Answer: 16 men
32 women
38 children
Step-by-step explanation:
Let x represent the number of men in the group.
Let y represent the number if women in the group.
Let z represent the number of children in the group.
A group of 86 people consist of men women and children. This means that
x + y + z = 86 - - - - - - - - - - - - 1
There are twice as many women than there are men. It means that
x = y/2
There are 6 more children than there are women. This means that
z = y + 6
Substituting x = y/2 and z = y + 6 into equation 1, it becomes
y/2 + y + y + 6 = 86
multiplying through by 2, it becomes
y + 2y + 2y + 12 = 172
5y = 172 - 12 = 160
y = 160/5 = 32
x = y/2 = 32/2
x = 16
z = y + 6 = 32 + 6
z = 38
There are 16 men, 32 women, and 38 children in the group.
Explanation:Let the number of men be M, the number of women be W, and the number of children be C.
From the given information, we have the following equations:
W = 2M (Twice as many women as men)
C = W + 6 (6 more children than women)
The total number of people is given as 86:
M + W + C = 86
Substituting the values of W and C in terms of M into the third equation, we have:
M + 2M + (2M + 6) = 86
5M + 6 = 86
5M = 80
M = 16
Substituting the value of M in the first equation, we have:
W = 2(16) = 32
Finally, substituting the value of W in the second equation, we have:
C = 32 + 6 = 38
Therefore, there are 16 men, 32 women, and 38 children in the group.
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Gaston claims to eat 6 dozen eggs every morning.If the hens in his town lay 2 eggs per day, what is the equation that represents the relationship between the total number of eggs Gaston eats each morning and the number of hens (h) needed to support his diet?
i put 72 eggs = 36h because that makes sense right? but it’s saying that the 36 hens is incorrect
Answer:
72 = 2h
Step-by-step explanation:
6 dozens = 6×12 = 72
72 = 2h
Each hen lays eggs, so h hens will lay 2×h eggs
The equation you've made implies every hen lays 36 eggs
72 = 2h is the equation,
Which simplifies to
h = 36
Jan has a 12 ounce milkshake. Four ounces in the milkshakes are vanilla, and the rest is chocolate. What equivalent fractions that represent the fraction of the milkshake that is vanilla
Answer:
Vanilla milkshake = 1/3 and Chocolate milkshake = 2/3
Step-by-step explanation:
Given data:
Total ounce of milkshake = 12 ounce
Vanilla milkshake = 4
Chocolate is the rest which can be interpreted as 12 - 4= 8 ounce
Representing as fractions
Vanilla milkshake = 4/12 (Reducing to lowest terms that is diving numerator and denominator by common factor in this case 4)
Vanilla milkshake = 1/3
Chocolate milkshake = 8/12 (Reducing to lowest terms that is diving numerator and denominator by common factor in this case 4)
Chocolate milkshake = 2/3
Demont used 4 gallons of gasoline in three days driving to work .Each day he used the same amount of gasoline. How many gallons of gasoline did he use each day?
Answer:
1 1/3 gallons per day
Step-by-step explanation:
To find gallons per day, divide gallons by days. ("per" means "divided by")
(4 gal)/(3 day) = (4/3) gal/day
Demont used 4/3 = 1 1/3 gallon each day.
To find out how many gallons of gasoline Demonte used each day, divide the total amount used (4 gallons) by the number of days (3), yielding approximately 1.33 gallons per day.
Demonte used 4 gallons of gasoline in three days driving to work and used the same amount of gasoline each day. To calculate the amount of gasoline he used each day, you divide the total gallons of gasoline by the number of days. This can be represented by the following equation:
Gallons per day = Total gallons used ÷ Number of days
Gallons per day = 4 gallons ÷ 3 days
Gallons per day = 1.33 gallons per day (approximately)
Therefore, Demonte used approximately 1.33 gallons of gasoline each day.
A researcher records the levels of attraction for various fashion models among college students. He finds that mean levels of attraction are much higher than the median and the mode for these data. a. What is the shape of the distribution for the data in this study? b. What measure of central tendency is most appropriate for describing these data? Why?
Answer:
a) Positively skewed
b) Median
Step-by-step explanation:
We are given the following in the question:
For a particular data, mean levels of attraction are much higher than the median and the mode for these data.
[tex]\text{Mean} > \text{Median}\\\text{Mean} > \text{Mode}[/tex]
a) Shape of data
Since the mean of data is greater than the median and mode of the data, thus, is a skewed data.
For a positively skewed data:
[tex]\text{Mean} > \text{Median} > \text{Mode}[/tex]
Thus, the given data is positively skewed data.
b) Measure of central tendency
Since it is a positively skewed data, median is a better measurement of central of tendency.
Advantage of median:
The median is less affected by outliers and skewed data than the mean.Final answer:
The data likely has a right-skewed distribution, making the median the most suitable measure of central tendency due to the impact of outliers.
Explanation:
a. What is the shape of the distribution for the data in this study?
The data distribution is likely skewed to the right, as the mean is much higher than the median and mode, indicating a long tail to the right.
b. What measure of central tendency is most appropriate for describing these data? Why?
In this case, the median is the most appropriate measure of central tendency because it is less affected by extreme values compared to the mean. Since the mean is much higher than the median and mode, it suggests outliers are pulling the mean upwards.
A car rental company charges an initial fee plus an additional fee for each mile driven. The charge depends on the type of car: economy or luxury. The charge E (in dollars) to rent an economy car is given by the function E -0.70M+14.95, where M is the number of miles driven. The charge L (in dollars) to rent a luxury car is given by the function L 1.05M+18.20 Let C be how much more it costs to rent a luxury car than an economy car (in dollars). Write an equation relating C to M. Simplify your answer as much as possible. Clear Undo Help Next > Explain
Answer:
C = 1.75M + 3.25
Step-by-step explanation:
Let E represent Economy
Let L represent Luxury
Let M be the number of miles driven
Let C be how much it cost to rent a luxury car than economy
E = -0.70M + 14.95
L = 1.05M + 18.20
C = L - M
C =(1.05M + 18.20) - (-0.70M + 14.95)
C = 1.05M + 18.20 + 0.70M - 14.95
collect like terms
C = 1.05M + 0.70M + 18.20 - 14.95
C = 1.75M + 3.25
The equation representing how much more it costs to rent a luxury car than an economy car, given the number of miles driven, is C = 1.75M + 3.25. This is derived by subtracting the equation for economy car costs from the equation for luxury car costs and simplifying.
Explanation:The value of C, which is the cost difference between renting a luxury and an economy car, can be found by finding the difference between the charge equations for the two types of cars. To find C in terms of M, subtract the equation for the economy car (E) from the equation for the luxury car (L).
So, C = L - E
Substitute the given equations for L and E into the equation for C:
C = (1.05M + 18.20) - (-0.70M + 14.95)
Simplify the equation by distributing the negative sign on the right side of the equation:
C = 1.05M + 18.20 + 0.70M - 14.95
Combine like terms:
C = 1.75M + 3.25
This equation represents how much more it costs to rent a luxury car than an economy car based on the number of miles driven.
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What is the missing reason in the proof?
Given: ∠ABC is a right angle, ∠DBC is a straight angle
Prove: ∠ABC ≅ ∠ABD
A horizontal line has points D, B, C. A line extends vertically from point B to point A. Angle A B C is a right angle.
A 2-column table has 8 rows. The first column is labeled Statements with entries angle A B C is a right angle, angle D B C is a straight angle, m angle A B C = 90 degrees, m angle D B C = 180 degrees, m angle A B D + m angle A B C = m angle D B C, m angle A B D + 90 degrees = 180 degrees, m angle A B D = 90 degrees, angle A B C is-congruent-to angle A B D. The second column is labeled Reasons with entries, given, given, definition of right angle, definition of straight angle, angle addition property, substitution property, subtraction property, and question mark.
definition of angle bisector
segment addition property
definition of congruent angles
transitive property
Answer:
Third option: Definition of Congruent angles.
Step-by-step explanation:
For this exercise it is important to know the definition Congruent angles.
Congruent angles are defined as those angles that have equal measure.
The symbol used for Congruent angles is the following:
≅
Keep the explanation above on mind.
In this case, you know that [tex]\angle ABC[/tex] measures 90 degrees (This is also known as "Rigth angle"):
[tex]\angle ABC=90\°[/tex]
And you can observe in the table attached that the measure of [tex]\angle ABD[/tex] is also 90 degrres:
[tex]\angle ABD=90\°[/tex]
Therefore, since they have exactly the same measure, these angles are congruent. Then:
[tex]\angle ABC[/tex] ≅ [tex]\angle ABD[/tex]
Based on this, you can identify that the missing reason number 8 is: Definition of Congruent angles.
Maria ordered a pizza. She ate 2/9 of it and gave the remaining pizza to her 3 brothers. What fraction of the whole pizza will each of Maria's brothers receive if they share the remaining pizza equally?
A. 7/9
B. 3/7
C. 1/3
D. 7/27
E. 2/27
Answer:
D 7/27
Step-by-step explanation:
If Maria ate 2/9 of the pizza, that means she DIDN'T eat 7/9 of the pizza. So far so good? Ok, then you just need to find out what is 1/3 of 7/9, because the three brothers are dividing the leftover pizza equally, right? Hint - "of" usually means multiply. And remember multiplying fractions is lovely - you simply multiply the numerators together, then multiply the denominators together (no common denominator mumbo jumbo). So...
1/3 * 7/9 = 7/27.
Maria's brothers will each receive option D. 7/27 of the pizza.
To determine the fraction of the whole pizza each of Maria's brothers will receive, if they share the remaining pizza equally, follow these steps:
Maria ate 2/9 of the pizza, so the remaining fraction of the pizza is 1 - 2/9 = 7/9.The remaining pizza (7/9) is shared equally among her 3 brothers.To find the fraction each brother gets, divide 7/9 by 3. This can be done by multiplying 7/9 by the reciprocal of 3 (which is 1/3): (7/9) * (1/3) = 7/27Therefore, each of Maria's brothers will receive option D. 7/27 of the whole pizza.
what is 5/6 y - 8 = 2
a. 12
b. 8 1/3
c. -7 1/5
d. 13
Answer:
[tex]a.\ 12[/tex]
Step-by-step explanation:
[tex]\frac{5}{6}y-8=2\\\\Add\ 8\ both\ sides\\\\\frac{5}{6}y-8+=2+8\\\\\frac{5}{6}y=10\\\\Multiply\ by\ 6\ both\ the\ sides\\\\\frac{5}{6}y\times 6=10\times 6\\\\5y=60\\\\divide\ by\ 5\ both\ the\ sides\\\\\frac{5y}{5}=\frac{60}{5}\\\\y=12[/tex]
Perform the indicated operation and simplify the result. 6a2/5b2 * 45b3/18a3 = ? answers:a)3ab b)(3b)/a c)3
Answer:
The answer to your question is [tex]\frac{3b}{a}[/tex] , check your options, maybe you forgot one.
Step-by-step explanation:
Original operation
[tex]\frac{6a^{2}}{5b^{2}} \frac{45b^{3}}{18a^{3}}[/tex]
Process
1.- Simplify 6 and 18 and 45 and 5
[tex]\frac{6}{18} = \frac{3}{9} = \frac{1}{3}[/tex]
[tex]\frac{45}{5} = \frac{9}{1} = 9[/tex]
Result
[tex]\frac{9}{3} = \frac{3}{1} = 3[/tex]
2.- Simplify a² and a³
[tex]\frac{a^{2}}{a^{3}} = \frac{1}{a}[/tex]
3.- Simplify b³ and b²
[tex]\frac{b^{3}}{b^{2}} = b[/tex]
4.- Join the results [tex]\frac{3b}{a}[/tex]
A very bright student is described as having an IQ that is three standard deviations above the mean. If this student's IQ is reported as a z-score, what would the z-score be?
a. z = m + 3
b. z = m + 3s
c. z = 3
d. cannot be determined from the information given
Answer:
Option C) z = 3
Step-by-step explanation:
We are given the following in the question:
IQ scores are normally distributed.
An IQ score is three standard deviations above the mean. Let x be the IQ score. Then, we can write,
[tex]x = \mu + 3\sigma[/tex]
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
[tex]z = \dfrac{\mu + 3\sigma-\mu}{\sigma} = \dfrac{3\sigma}{\sigma} = 3[/tex]
Thus, the z-score is 3.
Thus, the correct answer is
Option C) z = 3
The z-score for a student with an IQ three standard deviations above the mean would be z = 3.
Explanation:If a very bright student is described as having an IQ that is three standard deviations above the mean, and if this student's IQ is reported as a z-score, the z-score would be z = 3. This is because a z-score is a measure of how many standard deviations an observation is above or below the mean. When we say an observation is three standard deviations above the mean, we are describing a z-score of 3. Thus, the correct answer is c. z = 3.
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Write a numerical expression for the phase The quotient of 36 and the sum of -4 and -8 a numerical expression for this phrase is ? Simplified this is ?
The sum of -4 and -8 is -12, so the numerical expression for the given phrase is 36 / (-12) and the simplified expression is -3.
Explanation:To write a numerical expression for the phrase 'The quotient of 36 and the sum of -4 and -8,' we need to divide 36 by the sum of -4 and -8. The sum of -4 and -8 is -12, so the numerical expression is 36 / (-12).
Simplifying this expression, we get -3. Therefore, the simplified expression is -3.
On pet day 18 children brought a pet to school ⅔ of the pets were dogs 1\9 of the pets were cats how many dogs were there how many cats were there and how mant animals were neither dogs nor cats
Answer:
Step-by-step explanation:
On pet day 18 children brought a pet to school.
2/3 of the pets were dogs. This means that the number of pets that were dogs would be
2/3 × 18 = 12 dogs
1/9 of the pets were cats. This means that the number of pets that were cats would be
1/9 × 18 = 2 dogs
Total number of dogs and cats is
12 + 2 = 14
The number of animals that were neither dogs nor cats is
18 - 14 = 4
Final answer:
There were 12 dogs, 2 cats, and 4 animals that were neither dogs nor cats among the 18 pets that children brought to school on pet day.
Explanation:
On pet day, 18 children brought a pet to school. To find out how many dogs were there, we calculate two-thirds of 18, and for the cats, we calculate one-ninth of 18.
Dogs: ⅓ × 18 = 12 dogs
Cats: ⅙ × 18 = 2 cats
To determine how many animals were neither dogs nor cats, we subtract the number of dogs and cats from the total number of pets: 18 - (12 + 2) = 4 animals neither dogs nor cats.
So, there were 12 dogs, 2 cats, and 4 animals that were neither dogs nor cats.
Create at least 3 subtraction problems that have a common denominator of 20 using the fractions one sixth two fifths four sevenths three fourths three eights one half
Answer:
1. 1/2-2/5
2. 3/4-2/5
3. 1/2-3/4
Step-by-step explanation:
For you to be able to create such fractions you must make sure that the numerator is divisible by 20.
Clearly the number 2,4 and 5 can divide 20.so therefore any fraction formed with them will give the denominator 20
Write a system of equations (3 points) for the problem below and then solve it The candy shack has 20 lb. Of mixed white and dark chocolate worth $7.50 per pound. White chocolate alone sells for $8.00 per pound and dark chocolate sells for 6.00 per pound. How many pounds of each are in the mixture?
Answer: the mixture contained 15 pounds of white chocolate and 5 pounds of dark chocolate.
Step-by-step explanation:
Let x represent the number of pounds of white chocolate in the candy shack mixture.
Let y represent the number of pounds of dark chocolate in the candy shack mixture.
The candy shack has 20 lb of mixed white and dark chocolate. This means that
x + y = 20
The 20lb mixture is worth $7.50 per pound. This means that the total cost of the mixture is
20 × 7.50 = $150
White chocolate alone sells for $8.00 per pound and dark chocolate sells for 6.00 per pound. This means that
8x + 6y = 150 - - - - - - - - - - - - - -1
Substituting x = 20 - y into equation 1, it becomes
8(20 - y) + 6y = 150
160 - 8y + 6y = 150
- 8y + 6y = 150 - 160
- 2y = - 10
y = - 10/ - 2
y = 5
x = 20 - y = 20 - 5
x = 15
Can You Help Me With This??
100 Points and Brainliest For The Right Answer
Answer:
[tex]V=24,501.42\ m^3[/tex]
Step-by-step explanation:
we know that
The volume of the cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
where
r is the radius of the circular base of cylinder
h is the height of the cylinder
we have
[tex]r=34/2=17\ m[/tex] ----> the radius is half the diameter
[tex]h=27\ m\\\pi=3.14[/tex]
substitute the given values in the formula
[tex]V=(3.14)(17)^{2} (27)=24,501.42\ m^3[/tex]
Answer:
Answer = 24,501.42 m^3Step-by-step explanation
Givens
r is the radius = 17
h is the height of the cylinder = 27
pi = 3.14
Unknowns = Volume
Anwser = 24,501.42 m^3
Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range. y = x^2 +2x -5
Answer:
To find the x-intercept, substitute in 0 for y and solve for x . To find the y-intercept, substitute in 0 for x and solve for y -intercept(s): ( − 1 + √ 6 , 0 ) , ( − 1 − √ 6 , 0 ) y-intercept(s): ( 0 , − 5 )
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles?
Answer:
Step-by-step explanation:
x+x+(x+12)=180
3x=180-12=168
x=56
third angle=56+12=68
so angles are 56°,56°,68°
The larger angle is x + 12 i.e. 56 + 12 = 68⁰.
What is Triangle?A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices.
Let the first angle be x.
then second angle is equal to first i.e. x
and third angle = x + 12
we know that,
Sum of all angles of a triangle is 180⁰.
Now,
x + x + x + 12 = 180
3x = 180 -12
3x = 168
x = 168/3
x = 56
Thus, the larger angle is x + 12 i.e. 56 + 12 = 68⁰.
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Please help!
Two models are used to predict monthly revenue for a new sports drink. In each model, x is the number of $1-price increases from the original $2 per bottle price. Answer parts a and b below.
a. Identify the price you would set for each model to maximize monthly revenue.
Using Model A, the price should be $____ to maximize monthly revenue because the _-intercept occurs at x=_?
Model A
f(x)=-12.5x^2+75x+200
Model B
Model A's optimal price is $5, with a $3 increase, and Model B's optimal price is $6, with a $4 increase.
Let's walk through the step-by-step calculations for both Model A and Model B.
Model A:
Given Function:
f(x) = -12.5x^2 + 75x + 200
Completing the Square to Find Vertex:
f(x) = -12.5(x^2 - 6x - 16)
f(x)/(-12.5) = (x^2 - 6x - 16)
f(x)/(-12.5) + 16 + 9 = (x-3)^2
f(x)/(-12.5) + 25 = (x-3)^2 - 25
f(x) = (-12.5)[(x-3)^2 + 312.5]
Vertex Form:
f(x) = (-12.5)(x-3)^2 + 312.5
The vertex is at (3, 312.5).
Optimal Price Calculation:
The x-coordinate of the vertex indicates the optimal increase, which is $3. So, the optimal price is 3 + 2 = $5.
Y-intercept:
f(x) = -12.5(9) + 312.5 = 200
The y-intercept is $200.
X-intercepts:
Factorizing the original equation, we get x = 8 and x = -2.
Model B:
Symmetry Axis Calculation:
Midpoint between x-intercepts x = (-2 + 10)/2 = 4.
Optimal Price Calculation:
The optimal increase is $4, resulting in a price of 4 + 2 = $6.
Y-intercept:
The y-intercept is graphically determined to be between $180 and $210.
In summary, Model A's optimal price is $5, achieved with a $3 increase, while Model B's optimal price is $6, attained with a $4 increase.
In AABC, which ratio equals cos C?
Answer: the ratio that represents Cos C = a/b
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle,
AC represents the hypotenuse of the right angle triangle.
With m∠C as the reference angle,
BC represents the adjacent side of the right angle triangle.
AB represents the opposite side of the right angle triangle.
To determine m∠C, we would apply
the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos C = a/b
Estimate the value of the function at x = 4 given the following graph.
Yo sup??
The only way to solve this problem is by observing the graph closely and making some approximations.
We have to compare the value of x with the corresponding y value.
at x=4 you will find that the value of y is around 3.8-3.9
Therefore the answer is 3.8
Hope this helps.
Answer:
[tex]f(4) \approx 3.73[/tex]
Step-by-step explanation:
We can see that this function looks like a square root function but only shifted to the right by 1 and up by 2.
A square root function is:
[tex]f(x) = \sqrt{x}[/tex]
Shifting a function up means adding that value to the f(x):
[tex]f(x) = \sqrt{x}+2[/tex]
Shifting a function to the right means replacing a value x with the value (x-the value of shifting a function to the right):
[tex]f(x) = \sqrt{x-1}+2[/tex]
We can check that this really is a graph of a function [tex]f(x) = \sqrt{x-1}+2\\[/tex]:
[tex]f(1) = \sqrt{1-1}+2 = 0+2=2[/tex]
We can see on the graph that this really is the case : f(1)=2
Also,
[tex]f(2) = \sqrt{2-1}+2 = 1+2=3[/tex]
This is also the case if we check the graph.
So, now we have to estimate f(x) at x=4:
[tex]f(4) = \sqrt{4-1}+2 = \sqrt{3}+2[/tex]
where [tex]\sqrt{3} \approx 1.73[/tex] , hence:
[tex]f(4) \approx 1.73+2 = 3.73[/tex]
A house is valued at $118,000.00. The homeowner decides to add on a two-car garage that increased the value of the home by 15%.How much will the house be worth? Explian
Answer:
The value of the house after adding the garage is $135,700.
Step-by-step explanation:
Given,
value of house before adding garage = $118,200.00
we need to find the value of house after adding two car garage.
Solution,
Since after adding two car garage the value of the house increased by 15%.
So firstly we will find out the 15% of the value of the house after adding garage.
So we can say that;
15% of the value of the house after adding garage is equal to 15 divided by 100 the multiplied with the value of the house before adding garage.
15% of the value of the house after adding garage = [tex]\frac{15}{100}\times118,000=\$17,700[/tex]
Now, The value of the house after adding garage is equal to the sum of value of house before adding garage and 15% of value of house before adding garage.
We can frame it in equation form as;
The value of the house after adding garage = [tex]\$118,000+\$17,000=\$135,700[/tex]
Hence The value of the house after adding the garage is $135,700.
In which of the following cases is productive efficiency not satisfied? Assume we start at a point on the PPF between two products. Select the correct answer below: The economy switches to producing less of one product without increasing the production of the other product. The economy switches to producing at the point of intersection of the PPF and the vertical axis. The economy switches to producing more of one product and less of the other product but remains on the PPF. The economy switches to producing at the point of intersection of the PPF and the horizontal axis.
Answer:
A. The economy switches to producing less of one product without increasing the production of the other product
Step-by-step explanation:
PPC is the graphical representation of product combinations that an economy can produce, given resources & technology. It is downward sloping because given resources & technology, production of a good can be increased by decreasing production of other good.
It is based on assumption that resources are efficiently utilised. Points on PPC show resources efficient utilisation, Points under PPC show under utilisation, Points outside PPC are beyond country's productive capacity.
If country produces less of a good without increasing production of other goods, implying wasted resources & production below PPC. This case doesn't satisfy productive efficiency
Other cases : Producing more of a good & less of other is just re allocative movement on the PPC itself. Production point at PPF intersection with either axis implies economy is producing only the good on that axis.
In all the cases except A. satisfy the 'productive efficiency'
Simplify 2(x + 4) + 3(x - 4)
5x + 4
5x-4
5x
Answer:
5x - 4
Step-by-step explanation:
2( x + 4 ) + 3( x - 4)
Distribute the 2 into ( x + 4 ) so it comes out to be 2x + 8
now distribute 3 into ( x - 4 ) = 3x - 12
now combine like terms 2x + 8 + 3x - 12
2x and 3x can combine into 5x
-12 and 8 can combine into -4
so it comes out to be 5x - 4
What is the perimeter of a square whose diagonal is 3 square root 2? Show all work on how you got your answer
Answer:
12
Step-by-step explanation:
Given: Diagonal of square= [tex]3\sqrt{2}[/tex]
To find the perimeter of square, we need to find the length of sides of square.
∴ Using the formula of diagonal to find side of square.
Formula; [tex]Diagonal= s\sqrt{2}[/tex]
Where, s is side of square.
⇒ [tex]3\sqrt{2} = s\sqrt{2}[/tex]
Dividing both side by √2
⇒[tex]s= \frac{3\sqrt{2} }{\sqrt{2} }[/tex]
∴[tex]s= 3[/tex]
Hence, Length of side of square is 3.
Now, finding the perimeter of square.
Formula; [tex]Perimeter= 4s[/tex]
⇒[tex]Perimeter= 4\times 3[/tex]
∴ [tex]Perimeter= 12[/tex]
Hence, Perimeter of square is 12.
The perimeter of a square with a diagonal of 3 square root 2 units is 12 units.
Explanation:To find the perimeter of a square with a diagonal of 3√2, we can use the fact that the diagonal of a square divides it into two congruent right triangles. The length of each leg of the triangle is equal to one side of the square. We can use the Pythagorean theorem to find the length of the side of the square. Let's assume that the length of the side of the square is s.
Using the Pythagorean theorem, we have s2 + s2 = (3√2)2. Simplifying, we get 2s2 = 18. Dividing by 2, we have s2 = 9. Taking the square root of both sides, we get s = 3.
The perimeter of the square is equal to 4 times the length of one side, so the perimeter is 4 * s = 4 * 3 = 12 units.
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A square purple rug has a green square in the center. The side length of the green square is x inches. The width of the purple band that surrounds the green square is 2 in. What is the area of the purple band?
BLANK in^2
The area of the purple band is [tex]A = 4 - x^2[/tex]
The calculation is:Since both the shape contains the square so here the area square should be applied,
A = Total purple area - Total green area
[tex]A = (2)^2 - (x)^2\\\\A = 4 - x^2[/tex]
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Final answer:
The area of the purple band around the green square is calculated by finding the difference between the area of the larger purple square and the green square. It is determined by subtracting the green square's area (x²) from the total area of the larger square ((x + 4)²), resulting in an area of 8x + 16 square inches for the purple band.
Explanation:
To calculate the area of the purple band on the rug, we must first determine the dimensions of both the inner green square and the larger purple square that includes the band. The side length of the green square is given as x inches, and we know the width of the purple band surrounding it is 2 inches. To find the side length of the larger purple square, we add twice the width of the purple band (2 inches on each side) to the side length of the green square, giving us x + 2 + 2 or x + 4 inches.
The area of the larger purple square is therefore (x + 4)² square inches. The area of the inner green square is x² square inches. To find the area of just the purple band, we subtract the area of the green square from the area of the larger purple square.
So, the area of the purple band is (x + 4)² - x² square inches. Expanding this expression, we get x² + 8x + 16 - x² which simplifies to 8x + 16 square inches. Therefore, the area of the purple band around the green square is 8x + 16 in²
-5=x-3y
11=-3x+7y
This will be elimination
Answer:
Step-by-step explanation:
The given system of simultaneous equations is expressed as
-5=x-3y
11=-3x+7y
Rearranging both equations, it becomes
x - 3y = - 5- - - - - - - - - - 1
- 3x + 7y = 11 - - - - - - - - - -2
Multiplying equation 1 by 3 and equation 2 by1, it becomes
3x - 9y = - 15 - - - - - - - - - - -3
- 3x + 7y = 11 - - - - - - - - - - - 4
Adding equation 3 to equation 4, it becomes
- 2y = - 4
Dividing the left hand side and the right hand side of the equation by
- 2, it becomes
- 2y/ - 2 = - 4y/- 2
y = 2
Substituting y = 2 into equation 1, it becomes
x - 3 × 2= - 5
x - 6 = - 5
Adding 6 to left hand side and the right hand side of the equation, it becomes
x - 6 + 6= - 5 + 6
x = 1
Complete the proof of the Pythagorean theorem.
Given: Δ ABC is a right triangle, with
a right angle at ∠C
Prove: A²+B² =C²
Answer:
Statement
1. ΔABC is a right triangle, with a right angle at ∠C
2. Draw an altitude from point C to line AB
3. ∠CDB and ∠CDA are right angles.
4. ∠BCA ≅ ∠BDC
5. ∠B ≅ ∠B
6. ?
7. [tex]\frac{a}{x} = \frac{c}{a}[/tex]
8. a² = cx
9. ∠CDA ≅ ∠BCA
10. ∠A ≅ ∠A
11. ?
12. [tex]\frac{b}{y} = \frac{c}{b}[/tex]
13. b² = cy
14. a² + b² = cx + cy
15. ?
16. x + y = c
17. a² + b² = c²
Reason
1. Given
2. From a point not on a line, exactly one perpendicular can be drawn through the point to the line.
3. Definition of altitude
4. All right angles are congruent.
5. ?
6. AA Similarity Postulate
7. ?
8. ?
9. ?
10. ?
11. AA similarity Postulate
12. ?
13. ?
14. ?
15. Distributive Property
16. ?
17. ?
PLEASE FILL IN ALL THE QUESTION MARKS :)
To Determine:
So, here is the complete proof of the Pythagorean theorem.
Given: Δ ABC is a right triangle, with
a right angle at ∠C
Prove: A²+B² =C²
Answer:
Note: All the answers for the questions marks are filled with in bold text.
Statement
1. ΔABC is a right triangle, with a right angle at ∠C
2. Draw an altitude from point C to line AB
3. ∠CDB and ∠CDA are right angles.
4. ∠BCA ≅ ∠BDC
5. ∠B ≅ ∠B
6. AA Similarity Postulate
7. [tex]\frac{a}{x}\:=\:\frac{c}{a}[/tex]
8. a² = cx
9. ∠CDA ≅ ∠BCA
10. ∠A ≅ ∠A
11. ΔCBA ~ ΔDBA
12. [tex]\frac{b}{y}\:=\:\frac{c}{b}[/tex]
13. b² = cy
14. a² + b² = cx + cy
15. [tex]\left(CB\right)^2+\left(CA\right)^2=\left(AB\right)\left(DB+BA\right)[/tex]
16. x + y = c
17. a² + b² = c²
Reason
1. Given
2. From a point not on a line, exactly one perpendicular can be drawn through the point to the line.
3. Definition of altitude
4. All right angles are congruent.
5. Reflexive Property
6. AA Similarity Postulate
7. Polygon Similarity Postulate
8. Cross Multiply and Simplify
9. All right angles are Congruent
10. Reflexive Property
11. AA similarity Postulate
12. Polygon Similarity Postulate
13. Cross Multiply and Simplify
14. Addition Property of Equality
15. Distributive Property
16. Segment Addition Postulate
17. Substitution Property
Keywords: statement, reason
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It usually took josh 2/5 of an hour to ride his bike to work. But on Monday, his bike was broken, so he took the bus to work which took 5/8 of an hour. How much longer was it to take the bus to work?
Final answer:
To find the difference in time, subtract the bike time from the bus time by finding a common denominator and subtracting the fractions.
Explanation:
To compare the time it took Josh to bike to work with the time it took him to take the bus, we need to subtract the bike time from the bus time.
The time it took Josh to bike to work is given as 2/5 of an hour. We can represent this as a fraction, 2/5.
The time it took Josh to take the bus is given as 5/8 of an hour. This can also be represented as a fraction, 5/8.
To find the difference, we subtract the bike time from the bus time: 5/8 - 2/5. To do this, we need a common denominator, which in this case is 40.
Multiplying the numerator and denominator of 5/8 by 5, we get 25/40. Multiplying the numerator and denominator of 2/5 by 8, we get 16/40.
Now we can subtract the fractions: 25/40 - 16/40 = 9/40.
Therefore, it took the bus 9/40 of an hour longer than it took Josh to bike to work.
2. An 82 kg man on a diving board drops from rest 3.0 m above the surface of the water
and he comes to rest 0.55 s after reaching the water. What is the average net force on
the diver as he is brought to rest? Remember to first find the velocity of the man after he
falls 3.0 m off of the diving board.
The average net force on the man as he is brought to rest is: F = -1143.9N
The man on the diving board has a potential energy, P.E = mghWhen the man dives, he has a kinetic energy, K.E = (1/2)mv²Therefore, P.E = K.E
mgh = (1/2)mv²82 × 9.8 × 3 = (1/2)× 82 × v²v² = 58.8V = 7.67 m/sWhen the man comes to rest, the final velocity becomes, 0.
As, such, acceleration which is the rate of change of velocity becomes;
a = (0 - 7.67)/0.55a = -13.95 m/s².The force on the man; F = mass × acceleration.
F = 82 × -13.95F = -1143.9NRead more:
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The average net force on the diver as he is brought to rest is approximately 689.56 N.
First, we can find the velocity of the man just before he reaches the water using the kinematic equation:
d = vt + 1/2at²
Now, let's calculate the velocity of the man just before he reaches the water using the equation:
vf=0+(−9.8m/s2)×0.782s≈−7.664m/s
Since the velocity is negative, it means the man is moving downward.
After entering the water, the man comes to rest in 0.55 seconds. During this time, he decelerates due to the force of gravity, but this time in the opposite direction to his motion. We can use the equation:
Finally, we can determine the average net force using Newton's second law:
Given that the mass m of the man is 82 kg, we find:
F net = 82 kg × 14.025 m/s 2 ≈ 1147.35 N
Therefore, the average net force on the diver as he is brought to rest is approximately 1147.35 N.
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PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠E.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠E = °
Answer:
Step-by-step explanation:
Triangle DEF is a right angle triangle.
From the given right angle triangle,
DE represents the hypotenuse of the right angle triangle.
With m∠E as the reference angle,
EF represents the adjacent side of the right angle triangle.
DF represents the opposite side of the right angle triangle.
To determine m∠E, we would apply
the Tangent trigonometric ratio.
Tan θ = opposite side/adjacent side. Therefore,
Tan E = 8/5 = 1.6
E = Tan^-1(1.6)
W = 58.0° to the nearest tenth.