Question:
Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour and then walked from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the total distance Courtney walked was 8 kilometers.
Let b be the number of hours it took Courtney to walk from her house to the beach, and p the number of hours it took her to walk from the beach to the park.
Which system of equations represents this situation?
Answer:
CORRECT (SELECTED)
⎪b+p=2
⎨4b+5p=8
rewrite equation without fractions, do not use decimals in the answer.
7/9x +2 = 5/6
Answer:
Step-by-step explanation:
7/9x + 2 = 5/6.....multiply by the common denominator of 18
14x + 36 = 15 <=== re-written without fractions
14x = 15 - 36
14x = -21
x = -21/14
x = - 3/2...(or - 1 1/2)...ur solution
To rewrite the equation 7/9x + 2 = 5/6 without fractions, we multiply every term by the least common denominator (18) to get 14x + 36 = 15. Subtracting 36 from both sides and solving for x results in x = -21/14.
Explanation:In order to rewrite the equation without fractions, we can eliminate the fractions by finding the least common denominator (LCD) and multiplying every term in the equation by it.
The original equation is 7/9x + 2 = 5/6. The least common denominator for 9 and 6 is 18.Multiply each part of the equation by 18: 7/9x * 18 + 2 * 18 = 5/6 * 18. This simplifies to 14x + 36 = 15.Finally, subtract 36 from both sides to solve for x: 14x = 15 - 36, so x = -21/14.Learn more about Rewrite Equation here:https://brainly.com/question/31910848
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Convert z = 9cos200° + 9isin200° from polar form to rectangular form.
-8.46 - 3.08i
-2.09 – 6.84i
8.46 + 3.08i
2.09 + 6.84i
Answer:
z = -8.46 - 3.08i.
Step-by-step explanation:
cos 200 = -0.93969 so 9 * cos 200 = -8.46 to the nearest hundredth.
sin 200 = -0.3420 so 9 * sin 200 = -3.08 to nearest hundredth.
What is the reference angle for 120°? A. 30° B. 45° C. 60° D. 120° E. 240°
Answer:
C
Step-by-step explanation:
120° is an angle in the second quadrant.
The reference angle is the related acute angle in the first quadrant, that is
reference angle = 180° - 120° = 60° → C
Answer:
C
Step-by-step explanation:
Choose the missing exponent to create a polynomial: 3x^4+4x^2-9x^-?+2
?=Missing Value
A) 2
B) 3
C) -9
D) 7
E) 4
Answer:
C) -9
Step-by-step explanation:
Exponents in a polynomial must be positive integers. Since your ? has a minus sign in front, its value must be negative. The only such choice is C.
Add...- 3+(-3) =
Thank youuuu!!!!
Answer:
the answer is 0
Step-by-step explanation:
well - 3 plus 3 would just by 0 because if the number with the negative is the biggest then the answer is negative but if the positive number is the biggest then the answer would be positive because there is not a bigger number it would be 0 because 3 and -3 have pretty much the same value other then them being negative and positive
The distance from the equator to the north pole is almost 10,000 km. Roughly how many kilometers is: the distance around the earth at the equator? 1 degree of longitude?
Step-by-step explanation:
As the distance from the equator to the north pole is almost 10,000 km.
The reason is that the definition of a meter is [tex]1\:10,000,000th[/tex] of the distance from the North Pole to the equator. Thus, itʹs exactly [tex]10,000,000[/tex] meters from the North Pole to the equator, that is exactly 10,000 kmAs we know that
An equator is basically termed as an imaginary line around the middle of a planet - midway between the South and the North Pole, at [tex]0[/tex] degrees latitude.An equator cuts the planet into a Southern and a Northern HemisphereAs the planet Earth is outspread or widest at its Equator and the distance around the Earth at the Equator - its circumference - is [tex]24,901\:miles[/tex].
[tex]24,901\:miles\:=\:40,075\:kilometers[/tex]
So, the distance around the Earth at the Equator - its circumference - is [tex]40,075\:kilometers[/tex].
Also, at the equator, [tex]1^{0}[/tex] ( [tex]1\:degree[/tex] ) of longitude and latitude both cover about [tex]111[/tex] km, or just under [tex]70[/tex] miles.
Keywords: equator, longitude, north pole
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To save for a new car, Trafton invested $7,000 in a savings account that earns 6.5% interest, compounded continuously. After four years, he wants to buy a used car for $10,000. How much money will he need to pay in addition to what is in his savings account? (Round your answer to the nearest cent.)
Answer:
Trafton will need to pay $ 900 in addition to what is in his savings account, to buy the used car he wants.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Initial deposit = $ 7,000
Annual interest = 6.5% = 0.065 compounded continuously
Time of the investment = 4 years
Price of the used car Trafton wants to buy = $ 10,000
2. How much money will he need to pay in addition to what is in his savings account?
1. For answering the question, let's calculate how much money Trafton has in his savings account after 4 years, this way:
FV = PV * e ^ (i * t)
Where,
FV = Future value of the initial deposit after t time
PV = Initial deposit
e = Euler's number (2.7183)
i = 0.065 compounded continuously
t = 4 years
Replacing with the real values, we have:
FV = 7,000 * 2.7183^(0.065 * 4)
FV = 7,000 * 1.30 (Rounding to the nearest hundredth)
FV = $ 9,100
Now, we can elaborate how much money will Trafton need to pay in addition, as follows:
Money in addition = Price of the used car Trafton wants to buy - Future Value of the savings account after 4 years
Money in addition = 10,000 - 9,100
Money in addition = $ 900
Trafton will need to pay $ 900 in addition to what is in his savings account, to buy the used car he wants.
The value of a boat is $53,650. It loses 14% of its value every year. Find the approximate monthly percent decrease in value. Round your answer to the nearest hundredth of a percent.
Answer:
1.17
Step-by-step explanation:
this is because first you would do 14÷12 as 14 is yearly and you want to find the monthly percentage this gives you 1.1666666667. then the next step is to round it so you would round 1.1666666667 to 1.17 for hundredth of a percent
14÷12=1.1666666667
round 1.1666666667 to 1.17
hoped this helped
Please help..can't figure it out!
Answer:
B) y = x + 2 and y = -x - 4
Step-by-step explanation:
The equation of a line is represented with y = mx + b.
"x" and "y", when substituted, tell you if a point (x, y) is on the line.
"m" is slope, and tells if it goes up (positive slope) or down (negative)
"b" is the y-intercept, when the line hits the y-axis.
In the graph, we have two lines. One goes upwards (read from left to right), and the other goes downwards.
The graph that goes upwards hits the y-axis at positive "2".
The graph that goes downwards hits the y-axis at (negative) "-4".
Since the choices only have positive 1 or negative 1 as the slope, we only have to worry if it goes up or down.
Take the key information, slope and y-intercept, to write the equations.
"upwards slope, y-axis at 2"
y = x + 2
"downwards slope, y-axis at -4"
y = -x - 4
A designer is making a rectangular prism box with maximum volume, with the sum of its length, width, and height 8 in. The length must be 2
times the width. What should each dimension be? Round to the nearest tenth of an inch if necessary.
Answer:
width = 1.8 in
length = 3.6 in
height =[tex]8-3w =8-3(1.8)= 2.6 in[/tex]
Step-by-step explanation:
A designer is making a rectangular prism box with maximum volume, with the sum of its length, width, and height 8 in
Let l , w and h are the length , width and height
[tex]l +w+h=8\\l=2w[/tex]
Plug it in the first equation
[tex]2w+w+h=8\\3w+h=8\\h=8-3w[/tex]
volume the box is length times width times height
[tex]volume = (2w)(w)(8-3w)\\16w^2-6w^3[/tex]
To get maximum volume we take derivatived
[tex]v'=32w-18w^2[/tex]
set the derivative =0 and solve for w
[tex]0=32w-18w^2\\0=-2w(9w-16)\\w=0 , w= \frac{16}{9}[/tex]
width = 1.8 in
length = 2w= 3.6 in
height =[tex]8-3w =8-3(1.8)= 2.6 in[/tex]
A couple intends to have two children, and suppose that approximately 52% of births are male and 48% are female.
a. What is the probability both children are male?
b. What is the probability both children are female?
c. What is the probability they have exactly one male and exactly one female child?
a) Probability of both being males is 27%
b) Probability of both being females is 23%
c) Probability of having exactly one male and one female is 50%
Step-by-step explanation:
a)
The probability that the birth is a male can be written as
[tex]p(m) = 0.52[/tex] (which corresponds to 52%)
While the probability that the birth is a female can be written as
[tex]p(f) = 0.48[/tex] (which corresponds to 48%)
Here we want to calculate the probability that over 2 births, both are male. Since the two births are two independent events (the probability of the 2nd to be a male does not depend on the fact that the 1st one is a male), then the probability of both being males is given by the product of the individual probabilities:
[tex]p(mm)=p(m)\cdot p(m)[/tex]
And substituting, we find
[tex]p(mm)=0.52\cdot 0.52 = 0.27[/tex]
So, 27%.
b)
In this case, we want to find the probability that both children are female, so the probability
[tex]p(ff)[/tex]
As in the previous case, the probability of the 2nd child to be a female is independent from whether the 1st one is a male or a female: therefore, we can apply the rule for independent events, and this means that the probability that both children are females is the product of the individual probability of a child being a female:
[tex]p(ff)=p(f)\cdot p(f)[/tex]
And substituting
[tex]p(f)=0.48[/tex]
We find:
[tex]p(ff)=0.48\cdot 0.48=0.23[/tex]
Which means 23%.
c)
In this case, we want to find the probability they have exactly one male and exactly one female child. This is given by the sum of two probabilities:
- The probability that 1st child is a male and 2nd child is a female, namely [tex]p(mf)[/tex]
- The probability that 1st child is a female and 2nd child is a male, namely [tex]p(fm)[/tex]
So, this probability is
[tex]p(mf Ufm)=p(mf)+p(fm)[/tex]
We have:
[tex]p(mf)=p(m)\cdot p(f)=0.52\cdot 0.48=0.25[/tex]
[tex]p(fm)=p(f)\cdot p(m)=0.48\cdot 0.52=0.25[/tex]
Therefore, this probability is
[tex]p(mfUfm)=0.25+0.25=0.50[/tex]
So, 50%.
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Solve the following expression. 36 - {-49 + (32.9) ] =
Answer:
52.1
Step-by-step explanation:
The given expression is 36 - [-49 + 32.9]
First we have to simplify the numbers which are in parenthesis.
= 36 -(-16.1)
Here -(-16.1) = + 16.1
So, we get
= 36 + 16.1
= 52.1
The answer is 52.1
what is the orthocenter of a triangle on (-2,5), (6,5), and (4,-1)
Answer:
(4,3)
Step-by-step explanation:
The orthocenter of a triangle is the point of intersection of the altitudes of the triangle .
The vertices are:
A(-2,5), B(6,5), and C(4,-1)
Slope of (6,5), and (4,-1) is
[tex]m = \frac{5 - - 1}{6 - 4} = 3[/tex]
Slope of altitude through A is
[tex] - \frac{1}{3} [/tex]
The equation of the altitude through A is
[tex]y - 5 = - \frac{1}{3} (x - - 2)[/tex]
[tex]y = - \frac{1}{3} x + \frac{13}{3} [/tex]
The slope of A(-2,5), B(6,5) is zero because it is a horizontal line.
The equation of altitude through (4,-1) will be the vertical line x=4.
This implies that,
[tex]y = - \frac{4}{3} + \frac{13}{3} = 3[/tex]
Hence the orthocenter is (4,3)
Write and equivalent expression for 5x²-15x
Answer:
x-3
Step-by-step explanation:
5x²-15x
in order to get the equivalent of the equation, simplify to the lowest term.
To simplify to the lowest term, divide through by the common factor in the equation which is 5x
5x²÷5x - 15x÷5x
=x-3
Name a fourth point in plane TUY.
X
Y
Z
W
The answer is W, just took the test.
What is the answer to 5(a-b)?
Answer:
5xA-5xB
Step-by-step explanation:
Answer: 5a-5b
Step-by-step explanation: Distribute the 5 and carry the negative sign over
Question 6 of 10
2 Points
The solution set of an equation of a circle is all of the points that lie in the
circle
O
A
True
O
B. False
SUBMIT
It is true that the solution set of an equation of a circle is all of the points that lie in the circle
How to determine the true statement?The equation of a circle is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where:
Center = (a,b)
Radius = r
The points are represented by (x,y)
The (x,y) can take any value as long as it makes the equation (x - a)^2 + (y - b)^2 = r^2 to be true
Hence, it is true that the solution set of an equation of a circle is all of the points that lie in the circle
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Answer:
False
Step-by-step explanation:
What is the image point of (3,7) after translation right 5units and up 1 unit
Answer:
(8,8)
Step-by-step explanation:
The image point of (3,7) after translation 5 units to the right and 1 unit up is (8,8).
Explanation:Translation of a point in a coordinate plane involves moving the point to a new location without changing its orientation or size.
To find the image of a point (3,7) after a translation of 5 units to the right and 1 unit up, we simply add the translation amounts to the original coordinates.
For a rightward movement, we add 5 to the x-coordinate, and for an upward movement, we add 1 to the y-coordinate.
Therefore, the new position of the point after translation will be:
New x-coordinate = Original x-coordinate + Rightward translation = 3 + 5 = 8New y-coordinate = Original y-coordinate + Upward translation = 7 + 1 = 8So, the image point after the translation is (8,8).
Suppose a small airplane has a wingspan of 15 feet. Find the wingspan of a model of the airplane, in inches, if the scale factor is 1/60.
A) 3 inches
B) 4 inches
C) 6 inches
D) 12 inches
Answer: 3 inches
Step-by-step explanation:
1/60 = x/15,
x = 1/4
1/4 foot = 3 inches.
A fair coin is tossed in the air 50 times. It landed on tail 24 times. What is the experiment probability that the coin will NOT land on talis
Answer:50/50
Step-by-step explanation:
It’s a 50/50 chance because there is only two sides to a coin
a preschool has a student to teacher ratio of 5:2. The total number of students and teachers was 56 last year and is 70 this year. How many students and teachers were there for each of these two years?
Answer:
Step-by-step explanation:
student teacher ratio of 5:2....added = 7
so students make up 5/7 of the total people and teachers make up 2/7 of the total people.
Last year.....56 people
students : 5/7 * 56 = 280/7 = 40 students
teachers : 2/7 * 56 = 112/7 = 16 teachers
this year....70 total people
students : 5/7 * 70 = 350/7 = 50 students
teachers : 2/7 * 70 = 140/7 = 20 teachers
Final answer:
To find the number of students and teachers based on their ratio and total count, we applied the ratio of 5:2 to the total counts of 56 and 70 for the last year and this year, respectively. This calculation revealed there were 40 students and 16 teachers last year, and 50 students and 20 teachers this year.
Explanation:
The student has asked about finding the number of students and teachers at a preschool in two different years based on a given student-to-teacher ratio and the total count of students and teachers for those years.
Step-by-Step Solution:
First, understand the ratio of students to teachers is 5:2. This means for every 5 students, there are 2 teachers.
To solve for last year, we have a total of 56 individuals (students and teachers). Let's represent students as 5x and teachers as 2x, given their ratio. Therefore, 5x + 2x = 56, solving this gives us x = 8. This means there were 40 students (5*8) and 16 teachers (2*8) last year.
For this year, we have a total of 70 individuals. Using the same method, 5x + 2x = 70, we find that x = 10. This means there are 50 students (5*10) and 20 teachers (2*10) this year.
By understanding and applying the concept of ratios, we were able to find the number of students and teachers for both years.
In a certain card game, for every 4 44 blue cards, there are 3 33 yellow cards. There are a total of 84 8484 blue and yellow cards in the game. How many blue cards are in the game?
The total number of blue cards in the game = 48
Step-by-step explanation:
Total number of blue and yellow cards = 84
let the blue card denote B and yellow card as Y
B = 4
Y = 3
Total number of cards in one round = 7
number of rounds possible = total number of cards / number of cards in one round
= 84/7
= 12
number of blue cards = 12 x 4
= 48
The total number of blue cards in the game = 48
Answer:
48
Step-by-step explanation:
Khybar Inc. manufactures dental X-ray machines. The company can sell an X-ray machine which cost $508.17 to produce for
$1.295.75. Each of the company's two salespeople ears a different commission per sale, as shown in the table below.
Salesperson
Greg
Colleen
Commission/Sale
$243.15
$288.75
Last year, Greg sold 11 fewer X-ray machines than Colleen did. Khybar Inc.'s total expenses last year, not counting
production costs or commissions, came to $79,558.59. If Khybar Inc. broke even, how many X-ray machines were sold last
year in total?
The answer is B (153) on Edge.
The X-ray machines were sold last year in total is 157.
What is Commission?A commission is a sum of money that a salesperson receives for each transaction they make. If a salesman is compensated on commission, their pay is based on how much they sell. Salespeople are paid only on commission.
We have,
The company can sell an x-ray machine which cost $508.17 to produce for $1.295.75.
So, the number of x-ray machines that were sold last year by Khybar inc.
= 79558.59/508.17
= 156.5
= 157
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How many solutions does an equation have when the variable adds out and the final sentence is true?
Answer:
Infinitely many solutions
Step-by-step explanation:
If we have a system of equation like:
2x+y=4
6x+3y=12
If we make y the subject in the first equation and substitute into the second equation, we get:
6x+3(4-2x)=12
We expand to get:
6x+12-6x=12
6x-6x+12=12
Now the variable adds out to give:
12=12
This statement is true so the equation has infinitely many solution.
Answer:
infinite solutionsExplanation:
When the variable adds out means that after all the simplifications, at the end, it will not appear in the final sentence or expression.
Then, if the final sentence is true, and not variable appears, but only constants, the sentence is always true, no matter what value the variable takes.
That means that you can put any value for the variable in the original equation and the equation will be true; hence there are infinite solutions.
This is an example:
1. Equation:
3x + 5+ x² = 2 - ( - 4x - x²) + (3 - x)2. Remove the parenthesis:
3x + 5+ x² = 2 + 4x + x² + 3 - x3. Add like terms on the right side and transpose the variables to the left side:
3x + 5 + x² = 5 + 3x + x²3x + x² - 3x -x² + 5 = 54. Combine like terms on the left side:
5 = 5Thus, the variable added out and the final sentence is true. Hence, this equation has infinite solutions, which you can prove substituting the variable with any value.
The sum of two numbers is a hundred one number is at least 16 more than the other number. What are the numbers? Please help
Answer:
58 and 42.
Step-by-step explanation:
Let the 2 numbers be x and 100-x.
Also let x be the largest number, so
x ≥ 100 - x + 16 ( 'At least 16' means equal to 16 or greater than 16).
Add in x to both sides:
x + x ≥ 100 + 16
2x ≥ 116
x ≥ 58.
But since the sum of the 2 numbers is 100, x must be 58 and the other number is 42.
Find the equation of a line that is perpendicular to y=−12x−1 and passes through the point (3,2).
Answer:
y = (1/12)*x + 7/4
Step-by-step explanation:
y=−12x−1
Perpendicular line:
y = a*x + b
y = (1/12)*x + b
2 = (1/12) * 3 + b
2 = (3/12) + b
2 = 1/4 + b
2 - 1/4 = b
7/4 = b
Perpendicular line:
y = (1/12)*x + 7/4
A container is filled with 100 grams of bird feed that is 80% seed. How many grams of bird feed containing 5% seed must be added to get bird feed that is 40% seed?
Thank you!
Answer:
43.65 grams of bird feed containing 5% seed must be added to get bird feed that is 40% seed
Step-by-step explanation:
Let us assume the total capacity of the container = m grams
Here, given: 80% of m = 100 grams
[tex]\implies \frac{80}{100} \times m = 100\\\implies m = \frac{100 \times 100}{80} = 125[/tex]
or, the TOTAL CAPACITY of container = 125 grams
Now, the container already has 5 % seeds.
Calculating 5% of the capacity, we get:
[tex]\implies \frac{5}{100} \times 125 = 6.25[/tex]
So, the container already has 6.25 grams.
Now, the total filling of the container should be 40%.
Calculating 40% of the capacity, we get:
[tex]\implies \frac{40}{100} \times 125 = 50[/tex]
So, the weight of seeds that NEEDS To be in total = 50 grams.
Also, it already has 6.35 grams.
So, the weight of seeds to be added = 50 grams - 6.35 grams
= 43.65 grams
Hence, 43.65 grams of bird feed containing 5% seed must be added to get bird feed that is 40% seed.
43.75 grams of bird feed containing 5% seed must be added to get bird feed that is 40% seed
PercentagePercentage is a number or ratio that can be expressed as a fraction of 100.
Let the total mass of the container = x
Therefore,
80% of x = 100g of bird feed
80 / 100 × x = 100
80x = 10000
x = 10000 / 80
x = 125 grams
Therefore, 5% volume will be as follows;
5 / 100 × 125 = 625 / 100 = 6.25 gramsTherefore, 40% volume is as follows:
40 / 100 × 125 = 5000 / 100 = 50 gramsFinally, the weight to be added to make the bird feed 40% seed is as follows;
50 - 6.25 = 43.75 gramslearn more on percentage here: https://brainly.com/question/1691136
Manny runs 15 3/4 miles each week. Zander runs 5/6 as many miles each week as Manny.
How many miles does Zander run each week?
In these kinds of problems, take 15 and 3/4 (Manny's distance) and multiply it by the factor 5/6. (15 3/4 = 15.75)
(15.75) * (5/6) = 13.125 = 13 1/8
This should get you 13 and 1/8 miles for Zander's distance.
A gain of 56 points in a game as an integer
Answer:
+56
Step-by-step explanation:
Determine whether the statement is true or false.
Let A = {1, 3, 5, 7}
B = {5, 6, 7, 8}
C = {5, 8}
D = {2, 5, 8}
U = {1, 2, 3, 4, 5, 6, 7, 8}
Answer: I think it's True :)
Answer:
I feel like it true. Happy yo help!!!
Step-by-step explanation: