MATHEMATICS HIGH SCHOOL

Evaluate the function f(x)=2x-2 when x equals negative 1A. -4
B. -3
C. 0
D. 4

Answers

Answer 1
Answer: f(x)= -4. 
Just plug in -1 for your x in 2x-2 and solve like a normal equation. Think of f(x) a your y because that's basically what it is. If it helps, the equation is basically:
y=2x-2 so you would just solve for y by plugging in -1 into x.

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Which values are within the range of the piecewise-defined function?f(x) =
2 x + 2 x < - 3
X x = -3
- x - 2 X > -3
y = -6
y=-4
y=-3
y = 0
y = 1
y = 3

Answers

-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.

To learn more on function click:

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#SPJ7

Answer:

-6, -4, -3, 0

Step-by-step explanation:

I just did this question and got it right.

What would a model be for the math word problem Sammy has 50 pieces of gum. He wants to give 1/2 of the pieces to his brother and 3/4 of the pieces to his sister.

Answers

Answer: X = 1/2(y)

Z= 3/4(x)

But x= 1/2(y)

So z = 3/4 * 1/2(y)

Z = 3/8(y)

Total= 1/2(y) +3/8(y) + 1/8(y)

Step-by-step explanation:

3=c/5+2... how do I solve for c??

Answers

Primeiro Você IRA Dividir o c (APENAS Colocar 5 + 2 embaixo do c). Depois faça a soma 5 + 2 = 7. Então faça o mmc (mínimo múltiplo comum) entre 7 e 1(o 1 é invisível, mas continua estando embaixo do 3). Deu 7 o mmc. Transforme seus números em frações, com o denominador 7. Transforme os números em frações o 3 virá 21, pois você divide em baixo e multiplica em baixo, e o c continua normal, pois já estava em baixo de 7. Como é para descobrir uma incógnita você tira os denominadores e ficará 21 = c.

3 = c/5 + 2
3 = c/7
21/7 = c/7
21 = c
3 = c/5 + 2
3 - 2 = c/5
1 = c/5....multiply both sides by 5, causing the 5 on the right to cancel
5 = c

Can someone help me in this trig question, please? thanks A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates 5pi/12

Answers

The exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).

The position

Since the position of the carousel is (x, y) = (20cosθ, 20sinθ) and we need to find the position when θ = 5π/12 = 5π/12 × 180 = 75°

So, substituting the value of θ into the positions, we have

(20cos75°, 20sin75°)

The value of 20cos75°

20cos75° = 20cos(45 + 30)

Using the compound angle formula

cos(A + B) = cosAcosB - sinAsinB

With A = 45 and B = 30

cos(45 + 30) = cos45cos30 - sin45sin30

= 1/√2 × √3/2 - 1/√2 × 1/2

= 1/2√2(√3 - 1)

= 1/2√2(√3 - 1) × √2/√2

= √2(√3 - 1)/4

= (√6 - √2)/4

= (-√2 + √6)/4

So, 20cos75° = 20 × (-√2 + √6)/4

= 5 (-√2 + √6)

The value of 20sin75°

20sin75° = sin(45 + 30)

Using the compound angle formula

sin(A + B) = sinAcosB + cosAsinB

With A = 45 and B = 30

sin(45 + 30) = sin45cos30 + cos45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= 1/2√2(√3 + 1)

= 1/2√2(√3 + 1) × √2/√2

= √2(√3 + 1)/4

= (√6 + √2)/4

= (√2 + √6)/4

So, 20sin75° = 20 × (√2 + √6)/4

= 5(√2 + √6)

Thus, (20cos75°, 20sin75°) = 5 (-√2 + √6), 5(√2 + √6).

So, the exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).

Learn more about position here:

brainly.com/question/11001232
\bf \textit{the position of the rider is clearly }20cos\left( (5\pi )/(12) \right)~~,~~20sin\left( (5\pi )/(12) \right)\n\n-------------------------------\n\n\cfrac{5}{12}\implies \cfrac{2+3}{12}\implies \cfrac{2}{12}+\cfrac{3}{12}\implies \cfrac{1}{6}+\cfrac{1}{4}\n\n\n\textit{therefore then }\qquad \cfrac{5\pi }{12}\implies \cfrac{1\pi }{6}+\cfrac{1\pi }{4}\implies \cfrac{\pi }{6}+\cfrac{\pi }{4}\n\n-------------------------------

\bf \textit{Sum and Difference Identities}\n\nsin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta)\n\ncos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)\n\n-------------------------------\n\ncos\left( (\pi )/(6)+(\pi )/(4) \right)=cos\left( (\pi )/(6)\right)cos\left((\pi )/(4) \right)-sin\left( (\pi )/(6)\right)sin\left((\pi )/(4) \right)

\bf cos\left( (\pi )/(6)+(\pi )/(4) \right)=\cfrac{√(3)}{2}\cdot \cfrac{√(2)}{2}-\cfrac{1}{2}\cdot \cfrac{√(2)}{2}\implies \cfrac{√(6)}{4}-\cfrac{√(2)}{4}\implies \boxed{\cfrac{√(6)-√(2)}{4}}\n\n\nsin\left( (\pi )/(6)+(\pi )/(4) \right)=sin\left( (\pi )/(6)\right)cos\left( (\pi )/(4) \right)+cos\left( (\pi )/(6)\right)sin\left((\pi )/(4) \right)

\bf sin\left( (\pi )/(6)+(\pi )/(4) \right)=\cfrac{1}{2}\cdot \cfrac{√(2)}{2}+\cfrac{√(3)}{2}\cdot \cfrac{√(2)}{2}\implies \cfrac{√(2)}{4}+\cfrac{√(6)}{4}\implies \boxed{\cfrac{√(2)+√(6)}{4}}\n\n-------------------------------\n\n20\left( \cfrac{√(6)-√(2)}{4} \right)\implies 5(-√(2)+√(6))\n\n\n20\left( \cfrac{√(2)+√(6)}{4} \right)\implies 5(√(2)+√(6))

Find the oth term of the arithmetic sequence 16, 21, 26, ...

Answers

Answer:

31

Step-by-step explanation:

16+5=21

21+5=26

26+5=31

Which of the following are prime factorizations of the number 100? Check all that apply.A. 2, 5, 10
B. 5, 10, 2
C. 5, 2, 5, 2
D. 5, 2, 2, 5

Answers

Answer:

Use the factor tree to find the prime factorization of 100.

A factor tree of 100. 100 branches to 10 and 10. Both tens branch to 2 and 5.

What is the prime factorization of 100?

2 × 5

2 × 2 × 5 × 5

2 × 5 × 10

10 × 10

Step-by-step explanation:

smh.. people really keep getting it wrong and its B i took the test
Its C and D? I provided a picture showing how I did it. You just create a factor tree and circle all the prime numbers. Than you got your answer.
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