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Hitman42 [59]
2 years ago
8

A rectangle has a length of 2y inches and a width of y - 4 inches. If the perimeter of the rectangle is 22 inches, what is y? Wh

at is the length? What is the width?
Mathematics
1 answer:
kicyunya [14]2 years ago
7 0
P = 2( l + w)
Length: 2y
Width: y - 4
P= 22 inches
2(2y) + 2(y - 4) = 22
4y + 2y - 8 = 22
4y + 2y = 6y and add (-8) on both sides of the equation to equal: 6y = 30
Divide 6 from both sides of the equation and you get: y = 5
Check:
4(5) + 2(5) - 8 = 22
20 + 10 - 8 = 22
30 - 8 = 22 ✅
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Answer:

A base of ten raised to a negative exponent corresponds to a number that is between 0 and 1.

Step-by-step explanation:

A base of ten raised to a negative exponent, say - 1 will correspond to the number, 10^{- 1} = \frac{1}{10^{1}} = \frac{1}{10}.

Again, a base of ten raised to a negative exponent, say - 2 will correspond to the number, 10^{- 2} = \frac{1}{10^{2}} = \frac{1}{100}.

{Since we know the property of exponents as x^{- a} = \frac{1}{x^{a}}}

Therefore, all those numbers are between 0 and 1.

Hence, a base of ten raised to a negative exponent corresponds to a number that is between 0 and 1. (Answer)

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The endpoints of EF are E(2, 3) and F(8, 11). The midpoint of EF is M.<br> Find the length of EM.
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The midpoint of EF is M. The length of EM is 5

Given :

The endpoints of EF are E(2, 3) and F(8, 11).

M is the midpoint of EF

Lets find out the midpoint M using midpoint formula

(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\E (x_1,y_1) is (2,3)\\F(x_2,y_2) is (8,11)

Substitute the values inside the formula

(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\\\(\frac{2+8}{2} ,\frac{3+11}{2} )\\\\(5,7)

Midpoint M is (4,7)

Now to find out length of EM, we use distance formula

Distance = \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\\mathrm{The\:distance\:between\:}\left(2,\:3\right)\mathrm{\:and\:}\left(5,\:7\right)\\\sqrt{\left(5-2\right)^2+\left(7-3\right)^2}\\\sqrt{3^2+4^2} \\\sqrt{25}\\5

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2 years ago
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Answer:

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Therefore the co-ordinate of the point on the line segment from (-9,-1) to(-9,-10) into a ratio internally is (-9,-19).

Step-by-step explanation:

Given points are (-9,-1) and (-9,-10)

If a point divides the line segment by joining two points (x₁,y₁) and (x₂,y₂)  into a ratio m:n internally.

Then the point of the coordinate is (\frac{m.x_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}).

If a line segment is externally divided into a point by joining two points (x₁,y₁) and (x₂,y₂) with m: n ratio.

Then the point of the coordinate is (\frac{m.x_2-nx_1}{m-n},\frac{my_2-ny_1}{m-n}).

Internally

The co-ordinate of the point is (\frac{(-9)\times2+(-9)\times 1}{2+1},\frac{(-10)\times 2+(-1)\times 1}{2+1})

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Externally

The co-ordinate of the point is (\frac{(-9)\times2-(-9)\times 1}{2-1},\frac{(-10)\times 2-(-1)\times 1}{2-1})

                                                   =  (-9,-19)

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