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2 years ago

The width of the rectangle is 5x-4. The length of the rectangle is 5

Mathematics

1 answer:

drek231 [11]2 years ago

3 0

Answer:

The area of the rectangle A = 25x² - 20x

Step-by-step explanation:

Given

The width of the rectangle = w = 5x - 4

The length of a rectangle = l = 5x

To determine

The area of the rectangle = ?

Using the Formula to determine the area of the rectangle

$A = wl$

substitute w = 5x - 4 and l = 5x in the formula

$A = (5x-4) (5x)$

Apply distributive law: a(b-c) = ab - ac

$=\left(5x\right)\cdot \:5x-\left(5x\right)\cdot \:4$

$=5x\left(5x\right)-4\left(5x\right)$

as 5x(5x) = 25x² and 4(5x) = 20x, so

$=25x^2-20x$

Therefore, the area of the rectangle A = 25x² - 20x

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Kay has 28 coins which includes nickels and dimes if the total is 2.35$, how many of each coin does Kay have?

BaLLatris [955]

Answer:

19 dimes and 9 nickels

Step-by-step explanation:

Model the situation using two equations, then solve the system.

let n be number of nickels and d be number of dimes.

n + d = 28 <= This equation is about the number of coins.

0.05n + 0.10d = 2.35 <=This equation is about the worth in dollars.

Rearrange n + d = 28.

n = 28 - d

Now we can substitute this equation into the other one.

Sub n =28-d at the "d" variable for the equation 0.05n + 0.10d = 2.35

0.05n + 0.10d = 2.35

Now there is only one variable.

0.05(28 - d) + 0.10d = 2.35 <=distribute this

0.05(28 - d) + 0.10d = 2.35

1.4 - 0.05d + 0.10d = 2.35 <=combine like terms

1.4 + 0.05d = 2.35 <= begin to isolate d

0.05d = 2.35 - 1.4

0.05d = 0.95

d = 0.95/0.05

d = 19

Now that we know d=19, we can substitute it into any equation.

Choose the equation n + d = 28 because the numbers are easier.

n + d = 28

n + 19 = 28 <=isolate n

n = 28 - 19

n = 9

Since n=9 and d=19, Kay has 9 nickels and 19 dimes.

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Answer:

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