Harvey is studying the polynomial f(x) = (4x – 3)(x – 3)(x2 +5) and determines that the polynomial has four real roots. Do you agree or disagree with Harvey’s statement? Explain your reasoning.
A.yes because there are 4 roots
B.yes because complex solutions do not matter
C.yes because when I solve he gets 4 x intercepts
D.no because there are two complex solutions

Answers

Answer 1

Yes because when I solve he gets 4 x-intercepts. The x-intercept is a point where the y value is zero.

The degree of a polynomial always determines the number of roots such polynomial function will have;

Given the polynomial function studied by Harvey as g(x) = (4x – 3)(x – 3)(x2 +5)

Taking the product of the leading variables

g(x) = (4x – 3)(x – 3)(x2 +5)

g(x) = 4x(x) (x^2)

g(x) = 4x^4

Since the degree of the polynomial is 4, hence the polynomial has four real roots.

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Related Questions

what does it mean to use quotient powers?

Answers

When you are dividing like terms with exponents

When we use the concept of power and a denominator in it, we will describe the root in another form.

What is the definition of potency?

Potency is that which has power, strength, vigor and importance. In mathematics, power is the result of a number multiplied by itself one or more times. .

The base equation of the power is:

[tex]a^b = c[/tex]

Where:

a = base; b = exponent; c = power.

So from the definition of power we have that when a division in the power occurs we will have to be the same thing as writing a root.

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What is the common difference for this arithmetic sequence 45,40,35,30,25,

Answers

Answer:

-5

Step-by-step explanation:

fully simplify 124:72:48

Answers

Answer:

31:18:12

............................

Using substitution, which value of x makes this equation true?

3+x = 10

A. 13
B. 7
C. -7
D. -13

Answers

Answer:

The answer is B. 7

Step-by-step explanation:

3 + x = 10

3 + 7 = 10

B.

x=7.

Step by step:

x+3=10.

x=7.

(I subtracted 3 on both sides)

Hope this helped!! :)

2h(3m-4h)please help me

Answers

Answer:

6hm-8h^2

Step-by-step explanation:

2h(3m-4h)

2h*3m=6hm

2h*4h=8h^2

=6hm-8h^2

2——————————————————————-

There is a line that includes the point (-20, -7) and has a slope of 1. What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:

y=1x+13

Step-by-step explanation:

we can plug in the two points into the slope-intercept formula

-7=-20(1)+b

solve for the right side

-7=-20+b

add 20 to both sides

13=b

plug the y intercept into the equation

y=1x+13

Can you help me please?​

Answers

Answer:

B

Step-by-step explanation:

The Pythagoras theorem states that [tex]c^{2} = a^{2} + b^{2[/tex], where [tex]c[/tex] is the hypotenuse and a and b are the adjacent and opposite sides of the hypotenuse. If we made [tex]a[/tex] the subject of the expression, the expression will be re-written as [tex]a^{2} = c^{2} - b^{2}[/tex], which is the correct answer.

Question 1: Select the property shown
by the statement: 3a • 5b = 3.5 a.
b
A. Commutative
B. Associative
C. Reflexive
D. Symmetric
E. Transitive

Answers

Answer:

E BC itsay 3a 5b = 3.5 so it E

Merriam and Emmanuel assemble a new bookshelf. Its 1ft deep,4ft wide, and 8ft tall. They assemble it flat bit when they tip it up The shelf hits the ceiling. Why does it hit the ceiling

Answers

The maximum dimension of the shelf is given by the space diagonal

length of the shelf.

A possible reason why the shelf hits the ceiling is because the ceiling is

less than or equal to 9 feet from the ground.

Reasons:

The maximum height of the shelf is given as follows;

The diagonal of one of the side = √(8² + 4²)

The diagonal of the completed shelve = √((√(8² + 4²))² + 1²) = 9

The maximum extension of the shelve = 9 feet

Given that the shelf touches the ceiling, we have, that maximum height of

the ceiling = 9 feet.

Therefore, the shelf touches the ceiling because, height from the floor to

the ceiling is lesser than equal to 9 feet.

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https://brainly.com/question/9702103

Jacob followed a recipe that requires 2 cups of water for ever 3 cups of flour. If he
used 8 cups of flour, how many cups of water did he use?
2 2/3
4
5 1/3
12

Thank u SOOOOOOOOOO much if u helped me

Answers

Answer:

he used 5 1/3 everything else is to low or high

Can anyone help, im stuck

Answers

Answer:

The second one is right

Step-by-step explanation:

anyone help, im stuck

Answer:

The third one

Step-by-step explanation:

Since, 1 can be represented by x we can make an equation

2 can be represented y

and 4 can be represented by x

Since x + y = 180 and x + z = 180

y = z

Or 2 = 4

Brainliest please :)

Follow the steps to finish solving the equation -3x +18 = 7x

1. Add 3x to both sides to isolate the variable term.

2. Divide both sides by 10.

x=

Answers

It’s probs 1.8 but it could also be 1.8

Answer:

18/10

Step-by-step explanation:

got it right.

GIVING BRAINLIEST!! (ignore the answer i put i accidentally clicked on it) A line passes through the point (-2, 7) and has.a slope of -5.
What is the value of a if the point (a, 2) is also on the line?

Answers

the answer is -1 just believe me

Jack estimates that a piece of wood measures 4.5 cm. If it actually measures 4.72 cm, what is the percent error of Jack’s estimate? (Show all of your work)

Answers

Answer:

ion

Step-by-step explanation:srry

1238 round to the nearest 1000

Answers

Answer:

1,238.000

Step-by-step explanation:

PLEASE HELP What appears to be the range of the part of the exponential function graphed?
A- x ≤ 1
B- h(x) ≤ 1
C- x ≤ 5
D - h(x) ≤ 5

Answers

Answer:

A) Variable "x" is less than it equal to 1 because your domain can’t have [h(x)] because that’s your function and would be your range but in this case it’s your domain and your domain or else known as the variable "x" coordinate would have to be the number on the x axis that your line starts, your line begins on line 1 on the x axis which would be your domain

Hope this helps!

HELP ANSWER ASAP
ANSWER???

Answers

A proportional relationship means that two or more things are directly proportional, or that the quantities increase or decrease according to equivalent ratios. We can state this proportional relationship with the formula, y = kx. Y and x here are the quantities that are proportional to each other.

Proportional ur welcome :)

Sin x= cos y show that x+y=90

Answers

Answer:

just do sinx and cos y equal when x=y= multiple of pie by 4

Step-by-step explanation:

pie by 4 plus pie by 4 = 90

If I helped please mark brainliest it means a lot to my progression! <3 Thanks!

WILL GIVE BRAINLIEST!

Answers

Answer:

1 1/3

Step-by-step explanation:

it's bc the number is closer to one and not in the middle. have a great day

Answer:

The arrow is pointing to 1 1/3. From 1 to 2, there are 3 marks. These three marks are each 1/3. So, from 1 the next mark will be 1 1/3.

:)

A tank full of water is leaking at a constant rate for 30 minutes. The equation
y = -8x + 400
gives the amount of water in the tank, where y is the number of liters and x is
the number of minutes since the tank began to leak. Which statement is true?
A. There were 400 liters in the tank after 30 minutes, and it is
decreasing by 8 liters per minute.
B. There were 8 liters in the tank when the leak started, and it is
decreasing by 400 liters per minute.
C. There were 8 liters in the tank when the leak started, and it is
increasing by 400 liters per minute.
D. There were 400 liters in the tank when the leak started, and it is
decreasing by 8 liters per minute.

Answers

Answer:

A

Step-by-step explanation:

did the quiz

Answer:

D

Step-by-step explanation:

Mrs. Rashad Is baking 3 ples, She needs 1 /6 cups of strawberries for each ple. How many cups of strawberries does she need in all?

Answers

Answer: 3/6 or 1/2

Step-by-step explanation: 1/6 x 3 = 3/6 or simplified form 1/2.

Answer:

1/2 cups of strawberries is required.

Step-by-step explanation:

1 pie = 1/6 cups of strawberries

=> 3 pies = 1/6 x 3

=> 3 pies = 1/2 cups of strawberries.

Hoped this helped.

Suppose that you invest $15,000 into a high yield savings account that earns 2.1\% annual interest and is compounded monthly. If you do not deposit or withdraw any money from the account, how much money will be in the account after 8 years? Show your equation. Round your answer to the nearest cent. (5 Points )

Answers

Answer:

$17741.44

Step-by-step explanation:

Given:

Investment P = 15000Interest rate r = 2.1% PA or 0.021 PACompound number n = 12 PATime t = 8 years

Find the total amount:

A = P(1 + r/n)^(rn)A = 15000(1 + 0.021/12)^(8*12) = 17741.44

Write an equation of the line that passes through (-6,0) and $(0,-24)

Answers

Answer:

-4

Step-by-step explanation:

Y2 = -24 and Y1 = 0

X2 = 0 and X1 = -6

Y2-Y1/ X2- X1= -24 - 0/ 0 - (-6) = -4

y= -4x + c

y + 4x= c

Due in an hour help me
Please I have to pass

Answers

Answer:

A is answer

Step-by-step explanation:

What is Part 1 and Part 2? I think I have these correct.

Answers

Step-by-step explanation:

part 1. Alternate Exterior angle

part 2. 110°

HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE

10. What percent of 25 is 10? (1 point)
O10=r. 25: 40%
O 10=r. 25: 250%
025=x: 10; 40
025=r. 10; 250%

Answers

Answer:

40%

Step-by-step explanation:

To change a fraction into a percentage, multiply by 100% , then

[tex]\frac{10}{25}[/tex]

= [tex]\frac{10}{25}[/tex]  × 100%

= 0.4 × 100%

= 40%

A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is in control, package weight is normally distributed with a mean of 20 ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each Day Weight (ounces) Monday 23 22 23 24 Tuesday 23 21 19 21 Wednesday 20 19 20 21 Thursday 18 19 20 19 Friday 18 20 22 20 If he uses upper and lower control limits of 22 and 18 ounces, what is his risk (alpha) of concluding this process is out of control when it is actually in control (Type I error)

Answers

Using the normal distribution and the central limit theorem, it is found that his risk is of 0.0456.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean.  After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem:

Mean of 20 ounces and standard deviation of 2 ounces, hence [tex]\mu = 20, \sigma = 2[/tex].Sample of 4 packages, hence [tex]n = 4, s = \frac{2}{\sqrt{4}} = 1[/tex]

The risk is the probability of being more than 2 ounces from the mean, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Applying the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2}{1}[/tex]

[tex]Z = 2[/tex]

The risk is P(|Z| > 2), which is 2 multiplied by the p-value of Z = -2.

Looking at the z-table, Z = -2 has a p-value of 0.0228.

0.0228 x 2 = 0.0456

The risk is of 0.0456.

For more on the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213

Please help! 20 points! Will give brainliest!

Answers

Answer:

2 and 4 are correct

Step-by-step explanation:

Hope this helps!❄︎

What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.

Answers

Answer:

slope= 1/4

Step-by-step explanation:

8-5 over 8-(-4)= 3/12=0.25 = 1/4

I/4 8-5 over 8-(-4) = 3/12 = 0.25 = 1/4

What is the nth term rule of the quadratic sequence below?
-4,-3,0,5, 12, 21, 32,...
I need help quick!!

Answers

Answer:

The nth term = n^2 - 2n - 3.

Step-by-step explanation:

Here, we will be finding the nth term of a quadratic number sequence. A quadratic number sequence has nth term = an² + bn + c

Example 1

Write down the nth term of this quadratic number sequence.

-3, 8, 23, 42, 65...

Step 1: Confirm the sequence is quadratic. This is done by finding the second difference.

Sequence = -3, 8, 23, 42, 65

1st difference = 11,15,19,23

2nd difference = 4,4,4,4

Step 2: If you divide the second difference by 2, you will get the value of a.

4 ÷ 2 = 2

So the first term of the nth term is 2n²

Step 3: Next, substitute the number 1 to 5 into 2n².

n = 1,2,3,4,5

2n² = 2,8,18,32,50

Step 4: Now, take these values (2n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.

n = 1,2,3,4,5

2n² = 2,8,18,32,50

Differences = -5,0,5,10,15

Now the nth term of these differences (-5,0,5,10,15) is 5n -10.

So b = 5 and c = -10.

Step 5: Write down your final answer in the form an² + bn + c.

2n² + 5n -10

Example 2

Write down the nth term of this quadratic number sequence.

9, 28, 57, 96, 145...

Step 1: Confirm if the sequence is quadratic. This is done by finding the second difference.

Sequence = 9, 28, 57, 96, 145...

1st differences = 19,29,39,49

2nd differences = 10,10,10

Step 2: If you divide the second difference by 2, you will get the value of a.

10 ÷ 2 = 5

So the first term of the nth term is 5n²

Step 3: Next, substitute the number 1 to 5 into 5n².

n = 1,2,3,4,5

5n² = 5,20,45,80,125

Step 4: Now, take these values (5n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.

n = 1,2,3,4,5

5n² = 5,20,45,80,125

Differences = 4,8,12,16,20

Now the nth term of these differences (4,8,12,16,20) is 4n. So b = 4 and c = 0.

Step 5: Write down your final answer in the form an² + bn + c.

5n² + 4n

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