5x - 2y = 21

The area of a cross section through the center of a sphere is 46 square inches. Find the surface area of the sphere.

gavmur [86]

Answer:

184 in.^2

Step-by-step explanation:

The cross section through the center of a sphere is a circle whose radius is equal to the radius of the sphere.

area of circle

$A_{circle} = \pi r^2$

$\pi r^2 = 46$

$r^2 = \dfrac{46}{\pi}$

$r = \sqrt{\dfrac{46}{\pi}}$

$r = 3.83 ~in.$

surface area of sphere

$SA = 4 \pi r^2$

$SA = 4 \times \pi \times (3.83)^2$

$SA = 184~in.^2$

7 0

3 years ago

When you go to the store, does tax increase or decrease the cost of your items?

Musya8 [376]

yes because you have to pay more it's tricky

3 0

3 years ago

Write a real-world problem that is solved by an equation and then solve (show work).

ololo11 [35]

A company is selling books. It has to pay $500 to start printing the books, and once they have done that, the books sell at $14.99 each. How many books must they sell to make a profit?

First we would model an equation. X will be the amount of books sold, and Y will be profits (in dollars obv). They had to pay $500 before they could start selling, so we must account for that too.

This equation would be $y=14.99x-500$ because for every book sold, X increases by 1, increasing Y by 14.99

The answer would be 34 books sold in order to turn a profit. (500/14.99=

6 0

3 years ago

there are 11 pieces of pie left over in the cafeteria. if 6 pieces are apple and 5 are cherry, what fraction of the remaining pi

Leto [7]

Answer:

$\frac{6}{11}$

Step-by-step explanation:

we know that

To find what fraction of the remaining pieces are apple, divide the remaining pieces of apple by the total remaining pieces

we have that

the remaining pieces of apple is equal to 6

the total remaining pieces is 11

so

$\frac{6}{11}$

8 0

3 years ago

If y-3x=9, 7x+y=25, what is the value of x and y?

lianna [129]

$\bold{\rm{Given}}\text{ : If y - 3x = 9, 7x + y = 25, what is the value of x and y}?$

$\bold{\rm{Solution}} \text{: We'll solve this by substitution method}$

$\dashrightarrow y - 3x = 9 \\ \\ \dashrightarrow \boxed{y = 9 + 3x } \qquad .. \sf eq(1)$

$\text{we got the value of y now getting the value of x}$

$\looparrowright 7x + y = 25 \\ \\ \looparrowright 7x = 25 - y \\ \\ \looparrowright \boxed{x = \frac{25 - y}{7}} \qquad .. \sf eq(2)$

$\text{Now, putting y = 9 + 3x in eq(2)}$

$\hookrightarrow x = \frac{25 - y}{7} \\ \\ \hookrightarrow x = \frac{25 - 9 + 3x}{7} \\ \\ \hookrightarrow 7x = 25 - 9 + 3x \\ \\ \hookrightarrow 7x - 3x = 16 \\ \\ \hookrightarrow 4x = 16 \\ \\ \hookrightarrow x = \frac{16}{4} \\ \\ \star \quad \boxed{ \green{ \frak{ x = 4}}}$

$\text{Now we know the value of x, for getting y we need to put x in eq(1)}$

$: \implies y = 9 + 3x \\ \\ : \implies y = 9 + 3(4) \\ \\ : \implies y = 9 + 12 \\ \\ \star \quad \boxed{\frak{ \green{y = 21}}}$

$\text{Hence, values of x and y are} \: \frak{ \green{4}} \: \text{and} \: \frak{ \green{21}} \: \text{respectively}.$

4 0

2 years ago