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3 years ago

Is the term (X + 2) a factor of the polynomial shown below?

Mathematics

1 answer:

QveST [7]3 years ago

3 0

The correct answer is: No, the remainder is -114

Further explanation:

In order to check whether the given term is a factor of given polynomial or not we will put

x+2=0

x=-2

Given

$f(x)=x^3 - 10x^2 + 27^x - 12\\f(-2)=(-2)^3-10(-2)^2+27(-2)- 12\\=-8-10(4)-54-12\\=-8-40-54-12\\=-114$

As the remainder is -114, the term x+2 is not a factor of given polynomial

The correct answer is: No, the remainder is -114

Keywords: Polynomials, expressions

Learn more about polynomials at:

#LearnwithBrainly

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What pattern do you notice in the numbers below?

Andru [333]

Step-by-step explanation:

i think 48888 because i think so and you do to

4 0

3 years ago

Read 2 more answers

One number is 3 less than twice another. If their sum is 39 find the numbers

DedPeter [7]

Answer:

The numbers are 14 and 25

Step-by-step explanation:

Let one of the numbers be x. The second number we are told is 3 less than twice x. The second number will thus be;

2x - 3

The sum of the numbers is thus;

x + (2x - 3) = 3x - 3

But the sum of the numbers is said to be 39, therefore;

3x - 3 = 39

3x = 42

x = 14

The second number is thus;

2(14) - 3 = 28 - 3 = 25

5 0

3 years ago

For each set of probabilities, determine whether the events A and B are independent or dependent.

lozanna [386]

Answers:

(a) Independent
(b) Dependent
(c) Dependent
(d) Independent

========================================================

Explanation:

If events A and B are independent, then the two following equations must both be true

P(A | B) = P(A)
P(B | A) = P(B)

This is because the conditional probability P(A|B) means "P(A) when B has happened". If B were to happen, then P(A) must be the same as before. In other words, event B does not affect A, and vice versa.

For part (a), we have P(B) = 1/4 and P(B|A) = 1/4 showing that P(B|A) = P(B) is true, and therefore we can say the events are independent. We don't need the info that P(A) = 1/8.

------------------------

Unlike part (a), part (b) has the answer "dependent" because P(A) = 1/8 and P(A | B) = 1/3 differ in value. Event A starts off at probability 1/8, but then event B occurring means P(A) gets increased to 1/3. The prior knowledge about B changes the chances of A. The P(B) = 1/5 is unneeded.

------------------------

If A and B were independent, then,

P(A and B) = P(A)*P(B)

However,

P(A)*P(B) = (1/4)*(1/5) = 1/20

which is not the same as P(A and B) = 1/6. Therefore the two events are dependent.

------------------------

Refer back to part (a)

P(A) = 1/4 and P(A|B) = 1/4 are identical in value, so P(A|B) = P(A) which leads to the events being independent. Whether we know event B happened or not, it does not affect the outcome of event A. P(B) = 1/9 is unneeded.

7 0

2 years ago

The data set shown below has an outlier. Determine the outlier and then answer the questions as to what happens to the median, m

Pachacha [2.7K]

The mean is the average value of the given data set. When the outlier is removed the mean and the median of the data set are changed.

<h3>What are mean, median, and mode?</h3>

The mean is the average value of the given data set.
The median is the middle value of a given data set when the data is arranged in increasing order.
The mode is the number that is repeated the most number of times in a given data set.

The data set can be arranged as 12, 19, 19, 20, 21, 22, 22, 23, 24, 26, 27, 28, 29, 30, 32, 35, 48. Now, The means, median and mode for the data set is,

Mean = (29+19+35+27+21+48+23+12+24+26+20+28+30+22+19+32+22) / 17

Mean = 25.7

Median(The middle value when the data is arranged in increasing order) = 24

Mode = 19,22

The outlier in the data set is 48, therefore, the mean median and mode now will be,

12, 19, 19, 20, 21, 22, 22, 23, 24, 26, 27, 28, 29, 30, 32, 35

Mean = 24.3125

Median = 23.5

Mode = 19, 22

Hence, when the outlier is removed the mean and the median of the data set are changed.

Learn more about Mean, Median, and Mode:

brainly.com/question/15323584

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4 0

2 years ago

Expand and Combine like terms: <br> (4t^3-5)^2

arsen [322]

Answer: 16t^6−40t^3+25 is the answer

first lets set the equation as a binomial *remember 2 binomial= trinomial*

so its going to look something like..........

(4t^3-5) (4t^3-5)

now we do the foil method so 4t^3* 4t^3= 16t^6 (add exponents)

do the same for the other terms:

4t^3*-5= -20t^3

-5*4t^3= -20t^3

-5*-5= 25

now the whole equation is...

16t^6-20t^3-20t^3+25 (combine like terms like -20t^3 and -20t^3)

therefor the answer is... 16t^6-40t^3+25

4 0

3 years ago