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2 years ago

X22abab tobThe diagianKn showsrectangle. The shadeFind x.

Mathematics

1 answer:

Norma-Jean [14]2 years ago

5 0

Answer:

x = 28 cm

Step-by-step explanation:

Given:

Area of link shaded regions = 84 cm²

Required:

The value of x (diameter of the semicircle/length of the rectangle)

Solution:

Diameter of the semicircle = 2r = x

Length of rectangle (L) = 2r = x

Radius of semicircle (r) = ½x

Width of rectangle (W) = radius of semicircle = ½x

Use 3.14 as π

Area of the link shaded regions = area of rectangle - area of semicircle

Thus:

Area of the link shaded regions = (L*W) - (½*πr²)

Plug in the values

84 = (x*½x) - (½*3.14*(½x)²)

84 = x²/2 - (1.57*x²/4)

84 = x²(½ - 1.57/4)

84 = x²(0.5 - 0.3925)

84 = x²(0.1075)

Divide both sides by 0.1075

84/0.1075 = x²

781.4 = x²

√781.4 = x

27.9535329 = x

x = 28 cm

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Explain how the graph of y=|x+1|-2 will differ from the graph of y=|x|.

Natali5045456 [20]

$\bf ~~~~~~~~~~~~\textit{function transformations}\\\\\\f(x)= A( Bx+ C)+ D\\\\~~~~y= A( Bx+ C)+ D\\\\f(x)= A\sqrt{ Bx+ C}+ D\\\\f(x)= A(\mathbb{R})^{ Bx+ C}+ D\\\\f(x)= A sin\left( B x+ C \right)+ D\\\\--------------------\\\\\bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\\bullet \textit{ flips it upside-down if } A\textit{ is negative}$

$\bf ~~~~~~\textit{reflection over the x-axis}\\\\\bullet \textit{ flips it sideways if } B\textit{ is negative}\\~~~~~~\textit{reflection over the y-axis}\\\\\bullet \textit{ horizontal shift by }\frac{ C}{ B}\\~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}$

$\bf ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\\bullet \textit{ vertical shift by } D\\~~~~~~if\ D\textit{ is negative, downwards}\\\\~~~~~~if\ D\textit{ is positive, upwards}\\\\\bullet \textit{ period of }\frac{2\pi }{ B}$

with that template in mind,

$\bf y=\stackrel{A}{1}|\stackrel{B}{1}x\stackrel{C}{+1}|\stackrel{D}{-2}$

so is really just |x| but shifted some,

C/B = 1/1 = +1, horizontally to the right by 1 unit.

D = -2, vertically downwards by 2 units.

3 0

2 years ago

Mr. Walker asked his students to use the associative property to find an expression that is equivalent to (13 + 15 + 20) + (20 +

ozzi

HERES THE ANSWER AND EXPLINATION

⇒Associative property of Addition is applied for three real numbers.For, any three real numbers, A, B and C
≡A+B+C=A+(B+C)=(A+B)+C=(A+C)+B→→→Associative Property of Addition
that is , we can add any two numbers first and then the third number with them.
⇒Also, Commutative Property of Addition of two numbers says that for any two numbers , A and B
≡A+B=B+A
We have to find equivalent expression using Associative Property of the sum of set of three numbers
→→(13+15+20)+(20+47+18)
Answer Written by Jerry
→(20+13+15)+(20+47+18)
Answer Written by Layla
→(20+47+18)+(13+15+20)
The Expression Written by Keith and Melinda is Incorrect,because they haven't used the bracket Properly, as associative property says that you can add any two numbers first and then the third number among three numbers.
→→Number of Students who has applied the Associative property Correctly
Option B ⇒Two(Jerry, Layla)

8 0

2 years ago

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