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2 years ago

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Henry has a fenced yard in the shape of a rectangle with a perimeter that measures 242 feet. If the width of the yard measures 5

1 feet, what is the length?
_(blank)_ feet

1 answer:

neonofarm [45]2 years ago

4 0

Answer: Length = 70 feet

Concept:

Here, we need to know how to find the perimeter of a rectangle.

Perimeter (rectangle) = 2 (l + w)

l = length

w = width

Solve:

<u>Given information</u>

l = l

w = 51 feet

P = 242 feet

<u>Given expression</u>

P = 2 (l + w)

<u>Substitute values into the expression</u>

242 = 2 (l + 51)

<u>Divide 2 on both sides</u>

242 / 2 = 2 (l + 51) / 2

121 = l + 51

<u>Subtract 51 on both sides</u>

121 - 51 = l + 51 - 51

$\boxed{l=70}$

Hope this helps!! :)

Please let me know if you have any questions

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Find the area pf a trapezoid with a base of 26.7 ft , a height of 15.4 and top of 9.9 ft

evablogger [386]

Hello!

To find the area of the trapezoid, you use the formula A=1/2h(a+b), where a and b represent the two base lengths.

Since we already know the two bases and the height, we can just plug them into the equation to find the area.

A=1/2·15.4(26.7+9.9)
A=1/2·15.4(36.6)
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I hope this helps!

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2 years ago

Find the measure of each angle.

Feliz [49]

Answer:

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2 years ago

What is the coefficient in the expression 40a-61=17

zepelin [54]

Answer:

a = 1.95

Step-by-step explanation:

40a - 61 = 17

40a - 61 + 61 = 17 + 61

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2 years ago

Which of the following functions are homomorphisms?

Vikentia [17]

Part A:

Given $f:Z \rightarrow Z,$ defined by $f(x)=-x$

$f(x+y)=-(x+y)=-x-y \\ \\ f(x)+f(y)=-x+(-y)=-x-y$

but

$f(xy)=-xy \\ \\ f(x)\cdot f(y)=-x\cdot-y=xy$

Since, f(xy) ≠ f(x)f(y)

Therefore, the function is not a homomorphism.

Part B:

Given $f:Z_2 \rightarrow Z_2,$ defined by $f(x)=-x$

Note that in $Z_2$ , -1 = 1 and f(0) = 0 and f(1) = -1 = 1, so we can also use the formular $f(x)=x$

$f(x+y)=x+y \\ \\ f(x)+f(y)=x+y$

and

$f(xy)=xy \\ \\ f(x)\cdot f(y)=xy$

Therefore, the function is a homomorphism.

Part C:

Given $g:Q\rightarrow Q$ , defined by $g(x)= \frac{1}{x^2+1}$

$g(x+y)= \frac{1}{(x+y)^2+1} = \frac{1}{x^2+2xy+y^2+1} \\ \\ g(x)+g(y)= \frac{1}{x^2+1} + \frac{1}{y^2+1} = \frac{y^2+1+x^2+1}{(x^2+1)(y^2+1)} = \frac{x^2+y^2+2}{x^2y^2+x^2+y^2+1}$

Since, f(x+y) ≠ f(x) + f(y), therefore, the function is not a homomorphism.

Part D:

Given $h:R\rightarrow M(R)$ , defined by $h(a)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)$

$h(a+b)= \left(\begin{array}{cc}-(a+b)&0\\a+b&0\end{array}\right)= \left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right) \\ \\ h(a)+h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)+ \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)=\left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right)$

but

$h(ab)= \left(\begin{array}{cc}-ab&0\\ab&0\end{array}\right) \\ \\ h(a)\cdot h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)\cdot \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)= \left(\begin{array}{cc}ab&0\\-ab&0\end{array}\right)$

Since, h(ab) ≠ h(a)h(b), therefore, the funtion is not a homomorphism.

Part E:

Given $f:Z_{12}\rightarrow Z_4$ , defined by $\left([x_{12}]\right)=[x_4]$ , where $[u_n]$ denotes the lass of the integer $u$ in $Z_n$ .

Then, for any $[a_{12}],[b_{12}]\in Z_{12}$ , we have

$f\left([a_{12}]+[b_{12}]\right)=f\left([a+b]_{12}\right) \\ \\ =[a+b]_4=[a]_4+[b]_4=f\left([a]_{12}\right)+f\left([b]_{12}\right)$

and

$f\left([a_{12}][b_{12}]\right)=f\left([ab]_{12}\right) \\ \\ =[ab]_4=[a]_4[b]_4=f\left([a]_{12}\right)f\left([b]_{12}\right)$

Therefore, the function is a homomorphism.

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2 years ago

URGENT!! ILL GIVE<br> BRAINLIEST!!!! AND 100 POINTS!!!!!

Naddik [55]

The value of angle x is 113 degrees and y is 67 degrees.

What is angle?

In euclidean geometry, an angle is that the figure shaped by 2 rays, referred to as the perimeters of the angle, sharing a typical end point, referred to as the vertex of the angle. Angles shaped by 2 rays exist the plane that contains the rays.

Main body:

Given ;

∠C = 62°

∠A =51°

according to triangle sum property: Sum of angles of triangle is 180°

Using it,

62° +51° +∠y = 180°

113°+ ∠y =180°

∠y = 67°

∠x is equal to the sum of interior opposite angle ,so using it we get:

∠x = 61°+52°

∠x = 113°

Hence the value of ∠x is 113 degrees and y is 67 degrees.

To know more about angle , visit:

brainly.com/question/25770607

#SPJ1

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7 months ago