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diamong [38]
3 years ago
5

Which of the following equations matches the function shown above?

Mathematics
1 answer:
musickatia [10]3 years ago
7 0

Answer:

D, y = cos(x -π/2)

Step-by-step explanation:

When the cosine function is shifted right by π/2 units, it looks like the sine function. That is what we have here. To shift f(x) to the right, replace x by x-(amount of shift). Here, this means the graph is described by ...

y = 2cos(x -π/2)

_____

The vertical scale factor is 2 on the graph and in all answer choices.

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1. Suppose that a theater charges a school group $4.50 per student to show a special film. Suppose that the theater's operating
elixir [45]

The functions I(x) and E(x) of the theatre's income and expenses are illustrations of linear functions.

<h3>The equation of the theatre's income</h3>

The theatre charges $4.50 per student.

Assume the number of students is x, the equation of the theatre's income would be:

I(x) = 4.5x

<h3>The equation of the theatre's expenses</h3>

The theatre expense per student is $1.25, and the operating cost on the staff is $130

The equation of the theatre's expenses would be:

E(x) = 1.25x + 130

<h3>Complete the table</h3>

Using the formulas I(x) = 4.5x and E(x) = 1.25x + 130, the complete table is:

Students, x  0       10        20     30      40      50      60    70

Income, I      0      45        90     135     180    225    270   315

Expenses, E 130  142.5   155    167.5   180   192.5   205  217.5

<h3>The graph of the theatre's income and expenses</h3>

See attachment

<h3>The pattern by which theatre's income and expenses increase</h3>

The functions I(x) and E(x) are linear functions.

So, the pattern with which the functions increase is a linear pattern.

<h3>The number of students when the theatre's income and expenses are equal</h3>

This means that:

I(x) = E(x)

So, we have:

4.5x = 1.25x + 130

Subtract 1.25 from both sides

3.25x = 130

Divide both sides by 3.25

x = 40

Hence, the number of students is 40

<h3>The theatre profit</h3>

This is the difference between the theatre expenses and their income.

So, we have:

P(x) = E(x) - I(x)

This gives

P(x) = 1.25x + 130 - 4.5x

Simplify

P(x) = 130 - 3.25x

<h3>Solution to the inequalities</h3>

We have:

E(x) < 255

This gives

1.25x + 130 < 255

Subtract 130 from both sides and divide by 1.25

x < 100 students

Also, we have:

I(x) > 675

This gives

4.5x > 657

Solve for x

x > 146 students

Hence, the number of students for the inequalities are less than 100 and greater than 146

Read more about linear equations and inequalities at:

brainly.com/question/11234618

8 0
2 years ago
Evaluate -7a – 2b, if a = -1 and b = 2.
Roman55 [17]
Plug in a and be into the equations:
- 7( - 1) - 2(2) =  \\ 7 - 4 =  \\ 3
5 0
3 years ago
Read 2 more answers
-6(1+8a)=36-6a. anybody know this answer ?
Gwar [14]

Answer:

a=-1

If you need explanation please comment

5 0
3 years ago
Read 2 more answers
HELP PLS!!! I GIVE BRAINLIEST
emmainna [20.7K]

Based on the multiplication property of equality, the statement that completes the proof is: C. CD = b(sin A) and CD = a(sin B).

<h3>What is the Multiplication Property of Equality?</h3>

The multiplication property of equality is given as, if a/b = y, then a = yb. Both sides of the equation is multiplied by the same value.

In step 5 where the multiplication property of equality is applied, we would have:

sin(A) = CD/b

Multiply both sides by b

sin(A) × b = CD/b × b

b(sin A) = CD

CD = b(sin A)

This same property is applied to sin B = CD/a to get CD = a(sin B).

Therefore, the missing statement is: C. CD = b(sin A) and CD = a(sin B).

Learn more about the multiplication property of equality on:

brainly.com/question/1978763

#SPJ1

8 0
1 year ago
Write the expression as a square of a monomial.
frozen [14]

Answer:

The square of a monomial is (9x^2)^2

Step-by-step explanation:

Consider the provided monomial.

81x^4

We need to Write the expression as a square of a monomial.

The above expression can be written as:

9\times 9\times x^2\times x^2

9^2(x^2)^2

(9x^2)^2

Hence, the square of a monomial is (9x^2)^2

8 0
3 years ago
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