The ratio of the radii of two circles is 9:16. Then what is the ratio of their circumferences?

Answers

Answer 1

Answer: 56.52:100.48

circumference is the diameter × π
diameter is radius × 2

first circle ->

r = 9
d = 9 × 2 = 18
c = 18 × π ≈ 56.52

second circle ->

r = 16
d = 16 × 2 = 32
c = 32 × π ≈ 100.48

so the ratio of circurfremce for 2 circles that have a ratio of radii 9:16 would be 56.52:100.48

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Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level. 7h – 5(3h – 8) = –72Which statement is true about Pieter’s solution?
1. It cannot be a fraction or decimal because the depth of the well is a whole number.
2.It must be a positive number since it represents a number of hours.
3. It must be a negative number because the depth is below sea level.
4.It cannot be greater than –72 because that is the depth of the well.

Answers

Answer:

Option B is correct

It must be a positive number since it represents a number of hours.

Step-by-step explanation:

As per the statement:

Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level.

Given the equation as:

$7h-5(3h-8) = -72$

Using distributive property, $a\cdot (b+c) = a\cdot b+ a\cdot c$

$7h-15h+40 = -72$

Combine like terms;

$-8h+40 = -72$

Subtract 40 from both sides we have;

$-8h= -112$

Divide both sides by -8 we have;

h = 14 hours

Therefore, the statement is true about Pieter’s solution is, It must be a positive number since it represents a number of hours.

the answer is B It must be a positive number since it represents a number of hours.

Which of the following is the equation of a line parallel to the line y=3x+2, passing through the point (10,1)?A. 3x - y=29
B. 3x + y=29
C. -3x-y=29
D. 3x + y=29

Answers

Answer:

Option A

Step-by-step explanation:

We have to find the equation of a line parallel to y = 3x + 2 and passing through (10, 1)

Slope of the given line y = 3x + 2 is 3

So line parallel to this line will have same slope = 3

Now we assume this line is y = 3x + c

It is given that a point ( 10,1 ) lies on this line.

So we put x = 10 and y = 1 in this equation to get

y-intercept

1 = 30 + c

c = - 29

Equation of the line will be y = 3x - 29

or -3x + y = -29 ⇒ 3x - Y = 29

Option A is the answer.

I think it's A. One way you can identify if they are parallel is if both of the slopes are the same (also both have to have the same signs).

Chef Rita is cooking for a Sunday brunch. she knows that 22 pancakes can feed 8 people. She is wondering how many people she can feed with 55 pancakes. She assumes each person eats the same quantity of pancakes

Answers

Answer:

20 people

Step-by-step explanation:

22 pancakes = 8 people

55 pancakes = x people

=> Cross-multiply

=> 22 * x = 55 * 8

=> 22x = 440

=> 22x/22 = 440/22

=> x = 20

So, 55 pancakes can feed 20 people.

Simplify 8 -2/3 please (leave as fraction)

Answers

$8^{-(2)/(3)}=\left(2^3\right)^{-(2)/(3)}=2^{3\cdot(-(2)/(3))}=2^(-2)=\left((1)/(2)\right)^2=(1)/(4)$

$8^{-(2)/(3)}=\n \left((1)/(8)\right)^{(2)/(3)}=\n \sqrt[3]{\left((1)/(8)\right)^2}=\n \sqrt[3]{(1)/(64)}=\n (1)/(4)$

©Brian invests £1300 into his bank account.
He receives 10% per year simple interest.
How much will Brian have after 3 years?
Give your answer to the nearest penny where appropriate.