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3 years ago

The length of a rectangle is 7 inches less than twice the width, w, of the rectangle.

Mathematics

1 answer:

Ivan3 years ago

4 0

Answer:

Step-by-step explanation:

Let w represent the width of the rectangle.

The length of a rectangle is 7 inches less than twice the width, w, of the rectangle. It means that the length is (2w - 7) inches

Part A

The function that gives the area as a function of the width is

A(w) = w(2w - 7)

Part B:

If the area of the rectangle is 60 square inches, it means that

w(2w - 7) = 60

2w² - 7w = 60

2w² - 7w - 60 = 0

2w² + 8w - 15w - 60 = 0

2w(w + 4) - 15(w + 4) = 0

2w - 15 = 0 or w + 4 = 0

w = 15/2 or w = - 4

Since w cannot be negative, then

w = 15/2 = 7.5 inches

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lubasha [3.4K]

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2 years ago

Describe and correct the error(s) made in each of the problems below.

ladessa [460]

Answer:

$\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}$

$\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}$

Step-by-step explanation:

<u>Errors in Algebraic Operations </u>

It's usual that students make mistakes when misunderstanding the application of algebra's basic rules. Here we have two of them

When we change the signs of all the terms of a polynomial, the expression must be preceded by a negative sign
When multiplying negative and positive quantities, if the number of negatives is odd, the result is negative. If the number of negatives is even, the result is positive.
Not to confuse product of fractions with the sum of fractions. Rules are quite different

The first expression is

$1-x / (5-x)(-x)=x-1 / x(x-5)$

Let's arrange into format:

$\displaystyle \frac{1-x}{(5-x)(-x)} =\frac{x-1 }{ x(x-5)}$

We can clearly see in all of the factors in the expression the signs were changed correctly, but the result should have been preceeded with a negative sign, because it makes 3 (odd number) negatives, resulting in a negative expression. The correct form is

$\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}$

Now for the second expression

$5/s+2/5=2/s$

Let's arrange into format

$\displaystyle \frac{5}{s}+\frac{2}{5} =\frac{2}{s}$

It's a clear mistake because it was asssumed a product of fractions instead of a SUM of fractions. If the result was correct, then the expression should have been

$\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}$

6 0

2 years ago

Plz help :( what is 10,000,000(20)^10 !?

Sergio [31]

Answer: 102,400,000,000,000,000,000

Step-by-step explanation:

First do 20^10 = 10,240,000,000,000.

Then, multiply 10,240,000,000,000 * 10,000,000 to get 102,400,000,000,000,000,000.

<em>Hope it helps <3</em>

7 0

3 years ago