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3 years ago

Enter your answer and show all the steps that you use to solve this problem in the space provided.

Mathematics

1 answer:

Elan Coil [88]3 years ago

6 0

The circumference of the circle is 144.4 yards

Step-by-step explanation:

The circumference of a circle is C = 2πr, where

r is the radius of the circle
π is a constant ratio between the circumference of the circle and its diameter and its value is approximately 3.14

∵ The radius of a circle is 23 yards

- Use the rule above to find its circumference

∵ C = 2πr

∴ C = 2π(23)

∵ π ≅ 3.14

∴ C = 2(3.14)(23)

∴ C = 144.44 yards

- Round it to the nearest tenth

∴ C = 144.4 yards

The circumference of the circle is 144.4 yards

Learn more:

You can learn more about the circle in brainly.com/question/1952668

#LearnwithBrainly

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Which equation can be used to solve for the rate, r, for Sam to change all the light bulbs in the office building by himself?

Bad White [126]

Answer:

$\frac{3}{r}+\frac{3}{8}=1$

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Working together, Sam and Charlie can change all light bulbs in the office building in 3 hours. It would have taken Charlie 8 hours to do the job alone. Which equation can be be used to solve for the rate 'r', for Sam to change all the light bulbs in the office building by himself.

Let Sam can change the bulbs in the office alone in 'r' hours

Per hour work done by Sam alone = $\frac{1}{r}$

Let Sam takes he time to change the same bulbs in the office alone = 8 hours

Per hour work done by Sam = $\frac{1}{8}$

Since, Sam and Charlie complete the work together in time = 3 hours

Therefore, per hour work done by both = $\frac{1}{3}$

Equation for per work done by both will be,

Per hour work done by both = Per hour work done by Sam alone + Per hour work done by Charlie

$\frac{1}{r}+\frac{1}{8}=\frac{1}{3}$

Therefore, equation for the rate 'r' will be,

$\frac{1}{r}+\frac{1}{8}=\frac{1}{3}$

$\frac{3}{r}+\frac{3}{8}=1$

8 0

3 years ago

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What is the quotient of -8(^6)/4x(^-3)

Anna [14]

For this case we must find the quotient of the following expression:

$\frac {-8x ^ 6} {4x ^ {- 3}} =$

By definition of power properties we have:

$a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}$

Rewriting the expression we have:

$\frac{-8}{4}*x^6*x^3$

By definition of multiplication of powers of the same base we have to put the same base and add the exponents:

$-2x^{6+3}$

Answer:

$-2x ^ 9$

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3 years ago

What is the value of x? Enter your answer in the box. _____ units

krek1111 [17]

Answer:

x=28

Step-by-step explanation:

We can use similar triangles and proportions to solve this problem. Put the side of the small triangle over the same side of the larger triangle.

x 42

---------- = ----------

x+10 42+15

Simplify

x 42

---------- = ----------

x+10 57

Using cross products

57x = 42 (x+10)

Distribute

57x = 42x+420

Subtract 42x from each side

57x-42x = 42x-42x +420

15x = 420

Divide each side by 15

15x/15 = 420/15

x=28

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3 years ago

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Fred is 4 times as old as Nathan and is also 27 years older than Nathan. Let f be Fred's age and let n be Nathan's age.

bazaltina [42]

Answer:

The system of equations is

and

Fred's age is 36 years old and Nathan's age is 9 years old

Step-by-step explanation:

Let

f -----> Fred's age

n ----> Nathan's age

we know that

-----> equation A

----> equation B

equate the equations and solve for n

Find the value of f

therefore

Fred's age is 36 years old and Nathan's age is 9 years old

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What number would you add to the equation below to complete the square?x2 + 4x = 0?

julia-pushkina [17]

------------------------------------------------------------------
Equation
------------------------------------------------------------------
x² + 4x = 0

------------------------------------------------------------------
Add a constant
------------------------------------------------------------------
x² + 4x + (4/2)² - (4/2)² = 0 ← Add 2² to form perfect square

------------------------------------------------------------------
Evaluate bracket
------------------------------------------------------------------
x² + 4x + 2² - 2² = 0

------------------------------------------------------------------
Form the perfect square
------------------------------------------------------------------
(x + 2)² = 4

------------------------------------------------------------------
Square root both sides
------------------------------------------------------------------
(x+2) = $\pm$ √4

------------------------------------------------------------------
Evaluate the square root
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(x+2) = $\pm$ 2

------------------------------------------------------------------
Solve x
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x = 2 - 2 or x = -2 - 2

x = 0 or -4

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Answer: The constant to add is 4 and the value of x = 0 or -4
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