Answers
For a semi-circle with diameter 10, the circumference is 5π, perimeter is 5π + 10, and area is 25/2π. For a circle with radius 6 and a 90-degree cut, remaining circumference is 9π, perimeter is 12π, and remaining area is 27π.
Semi-circle with Diameter 10:
a. Circumference:
The circumference of a circle is given by the formula C = π × d, where d is the diameter. For a semi-circle, it's half of the circumference of a full circle. Thus, C(semi-circle) = π × 10/2 = 5π.
b. Perimeter:
The perimeter of a shape is the sum of all its sides. For a semi-circle, it includes the curved boundary and the diameter. Therefore, P(semi-circle) = 5π + 10.
c. Area:
The area of a semi-circle is given by A(semi-circle) = 1/2 × π × r^2, where r is the radius. Substituting the given diameter, A(semi-circle) = 1/2 × π × (10/2)^2 = 25/2 × π.
Circle with Radius 6 and a 90-Degree Cut:
a. Circumference:
For the full circle, C(circle) = 2π × r = 2 × π × 6 = 12π. Since a 90-degree cut removes a quarter of the circle, the remaining circumference is C(remaining) = 3/4 × 12π = 9π.
b. Perimeter:
The perimeter includes the cut portion, so P(circle) = 12π.
c. Area:
The area of the circle is A(circle) = π × r^2 = π × 6^2 = 36π. With the cut, A(remaining) = 3/4 × 36π = 27π.
Related Questions
Amelia opened a new savings account at a local bank. She made a beginning deposit of $1,000. The account earns 2% simple interest. If Amelia makes no additional deposits or withdrawals, what is the total amount that Amelia will have in her account at the end of 5 years?
Answers
Answer:
Step-by-step explanation:
We would apply the formula for determining simple interest which is expressed as
I = PRT/100
Where
I = interest at the end of t years
r represents the interest rate.
P represents the principal or initial amount deposited.
t represents the number of years of investment.
From the information given,
P = 1000
R = 2%
T = 5 years
Therefore,
I = (1000 × 2 × 5)/100
I = $100
The total amount in the account after 5 years would be
1000 + 100 = $1100
In AABC, which ratio equals cos C?
Answers
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
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
Answers
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.
What similarity statement can you write relating the three triangles in the diagram?
The image is a right angled triangle YHB such that angle H is 90 degree. From the vertex H a perpendicular HD is drawn on side YB.
A. YHB ≅ YDH ≅ HDB
B. YHB ~ YDH ~ HDB
C. YHD ~ HYB ~ HDB
D. YHB = YDH = HDB
Answers
The similarity statement relating the three triangles in the diagram is 'YHB ~ YDH ~ HDB'. This is because they are all similar triangles, sharing the same shape but differing in sizes due to scale.
Explanation:In this case, the answer would be 'YHB ~ YDH ~ HDB'. We are looking for a similarity statement, which states that all three triangles are similar. Similar triangles are triangles that have the same shape, but can be different sizes, i.e. they are scaled versions of each other. Since HD is a perpendicular drawn from right angle H in triangle YHB, this creates two triangles (YDH, HDB) that are respectively similar to the original triangle YHB as each of the two triangles include one of the acute angles of triangle YHB and their own right angles. Therefore, YHB ~ YDH ~ HDB.
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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 ?
Answers
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.
Can You Help Me With This??
100 Points and Brainliest For The Right Answer
Answers
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
A seven-year medical research study reported that women whose mothers took the drug
DES during pregnancy were twice as likely to develop tissue abnormalities that might lead
to cancer as were women whose mothers did not take the drug.
a. This study involved the comparison of two populations. What were the populations?
b. Do you suppose the data were obtained in a survey or an experiment?
c. For the population of women whose mothers took the drug DES during pregnancy, a
sample of 3980 women showed 63 developed tissue abnormalities that might lead
to cancer. Provide a descriptive statistic that could be used to estimate the number of
women out of 1000 in this population who have tissue abnormalities.
d. For the population of women whose mothers did not take the drug DES during pregnancy,
what is the estimate of the number of women out of 1000 who would be
expected to have tissue abnormalities?
e. Medical studies often use a relatively large sample (in this case, 3980). Why?
Answers
Answer:
Step-by-step explanation:
a) The two populations were i) the pregnant mothers who took the drug ii) the pregnant mothers who did not take the drugs
b) The data must have been obtained in a survey because experiment was not done.
c) 63 out of 3980 developed abnormalities in I case.
Hence out of 1000 abnormalities estimated = [tex]\frac{63}{3980} *1000\\=15.829\\[/tex]
i.e. approximately 16
d) Mothers who did not take drug
(information incomplete)
e) Medical hypothesis testing requires accurate results and hence sample sizes should be very large.
The mentioned study compares two populations: women exposed to DES during their mother's pregnancy and women who weren't. The data seems to be from a survey, is calculated with available information to be around 15.8 per 1000 women for the first population and half that for the second. Medical studies use large samples for higher statistical reliability.
Explanation:a. The two populations in this study are women whose mothers took the drug DES during pregnancy and women whose mothers did not take the drug DES during pregnancy.
b. The data is most likely obtained through a survey, since medical research often relies on observations, health histories, and existing data rather than conducting an experiment. This would also protect subjects' safety and uphold ethical considerations.
c. To provide a descriptive statistic, we would use the rate of occurrence in the sample to estimate the rate in the overall population. In the sample of 3980 women, 63 developed tissue abnormalities. This is a rate of (63/3980) * 1000 ≈ 15.8 per 1000 women.
d. This question does not provide specific data for the second population, but based on the statement that women from the first group are twice as likely to develop abnormalities, we can estimate that the occurrence of abnormalities in the second population would be half as frequent. This would be approximately 7.9 out of 1000 women.
e. Large sample sizes are often used in medical studies to ensure the results are statistically significant and more reliable. This helps to avoid anomalies and provides a more accurate representation of the population.
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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 :)
Answers
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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Simplify 2(x + 4) + 3(x - 4)
5x + 4
5x-4
5x
Answers
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
Perform the indicated operation and simplify the result. 6a2/5b2 * 45b3/18a3 = ? answers:a)3ab b)(3b)/a c)3
Answers
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]
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
Answers
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.
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
Answers
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
The Graduate Management Admission Test (GMAT) is a standardized test used by schools to determine the aptitude of individuals who are applying for MBA programs. The range of the GMAT score is 200-800. Brian has recently taken the exam and scored 720. This is an example of __________ data.
Answers
Answer:
Interval data
Step-by-step explanation:
Brian's score is an interval data because it appears within the GMAT range of score, which is 200-800
what does Martin Luther King Jr. mean when he said: "Let freedom ring"?
Answers
Answer:
Through the expression, "let freedom ring", Martin Luther King Jr. was emphasizing on the need for community effort throughout the nation in order to counteract segregation. Let freedom ring is a metaphor for the action of spreading equality
Step-by-step explanation:
Answer:this isn’t in the right spot it’s in math. But when mlk says this he wants equality for all people through the country and this is the metaphor he uses. He wants justice and freedom to be granted to all.
Step-by-step explanation:
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
Answers
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
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
Answers
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.
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
Answers
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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Trey drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 12 hours. When Trey drove home, there was no traffic and the trip only took hours. If his average rate was 20miles per hour faster on the trip home, how far away does Trey live from the mountains?
Do not do any rounding.
Answers
Question was Incomplete;Complete question is given below;
Trey drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 12 hours. When Trey drove home, there was no traffic and the trip only took 8 hours. If his average rate was 20miles per hour faster on the trip home, how far away does Trey live from the mountains?
Do not do any rounding.
Answer:
Trey lives 480 miles from the mountain.
Step-by-step explanation:
Given:
Time taken to drove the mountain =12 hours
Time taken to return back from mountain = 8 hours.
Let the speed at which he drove to mountain be denoted by 's'.
Speed on the trip to home = [tex]s+20[/tex]
We need to find the distance Trey live from the mountains.
Solution:
Let the distance be denoted by 'd'.
Now we know that;
Distance is equal to speed times Time.
framing in equation form we get;
distance from home to mountain [tex]d=12s[/tex]
Also distance from mountain to home [tex]d = (s+20)8=8s+160[/tex]
Now distance is same for both the trips;
so we can say that;
[tex]12s=8s+160[/tex]
Combining the like terms we get;
[tex]12s-8s=160\\\\4s=160[/tex]
Dividing both side by 4 we get;
[tex]\frac{4s}{4}=\frac{160}{4}\\\\s=40\ mph[/tex]
Speed while trip to mountain = 40 mph
Speed while trip to home = [tex]s+20=420+20=60\ mph[/tex]
So Distance [tex]d=12s=12\times40 = 480\ miles[/tex]
Hence Trey lives 480 miles from the mountain.
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
Answers
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
Please help asap need it done. What is the measure of ∠CED and ∠ACD?
Answers
Answer:
[tex]m\angle CED= 64\°[/tex]
[tex]m\angle ACD=124\°[/tex]
Step-by-step explanation:
In the figure given:
∠ABC = 93°
∠BAC = 31°
∠CDE = 60°
To find ∠CED and ∠ACD.
Solution:
In triangle ABC, we are given two vertex angles. We can find the third angle as angle sum of triangle = 180°.
∠ABC = 93° , ∠BAC = 31°
∠BCA= [tex]180\°-(93\°+31\°)[/tex]
∠BCA = 56°
[tex]m\angle BCA+m\angle ACD=180\°[/tex] [Supplementary angles forming a linear pair]
[tex]m\angle ACD=180\°-56\°[/tex]
[tex]m\angle ACD=124\°[/tex] (Answer)
In triangle CDE:
[tex]m\angle CDE+m\angle CED = m\angle ACD[/tex] [Exterior angle theorem :Exterior angle of a triangle is equal to sum of opposite interior angles ]
[tex]60\°+m\angle CED = 124\°[/tex]
[tex]m\angle CED= 124\°-60\°[/tex]
[tex]m\angle CED= 64\°[/tex] (Answer)
Answer:
m\angle CED= 64\°
m\angle ACD=124\°
Step-by-step explanation:
get an A!
What is the greatest common factor of the expression 63r^2t^3+42r^3t^5
Question 4 options:
10r^3t^5
21r^2t^3
7r^2t^3
3r^5t^8
Answers
Answer:
the gcf is 21r^2t^3
Step-by-step explanation:
21r^2t^3(3+2rt^2)
The greatest common factor of the expression 63r²t³+42r³t⁵ is 21r²t³, determined by finding the highest common power of each factor.
To find the greatest common factor (GCF) of the expression 63r²t³+42r³t⁵, we need to identify the highest powers of each factor that divide both terms.
Firstly, look at the numerical coefficients 63 and 42, the GCF of which is 21.For the variable r, the smallest power in the expression is r².For the variable t, the smallest power in the expression is t³.Thus, the GCF of the expression 63r²t³+42r³t⁵ is 21r²t³.
what is the solution of the following equation if x=10
Answers
Answer:
pictured and shown and solved
HELP MEEEEEEEEEEE PLZZZZZZ I NEEEEED ANSWER RIGHT NOWWWWW
Answers
Answer:
Therefore the measure of∠ A is 60.07.
Step-by-step explanation:
Given:
In Right Angle Triangle ABC
∠ B = 90°
BC = 13 ....Side opposite to angle A
AC = 15 .... Hypotenuse
To Find:
m∠A = ?
Solution:
In Right Angle Triangle ABC ,Sine Identity,
[tex]\sin A = \dfrac{\textrm{side opposite to angle A}}{Hypotenuse}\\[/tex]
Substituting the values we get
[tex]\sin A = \dfrac{BC}{AC}=\dfrac{13}{15}=0.8666\\\\A=\sin^{-1}(0.8666)=60.065\\\\m\angle A=60.07\°[/tex]
Therefore the measure of∠ A is 60.07
PLEEEEASE!!!! HELPP!!!
In △FEG , point H is between points E and F, point J is between points F and G, and HJ¯¯¯¯¯∥EG¯¯¯¯¯ . EH=8 , HF=12 , and FG=30 . What is FJ ? Enter your answer in the box.
Answers
Answer:
[tex]FJ=18\ units[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
△FEG is similar with △FHJ -----> by AA Similarity Theorem
so
[tex]\frac{FE}{FH}=\frac{FG}{FJ}[/tex]
we have
[tex]FE=HF+EH=12+8=20\ units\\FH=HF=12\ units\\FG=30\ units[/tex]
substitute the given values
[tex]\frac{20}{12}=\frac{30}{FJ}\\\\FJ=12(30)/20\\FJ=18\ units[/tex]
Answer: Fj = 18
Step-by-step explanation:
Hello! So i just took the test and I got this wrong but the answer is 18 down below is a screenshot so you know 18 is the correct answer :) Hope this helps ^.^
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
Answers
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.
Terrence finished a word search in 3/4 the time it took Frank. Charlotte finshed the word search in 2/3 the time it took Terrence. Frank finished the word search in 32 min. How long did it tack Charlott to finish the word search
Answers
Answer: Charlotte finished the word search in 16 minutes.
Step-by-step explanation:
Frank finished the word search in 32 minutes.
Terrence finished a word search in 3/4 the time it took Frank. This means that the time it took Terrence to finish the word search would be
3/4 × 32 = 24 minutes.
Charlotte finished the word search in 2/3 the time it took Terrence. This means that the time it took Charlotte to finish the word search would be
2/3 × 24 = 16 minutes
A castle has to be guarded 24 hours a day. Five knights are ordered to split each day's guard duty equally. How long will each knight spend on guard duty in one day? Write your answer in minutes:
Answers
Answer:
Each knight will guard 288 minutes in one day.
Step-by-step explanation:
Given:
A castle has to be guarded 24 hours a day. Five knights are ordered to split each day's guard duty equally.
Now, to find the minutes will each night spend on guard duty in one day.
As, in 1 hour there are 60 minutes.
Thus, in 24 hour there are 60 × 24 = 1440 minutes.
Total minutes for guarding = 1440 minutes.
So, there are knights ordered for guarding are = 5.
And each day's guard duty equally.
Now, to get the minutes will each night spend on guard duty in one day we divide the total minutes for guarding by number of knights that is 5:
[tex]1440\div5[/tex]
[tex]=288\ minutes.[/tex]
Therefore, each knight will guard 288 minutes in one day.
The registrar has nominal-level data on students' racial classification. What would be an appropriate measure of central tendency to report?
Answers
Answer:
In this case the Central Tendency measure that would be appropriate to report is Mode.
Step-by-step explanation:
Central Tendency measures are listed as follows:
i.) Mean
ii) Median
iii) Mode.
In the case that the data collected of a population is qualitative and not quantitative then the best Central Tendency measure to qualify the data is Mode of the data.
In the given example the data collected is of the students' racial classification which is not quantitative and purely qualitative. Therefore in case it is proper to take the Central Tendency measure to be reported as the Mode.
Tony and Maria are two star-crossed lovers trying to get on a committee of 4 people. If there are 9 people eligible for this committee, how many ways can exactly one of Tony and Maria be selected for the committee?
Answers
Answer:
The number of ways Tony and Maria can both be selected for the committee is 8 ways.
Step-by-step explanation:
i) Tony and Maria have to be on the committee together or not at all.
ii) Let us consider Tony and Maria as combined as one person.
Therefore now we can say that the number of eligible people for the committee = 9 - 1 = 8.
iii) therefore the number of ways that both Tony and Maria can be selected for the committee are
= 8C1 = [tex]\hspace{0.2cm}\binom{8}{1} = \frac{8!}{1! (8-1)!} = \frac{8!}{1!\times 7!} = \frac{8}{1} = \hspace{0.1cm}8 \hspace{0.1cm}ways[/tex]
The number of ways to select exactly one of Tony and Maria is 70.
It is given that,
The number of eligible people is 9.The number of members required for the committee is 4.Exactly one of Tony and Maria be selected for the committee.Explanation:
Excluding Tony and Maria from the 9 people. The number of remaining people is 7.
Exactly one of Tony and Maria be selected for the committee. So, one person is selected from 2 and 3 people are selected from the remaining 7 people.
[tex]\text{Number of ways}=^2C_1\times ^7C_3[/tex]
[tex]\text{Number of ways}=\dfrac{2!}{1!(2-1)!}\times \dfrac{7!}{3!(7-3)!}[/tex]
[tex]\text{Number of ways}=2\times 35[/tex]
[tex]\text{Number of ways}=70[/tex]
Thus, the number of ways to select exactly one of Tony and Maria is 70.
Learn more:
https://brainly.com/question/541625
The ratio of the number of the model cars that Jim owns to the number of cars Terrence owns is 4:3. Terrence owns 36 model cars. How many model cars does Jim own? Will the ratio change if Jim and Terrence each sell ten of their model car?
Answers
Answer:
Answer in explanation
Step-by-step explanation:
The ratio of their ownership is 4:3 I.e J to T
Now we know that Terrence has 36 model cars. To find the number of model cars Jim own, we need to find the unit ownership. This is the same as 36/3 which is 12 cars.
This means Jim has 12 * 4 = 48 model cars.
Now we are looking at them selling 10 of their cars each. This would bring the number of model cars owned to be 38 and 26 respectively.
The ratio here would now be 38:26 which is same as 19:13. Of course this is different from 4:3, hence we can conclude that the ratio will indeed change
Final answer:
Jim owns 48 model cars.
If both Jim and Terrence sell ten cars each, Jim will have 38 cars, Terrence will have 26, and the ratio of Jim's cars to Terrence's cars will change to 19:13.
Explanation:
The ratio of the number of model cars that Jim owns to the number of cars Terrence owns is 4:3. If Terrence owns 36 model cars, we can set up a proportion to find out how many model cars Jim owns.
Because Terrence's part of the ratio corresponds to 36 cars, we have:
Jim's cars / Terrence's cars = 4/3
Jim's cars / 36 = 4/3
Cross-multiplying to solve for Jim's cars:
(Jim's cars) * 3 = 4 * 36
Jim's cars = (4 * 36) / 3
Jim's cars = 144 / 3
Jim's cars = 48
Therefore, Jim owns 48 model cars.
If Jim and Terrence each sell ten of their model cars, Jim will have 38 model cars and Terrence will have 26. The new ratio will be:
38 / 26, which simplifies to 19 / 13, different from the original ratio of 4/3.
So, yes, the ratio will change if they both sell ten of their cars.