At which root does the graph of f(x) = (x – 5)3(x + 2)2 touch the x-axis?
-5
-2
Ο Ο Ο Ο
2
5

Answers

Answer 1

Answer:

At x = -2 the graph of this polynomial will touch the x-axis.

Step-by-step explanation:

Recall the behavior difference between power functions of even and odd power. Odd powers are associated with the crossing of the x-axis, while even powers are associated with "touching" of the x axis.

in this cases, since they give you the function in factor form, the actual roots (x-values where the function adopts value zero) of the function are evident :

[tex]f(x)=(x-5)^3\, (x+2)^2[/tex]

It has a root at x = 5 [notice that at such x-value the factor (x-5) becomes zero], and this root is of multiplicity "3" (given by the power associated with the binomial factor for this root)

and has another root at x = -2  [notice that at such x-value the factor (x+2) becomes zero], and this root is of multiplicity "2" (given by the power associated with the binomial factor for it)

It is just the second root analyzed the one that shows an even power (2) associated to its binomial factor, and therefore it is at x= -2 that the graph of this function will show as "touching" the x axis.


Related Questions

Please help! Correct answer only!

In a raffle, one ticket out of 250 will win a $230 prize. The rest will win nothing. If you have a ticket, what is the expected payoff?

$__

Answers

Answer:

$0.92

Step-by-step explanation:

Since only one ticket out of the 250 wins a 230 dollar prize, the expected payoff is 230/250=0.92. Hope this helps!

Find the circumference of this circle:
7 cm
Write appropriate units with your answer, and round your answer to 2 decimal places.

Answers

I used 3.14 for pie so my answer may very slightly.
Answer: 43.96
Reasoning/Work:
(formula): C= 2(pie, 3.14)r
2x3.14x7
43.96

Plz help...it’s a math question and I suck at math would mean a lot to me thx <3

Answers

Answer:

Read below

Step-by-step explanation:

11. YX = 4.5

    RQ corresponds to ZY. If RQ is 4 and ZY is 3, then ΔQRP was dilated by  0.75 to form ΔYZX. (3/4 = 0.75). Using this knowledge, we can find the length of YX by multiplying 6 by 0.75. (YX corresponds to QP). 6 × 0.75 = 4.5.

12. 55°

    All of a triangle's angles must add up to 180°. ∠Q is 88°. ∠Z is 37°. ∠Z is congruent to ∠R because corresponding angles in similar triangles are congruent. So, 88° + 37° = 125°. We need to get to 180°, so 180° - 125° = 55°.

13. 4.2

    BC corresponds to DF. We need to find the scale factor, so divide 2.7 by 3.6. That equals 0.75. AC corresponds to EF. EF is 5.6, so multiply 5.6 by 0.75. That equals 4.2.

I hope this helps :))

Vx
Below is a scale drawing of a stage that Syla is designing,
8 cm
5 cm
Using the scale 1 cm: 7 m, Syla calculated the width, or the shorter side of the stage, to be 35 m. She decides to change the
scale to 1 cm 10 m. What is the width of the new stage?
35 m
50 m
56 m
80 m
Save and Exit
Next
Submit
Mark this and return
PA-Common Core...

Answers

Answer:

I beleive the new stage would be 50 meters wide

Step-by-step explanation:

I took the quiz on ed

Find the volume of the prism.

Answers

Answer:

792

Step-by-step explanation:

mark me brainliest!

12*11*6=792

v=l*w*h

*= times

Find x 4sqrt3 2sqrt3 8 8sqrt3

Answers

Answer:

8

Step-by-step explanation:

sin 30° = 1/2

sin is opponent/hypotenuse

so

opp/hyp = 4/x = 1/2

x = 4 * 2 = 8

Answer:

[tex]\displaystyle x=8[/tex]

Step-by-step explanation:

[tex]\displaystyle x=\frac{sin(90) \times 4 }{sin(30)}[/tex]

[tex]\displaystyle x=8[/tex]

One sheet of paper is 9 x 10 to the power of -3 to cm thick. Mark wants to put 500 sheets of paper into the paper tray of his printer. The paper tray is 4 cm deep. Is the paper tray deep enough for 500 sheets of paper? You must explain your answer. Input note: write down the thickness of the 500 sheets of paper.

Answers

Answer:

The paper tray is not deep enough.

Step-by-step explanation:

500 * 9 * 10^-3

= 500 * 0.009

= 4.5 cm which is greater than the depth of the paper tray (4 cm).

The paper tray is not enough for sheets of paper.

The thickness of 500 sheets of paper is 45 cm.

What is multiplication?

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

One sheet of paper is [tex]9[/tex] × [tex]10^{-3}[/tex] to the power of -3 to cm thick.

Mark wants to put 500 sheets of paper into the paper tray of his printer.

The thickness of 500 sheets of paper is

 [tex]9[/tex] × [tex]10^{-3}[/tex] × 500 = 45 cm

But the paper tray is 4cm deep

45 cm > 4 cm

So the paper tray is not enough for sheets of paper.

Find out more information about multiplication here

https://brainly.com/question/14059007

#SPJ2

Can someone plz help me out! With this problem I really need help ASAP! I will mark you as brainiest! Help help ASAP!

Answers

Answer:

John = 82 Billy = 82 Gregg = 80 Bob = 55

Step-by-step explanation:

John = (3x38)+(2x0)-(2x8)-(2x8)

Billy = (3x30)+(2x4)-(2x3)-(2x5)

Gregg = (3x30)+(2x3)-(2x4)-(2x4)

Bob = (3x25)+(2x6)-(2x9)-(2x7)

What is the equation for the graph shown?

Answers

Answer:

y = -2x + 6

Step-by-step explanation:

The graph is a line Then it has an equation of the form : y = my + p

where m is the slope and p is the y-intercept.

the line crosses the y-axis at the point (0,6) then

p = 6

the line is going down then

m is negative

the only provided equation that verify: m < 0 and p = 6 is  y = -2x + 6

Answer:

y = -2x + 6

Step-by-step explanation:



Solve for X.
X/3=5/8
4 4/5
17/8
8/15

Answers

Answer:

x = [tex]\frac{15}{8}[/tex]

OR

x = [tex]1 \frac{7}{8}[/tex]

Step-by-step explanation:

[tex]\frac{x}{3} = \frac{5}{8}[/tex]

Cross Multiplying

x × 8 = 5 × 3

8x = 15

Dividing both sides by 8

x = [tex]\frac{15}{8}[/tex]

OR

x = [tex]1 \frac{7}{8}[/tex]

Determine the number of solutions for the quadratic function f(x) = -x^2 + 3x - 9.

Answers

Answer:

0

Step-by-step explanation:

Rewrite the equation as x^2-3x+9=0

find the determinant.

D = b^2-4ac = (-3)^2-4*1*9 <0

no solution

Which angle measures approximately 152°?

Answers

Answer:

The answer is YZC, so the third option

Step-by-step explanation:

The explanation for this one is fairly simple, as the lines are already drawn out for you!

The line labeled C lines up with 152 on the protractor, and after connecting that to the base point Z in the middle and then the base line of Y, you get YZC

Hopefully I helped you!

Answer:

yzc

Step-by-step explanation:

i took the test and got it right

Find the SURFACE AREA of this composite solid. Show work

Answers

Answer:

8

Step-by-step explanation:

4+4

6-6+8

g(x) = 1/3 * (2/9)^x. Does the function model growth or decay?

Answers

The function models Exponential Decay due to the fact that as

x -> infinity, y-> 0

Answer:

It Decays

Step-by-step explanation:

Why because Kahn Acadmey  said so

how old am I?
16
17
4

Answers

Answer:

16

Step-by-step explanation:

(if u are 4, i'm gonna scream)

Answer:

16

Step-by-step explanation:

If you are 4, just no.

PLEASE HELP!!!!! PLEASE

Answers

Answer: d. (if a polygon has congruent angles, then it is regular)

Step-by-step explanation:

Converses follow the format of "if q, then p" (while  the original conditional is "if p, then q")

Just because there are clouds does not mean its raining (cloudy days)

just because it has four equal sides does not make it a square (rhombi have four equal sides but are not squares)

just because you cannot see the sun does not mean it is not daytime (solar eclipses)

if a polygon is regular, it must have congruent angles

A pipe cleaner lay across a wire shelf. The wires that make up the shelf are parallel, and the pipe cleaner is a transversal. The parallel wires are labeled a, b, and, c, and the angles are labeled with numbers.



The measure of one angle is 130°. Which statement is true regarding the 130° angle and angle 3?


They are same-side interior angles, so angle 3 measures 50°.

They are alternate interior angles, so angle 3 also measures 130°.

They are corresponding angles, so angle 3 also measures 130°.

They are alternate exterior angles, so angle 3 measures 50°.

Answers

Answer:

They are alternate interior angles, so angle 3 also measures 130°.

Step-by-step explanation:

Notice that the pair of angles are inside parallels, and at different sides of the transversal. So, those angles are alternate interior angles by definition, which means they are congruent.

Therefore, the right answer is B.

What equation represents three less than 1/5 of a number is 28

Answers

the answer is x÷5-3 = 28

Answer:

(28+3)×5=x

Step-by-step explanation:

28+3= [tex]\frac{1}{5}[/tex] of x

31 is 1/5 of x

x is 155

Checking:

155÷5-3=28

31-3=28

x is 155

Alternate solution:

(28+3)×5=x

Esme buys jackets for $500 each and prices them for $700 each. If the selling price is reduced by 20%, what's the profit percentage?

Please help!!! Imma mark you the brainliest!!​

Answers

12%

The cost Esme increased was 200, but then she reduced 20%of 700, which gives 140 dollars reduced. So, we subtract 140 from 200, which is 60 to find the actual increase.

Now, we follow the simple rules of percentage change

Increase divided by original times 100.

So, 60 divided by 500( not 700) times 100 = 12

12% is the very correct answer ever


Linda made 5 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 5 necklaces was $18.50. If the beads cost $1.50 for each necklace, how much did each pendant cost?

Answers

1.50 for beads x 5 necklaces = 7.50

Total.

18.50 -7.50 = 11.00

11.00 / 5 = $2.20 for was pendant

please help me on this!

Answers

Answer:

The rocket reached its maximum height at 1.25 seconds.

Step-by-step explanation:

What is the volume of this rectangular prism? 30.75 cm^3

61.5 cm^3

147.6 cm^3

295.2 cm^3

Answers

This question is incomplete. Because it lacks the diagram of the Rectangular prism. Find attached to this answer the appropriate diagram.

Answer:

295.2 cm³

Step-by-step explanation:

A Rectangular Prism is a 3 dimensional geometric shape.

The formula used to calculate the volume of the Rectangular Prism = Length × Width × Height

Length = 15cm

Height = 4.8cm

Width = 4.1cm

Volume of the Rectangular Prism = 15cm × 4.8cm × 4.1cm

= 295.2 cm³

Answer:

295.2

Step-by-step explanation:

Got it right on the test. Your welcome and have a great day and God bless you all.

Define: slant height

Answers

Answer:

The slant height which is the distance from the top, down the side, to a point on the base circumference.

Step-by-step explanation:

Which algebraic expression is equivalent to the expression below?
3(5x + 7) – 6(4 – 2x)
270 - 3
27r - 12
12r + 3
12. + 27
ha

Answers

Answer:

[tex] \boxed{27x - 3} [/tex]

Step-by-step explanation:

[tex] = > 3(5x + 7) - 6(4 - 2x) \\ \\ = > (3 \times 5x) + (3 \times 7) - (6 \times 4) - (6 \times ( - 2x)) \\ \\ = > 15x + 21 - 24 - ( - 12x) \\ \\ = > 15x - 3 + 12x \\ \\ = > 27x - 3[/tex]

Answer: 27x=3

Step-by-step explanation: 3(5x+7) -6(4-2x) = 3(5x+7) + (-6)(4+(-2x)) = 15x + 21 + (-24) + 12x =15x + 12x + (-24) + 21 =27x + (-3) =27x-3 hope this helps

What is the value angle marked x?

Answers

Answer: x =104

Step-by-step explanation:

If we draw the black line shown in the figure, two isosceles triangles are formed, and the base angles of the isosceles triangles are the same. The red angles are the same and the green ones too. The 104 degree angle is the sum of the red angle and the green angle, and x is also the sum of the red angle and the green angle, therefore x = 104.

What is the slope?

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Answer:

slope = [tex]\frac{1}{4}[/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 ) = (0, 2) and (x₂, y₂ ) = (4, 3) ← 2 points on the line

m = [tex]\frac{3-2}{4-0}[/tex] = [tex]\frac{1}{4}[/tex]

how can you find dictance between points and cordinte plances

Answers

Answer:

Distance = [tex]\sqrt{(x^{2}-x,)^{2} +(y^{2} -y,)^{2}[/tex]

I need help please!!​

Answers

Answer:

8

Step-by-step explanation:

x = 8

f(8) = |8|

f(8) = 8

Does this help?

VX
What is the value of x in the equation below?
-3-(-8)-(-2)
4-13

Answers

Answer: 0

I didn't see an 'x' so I was very confused but I simplified and got "0"

The answer to your question is 0

Anyone know how this can be solved?​

Answers

Answer:

127.235cm^2

Step-by-step explanation:

A = πr²/2 = 40.5 * π [cm²] ≈ 127.235 [cm²]

Answer:

[tex]127.251 {cm}^{2} [/tex]

Step-by-step explanation:

[tex] \frac{180}{360} \times \pi {r}^{2} \\ \frac{1}{2} \times 3.142 \times 9 \times 9 \\ = \frac{254.502}{2} \\ = 127.251 {cm}^{2} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

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