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jenyasd209 [6]
3 years ago
9

ABC Bookstore sells packages of books that include both new and used books. New books cost $20 and used books cost $8. The books

tore wants to sell packages that have 36 books total, and the store charges $456 for each package. How many new and used books will be in each Package?
Mathematics
1 answer:
evablogger [386]3 years ago
5 0

Answer:

There are 14 new books and 22 old books in the package.

Step-by-step explanation:

New books cost $20 and used books cost $8. The bookstore wants to sell packages that have 36 books total, and the store charges $456 for each package.

If the number of new books in the package is x and that of old books in the package is y, then we can write two simultaneous equations as

x + y = 36 ........... (1) and

20x + 8y = 456

⇒ 5x + 2y = 114 ............ (2)

Now, solving equations (1) and (2) we get,

5x + 2(36 - x) = 114

⇒ 3x + 72 = 114

⇒ 3x = 42

⇒ x = 14

Then, y = 36 - x = 22.

Therefore, there are 14 new books and 22 old books in the package. (Answer)

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Answer:

314 cm²

Step-by-step explanation:

It's not the point O, but the circle O, a point has no area.

The area of a circle is given by the formula A = π r²

We don't have r (radius), but we have the diameter, which is double the radius.  So, r = d / 2 = 20 cm / 2 = 10 cm

Now, we can plug r directly into the equation:

A = π r² = π 10² = 100π = 314 cm²

7 0
4 years ago
Given: WY=ZX<br><br> A is the midpoint of WY.<br><br> A is the midpoint of ZX.<br><br> Prove: WA =ZA
navik [9.2K]

Answer:

Given information: WY=ZX, A is the midpoint of WY and A is the midpoint of ZX.

To prove :  WA =ZA

Proof:

A is the midpoint of WY, it means A divides WY in two equal parts.

WA=AY

So, WY is twice of WA.

WY=2WA            .... (1)

A is the midpoint of ZX, it means A divides ZX in two equal parts.

ZA=AX

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Substitute the values from equation (1) and (2).

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3 years ago
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
hram777 [196]

Write the system in augmented-matrix form:

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Multiply through row 1 by 1/2:

\left[\begin{array}{ccc|c}1&1&2&8\\5&-2&3&-1\\1&2&-3&-9\end{array}\right]

Add -1(row 1) to row 3, and add -5(row 1) to row 2:

\left[\begin{array}{ccc|c}1&1&2&8\\0&-7&-7&-41\\0&1&-5&-17\end{array}\right]

Swap rows 2 and 3:

\left[\begin{array}{ccc|c}1&1&2&8\\0&1&-5&-17\\0&-7&-7&-41\end{array}\right]

Add -7(row 2) to row 3:

\left[\begin{array}{ccc|c}1&1&2&8\\0&1&-5&-17\\0&0&-42&-160\end{array}\right]

Multiply through row 3 by -1/42:

\left[\begin{array}{ccc|c}1&1&2&8\\0&1&-5&-17\\0&0&1&\frac{80}{21}\end{array}\right]

Add 5(row 3) to row 2:

\left[\begin{array}{ccc|c}1&1&2&8\\0&1&0&\frac{43}{21}\\0&0&1&\frac{80}{21}\end{array}\right]

Add -1(row 2) and -2(row3) to row 1:

\left[\begin{array}{ccc|c}1&0&0&-\frac53\\0&1&0&\frac{43}{21}\\0&0&1&\frac{80}{21}\end{array}\right]

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Answer:

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3 years ago
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(x-4)(x-3)

FOIL to check

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