E 125° G F mZGFH = [?]° H​

Answer:

181

Step-by-step explanation:

Area of a semicircle: 1/2 (pi • r^2)

1/2(3.14 • 100)

1/2 ( 314 )

157

Triangle:

(6 • 8) ÷ 2

48 ÷ 2

24

Add the area of the triangle & semicircle together: 157 + 24 = 181

Hope this helps! Have a great day!

-6, -4, -3, and 0 are the values which are within the range of the piecewise-defined function.

Correct options: a) y = -6, b) y = -4, c) y = -3, d) y = 0

Here, we have, to determine which values are within the range of the piecewise-defined function, we need to evaluate the function for each given value of y.

Given piecewise-defined function:

f(x) =

2x, x < -3

x, x = -3

-x - 2, x > -3

Let's evaluate the function for each value of y:

a) y = -6

For y = -6, we need to find x such that f(x) = -6.

-6 is in the range of the function if there exists an x such that f(x) = -6.

For x < -3: f(x) = 2x

2x = -6

x = -3

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = -6

x = 4

Since there is a value of x (-3) that satisfies f(x) = -6, option a) y = -6 is correct.

b) y = -4

For y = -4, we need to find x such that f(x) = -4.

-4 is in the range of the function if there exists an x such that f(x) = -4.

For x < -3: f(x) = 2x

2x = -4

x = -2

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = -4

x = 2

Since there is a value of x (-3) that satisfies f(x) = -4, option b) y = -4 is correct.

c) y = -3

For y = -3, we need to find x such that f(x) = -3.

-3 is in the range of the function if there exists an x such that f(x) = -3.

For x < -3: f(x) = 2x

2x = -3

x = -1.5

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = -3

x = 1

Since there is a value of x (-3) that satisfies f(x) = -3, option c) y = -3 is correct.

d) y = 0

For y = 0, we need to find x such that f(x) = 0.

0 is in the range of the function if there exists an x such that f(x) = 0.

For x < -3: f(x) = 2x

2x = 0

x = 0

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = 0

x = -2

Since there is a value of x (-3) that satisfies f(x) = 0, option d) y = 0 is correct.

e) y = 1

For y = 1, we need to find x such that f(x) = 1.

1 is in the range of the function if there exists an x such that f(x) = 1.

For x < -3: f(x) = 2x

2x = 1

x = 0.5

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = 1

x = -3

Since there is no value of x that satisfies f(x) = 1, option e) y = 1 is incorrect.

f) y = 3

For y = 3, we need to find x such that f(x) = 3.

3 is in the range of the function if there exists an x such that f(x) = 3.

For x < -3: f(x) = 2x

2x = 3

x = 1.5

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = 3

x = -5

Since there is no value of x that satisfies f(x) = 3, option f) y = 3 is incorrect.

Correct options: a) y = -6, b) y = -4, c) y = -3, d) y = 0

The correct values within the range of the piecewise-defined function are -6, -4, -3, and 0.

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Answer:

-6, -4, -3, 0

Step-by-step explanation:

I just did this question and got it right.

Answer:

3w + 52 ≥ 90

Step-by-step explanation:

If she volunteers 3 hours per week for w weeks, then the number of hours from tutoring is 3w.  Add the 52 hours from her summer volunteering, and her total hours is 3w + 52.  This needs to be at least 90 hours for her to graduate, so:

3w + 52 ≥ 90

Answer:

Option A.

Step-by-step explanation:

The question asked for a unit rate. This means that there should be no denominator higher than 1. Option A is the only one which have a denominator of 1.

Answer:

3.9-21=-17.1

Step-by-step explanation:

3.9-21

3.9+-21

=-17.1

Replace f(x) with 0 and solve for x. We do this because the x intercepts always occur when y = 0. Keep in mind that y = f(x).

f(x)=x^3-9x^2+20x

0=x^3-9x^2+20x

x^3-9x^2+20x = 0

x(x^2-9x+20) = 0 .... factor out GCF x

x(x-5)(x-4) = 0 ... factor the stuff inside

x = 0 or x-5 = 0 or x-4 = 0 ... zero product property

x = 0 or x = 5 or x = 4

The roots or zeros are 0, 5, 4

Answer: Choice D