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2 years ago

Let f(x) = |x|, ????????(x) = f(x − 3), and h(x) = f(x + 2), where x can be any real number.

Mathematics

1 answer:

ra1l [238]2 years ago

5 0

Answer:

g(x)= |x-3|

h(x) = |x+2|

Step-by-step explanation:

1. Let g(x)=f(x-3), we can write the function in terms of |x| as:

g(x)= |x-3|

2. Let h(x)=f(x+2), the function can be rewrite in terms of |x| as:

h(x) = |x+2|

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When using the given diagram to determine the area of the pentagon by decomposition, which statements are correct?:

pogonyaev

Answer:

Options (B) and (E)

Step-by-step explanation:

Area of ΔABC = $\frac{1}{2}(\text{Base})(\text{Height})$

= $\frac{1}{2}(14)(6)$

= 42 in²

Area of trapezoid ADEC = $\frac{1}{2}(b_1+b_2)h$

[Here, $b_1$ and $b_2$ are the parallel sides and 'h' is the height of the isosceles trapezoid given]

= $\frac{1}{2}(10+14)(8)$

= 96 in²

Area of the pentagon = Area of triangle ABC + Area of trapezoid ADEC

= 42 + 96

= 138 in²

Therefore, Options (B) and (E) are the correct options.

6 0

2 years ago

The first step to solve the equation x/4-3/4=16 is shown below

Sladkaya [172]

Answer:

i think it is A because that seems like the one making the most sense

Step-by-step explanation:

7 0

2 years ago

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of t

Makovka662 [10]

Answer:

132.233 ft2

Step-by-step explanation:

Let's call the width of the rectangle 'w' and the length 'x'. So the area of the semicircle is:

$A_1 = \pi*radius^2/2$

$A_1 = \pi*(w/2)^2/2$

$A_1 = \pi/8*w^2$

And the area of the rectangle is:

$A_2 = w*x$

If the perimeter of the window is 41 feet, we have:

$Perimeter = length + 2*width + \pi*radius$

$41 = x + 2*w + \pi*w/2$

$x = 41 - w(2 + \pi/2)$

Now, the equation for the total area of the window is:

$A = A_1 + A_2 = \pi/8*w^2 + w*x$

$A = \pi/8*w^2 + w*(41 - w(2 + \pi/2))$

$A = (\pi/8-2 - \pi/2)*w^2 + 41w = -3.1781w^2 + 41w$

To find the maximum area, we can find the x-coordinate of the vertex of the quadratic equation:

$x\_vertex = -b / 2a = -41 / (-3.1781*2) = 6.45$

So the width that gives us the maximum area of the window is 6.45 feet, and the area will be:

$A = -3.1781w^2 + 41w = -3.1781*(6.45)^2 + 41*6.45 = 132.233\ ft^2$

3 0

2 years ago

Plz answer with work

V125BC [204]

Answer:

Calculate 93% of 29.96.

Your final answer is approximately 27.86

6 0

1 year ago

Answer 17 and 18 for 15 points<br><br><br>

Mkey [24]

17. 62 degrees

18. 38 degrees

5 0

2 years ago