Find all zeros of ƒ(x) = 2x^4 – 72x^2. Then determine the multiplicity at each zero. State whether the graph will touch or cross the x-axis at the zero.

Answers

Answer 1

Answer: See below

Step-by-step explanation:

To find the factor,

f(x) = 0

[tex]\begin{aligned}&2 x^{4}-72 x^{2}=0 \\&2 x^{2}\left(x^{2}-36\right)=0 \\&x^{2}\left(x^{2}-36\right)=0 \\&x \times x \times(x-6) \times(x+6)=0 \\&\mathrm{x}=0,0,6,-6\end{aligned}[/tex]

So,

x = 0 multiplicity 2

x = -6 multiplicity 1

x = 6 multiplicity 1

For an even multiplicty, the graph touches the x-axis, and for an odd multiplicty, the graph crosses the x-axis

Therefore,

x = 0 multiplicty 2, Touch

x = -6 multiplicty 1, Cross

x = 6 multiplicty 1, Cross


Related Questions

The following table shows the salary of 7 people in an office last year.

Name Income
Andy £9500
Bevan £25000
Cheryl £13250
Deva £75000
Elliott £18750
Frankie £27500
Grace £15000
a) Work out the mean income to 2 DP.
b) Deva was given a large bonus for 30 years service.
Excluding Deva's income, what was the mean income for the remaining 6 workers to 2 DP?

Answers

184000 / 7 = 26285.71
109000 / 6 = 18166.67

Ben spent 1/6 of his money on a burger, fries, and a drink. Then he spent half of the money he had left: $5 on a magazine, $8.25 on a bookmark, and $10.50 on a book. How much money did he have to begin with?

Please answer asap and please explain your answer.

Answers

Answer:

$57

Step-by-step explanation:

I'm not a good person explaining answers, so I will just give the equation.

[2(5+8.25+10.50)+ 23.75) x 4]  ÷ 5

Hope this helps :)

3 (– 8) = 3x – 24
No Solution
Infinite Solutions
X = -16 D
x = 0​

Answers

Answer:

B Infinite Solutions

Step-by-step explanation:

3 (x - 8) = 3x - 24

3x - 24 = 3x - 24

    + 24        + 24

3x = 3x

x = x

Infinite solutions

Strategic planning answers the question "__________"

Answers

Step-by-step explanation:

Where do you want to go from here?

What do you want to accomplish?

What obstacles will you have to overcome?

What problems will you have to solve?

What additional knowledge, skills, or resources will you require to achieve your strategic objectives?

The required Strategic planning answers the question "Where do we want to go and how do we get there?"

What is Strategic planning?

Strategic planning is the process of defining an organization's vision, mission, values, goals, and objectives, and developing a roadmap to achieve them.

Here,

"Where do we want to go and how do we get there?"

Strategic planning is the process of defining an organization's vision, mission, values, goals, and objectives, and developing a roadmap to achieve them. It involves assessing an organization's current situation, identifying strengths, weaknesses, opportunities, and threats, and developing strategies to leverage strengths, address weaknesses, seize opportunities, and mitigate threats.

The end result is a plan that sets the direction for the organization and guides decision-making and resources allocation to achieve its goals and objectives.

Learn more about Strategic planning here:
https://brainly.com/question/30562644
#SPJ2

A bowl has 8 green and 15 red grapes, Henry randomly choses a grape and eats it. What is the probabilty that both grapes are green?

Answers

Answer:

like 30% cause there are more red grapes then green

Step-by-step explanation:

I'm not sure cause I don't see any answer choices

What is 2(5+5) + 3(2+3)?

Answers

Step-by-step explanation:

[tex]2(5 + 5) + 3(2 + 3)[/tex]

[tex]2(10) + 3(5)[/tex]

[tex]20 + 15[/tex]

[tex]35[/tex]

i-Ready
»Evaluate (8+t)³ - 6 when t = 2.
The value of the expression is
Practice: Numeric and Algebra

Answers

Answer:

994

Step-by-step explanation:

8+t(3) - 6 = 1000-6= 994

What is the volume of a right circular cylinder with a radius of 4 m and a height of 4 m? 8π m³ 16π ​m³ ​64π ​m³ 256π m³

Answers

Answer: 64

Step-by-step explanation:

What additional piece of information must be known in order to calculate the volume of the cylinder below?
in.
the diameter of a base
the height of the cylinder
the area of a base
Othe radius of a base

Answers

Answer:

the height of the cylinder

Step-by-step explanation:

Please Help me

A farm grew 19.8 tons of wheat in 2013. The farm's wheat output increased by 9.8%
from 2013 to 2014 and by 5.1% from 2014 to 2015. Which expression represents a
strategy for estimating the total output of wheat, in tons, in 2015?

A) 20 + 10 + 5
B) 20(10)(5)
C) 20 + 1.1 + 1.05
D 20(1.1)(1.05)

Answers

D because it shows the . of each percentage

I WILL GIVE BRAINLIEST ANSWER TO THE PERSON WHO GETS THIS QUESTION CORRECT

Answers

Answer: y = -2x + 1

Step-by-step explanation:

The formula for slope-intercept form is y = mx + b. Keep y and x as the variables. Replace m with the slope, which can be found by doing rise/run, and replace b with the y-intercept. The y-intercept is the spot where the line intersects the y-axis.

Hope this helps! Have a great day! :)

NO LINKS!!! Please help me with this problem​

Answers

#RS

[tex]\\ \rm\Rrightarrow \dfrac{RS}{TS}=\dfrac{FG}{EF}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{RS}{12}=\dfrac{45}{18}=\dfrac{5}{2}[/tex]

[tex]\\ \rm\Rrightarrow RS=\dfrac{12(5)}{2}=6(5)=30[/tex]

#QR

[tex]\\ \rm\Rrightarrow \dfrac{HG}{EF}=\dfrac{QR}{TS}[/tex]

[tex]\\ \rm\Rrightarrow QR=TS=12[/tex]

#QU

[tex]\\ \rm\Rrightarrow \dfrac{UQ}{QR}=\dfrac{DH}{HG}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{UQ}{12}=\dfrac{45}{18}=\dfrac{5}{2}[/tex]

[tex]\\ \rm\Rrightarrow UQ=30[/tex]

Answer:

RS = 30, QR = 12, QU = 30

Step-by-step explanation:

Step 1:  Determine RS

We can see that RS on the left shape corresponds to FG on the right shape that is also larger.  We can use other sides to help us determine the ratio which will then give us the length of RS.  We can also see that the shape has been flipped so EF would match to ST.

[tex]RS/ST = FG/EF[/tex]

[tex]RS/12 = 45/18[/tex]

[tex]RS * 18 = 12 * 45[/tex]

[tex]\frac{18*RS}{18} = 540 / 18[/tex]

[tex]RS = 30[/tex]

Step 2:  Determine QR

We can see that QR on the left shape corresponds to HG on the right shape that is also larger.  We can use other sides to help us determine the ratio which will then give us the length of QR.  We can also see that the shape has been flipped so EF would match to ST.

[tex]QR/ST = HG/EF[/tex]

[tex]QR/12 = 18/18[/tex]

[tex]QR * 18 = 12 * 18[/tex]

[tex]\frac{18 * QR}{18} = 216 / 18[/tex]

[tex]QR = 12[/tex]

Step 3:  Determine QU

We can see that QR on the left shape corresponds to DH on the right shape that is also larger.  We can use other sides to help us determine the ratio which will then give us the length of QU.  We can also see that the shape has been flipped so EF would match to ST.

[tex]QU/ST = DH/EF[/tex]

[tex]QU/12 = 45/18[/tex]

[tex]QU * 18 = 12 * 45[/tex]

[tex]\frac{18*QU}{18} = 540/18[/tex]

[tex]QU = 30[/tex]

Answer:  RS = 30, QR = 12, QU = 30

plllsss answer! I don't understand this question.

Answers

Answer:

  C and D

Step-by-step explanation:

Population density is the ratio of population to area. Its units are persons per square mile. Here, you're being asked to compare the population densities of several countries to the average population density in several US states.

__

average

The idea of "average population density of the 10 states listed" is somewhat ambiguous. It could mean either of (a) the ratio of the total of the states' population to the total of their land area, or (b) the average of the population densities of the states. (In the attached, we computed both, but the answer remains the same using either number.)

When there are numerous identical calculations to be performed, it is convenient to let a spreadsheet do them. The attached spreadsheet shows the population densities for the 10 states and 5 countries listed.

Depending on how you define it, the average population density of the 10 states is about 10.5 or about 15.7 people per square mile. (15.7 is the average of the density numbers, found using the spreadsheet AVERAGE function.)

__

countries

The 5 countries have population densities ranging from about 7.7 to 236 people per square mile. Two of the countries have density below 10.5, so are the answers to the question asked.

  Canada (C) and Iceland (D) have population density below the US state average.

Hey could you guys help me answer this and explain it to me? It’s math

Answers

Answer:

C. 8

Step-by-step explanation:

d = 8

4 + [tex]\frac{d}{2}[/tex]

Substitute d for 8

4 + 8/2

Simplify

4+4

Simplify

8

Answer:

c = 8

Step-by-step explanation:

if d = 8, that would mean that

4 + 8/2 (because 8 has substituted for d)

then you do 8 ÷ 2 = 4

4 + 4 = 8

Select the correct answer. Which system of equations has a solution of (-2,-2,-2) ​

Answers

Answer:

[B] [tex]\begin{bmatrix}x+2y=-6\\ y+2z=-6\\ x-y-z=2\end{bmatrix}[/tex]

Step-by-step explanation:

Going through all answer choice to find the solution:

[A]  [tex]\begin{bmatrix}x+y=0\\ y-z=-2\\ x+y-z=-4\end{bmatrix}[/tex]

[tex]\mathrm{Isolate\;x\;for\;x+y=0;x=-y}[/tex]

[tex]\mathrm{Substitute\:}x=-y[/tex]

[tex]\begin{bmatrix}y-z=-2\\ -y+y-z=-4\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}y-z=-2\\ -z=-4\end{bmatrix}[/tex]

[tex]\mathrm{Isolate\;z\;for\;-z=-4;z=4}[/tex]

[tex]\mathrm{Substitute\:}z=4[/tex]

[tex]\begin{bmatrix}y-4=-2\end{bmatrix}[/tex]

[tex]\mathrm{Isolate\;y\;for\;y-4=-2;y=2}[/tex]

[tex]\mathrm{For\:}x=-y[/tex]

[tex]\mathrm{Substitute\:}z=4,\:y=2[/tex]

[tex]x=-2[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=-2,\:z=4,\:y=2[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[B] [tex]\begin{bmatrix}x+2y=-6\\ y+2z=-6\\ x-y-z=2\end{bmatrix}[/tex]

[tex]\begin{bmatrix}y+2z=-6\\ z-y-z=2\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}y=-2[/tex]

[tex]\begin{bmatrix}-2+2z=-6\end{bmatrix}[/tex]

[tex]\mathrm{For\:}x=-6-2y[/tex]

[tex]\mathrm{Substitute\:}z=-2,\:y=-2[/tex]

[tex]x=-6-2\left(-2\right)[/tex]

[tex]x=-2[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=-2,\:z=-2,\:y=-2[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[C] [tex]\begin{bmatrix}3x-y=-8\\ y-3z=-8\\ x+y+z=-8\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}x=\frac{-8+y}{3}[/tex]

[tex]\begin{bmatrix}y-3z=-8\\ \frac{-8+y}{3}+y+z=-8\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}y-3z=-8\\ z+\frac{-8+4y}{3}=-8\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}y=-8+3z[/tex]

[tex]\begin{bmatrix}z+\frac{-8+4\left(-8+3z\right)}{3}=-8\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}\frac{15z-40}{3}=-8\end{bmatrix}[/tex]

[tex]\mathrm{For\:}y=-8+3z[/tex]

[tex]\mathrm{Substitute\:}z=\frac{16}{15}[/tex]

[tex]y=-8+3\cdot \frac{16}{15}[/tex]

[tex]y=-\frac{24}{5}[/tex]

[tex]\mathrm{For\:}x=\frac{-8+y}{3}[/tex]

[tex]\mathrm{Substitute\:}z=\frac{16}{15},\:y=-\frac{24}{5}[/tex]

[tex]x=\frac{-8-\frac{24}{5}}{3}=x=-\frac{64}{15}[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=-\frac{64}{15},\:z=\frac{16}{15},\:y=-\frac{24}{5}[/tex]

[tex]x=-\frac{64}{15}=-4.26666666667, z=\frac{16}{15}=1.06666666667,y=-\frac{24}{5}=-4.8[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[D] [tex]\begin{bmatrix}x-2y+z=0\\ 2y+9z=-20\\ x-y+z=0\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}y=\frac{-20-9z}{2}[/tex]

[tex]\begin{bmatrix}x-2\cdot \frac{-20-9z}{2}+z=0\\ x-\frac{-20-9z}{2}+z=0\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}x+20+10z=0\\ x+\frac{20+11z}{2}=0\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}x=-10z-20[/tex]

[tex]\begin{bmatrix}-10z-20+\frac{20+11z}{2}=0\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}\frac{20-9z}{2}-20=0\end{bmatrix}[/tex]

[tex]\mathrm{For\:}x=-10z-20[/tex]

[tex]\mathrm{Substitute\:}z=-\frac{20}{9}[/tex]

[tex]x=-10\left(-\frac{20}{9}\right)-20[/tex]

[tex]x=\frac{20}{9}[/tex]

[tex]\mathrm{For\:}y=\frac{-20-9z}{2}[/tex]

[tex]\mathrm{Substitute\:}x=\frac{20}{9},\:z=-\frac{20}{9}[/tex]

[tex]y=\frac{-20-9\left(-\frac{20}{9}\right)}{2}=0[/tex]

[tex]y=0[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=\frac{20}{9},\:z=-\frac{20}{9},\:y=0[/tex]

[tex]x=\frac{20}{9}=2.22222222222,\:z=-\frac{20}{9}-2.22222222222,\:y=0[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Kavinsky

Can someone help me please

Answers

Answer:

6.75 kg

Step-by-step explanation:

6/8 = 0.75

0.75 x 9 = 6.75

Answer:

6 3/4 kg

Step-by-step explanation:

9 x 6/8 = 6 3/4

The bigger the payment that you make on your credit card bill, the
А less interest you wil have to pay in total
B more interest you will have to pay in total C higher your APR
D lower your annual fee

Answers

Answer:

A I think

Step-by-step explanation:

subtract x-3 from 3-x + 4​

Answers

Answer:

-2x + 10

Step-by-step explanation:

3 - x + 4 - (x - 3)

1. Combine like terms:

-x + 7 - (x - 3)

2. Apply the distributive law - (a - b) = -a + b :

-x + 7 -x + 3

3. Combine like terms:

-2x + 10

hope this helps!

Find A in degrees.
a = 11
b = 12
C = 20
B
A
N
A =[? ] degrees
Round to the nearest tenth.
Enter

Answers

Answer:

28.2°

Step-by-step explanation:

formula for an included angle (law of cosines)

[tex] - \cos( \frac{ {a }^{2} + {b}^{2} - {c}^{2} }{2ab} )[/tex]

(the variables change depending on the question, this one is switched, for example...it is actually b squared+ c squared - a squared over 2(bc) in this case)

after you plug it all in, you get cos⁻¹(0.88125), and an answer to the nearest tenth of 28.2

If you found this answer helpful, I would greatly appreciate brainliest :D.

Raise 10 to the 3rd power then multiply the result by a

Answers

Answer:

1000a

Step-by-step explanation:

[tex] 10^3 \times a = 10 \times 10 \times 10 \times a = 1000 \times a = 1000a [/tex]

250 employees in an organization were surveyed about their hair color and height the data collected is presented in the table if a person is selected at random what is the probability that the person is at least 175 cm tall

Answers

1) There are 90 + 74 people who are "at least 175 cm tall" (164 ppl)

2) probability is 164/250 = 0.656

D. 0.656

A display case of hat pins are marked 5 for $3. If Patty has $21, how many hat pins can Patty get? (assume no other taxes and fees)

Answers

Answer: 35

Explanation: If patty has $21, and $3 is the price for 5 hat pins, then: 21/3=7, so she can buy 7 packages which cost $3 and contain 5 pins, and because the question asked the number of pins, we will multiply 7 • 5 and that equals 35

Solve the equation: (a + 2)^4- 20(a + 2)^2+ 64 = 0

Answers

Answer:

Answer is 7.

Step-by-step explanation:

(a + 2)^4- 20(a + 2)^2+ 64 = 0

2a^4- 20(2a)^2+ 64 = 0

16a-20(4a)+64=0  

-4a    -64  -4a          -64

12a-84=0

    +84 +84

12a=84

84/12=7

The answer is 7
If needed to be solved to show proof text me

A right triangular prism, with measurements in inches (in.), is shown.
3 in.
4 in.
5 in.
What is the volume, in cubic inches, of the right triangular prism?

Answers

Answer:

The volume is 30 cubic inches

Step-by-step explanation:

If it helped mark brainliest :)

Answer:

I would I don't know cause I am only in six grade


Which situation will yield variability?

A. How many days are in June?
B. How many minutes the avengers movie lasts?
C. How many texts do you receive each month?
D. How fast the speed limit is on Grand parkway?
I will give brainliest

Answers

Answer:

A) 30

B) 2h 23m

C) 13-17

D) 70 MPH

Step-by-step explanation:
D) It is a safe speed for people to go

I need help on shehidbdornd Fr

Answers

Answer:

A factory makes aquariums. Each aquarium is in the shape of a triangular prism, as shown below. If the factory makes 126 aquariums, how much water will be needed to fill all of them (in cubic feet)?

Step-by-step explanation:

The distance, d, an object travels is represented by the equation d = rt, where r represents the average rate of speed and t represents time. Determine the units of t if d is measured in feet and r is measured in feet per second.

A.
square feet

B.
seconds

C.
feet per second

D.
feet per second squared

Answers

Answer:

B. seconds

Step-by-step explanation:

We have d=rt

means that t= [tex]\frac{d}{r}[/tex]

Given the units of each:

d: feet

r: feet/second

Replace each with its unit:

 t=    [tex]\frac{feet}{\frac{feet}{second} }[/tex]   =  [tex]\frac{feet.second}{feet}[/tex]  = second

So the unit of t is seconds (option B.)

Answer:

B. seconds

Step-by-step explanation:

Given

d = rtunit of d = feetunit of r = feet per second

To Find :

unit of t

Solving :

Since d = rt, we can rearrange it and rewrite it as t = d/rNow substitute the units in place of d and rt = d/rt = feet/feet per secondt = (feet)/(feet)(second)⁻¹t = seconds

IMPORTANT: every " a, b, c and + , -" are meant to be exponents

Answers

The expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is an algebraic expression, and the result of simplifying the expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is 1

How to simplify the expression?

The expression is given as:

[tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex]

Apply the power rule of indices

[tex](x^{a-b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex]

Expand the exponents of the expression

[tex]x^{a^2-b^2} \cdot x^{b^2 - c^2} \cdot x^{c^2 - a^2[/tex]

Apply the product rule of indices

[tex]x^{a^2-b^2+b^2 - c^2+c^2 - a^2[/tex]

Collect like terms

[tex]x^{a^2- a^2-b^2+b^2 - c^2+c^2[/tex]

Evaluate the differences

[tex]x^{0-0 - 0[/tex]

This gives

[tex]x^{0[/tex]

Evaluate the exponent

1

Hence, the result of simplifying the expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is 1

Read more about simplifying expressions at:

https://brainly.com/question/723406

What is 125.1 ÷ 6 and if you do how do you do it?

Answers

ans = 20.85

hope it helps...!!!

WILL MARK BRAINLIEST!!!!!
For which shape is 180 degrees the smallest angle of rotational symmetry?

Answers

The shape with a rotational symmetry would remain the same when rotated

The shape with the smallest angle of rotational symmetry of 180 degrees is shape D

How to determine the shape?

To do this, we simply examine each of the options

Shape A: Cross

The shape has 4 equal sides.

So, the smallest angle of rotational symmetry is:

Angle = 360/4

Angle = 90

The smallest angle of rotational symmetry is 90 degrees

Shape B: Star

The shape has 5 vertices.

So, the smallest angle of rotational symmetry is:

Angle = 360/5

Angle = 72

The smallest angle of rotational symmetry is 72 degrees

Shape C: Composite figure

This shape has a square and a triangle merged together at two ends

This means that the smallest angle of rotational symmetry is a complete rotation of 360 degrees

Shape D: Circle

The circle is divided into two equal segments.

The angle on the straight line of each segment is:

Angle = 360/2

Angle = 180

The smallest angle of rotational symmetry is 180 degrees

Hence, the shape with the smallest angle of rotational symmetry of 180 degrees is shape D

Read more about rotational symmetry at:

https://brainly.com/question/12214455

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