All categories

3 years ago

If you divide a polynomial f(x) by the factor (x - 4), the remainder will be equal to f(-4). true or false ?

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

5 0

Answer:

<h3>FALSE</h3>

Step-by-step explanation:

Given the polynomial f(x) divided by x-4

To check whether the remainder will be equal to f(-4), we need to get whether the value of x is -4 if we set x-4 to zero as shown;

x- 4 = 0

Add 4 to both sides

x - 4 + 4 = 0+4

x = 4

Since the value of x is 4 not -4 hence the remainder will NOT be equal to f(-4). The answer is false

You might be interested in

5/6-1/8 Solve by finding a common denominator A)30/48 B)34/48 C)38/48 D)42/48

GrogVix [38]

Answer:

B) 34/48

Step-by-step explanation:

The easiest common denominator to find is the product of the denominators you have.

The difference is ...

$\dfrac{5}{6}-\dfrac{1}{8}=\dfrac{5}{6}\cdot\dfrac{8}{8}-\dfrac{1}{8}\cdot\dfrac{6}{6}\\\\=\dfrac{40-6}{48}=\boxed{\dfrac{34}{48}}$

Additional comment

The difference numerator and denominator have a common factor of 2, so can be reduced to 17/24. The denominator 24 could have been used as the common denominator from the start.

5/6 -1/8 = 20/24 -3/24 = 17/24 . . . . reduced result

Using the least common denominator does not always result in a reduced sum or difference. If some other denominator is used (as here), then you can be assured that the result will need to be reduced to get to lowest terms.

8 0

2 years ago

Cain measured his couch and found it is 3 3/4 meters long what is the length as a decimal

11Alexandr11 [23.1K]

3 3/4
= 3+ 3/4
= 3+ 0.75
= 3.75

The length as a decimal is 3.75 m~

5 0

3 years ago

Solve 5n + 6 = -3n - 10

Verizon [17]

Hi there! :)

Answer:

$\huge\boxed{n = -2}$

5n + 6 = -3n - 10

Solve for n:

Add 3n to both sides:

5n + 3n + 6 = -3n + 3n - 10

8n + 6 = -10

Subtract 6 from both sides:

8n + 6 - 6 = -10 - 6

8n = -16

Divide both sides by 8:

8n/8 = -16/8

n = -2.

3 0

3 years ago

Read 2 more answers

What type of number is 302.14

kondor19780726 [428]

302.14 is a decimal number

Explanation:

302.14 is a decimal type of number.

A decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point. The dot in a decimal number is called a decimal point. The digits following the decimal point show a value smaller than one.

Decimals are based on the preceding powers of 10. Thus, as we move from left to right, the place value of digits gets divided by 10, meaning the decimal place value determines the tenths, hundredths and thousandths. A tenth means one tenth or 1/10. In decimal form, it is 0.1. Hundredth means 1/100. In decimal form, it is 0.01.

Similarly, 302.14 has a decimal place value of hundred.

3 0

3 years ago

The quality-control department of Starr Communications, the manufacturer of video-game cartridges, has determined from records t

notsponge [240]

Answer: (A) The probability that a cartridge purchased will have a video or audio defect is 1.9%

(B) The probability that a cartridge purchased will not have a video or audio defect is zero.

Step-by-step explanation: The data given shows that 1.2% (or 120) cartridges have video defects, 0.9% have audio defects (or 90) and 0.2% (or 20) have both audio and video defects.

The possible outcomes for all events (audio defects and video defects) is derived as 120 plus 90 which is equals 210 possibilities (or possible outcomes).

Therefore the probability of having an audio defect is calculated as follows;

P(Audio) = Number of required outcomes/Number of all possible outcomes

P(Audio) = 90/210

P(Audio) = 3/7

Also the probability of having a video defect is derived as follows;

P(Video) = Number of required outcomes/Number of all possible outcomes

P(Video) = 120/210

P(Video) = 4/7

However we should take note of the fact that 0.2% or 20 of the cartridges in the sample size has both audio and video defects. Hence the probability that a cartridge has both audio and video defects is calculated as;

P(Audio and Video) = Number of required outcomes/Number of all possible outcomes

P(Audio and Video) = 20/210

P(Audio and Video) = 2/21

To calculate the probability that a cartridge bought would have either an audio or a video defect would mean to add both probabilities together, but we MUST SUBTRACT the probability of having both an audio defect and video defect (that is P{Audio and Video}). The reason is that this is already included in both probabilities and we need to avoid double counting. Hence we have;

(A); P(Video OR Audio defect) = P(Audio) + P(Video) - P(Audio and Video)

P(Video OR Audio defect) = (3/7 + 4/7) - 2/21

P(Video OR Audio defect) = 1 - 2/21

P((Video OR Audio defect) = 19/21

Therefore the probability that a cartridge purchased will have a video or audio defect is 190, or better still 1.9%.

(B): From all possibilities shown, which is 210 possibilities of either events, we have determined that 120 will be the probability of having an audio defect and 90 will be the probability of having a video defect. Therefore the probability that a cartridge purchased will not fall into any of either possibilities is zero.

6 0

3 years ago