(a) The graph of y=h(x) is shown. Draw the graph of y=-h(x)+3(b) The graph of y = g(x) is shown. Draw the graph of y = 2g (x+4).

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The length of a rectangle is 3 inches more than twice its width, and its area is 65 square inches. What is the width?If w = the width of the rectangle, which of the following expressions represents the length of the rectangle?

2w + 3
2(w + 3)
3(2w)

Answers

Let L be the length of the rectangle and W be its width. Translating the first sentence into mathematical expressions, we get, L=2W+3. To get the area of a rectangle, we will use the formula A=L*W. Since we are already given with the area, we will substitute this value to the formula, together with the expression of L in terms of W. Thus, 65=(2W+3)*(W). Further simplification would yield

65=2W^2+3W
2W^2+3W-65=0

We have a quadratic equation, hence, we will solve for its factors. We have,

(2w+13)(w-5)=0

The two roots of the equation are: -13/2 and 5. Since we can only have positive numbers for dimensions, the width of the rectangle is 5 in.

The expression for the length of the rectangle is 2W+3.

Giselle graphs the function f(x) = x2. Robin graphs the function g(x) = –x2. How does Robin’s graph relate to Giselle’s?

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g(x)=-x2
= -(f(x))
so, g(x) = -f(x), so g(x) is reflection of f(x) over x-axis

Answer:

g(x)=-x2

= -(f(x))

so, g(x) = -f(x), so g(x) is reflection of f(x) over x-axis

A metal washer is made by cutting out a circle 13.2 mm in diameter from a larger circle. To the nearest tenth, what is the area of the washer

Answers

The standard formula of area of the circle is (pi * r^2)
here r is radius.

So the radius of this washer is equal to 6.1 mm (13.2 / 2)
Therefore the area of the washer
pi * 6.1^2
116.9 mm^2

Use the distributive property to find the value of 8(10 + 9).
152
82
89
97