How are the following ratios equivalent? 4:5 and 8:10

The length of each side of a regular pentagon is increased by 8 inches, so the perimeter is now 65 inches. What is the original

evablogger [386]

Here as the Pentagon is regular so it's all sides will be of equal length . And if we assume It's each side be s , then it's perimeter is going to be (s+s+s+s+s) = 5s.And as here , each side is increased by 8 inches and then it's perimeter is 65 inches , so we got that it's side after increament is (s+8) inches and original length is s inches . And if it's each side is (s+8) inches , so it's perimeter will be 5(s+8) and as it's equal to 65 inches . So , 5(s+8) = 65

${:\implies \quad \sf 5(s+8)=65}$

${:\implies \quad \sf 5s+5\times 8=65}$

${:\implies \quad \sf 5s+40=65}$

${:\implies \quad \sf 5s=65-40}$

${:\implies \quad \sf 5s=25}$

${:\implies \quad \sf s=\dfrac{25}{5}=5}$

${:\implies \quad \bf \therefore \quad \underline{\underline{s=5\:\: Inches}}}$

As we assumed the original side to be s .

Hence, the original side's length 5 inches 

8 0

1 year ago

Manuela solved the equation 3−2|0.5x 1.5|=2 for one solution. her work is shown below. 3−2|0.5x 1.5|=2 −2|0.5x 1.5|=−1 |0.5x 1.5

irakobra [83]

The other solution to the absolute value equation 3 − 2|0.5x + 1.5| = 2 is x = -4

<h3>How to determine the solution?</h3>

The equation is given as:

3 − 2|0.5x + 1.5| = 2

Subtract 3 from both sides

-2|0.5x + 1.5| = -1

Divide both sides by -2

|0.5x + 1.5| = 0.5

Expand the equation

0.5x + 1.5 = 0.5 or 0.5x + 1.5 = -0.5

Subtract 1.5 from both sides

0.5x = -1 or 0.5x = -2

Divide both sides by 0.5

x = -2 or x = -4

Hence, the other solution to the absolute value equation 3 − 2|0.5x + 1.5| = 2 is x = -4

Read more about absolute value equation at:

brainly.com/question/26954538

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4 0

1 year ago

What is the coefficient b makes the equation true for any real number x -3 (2x-3) + 5x = bx + 9

QveST [7]

Answer:

b = 0

Step-by-step explanation:

x -3 (2x-3) + 5x = bx + 9

x - 6x +9 + 5x = bx + 9

-9 -9

x - 6x + 5x = bx

-5x + 5x = bx

0 = bx

b/x 0/x

b = 0

3 0

1 year ago

SHORT ANSWER Graph and label point W(4, –1) on the coordinate plane.

Lunna [17]

Answer:

Step-by-step explanation:

a coordinate point is (x, y) so for point W (4, -1), 4 is the x-coordinate and -1 is the y-coordinate.

Start at the origin (O). Go 4 units to the right (along the x-axis in a positive direction) and then 1 unit down (in the y plane in a negative direction).

4 0

1 year ago

A pen talking pyramid has a volume of 1536in what is the volume of the pentagonal pyramid if measures are multiplied by 1/4

Natasha2012 [34]

$\bf \textit{volume of a pyramid}\\\\
V=\cfrac{1}{3}Bh\qquad 
\begin{cases}
B=\textit{area of its base}\\
h=height\\
----------\\
B=\frac{1}{4}B\\\\
h=\frac{1}{4}h
\end{cases}\implies V=\cfrac{1}{3}\cdot \cfrac{B}{4}\cdot \cfrac{h}{4}
\\\\\\
V=\cfrac{1}{3}\cdot \cfrac{1}{4\cdot 4}Bh\implies V=\cfrac{1}{16}\left( \cfrac{1}{3}Bh \right)$

so, you'd end up with a pyramid with a volume "one sixteenth" of the original then

now, the original had a volume of 1536, the quarterized version will then just be one sixteenth of that, or 1536 * 1/36

7 0

2 years ago