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2 years ago

By using the remainder theorem, determine the remainder when

Mathematics

2 answers:

lora16 [44]2 years ago

4 0

Answer:

C) -123

Step-by-step explanation:

x + 4 = 0

x = -4

3(-4)³ − (-4)2 − 20(-4) + 5

-123

Greeley [361]2 years ago

3 0

Answer:

-123

Step-by-step explanation:

The remainder theorem says that when a polynomial is divided by a linear factor x - c (note the minus sign), the remainder is the value of the polynomial at x = c.

When a polynomial P(x) is divided by x - c, the remainder is P(c). In other words, to find the remainder, plug in c for x.

You're dividing by x + 4 which is the same thing as x - (-4) -- the role of c is being played by -4.

3(–4)^3 – (–4)^2 – 20(–4) + 5 = –123

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In a rational function, is the horizontal shift represented by the vertical asymptote?

ziro4ka [17]

<h3>Short Answer: Yes, the horizontal shift is represented by the vertical asymptote</h3>

A bit of further explanation:

The parent function is y = 1/x which is a hyperbola that has a vertical asymptote overlapping the y axis perfectly. Its vertical asymptote is x = 0 as we cannot divide by zero. If x = 0 then 1/0 is undefined.

Shifting the function h units to the right (h is some positive number), then we end up with 1/(x-h) and we see that x = h leads to the denominator being zero. So the vertical asymptote is x = h

For example, if we shifted the parent function 2 units to the right then we have 1/x turn into 1/(x-2). The vertical asymptote goes from x = 0 to x = 2. This shows how the vertical asymptote is very closely related to the horizontal shifting.

7 0

2 years ago

Can somebody explain how to do this question

evablogger [386]

Answer:

The answer is D

Step-by-step explanation:

Remember:

Contrapositive means that if you reverse the hypothesis and the conclusion the statement will mean the same thing

7 0

2 years ago

A plumbing supply company has fixed costs of $9,000 per month and average variable costs of $9.30 per unit manufactured. The com

nekit [7.7K]

Answer:

8710 units

Step-by-step explanation:

<em>Step 1: Write all the data</em>

Fixed cost: $9000

Average variable cost: 9.3 per unit

Total cost: 90,000

Total units: x

<em>Step 2: Find the total variable cost</em>

Average variable cost is per unit so it has to be multiplied by the number of units to find the total variable cost.

Total variable cost = average variable cost per unit x number of units

Total variable cost = 9.3x

<em>Step 3: Make the formula for finding x</em>

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Rounded off to 8710 units

3 0

2 years ago

1/f - 1/u = 1/v then f

german

Answer:

1/V

Step-by-step explanation:

8 0

2 years ago

What is the equation of a sine function with an amplitude of 2 and a period of 4

antiseptic1488 [7]

Answer: C

Step-by-step explanation:

For this problem, we need to know the standard form of a sine function and the meaning of each part.

Standard form: $y=asin[b(x-h)]+k$

a=amplitude

b=period

h=phase shift

k=vertical replacement/shifting

Now that we know the standard form and the components, we know that we can forget about k and plug in 0 for h. This would leave us with $y=asin[b(x)]$ . We know that the amplitude is 2, therefore, a=2. To find the period, you divide 2π by the given period. $\frac{2\pi }{b} =\frac{2\pi }{4\pi } =\frac{2}{4} =\frac{1}{2}$ , therefore, b=1/2.

$y=asin[b(x)]$ [plug in a=2]

$y=2sin[b(x)]$ [plug in b=1/2]

$y=2sin(\frac{1}{2}x)$

Therefore, C is the correct answer.

7 0

2 years ago