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3 years ago

John is 14 years older than Sam and the product of their ages is 240. How old is Sam?

Mathematics

1 answer:

Shtirlitz [24]3 years ago

3 0

Answer:

A.) 10 years old

Step-by-step explanation:

Sam: John - 14

S = J - 14

S x J = 240

10 = J - 14

0 = J - 14 - 10

-J = -24

J = 24

10 x 24 = 240

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Find the length of the arc and express your answer as a fraction times pie

Elina [12.6K]

Solution:

Given a circle of center, A with radius, r (AB) = 6 units

Where, the area, A, of the shaded sector, ABC, is 9π

To find the length of the arc, firstly we will find the measure of the angle subtended by the sector.

To find the area, A, of a sector, the formula is

$\begin{gathered} A=\frac{\theta}{360\degree}\times\pi r^2 \\ Where\text{ r}=AB=6\text{ units} \\ A=9\pi\text{ square units} \end{gathered}$

Substitute the values of the variables into the formula above to find the angle, θ, subtended by the sector.

$\begin{gathered} 9\pi=\frac{\theta}{360\degree}\times\pi\times6^2 \\ Crossmultiply \\ 9\pi\times360=36\pi\times\theta \\ 3240\pi=36\pi\theta \\ Divide\text{ both sides by 36}\pi \\ \frac{3240\pi}{36\pi}=\frac{36\pi\theta}{36\pi} \\ 90\degree=\theta \\ \theta=90\degree \end{gathered}$

To find the length of the arc, s, the formula is

$\begin{gathered} s=\frac{\theta}{360\degree}\times2\pi r \\ Where \\ \theta=90\degree \\ r=6\text{ units} \end{gathered}$

Substitute the variables into the formula to find the length of an arc, s above

$\begin{gathered} s=\frac{\theta}{360}\times2\pi r \\ s=\frac{90\degree}{360\degree}\times2\times\pi\times6 \\ s=\frac{12\pi}{4}=3\pi\text{ units} \\ s=3\pi\text{ units} \end{gathered}$

Hence, the length of the arc, s, is 3π units.

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1 year ago

A painter leans a 25-foot ladder against the wall. The bottom of the ladder is 20 feet from the base of the wall. The painter th

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Marcus has created a budget for his upcoming trip to the theme park. Admission is 40% of the budget. He plans to spend 32% of his money on food, 23% on souvenirs, and save 5% for emergencies. He knows the admission will be $6 less than he will spend on food and souvenirs. How much money will Marcus need to take to the park?

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3 years ago

(05.05)Polygon ABCD has the following vertices:

Kaylis [27]

Answer is option b)38.5 sq.units

Given vertices are A(-4,2) ,B(3,2),C(3,-5) and D(-4,-2)

Area of polygon is defined in the image.

If you have any doubts see the image or ask in comments box.

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THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.

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3 years ago

Help please! A. B. C. D.

elixir [45]

Answer:

b = 175; which is the initial # of pages to start

Step-by-step explanation:

you can find the slope to find b or y-intercept (x=0) for equation

y=mx+b

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(x1,y1) = (9, 100)

(x2, y2) = (15, 50)

m = (50-100) / (15-9) = -50/6 = -25/3

let use point (15, 50)

y=mx+b

50 = -25/3*x + b

50 = (-25/3)*(15) + b

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Graph The Solution set to the inequality - s/2 > 9 A B C Or D

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4 years ago

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