Is (x 5) a factor of f(x) = x3 − 4x2 3x 7? explain your reasoning.

Answers

Answer 1

(x+5) is not a factor of f(x) because x = -5 does not satisfy the given equation f(x) = x³ - 4x² + 3x + 7.

Step 1. First we solve the equation x +5 = 0, we get

x = -5

Step 2. By putting the value of x = -5 in f(x) check whether we get a zero or a number other than zero.

If we get zero then x+5 is a factor of f(x) and if we get a number other than zero then x+5 is not a factor of f(x)

f(-5) =  (-5)³ − 4(-5)² + 3(-5) + 7 = - 233

Since we got -233 and not 0. Therefore, (x+5) is not a factor of f(x).

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Related Questions

What is the median of the following 9 numbers: 23, 15, 32, 27, 19, 11, 30, 19, 22?

Answers

The median of the following 9 numbers 23, 15, 32, 27, 19, 11, 30, 19, 22 will be 22.

What is a median?

The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.

The median for odd data will be

Median = [(n + 1) / 2]th

The median for even data will be

Median = {[n / 2 + (n + 2)/ 2] / 2}th

The data is given below.

23, 15, 32, 27, 19, 11, 30, 19, 22

Arrange the data in ascending order. Then we have

11, 15, 19, 19, 22, 23, 27, 30, 32

Then the median of the following 9 numbers is calculated as,

Median = [(9 + 1) / 2]th

Median = (10 / 2)th

Median = 5th

Median = 22

The median of the following 9 numbers 23, 15, 32, 27, 19, 11, 30, 19, 22 will be 22.

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Create a word problem for 4 x 8 = ?
and solve it using a bar model?

Answers

Answer:

Jackie has been assigned to hand out papers to all the students in her class. Each student gets 4 pieces of paper, and there are 8 total students. How many papers total does Jackie need to get?

(I cannot show a picture of a bar model, apologies)

Using traditional methods it takes 8.5 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 21 students and observed that they had a mean of 8.8 hours with a variance of 1.21. Is there evidence at the 0.05 level that the technique performs differently than the traditional method? Assume the population distribution is approximately normal. Step 1 of 5 : State the null and alternative hypotheses

Answers

There is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.

What are the hypothesis tested?

At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:

[tex]H_0: \mu = 8.5[/tex]

At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:

[tex]H_1: \mu \neq 8.5[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:

|z| = 1.96.

(p-value of 1 - (0.05/2)).

Hence the decision rule is given as follows:

|z| < 1.96 -> do not reject the null hypothesis -> not enough evidence.|z| > 1.96 -> reject the null hypothesis -> enough evidence.

What is the test statistic?

The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.

The equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.

The parameters for this problem are given as follows:

[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]

Hence the test statistic is of:

[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}[/tex]

z = 1.24.

|z| < 1.96, hence there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.

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Find the value of x such that the data set has the given mean.

100, 122, 103, 113, 109, x; mean 102

Answers

Answer:

[tex]mean = \frac{sum}{number} \\ 102 = \frac{(100 + 122 + 103 + 113 + 109 + x)}{6} \\ 612 = 547 + x \\ x = 65[/tex]

Wyatt is joining the Shorewood Sharks swim team. He has been taking swimming lessons for several years at the community pool. The community pool is shaped like a rectangular prism and holds 480,000 liters, or 480 cubic meters, of water. It is 12 meters wide and 2 meters deep. The Shorewood Sharks practice in the pool at Shorewood High School. The high school's pool is also shaped like a rectangular prism. It is 15 meters wide, 2.5 meters deep, and holds 937,500 liters, or 937.5 cubic meters, of water. How much longer is the high school's pool than the community pool? Write your answer as a whole number or decimal. Do not round.

Answers

Answer:

11.25 m

Step-by-step explanation:

Since the volume of  a rectangular prism, V = lwh where l = length, w = width and h = depth,

So, l = V/wh

Now, for the length of the community pool, its volume, V = 480 m³, h = 2 m and w = 12 m

So, l = V/wh

= 480 m³/(12 m × 2 m)

= 480 m³/24 m²

= 20 m

Also, for the length, l' of the Shorewood High School pool, its volume, V' = 937.5 m³, its depth, h' = 2.5 m and its width, w' = 15 m

So, l' = V'/w'h'

= 937.5 m³/(15 m × 2 m)

= 937.5 m³/30 m²

= 31.25 m

So, the difference in length of the pools is l' - l = 31.25 m - 20 m = 11.25 m

So, the high school's pool is 11.25 m longer than the community pool.

How do you find the mean and standard deviation of a simple random sample?

Answers

The steps of finding mean and standard deviation of a simple random sample are given below.

What is standard deviation and mean?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

There are various mean types in mathematics, particularly in statistics. Each mean serves to summarize a specific set of data, frequently to help determine the overall significance of a specific data set.

The steps of finding mean and standard deviation of a simple random sample are:

Divide the population standard deviation (σX) by the square root of the sample size (n) to get the standard deviation of the sample mean (σX):  = σ/n.

How to determine sample means

Add up the examples' components. You must first count the number of sample items in each data set and then add up all of the sample items. ...

Sum divided by the quantity of samples.

The outcome is the mean.

To determine the variance, use the mean.

To determine the standard deviation, use the variance.

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which number is a composite
11, 5 , 9, or 2
(i need an answer asap

Answers

Answer:

2

Step-by-step explanation:

Which expression is the factored form of X^3 2x^2 5x 6?

Answers

The factors of the given equation x³ - 2x² - 5x + 6 is (x - 1)(x + 2)(x - 3) with the help of synthetic division.

Let f(x) = x³ - 2x² - 5x + 6

Substitute x = 1

f(1) = (1)³ - 2(1)² - 5(1) + 6

⇒ f(1) = 1 - 2 - 5 + 6

⇒ f(1) = -1 + 1

⇒ f(1) = 0

As x = 1 is the root of the given equation therefore one of the factor of the given equation is (x-1)

Now use long division method, we get (x² - x - 6) as another factor.

⇒ f(x) = (x - 1)(x² - x - 6)

⇒ f(x) = (x - 1)(x² - 3x + 2x - 6)

⇒ f(x) = (x - 1)(x(x-3) + 2(x-3))

⇒ f(x) = (x - 1)(x - 3)(x + 2)

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There are 3 boys for every 5 girls in a kindergarten class. How many total students are there if there are 6 boys?

Answers

Answer:

16 students

Step-by-step explanation:

It is a 3 to 5 ratio, so if there are six boys, there are 10 girls. Six plus ten is 16 students.

You have a cup with 17 coins inside. The total inside the cup is $5. 50. Determine how many half dollars and quarters are inside the cup. Use a system of equations. Be sure to define the variables and show all work

Answers

There are 8 half dollars and 9 quarters inside the cup.

We can set up a system of equations to represent the number of half dollars (h) and quarters (q) in the cup and the total value of the coins.

Let h be the number of half dollars and q be the number of quarters.

The first equation represents the total number of coins in the cup:

h + q = 17

The second equation represents the total value of the coins:

0.5h + 0.25q = 5.50

To solve for h and q, we can use either the substitution or elimination method.

By substitution, we can solve for one variable in terms of the other in one of the equations and substitute it into the other equation.

So, q = 17 - h

then substitute it into the second equation:

0.5h + 0.25(17 - h) = 5.50

By solving for h, we get h = 8, then we can substitute it back into the first equation to get q = 9

So, there are 8 half dollars and 9 quarters inside the cup.

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Peggy completed 5/6 of the math homework and Al completed 4/5 of the homework. Did Peggy or Al complete more hoof the math homework?

Answers

Peggy completed more of the math homework than Al

What does division of fractions mean?

A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.

we know that

In order to be able to compare fractions more easily it is recommended that both have the same denominator

Peggy

5/6 x 5 = 25/30

Al

4/5 x 6 = 24/30

Peggy completed more of the math homework

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How do you make a truth table?

Answers

If we want to create a truth table , for say expression  (P ∨ Q)∧(~P⇒Q) , then we will create different columns having the column head as , P , Q , ~P , P ∨ Q,~P⇒Q and  (P ∨ Q)∧(~P⇒Q) and then perform the logical operation on them.

Truth table is a medium  used to perform logical operations on expressions. These operations consists of Boolean algebra or Boolean functions expressions.

On performing these logical operation we get to know whether the propositional expression is correct or incorrect, based on the input values. This  entire process is based on Boolean algebra and the table is made up of rows and columns for one or more input values.

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Finding the slope ?identify the slope

Answers

the slope of the given straight line will be -3

What is the slope of line?

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.

We know that formula two find the slope of the line joining two points which is

Slope is = y2-y1/x2-x1

=9-0/0-3

=-3

Hence the slope of the given straight line will be -3

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whats the answer for this question i need help

Answers

The answer for it is r = -4 :))

Given P(A) = 0.32, P(B) = 0.2 and P(AU B) = 0.366, find the value of
P(An B), rounding to the nearest thousandth, if necessary.

Answers

By using formula, P(A n B) = 0.346. Rounded to the nearest thousandth, P(A n B) = 0.346

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In between 0 and 1, the closer the probability is to 1, the more likely the event is to occur. The probability of an event is usually represented by the letter P, followed by the event in parentheses.

What is rounding off?

Rounding off is a mathematical operation that is used to reduce the number of digits in a number while maintaining its value within a certain degree of accuracy. When we round off a number, we look at the digit that is immediately to the right of the last digit that we want to keep. If the number is less than 5, we keep the last digit as it is, but if the number is greater than or equal to 5, we add 1 to the last digit.

We can use the formula of conditional probability to find the value of P(A n B).

P(A n B) = P(A U B) - P(A) - P(B) + P(An B)

We know that:

P(A U B) = P(A) + P(B) - P(A n B)

So we can substitute this in the first equation:

P(A n B) = P(A U B) - P(A) - P(B) + P(An B)

P(An B) = P(A U B) - P(A) - P(B) + P(An B)

Now we can substitute the given values:

P(An B) = 0.366 - 0.32 - 0.2 + P(An B)

P(An B) = 0.346 + P(An B)

To find P(An B) we can subtract 0.346 from both sides of the equation:

P(An B) = P(An B) - 0.346

P(An B) = P(An B) - 0.346

So, P(An B) = 0.346

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Nathan had 58 pieces of gum that he wants to make last six days how much can he chew each day so that the gum last him six days between what two whole numbers does your answer lie

Answers

Natha can chew between 9 to 10 chewing gum each day so that it could last for 6 days.

What is a unitary method?

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Nathan had 58 pieces of gum that he wants to make last six days.

Therefore, The number of chewing gums he can chew is the total number of chewing gums he has divided by the total number of days which is,

= (58/6).

= 9.66 chewing gums but it should be a whole number.

So, Nathan can chew between 9 to 10 chewing gums each day.

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1.) Select all shapes that are quadrilaterals. A D C С B H E G F​

Answers

Abcdefghijklmnopqrstuvwxyz

Slope = -7; (4, -30) step by step​

Answers

Answer:

the equation of the line is y = -7x - 2.

Step-by-step explanation:

To find the equation of the line with slope -7 that passes through the point (4, -30), we can use the point-slope form of a line.

The point-slope form of a line is:

y - y1 = m(x - x1)

where:

(x1, y1) is a point on the line

m is the slope of the line

Substituting the given values, we get:

y - (-30) = (-7)(x - 4)

Expanding the right side, we get:

y + 30 = -7x + 28

Combining like terms, we get:

y = -7x - 2

So the equation of the line is y = -7x - 2.

PLEASE HELP!!! I WILL MARK BRAINLEST. please help me guys

Answers

the answer is the last one
Option 2 because there are multiple inputs that = different outputs; therefore, option 2 is a relation, not a function.

What is a mark up in math?

Answers

A mark up in math is how much a retailer increases, or gets over what they payed for it, Example: if I bought a bag of candy for $10, but then sold it for $15, that would be a mark up! Another example: if your product costs $50, and the selling price is $75, then the markup percentage would be 50%, $75-$50/50 Hope this helps! :)

What is the perimeter of kite KLMN? StartRoot 2 EndRoot + StartRoot 5 EndRoot units StartRoot 14 EndRoot units 2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units 4 StartRoot 5 EndRoot units
HELP PLEEEEAASEEE

Answers

Answer:

C.  2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units

Step-by-step explanation:

Answer:

The Answer is C.

Step-by-step explanation:

2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units

What is the relationship between multiplying and factoring?
You multiply numbers or expressions to produce a
[Select]
numbers or [Select]
produce it.
✓. You factor a product into the
✓that were multiplied to

Answers

Polynomial factoring is the opposite of polynomial multiplication. A polynomial's leftover will be 0 if it is divided by its factors after factoring.

What do "multiply" and "factor" mean?

A multiple is a number that is the result of multiplying the provided number by other numbers, as opposed to a factor, which divides the given number perfectly without leaving a remainder.

What connection exists between the factor theorem and the division of polynomials?

When a polynomial f(x) is divided by (x - c), and (x - c) is a factor of the polynomial f(x), the remainder of the division is simply equal to 0. Therefore, if the remainder of a division like the ones mentioned above equals zero.

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What is the discriminant of the quadratic equation 3x^2+8x+4=0

Answers

Using this formula b^2-4ac
a=3, b=8, c=4
8^2-4x3x4 = 64 - 48
=16
x>0 two roots
16>0 so two real roots

A quadrilateral has vertices (-5,1) (-2,5) (2,2) (-1,-2). Determine if it is a square by using the distance formula to calculate the length of the diagonals, and the slope formula to determine if the diagonals are perpendicular

Answers

Length of diagonals are :

[tex]D_1 = \sqrt{ (-5-(-1))^2 + (1-(-2))^2 }\\\\D_1 = 5\ units[/tex]

[tex]D_2 = \sqrt{(-2 -2 )^2 + (5-2)^2}\\\\D_2 = 5 \ units[/tex]

Now, Slope of both the diagonal is :

[tex]m_1 =\dfrac{1-(-2)}{-5-(-1)} \\\\m_1 = -\dfrac{3}{4}\\\\m_2 = \dfrac{5-2}{-2-2}\\\\m_2 = -\dfrac{3}{4}[/tex]

Now, product of slopes are :

[tex]m_1 \times m_2 = \dfrac{-3}{4} \times \dfrac{-3}{4}\\\\m_1 \times m_2 = \dfrac{9}{16}[/tex]

Since, the product of slope is not equal to -1 . It means that the slopes are not perpendicular.

Therefore, this quadrilateral is not square.

EASY POINTS!!!

Which value for x makes the following number sentence true?

10x - 4x = 36
A. 216
B. 30
C. 6
D. 3

Answers

Simplify
10x - 4x = 36
6x = 36
Divide by 6

Solution: x = 6

Answer:

C. 6

Step-by-step explanation:

10x - 4x = 36

1. Take away 4x from each side

6x = 36

2. Divide by six

x = 6

I have two fair dice each numbered 1 to 6 I throw both dice and add the two numbers together. What is the probability that the number I get is a multiple of 5 .

Answers

Answer:

7 / 36

Step-by-step explanation:

Using the sample space attached,

Required outcome = multiple of 5 from the sun of two rolled dice = 7

Total possible outcomes =(number of faces)² = 6² = 36

Therefore, the probability of obtaining a sum which is a multiple of 5 is :

P(sum which is a multiple of 5) :

Required outcome / Total possible outcomes

= 7 / 36

A car moving on a road with velocity 30 m/ ,
when brake are applied it velocity decreae at a rate
of 6 meter per econd. Find the ditance it will cover before coming to ret

Answers

the distance it will cover before coming to rest is 75m. Solved using the concept of velocity.

What is velocity?

Simply said, velocity is the rate of movement in a certain direction. such as the speed of a car driving north on a highway or the pace at which a rocket takes off.

Due to the fact that it includes both magnitude and direction, velocity is a vector quantity. Since acceleration is only the rate at which velocity changes, acceleration is likewise a vector quantity.

Given that,

initial velocity (u) = 30 m/s

acceleration (a) = - 6 m/s²

As we know,

v² = u² + 2as

or, 0 = (30)² + 2 × (-6) × s

or, s = 75 m

Hence, the distance it will cover before coming to rest is 75m

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35 POINTS Complete the sentence.
Statistics is the result of __________ data.

Answers

Answer:

analysis (i got to put a bunch of random stuff here cs the limit)


The weights of 2-pound bags of Best Dog Food are approximately normally distributed with a given mean ul and
standard deviation o. According to the Empirical Rule, what percentage of the bags will have weights within 3 standard deviations of the mean?

Answers

Answer: 99.7%

Step-by-step explanation:

Edg 2020

If the length of the American flag is 1.8 yards, find the hight

Answers

The flag uses a scale of
L:H=3:2
L=1.8
1.8/3
0.6=1 unit
2 units make up the height so
0.6 * 2 = 1.2
height =1.2 yards
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