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

Describe how to transform the graph of f(x) = ⎜x⎟ to obtain the graph of the related function g(x). Then draw the graph of g.

Answers

Answer:

ssss

Step-by-step explanation:

dddd

I need help I don't understand​

Answers

Answer:

2nd one

Step-by-step explanation:

I know this because I learned about this

Like terms can be ________

this is fill - up question


Answers

Answer:

.the same variables and same powers

Step-by-step explanation:

In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers.

HOPE IT HELPS...............

find the square root of each by division method:
a) 225 b) 961 c) 3969 d) 10404
If you can give the correct answer first, I'll mark the brainliest.

Answers

Refer to the attachment

Answer:

[tex]\sqrt[2]{225} =15[/tex], [tex]\sqrt[2]{961} =31[/tex], [tex]\sqrt[2]{3969} =69[/tex], [tex]\sqrt[2]{10404} =102[/tex]

Step-by-step explanation:

[tex]\sqrt[2]{225} =\sqrt{15*15}=15[/tex]

[tex]\sqrt[2]{961}=\sqrt{31*31} =31[/tex]

[tex]\sqrt[2]{3969} =\sqrt{69*69} =69[/tex]

[tex]\sqrt[2]{10404} =\sqrt{102*102}=102[/tex]

Write an equation for each line in slope-intercept form.​

Answers

Answer:

Line 1 : y = -2x - 5

Line 2 : y = -3x + 3

Step-by-step explanation:

note the slope, and then note the y intercept

Answer:

y = - 2x - 5 and y = - 3x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = - 2, - 1) and (x₂, y₂ ) = (0, - 5) ← 2 points on the line

m = [tex]\frac{-5-(-1)}{0-(-2)}[/tex] = [tex]\frac{x- 5+1}{0+2}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

The line crosses the y- axis at (0, - 5 ) ⇒ c = - 5

y = - 2x - 5 ← equation of line 1

Repeat with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (1, 0) ← 2 points on line 2

m = [tex]\frac{0-3}{1-0}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3

The line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = - 3x + 3 ← equation of Line 2

Is (1,0) (3,0), (1,1) (3,1) (1,3) a function

Answers

Answer:

yes

Step-by-step explanation:

Emma has addressed seven invitations to her
birthday party. This is one more than half of the
invitations that she intends to send. How many
invitations does she intend to send?

Answers

Answer:

12

Step-by-step explanation:

This can be solved by working backwards.

7 is one more than half the number of invitations.

Subtract 1.  6 is half the number of invitations.

Double.

12 is the full number of invitations.

Algebra (if you must!):

x = number of invitations

x/2 + 1 = 7

Subtract 1.

x/2 = 6

Multiply by 2.

x = 12

Answer:

12

Step-by-step explanation:

7-1=6

6x2=12

PLS HELPP me asap no bots

Answers

PART A

Cutting in one minute = 105 ÷ 3 = 35 cuts

Now for six machine = 35 × 6 = 210 parts.

So, the option C. 210 parts is correct answer.

PART B

As, 20 × 3 = 60 seconds

Parts can be stamped in one minute = 24 × 3 = 72

So, time required [tex] = \frac{4320}{72} \\ = 60 \: minutes[/tex]

So, the option D. 60 minutes is c correct answer

Select the correct answer.
Which statement is a converse of p?
p: If every fourth card drawn is a spade, then 25% of the cards in a deck would be spades.
A. If 25% of the cards in a deck are spades, then every fourth card drawn would be a spade.
B. If every fourth card drawn isn't a spade, then 25% of the cards in a deck aren't spades.
C. If 25% of the cards in a deck aren't spades, then every fourth card drawn wouldn't be a spade.
D. If every fourth card drawn isn't a spade, then 75% of the cards in a deck are spades.

Answers

C is the correct answer.

How do I know which region to shade for this inequality
y ≤ 2x + -4?

Answers

Answer:

You look at the sign between y and 2x

Step-by-step explanation:

To find which way to shade, look at your symbol. The symbol you have is a less than or equal to, you shade to the left. Because it has the line underneath, you have a closed circle. (This is for line plots so I don't know if this completely helps)

Hopefully it does help though!!

3) Solve this system using elimination method. Upload your work
8x + 14 y = 4
-6x - 7y=-10

Answers

Answer:

y = -2 and x = 4

Step-by-step explanation:

8x + 14y = 4

-6x - 7y = -10

First, find the lowest common multiple of 8 and 6 (which is 24). Multiply the first equation by 3:

8x + 14y = 4

3(8x + 14y) = 3(4)

24x + 42y = 12

Multiply the second equation by 4:

-6x - 7y = -10

4(-6x - 7y) = 4(-10)

-24x - 28y = -40

Now, add the two equations together:

24x + 42y = 12

-24x - 28y = -40

24x + -24x = 0

42y + -28y = 14y

12 + -40 = -28

14y = -28

Divide both sides by 14:

14y ÷ 14 = -28 ÷ 14

y = -2

Plug this known variable back into the first equation:

8x + 14(-2) = 4

8x + (-28) = 4

8x - 28 = 4

Add 28 to both sides:

8x - 28 + 28 = 4 + 28

8x = 32

Divide both sides by 8:

8x ÷ 8 = 32 ÷ 8

x = 4

So y = -2 and x = 4.

Hope this helps!

3/10 = ___ x 1/10
pls help i'll give brainiest

Answers

Answer:

1/10 x 30/10=30/100 then simplify =3/10  

Step-by-step explanation:

Hope I helped please mark brainliest!

The answer is 3

1 3
—-x 3 = ——
10 10

3 is equivalent to 3/1=3 You have to see how many times can 1 go into 3 which is 3 (1x3=3)
—-
1

. A National Institute of Health survey of 40467 U.S adults found that 3156 of them experienced at least one major depressive episode in the previous year. Make a 95% confidence interval for the proportion of all U.S. adults who experienced depression in that year. (Source: https://www.nimh.nih.gov/health/statistics/major-depression)

Answers

Using the confidence interval for sample proportion formula, the C.I is (0.075; 0.081)

Using the relation :

[tex]p ± z_{crit} \sqrt{ \frac{p(1 - p)}{n} } [/tex]

Sample size, n = 40467

Sample proportion, p = 3156/40467 = 0.078

Zcrit at 95% = 1.96

Margin of Error = [tex] 1.96 \sqrt{ \frac{0.078(0.922)}{40467} } [/tex]

Margin of Error = 0.0026128

Lower boundary = 0.078 - 0.0026128 = 0.075

Upper boundary = 0.078 + 0.0026128 = 0.081

Hence, the confidence interval is (0.075; 0.081)

Learn more :

Triangle PIN is rotated -270 degrees about the origin.

Draw the image of this rotation.

Answers

If triangle PIN  is rotated -270 degrees about the origin, the new point is at:

P'(-3, 2), I'(7, 7) and N'(7, -2)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.

If a point A(x, y) is rotated -270 degrees about the origin, the new point is at A'(-y, x).

The triangle PIN has vertices at P(2, 3), I(7, -7) and N(2, -7). If it is rotated -270 degrees about the origin, the new point is at:

P'(-3, 2), I'(7, 7) and N'(7, -2)

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Answer:

P=(-3,2)

I=(7,7)

N=(7,2)

Step-by-step explanation:

khan

What does "for example" tell readers about the sentence it introduces?
1. that they're about to be introduced to a new idea
2. that it's a sentence that will show them a similarity
3. that it's sentence will show them a difference
4. that they're about to hear an example of the idea in the previous sentence

Answers

Answer:

The answer is option 4., but this question does not belong in the math section.

How many times does 6 go into 719 divison with partial quotient

Answers

119.833333333 times it goes into 719 119.833333333 times

Answer:

119 R5

Step-by-step explanation:

we first divide 7 by 6 and we get that it goes in once

so 1__

then after we do 7 - 6 and get a remainder of 1

we drop the 1 next to the other one and get 11

then we divide 11 by 6 and we get that it goes in once

so 11_

then after we do 11 - 6 we get a remainder of 5

we drop the 5 next to the nine and get 59

then we divide 59 by 6 and get 9

so 119

then after we do 59 - 54 and get a remainder of 5

so our answer is 119 R5

hey guys can u check my answers, if you see one thats not correct pls correct me!

Answers

Answer:

b. 300 c. 18 d. 30

Step-by-step explanation:

b. 400/4=100, 100*3=300

c.0.3*10=3, 3*6=18

d.0.75*10=7.5, 7.5*4=30

Answer:

B C and D are incorrect

Step-by-step explanation:

1/2 • 13 is 6.5

3/4 • 400 = 300

(0.3)•60 = 18

(0.75) • 40 = 30

Brainliest please

What is the measure of _____?​

Answers

Answer:

112°

Step-by-step explanation:

3x+22+2x+8=180

5x+30=180

5x=150

x=30

3x+22

3(30)+22

90+22

112

(Score for Question 3:
of 3 points)
3. Describe the transformation that takes
(x)=x+1 to g(x) = -x +4.
Answer:

Answers

Answer:

It's a rotation of 90 degrees - doesn't matter which way - around the intersection of the two lines

Step-by-step explanation:

Claim: it's a 90 degree rotation around the intersection of f and g.

It's easy to spot the two lines  are perpendicular. Let's assume the rotation doesn't happen at the point of intersection [tex]x_0[/tex], but slightly to the side, around let's say, [tex]x_0+\epsilon[/tex]; the new line will coincide with [tex]g(x)[/tex] if and only if [tex]\epsilon = 0[/tex], ie only the rotation happens around the intersection.

х
4.
1
6 11
y
-3
-2
-1
0
slope:

Answers

Answer:

slope = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, - 3) and (x₂, y₂ ) = (11, 0) ← 2 ordered pairs from the table

m = [tex]\frac{0-(-3)}{11-(-4)}[/tex] = [tex]\frac{0+3}{11+4}[/tex] = [tex]\frac{3}{15}[/tex] = [tex]\frac{1}{5}[/tex]

Which function has the smallest y-intercept value?
A
у
4
4
h(x)
2.
X
- 2
2.
4
+2
4
OB.
(x) =
= 2 + 10
A linear function, f, with an x-intercept of 3 and a y-Intercept of 6.
OC.
OD.
х
1
2
3
4
g(x)
1
-4
-9
-14

Answers

Answer:

Could you... put it normally?

Step-by-step explanation:

It's kinda confusing to read, so much understand

Divide 5097 by 10 and write the answer as a mixed number

Answers

If it is a mixed number it should be 509 7/10

help only answer if you know!!!!

Subtract.

18 7/12−9 4/12

8

8 1/3

9

9 1/4

Answers

Answer:

9 1/4

Step-by-step explanation:

I hope this helps! it should be correct

18 7/12 - 9 4/12
18-9= 9
9 3/12
9 3/12:3
9 1/4

NEED HELP show your work

Simplify the expression √8x^5 / z1

Answers

Answer:

3/4

Step-by-step explanation:

How can the careers or hobbies of your family members help you earn
scholarship awards?

Answers

The careers or hobbies of my family members can help me earn scholarship awards as some employers and associations offer scholarships to participants and family members.

That is, certain hobbies, skills or careers that members of my family have may involve them in certain jobs or groups that, in turn, offer the possibility of accessing scholarships and other benefits.

Thus, social and labor groups always tend to expand the opportunities of those who participate in them, as well as those of their closest people.

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4, 13, 5, 8, R, 5, 11

In the data set shown, R is an integer. If the median of the data set is 8 and R < 11, what is a possible value

of R?

Answer:

Answers

Answers:

R can be either 8, 9 or 10

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

Explanation:

Let's exclude the R value for now.

The set {4,13,5,8,5,11} sorts to {4,5,5,8,11,13}.

Now we'll include R back in. We're told that R is an integer and it's smaller than 11. The possible values R can take on are: {10, 9, 8, 7, ...} The countdown continues forever into the negative territory.

If R < 4, then we go from {4,5,5,8,11,13} to {R,4,5,5,8,11,13}. That R is guaranteed to be the min value since R is less than the smallest value of the previous set. Note that the middle-most item of the second set is 5; however, we want the median to be 8 instead. This allows us to rule out the case that R < 4.

So we've determined that 4 < R < 11. Because R is an integer, we can say it takes on the values from the set {5,6,7,8,9,10}

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

If R = 5, then {4,5,5,8,11,13} updates to {4,5,5,5,8,11,13} after adding in that R value. We can see the median is 5, so we can rule out the case that R = 5.

Similarly, we can rule out R = 6 as well. The set {4,5,5,8,11,13} updates to {4,5,5,6,8,11,13} in which the median is 6.

If R = 7, then the median is 7 for similar reasoning and we can rule out this R value.

So we've ruled out the cases that R = 5, R = 6 and R = 7.

If we tried R = 8, then {4,5,5,8,11,13} becomes {4,5,5,R,8,11,13} = {4,5,5,8,8,11,13}. This set has a median of 8 and R = 8 is one of the answers.

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

Now let's consider the possibility that 8 < R < 11.

If for instance R = 9, then {4,5,5,8,11,13} becomes {4,5,5,8,9,11,13} to show that this set also has a median of 8. R = 9 is another answer.

The same idea happens when R = 10 as well because we get {4,5,5,8,10,11,13}. R = 10 is another answer.

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

In short, R can be any of the following values: 8, 9, 10

If the simple interest on 4,000 for 10 years is 2,400 then what is the interest rate

Answers

Answer:

6%

Step-by-step explanation:

I =Prt I being interest paid, P is Principal, r is rate, t is term

2400=4000x r x 10

2400=40000r

2400/40000=.06 convert to percentage by multiplying by 100 x. 06=6

Someone please help! Thank you in advance!

Answers

Answer:

58ft

Step-by-step explanation:

100-60=40

40+18=58

the answer is 58ft

(brainliest plz)

YES I WILL MARK BRAINLIST:D

Sarah is going to the food truck with her friends. Hot dogs cost $2 and drinks cost $3. She has a total of $24 that she can spend. The equation 2x+3y=24 represents this scenario.

Determine the amount of hotdogs that can be purchased if Sarah orders 4 drinks.

Question 4 options:

4 hotdogs


7 hotdogs


6 hotdogs


5 hotdogs

Answers

The answer is 6 hotdogs. If you plug in the number of drink for y you get 12. 24-12=12. 12/2=6

Answer:

6 hotdogs

Step-by-step explanation:

:)

simplify-3 divided by (-2/5)

Answers

Decimal form: 7.5

Fraction form: 15/2

Improper fraction: 7  1/2

Hope this is enough! :D

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