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4 years ago

The perimeter of a rectangle is represented by

1 answer:

8 0

The perimeter of a rectangle is represented by 4x^2 + 5x − 2. The perimeter of a smaller rectangle is represented by x^2 + 3x + 5. Which polynomial expression BEST represents how much larger the first rectangle is than the smaller rectangle?

A) 3x^2 + 2x − 7

B) 3x^2 + 2x − 3

C) 3x^2 + 8x + 3

D) 5x^2 + 8x − 7

<h3><u>Answer:</u></h3>

Option A

The polynomial expression best represents how much larger the first rectangle is than the smaller rectangle is $3 x^{2}+2 x-7$

<h3><u>Solution:</u></h3>

Perimeter of a rectangle is represented by 4x^2 + 5x − 2

Perimeter of a smaller rectangle is represented by x^2 + 3x + 5

To Find : Polynomial expression that represents how much larger the first rectangle is than the smaller rectangle.

Which means we have to find difference between perimeter of both rectangles

Subtract the equation of perimeter of smaller rectangle from equation of perimeter of a larger rectangle

Difference = perimeter of a larger rectangle - perimeter of smaller rectangle

$\text {Difference }=\left(4 x^{2}+5 x-2\right)-\left(x^{2}+3 x+5\right)$

On removing the brackets we get,

$\begin{array}{l}{\text { Difference }=4 x^{2}+5 x-2-x^{2}-3 x-5} \\\\ {\text { Difference }=3 x^{2}+2 x-7}\end{array}$

Thus option A is correct

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Match each pair of points to the equation of the line that is parallel to the line passing through the pointsB(5,2) and C(7,-5)Y

a_sh-v [17]

we will select each points and find equation of line

option-A:

points are B(5,2) and C(7,-5)

x1=5,y1=2 , x2=7 , y2=-5

Firstly, we will find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{-5-2}{7-5}$

$m=-3.5$

we can use point slope form of line

$y-y_1=m(x-x_1)$

we can plug values

$y-2=-3.5(x-5)$

$y=\frac{-7}{2}x+\frac{39}{2}$ ...........Answer

option-B:

points are D(11,6) and E(5,9)

x1=11,y1=6 , x2=5 , y2=9

Firstly, we will find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{9-6}{5-11}$

$m=-0.5$

we can use point slope form of line

$y-y_1=m(x-x_1)$

we can plug values

$y-6=-0.5(x-11)$

$y=\frac{-1}{2}x+\frac{23}{2}$ ...........Answer

option-C:

points are F(-7,12) and G(3,-8)

x1=-7,y1=12 , x2=3 , y2=-8

Firstly, we will find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{-8-12}{3+7}$

$m=-2$

we can use point slope form of line

$y-y_1=m(x-x_1)$

we can plug values

$y-12=-2(x+7)$

$y=-2x-2$ ...........Answer

option-D:

points are H(4,4) and I(8,9)

x1=4,y1=4 , x2=8 , y2=9

Firstly, we will find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{9-4}{8-4}$

$m=1.25$

we can use point slope form of line

$y-y_1=m(x-x_1)$

we can plug values

$y-4=1.25(x-4)$

$y=\frac{5}{4}x-1$ ...........Answer

option-E:

points are J(7,2) and K(-9,8)

x1=7,y1=2 , x2=-9 , y2=8

Firstly, we will find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{8-2}{-9-7}$

$m=-\frac{3}{8}$

we can use point slope form of line

$y-y_1=m(x-x_1)$

we can plug values

$y-2=\frac{3}{8}(x-7)$

$y=\frac{3}{8}x-\frac{5}{8}$ ...........Answer

option-F:

points are L(5,-7) and M(4,-12)

x1=5,y1=-7 , x2=4 , y2=-12

Firstly, we will find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{-12+7}{4-5}$

$m=5$

we can use point slope form of line

$y-y_1=m(x-x_1)$

we can plug values

$y+7=5(x-5)$

$y=5x-32$ ...........Answer

7 0

3 years ago

Read 2 more answers

Which of the prisms below must have symmetry with respect to a point? (Select all that apply.

evablogger [386]

Answer:

Option III

Step-by-step explanation:

All regular figures have a point at which one can draw a line of symmetry. A figure classifies are regular if all of its sides and angles are congrunet. It is given that figure (III) has a regular base, thus it is most probable that it has symmetry with respect to a point.

5 0

3 years ago

Please answer this fast

fomenos

Answer:

CD = 2 units

Step-by-step explanation:

in the given right triangle ΔCDE,

By applying tangent rule,

tan(∠E) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$