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Goryan [66]
3 years ago
10

A rectangle has a width of 9 inches and a length of 15 inches. If the rectangle is enlarged by a scale factor of 3/2, what is th

e perimeter of the dilated rectangle
Mathematics
1 answer:
asambeis [7]3 years ago
6 0

Answer:

P = 48 in²

Step-by-step explanation:

Given: A rectangle; Width = 9 inches, length = 15 inches, enlarged by a scale factor of \frac{3}{2}

To find: Perimeter of the dilated rectangle

Formula: P=2(l+w)

Solution: After a dilation with a scale factor of one-half, then the lengths on the image would be one-half , one-half , and one-half . To find the perimeter of an enlarged figure, you can multiply the original figure's perimeter by the scale factor.

P=2(l+w)=2 × (15+9)=48in

Therefore, the perimeter of the detailed rectangle that was enlarged is 48 in²

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Use a graph in a (-2π, 2π, π/2) by (-3, 3, 1) viewing rectangle to complete the identity.
yaroslaw [1]

First, notice that:

2\tan (\frac{x}{2})=2\cdot(\pm\sqrt[]{\frac{1-cosx}{1+\cos x})}

And in the denominator we have:

1+\tan ^2(\frac{x}{2})=1+\frac{1-\cos x}{1+\cos x}=\frac{1+cosx+1-\cos x}{1+cosx}=\frac{2}{1+\cos x}

then, we have on the original expression:

\begin{gathered} \frac{2\tan(\frac{x}{2})}{1+\tan^2(\frac{x}{2})}=\frac{2\cdot\pm\sqrt[]{\frac{1-\cos x}{1+cosx}}}{\frac{2}{1+\cos x}}=\frac{2\cdot(\pm\sqrt[]{1-cosx})\cdot(1+\cos x)}{2\cdot(\sqrt[]{1+cosx})} \\ =(\sqrt[]{1-\cos x})\cdot(\sqrt[]{1+\cos x})=\sqrt[]{(1-\cos x)(1+\cos x)} \\ =\sqrt[]{1-\cos^2x}=\sqrt[]{\sin^2x}=\sin x \end{gathered}

therefore, the identity equals to sinx

8 0
1 year ago
Peter is reading a 193-page book. He has read three pages more than one fourth of the number of pages he hasnt yet read. How man
Anit [1.1K]
<span>Let n = the number of pages not read
Then the number of pages read = n/4 + 3
Since the total number of pages is 193, we have

n + n/4 + 3 = 193
5n/4 = 190
n = 152
At 8 pages per day it will take 152 pages/ 8 pages/day = 19 days

</span>
5 0
3 years ago
What is the value of d to the nearest tenth?
Ghella [55]

Answer: d=13.8

Step-by-step explanation:

A line that cuts a circle at two points is called "secant".

There is a theorem known as "Intersecting Secant Theorem". This is the theorem you need to use to find the value of "d".

According the Intersecting Secant Theorem:

(14)(14+20)=(16)(16+d)\\(14)(34)=(16)(16+d)

Having this expression, the next step is to solve for "d":

Use Distributive property:

476=256+16d

Subtract 256 from both sides:

476-256=-256+256+16d

220=16d

Divide both sides by 16:

\frac{220}{16}=\frac{16d}{16}\\\\13.75=d

The value of "d" rounded to the nearest tenth is:

d=13.8

6 0
3 years ago
A cone shaped building has a height of 11.4 meters and a base with a diameter of 12 meters . The building will be filled with ro
Vlad1618 [11]

Answer:

The answer to your question is  $ 8591.04

Step-by-step explanation:

Data

height = 11.4 m

diameter = 12 m

cost = $20/ft³

Process

1.- Calculate the volume of the cone

Formula

Volume = 1/3 πr²h

Substitution

Volume = 1/3 (3.14)(12/2)²(11.4)

Simplification

Volume = 1/3(1288.66)

Volume = 429.55 m³

2.- Calculate the cost

                $20 ----------------- 1 m³

                   x   ----------------- 429.55 m³

                   x = (429.55 x 20)/ 1

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8 0
3 years ago
Which relationship has a zero slope
vesna_86 [32]

Answer:

The first table.

Step-by-step explanation:

A slope of 0 means that as x increases, y stays the same.  In the first table, all of our y-values are 2; this means that y stays constant.  

To prove it, we use our formula for slope:

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

The slope of the line between the first two points is

(2-2)/(-3--1) = 0/-2 = 0

The slope of the line between the second pair of points is

(2-2)/(-1-1) = 0/-2 = 0

The slope of the line between the next pair of points is

(2-2)/(1-3) = 0/-2 = 0

Since the slope between each pair of points is 0, the slope of the entire line is 0.

4 0
3 years ago
Read 2 more answers
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