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3 years ago

Rewrite the rational expression with the given denominator -3/q = ?/6q

Mathematics

1 answer:

allochka39001 [22]3 years ago

7 0

Answer:

The answer is -18.

Step-by-step explanation:

Because to find this answer you have to multiply Q by 6 which gives you the denominator 6q. Then to get the numerator you have to multiply -3 by 6 also and that's how you get your answer of -18/6q.

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A rectangle has the length of 22 inches less than 7 times the width. If the area of the rectangle is 3197 square inches, find th

Nikolay [14]

The length of rectangle is 139 inches

Solution:

Given that, area of the rectangle is 3197 square inches

Let "L" be the length of rectangle and "W" be the width of rectangle

Also given that rectangle has the length of 22 inches less than 7 times the width

Length = 7 times width - 22

L = 7W - 22

The area of rectangle is given as:

$\text {Area of rectangle }=\text { length } \times \text { width }$

Substituting the values we get,

$\begin{array}{l}{3197=(7 W-22)(W)} \\\\ {3197=7 W^{2}-22 W} \\\\ {7 W^{2}-22 W-3197=0}\end{array}$

On solving the above quadratic equation using quadratic formula,

$\text {For the quadratic equation } a x^{2}+b x+c=0 \text { where } a \neq 0$

$x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$

$\begin{array}{l}{\text {Here in } 7 \mathrm{W}^{2}-22 \mathrm{W}-3197=0} \\\\ {a=7 ; b=-22 ; c=-3197}\end{array}$

Substituting in above quadratic formula,

$\begin{array}{l}{W=\frac{-(-22) \pm \sqrt{\left((-22)^{2}-4(7)(-3197)\right)}}{2 \times 7}} \\\\ {W=\frac{22 \pm \sqrt{90000}}{14}=\frac{22 \pm 300}{14}} \\\\ {W=\frac{22+300}{14} \text { or } W=\frac{22-300}{14}} \\\\ {W=23 \text { or } W=-19.85}\end{array}$

Since width of rectangle cannot be negative, ignore negative value of "W"

So width W = 23 inches

Length L = 7W - 22 = 7(23) - 22 = 139 inches

Thus length of rectangle is 139 inches

8 0

4 years ago

Find the area of a trapezoid , given the bases b1 = 14 mi and b2 = 25 mi and hight h= 6 mi

elena55 [62]

Answer:

area = 117

Step-by-step explanation:

The area (A) of a trapezoid is calculated using the formula

A = $\frac{1}{2}$ h (b₁ + b₂ )

here h = 6, b₁ = 14 and b₂ = 25

A = $\frac{1}{2}$ × 6 × (14 + 25) = 3 × 39 = 117

3 0

3 years ago

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Rasek [7]

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5 0

3 years ago

Insert a parentheses 4 + 3 * 7 - 4

lana66690 [7]

(4+3)(7-4) if you want the products to multiply each other
4+3(7-4) if you want to use the distributive property and simply have 3 multiplied but the simplification of 7-4 which is 3

3 0

3 years ago

Read 2 more answers

What is 7x + 6x = ?

viva [34]

Answer:

Step-by-step explanation:

Two ways to solve

1.) Expand each term in the equation

7x = x · x · x · x · x · x · x

6x = x · x · x · x · x · x

Count all the x’s ⇒ There are 13 x’s ⇒ 13x

2.) Add the coefficients

7 + 6 = 13
7x + 6x = 13x

Hence,

Answer = 13x

8 0

3 years ago