Simplify the expression. 7 √x • 7 √x • 7 √x

1 answer:

8 0

Answer:

√7x−49√x

Explanation:

First of all, expand by multiplying √7x⋅√x and √7x⋅7√7respectively:

√7x(√x−7√7)=√7x⋅√x−√7x⋅7√7

... you can express √7x as √7⋅√x...

=√7⋅√x⋅√x−√7⋅√x⋅7⋅√7

=√7⋅(√x)2−(√7)2⋅√x⋅7

... the operations squaring and taking the square root "eliminate each other"...

=√7⋅x−7⋅√x⋅7

=√7x−49√x

Hope that this helped!

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The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 50 ft². Find the dimensions

Mariulka [41]

Answer

Length = 10 ft

Width = 5 ft

Explanation

Area of the rectangle given = 50 ft²

Let the width of the rectangle be x

So this means the length of the rectangle will be 3x - 5

What to find:

The dimensions of the rectangle.

Step-by-step solution:

Area of a rectangle = length x width

i.e A = L x W

Put A = 50, L = 3x - 5, W = x into the formula.

$\begin{gathered} 50=(3x-5)x \\ 50=3x^2-5x \\ 3x^2-5x-50=0 \end{gathered}$

The quadratic equation can now be solve using factorization method:

$\begin{gathered} 3x^2-5x-50=0 \\ 3x^2-15x+10x-50=0 \\ 3x(x-5)+10(x-5)=0 \\ (3x+10)(x-5)=0 \\ 3x+10=0\text{ }or\text{ }x-5=0 \\ 3x=-10\text{ }or\text{ }x=5 \\ x=-\frac{10}{3}\text{ }or\text{ }x=5 \end{gathered}$

Since the dimension can not be negative, hence the value of x will be = 5.

Therefore, the dimensions of the rectangle will be: