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jek_recluse [69]
3 years ago
11

The perimeter of a given rectangle is equal to the circumference of a given circle. The circle has radius 30 inches; the width o

f the rectangle is 8π inches. What is the length of the rectangle?
A. 7π inches

B. 44π inches

C. (30−8π) inches

D. 22π inches

E. 14π inches
Mathematics
2 answers:
Arte-miy333 [17]3 years ago
7 0
The answer to this question will be E
Nutka1998 [239]3 years ago
4 0
The answer to this is E
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A cell phone and phone case cost $110 in total. The cell phone costs $100 more
Olegator [25]

Answer:

Step-by-step explanation:

p + c = 110

p = c + 100

c + 100 + c = 110

2c + 100 = 110

2c = 110 - 100

2c = 10

c = 10/2

c = 5 .......cost of the phone case

p = c + 100

p = 5 + 100

p = 105 <=== cost of the phone

3 0
3 years ago
Find the angle θ between u = &lt;7, –2&gt; and v = &lt;–1, 2&gt;.
Dmitry_Shevchenko [17]

The angle between two vectors is:

CosФ = u - v / Magnitude(u) x magnitude(v)

Magnitude of u = SQRT(7^2 + -2^2) = SQRT(49 +4) = SQRT(53)

Magnitude of v = SQRT(-1^2 +2^2) = SQRT(1 +4) = SQRT(5)

u x v = (7 x -1) + (-2 x 2) = -7 + -4 = -11

cosФ = -11 / sqrt(53) x sqrt(5)

cosФ = -11sqrt265) / 265

Ф =cos^-1(-11sqrt265) / 265)

Ф=132.51 degrees.

7 0
3 years ago
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Slove for the value of x to the nearest whole number?
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Answer:

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Step-by-step explanation:

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3 0
2 years ago
How do you find the radius of a circle​
tia_tia [17]

Answer:

To calculate the radius of a circle by using the circumference, take the circumference of the circle and divide it by 2 times π.

3 0
3 years ago
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Working alone, Henry takes 3 hours less than Mary to clean the carpets in the entire office. Working together, they can clean th
Sati [7]

Answer:

It would take Henry 3 hours to clean the office carpets if Mary were not there to help

Step-by-step explanation:

Assume that it takes Henry t hours to clean the carpets

∵ Henry takes 3 hours less than Mary to clean the carpets

∵ Henry takes t hours

- That means add 3 to t to find Mary time

∴ Mary takes t + 3 hours

∵ The rate of Henry is \frac{1}{t}

∵ The rate of Mary is \frac{1}{t+3}

∵ Working together, they can clean the carpets in 2 hours

- Add the two rates and equate the answer by \frac{1}{2} (their rate together)

∴ \frac{1}{t}+\frac{1}{t+3}=\frac{1}{2}

Multiply the two denominators and multiply each numerator by the other denominator to add the two fractions of the left hand side

∵ \frac{(1)(t+3)}{t(t+3)}+\frac{(1)t}{t(t+3)}=\frac{1}{2}

∴  \frac{(t+3)}{t(t+3)}+\frac{t}{t(t+3)}=\frac{1}{2}

- Add the two fractions in the left hand side

∴ \frac{t+3+t}{t(t+3)}=\frac{1}{2}

∴  \frac{2t+3}{t^{2}+3t}=\frac{1}{2}

Use the cross multiplication

∵ (t² + 3t)(1) = 2(2t + 3)

∴ t² + 3t = 4t + 6

- Subtract 4t from both sides

∴ t² - t = 6

- Subtract 6 from both sides

∴ t² - t - 6 = 0

- Factorize it into two factors

∴ (t - 3)(t + 2) = 0

Equate each factor by 0 to find t

∵ t - 3 = 0

- Add 3 to both sides

∴ t = 3

OR

∵ t + 2 = 0

- Subtract 2 from both sides

∴ t = -2 ⇒ reject this answer because there is no - ve time

∴ t = 3

∴ Henry would take 3 hours to clean the carpets alone

It would take Henry 3 hours to clean the office carpets if Mary were not there to help

8 0
3 years ago
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