For the polynomial function ƒ(x) = x4 − 16x2, find the zeros. Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept.

QUESTION POSTED AT 10/10/2019 - 07:33 PM

Answered by answersmine AT 10/10/2019 - 07:33 PM

Our function f(x) can be rewritten if we factor out a common x^2 from each term:
f(x) = x^2(x^2-16)
Now inside the parentheses we have a polynomial of the form a^2 - b^2, or the difference of two perfect squares, which can be factored as (a+b)(a-b) so we have:
f(x)=x^2(x-4)(x+4)
Setting our function equal to zero gives us the roots x = 0, x = 4, and x = -4.
The multiplicity of the root zero is two since it occurs twice, and the others are one since they occur only once. If you graph the function you can see that it will only touch the x-axis at x = 0, but will cross the x-axis at x = 4 and x = -4.
Post your answer

Related questions

Find the distance between these points. C(0, 4), T(-6, -3) √(37) √(85) √(109)

The distance between 2 points C and T with their coordinates given is as follows:

C(x₁ , y₁) and T(x₂ , y₂) OR C(0,4) and T(-6,-3)


CT=√[(x₂ - x₁)² + (y₂ - y₁)²] =√[(-6-0)² + (-3 - 4)²]


CT=√[(36) + (49)} = CT = √85 

ANSWERED AT 17/10/2019 - 09:19 AM


QUESTION POSTED AT 17/10/2019 - 09:19 AM

If a+b+c=-9, and x+y=8, what is -4a+6x-4c+6y-4b

Hey there! 

For this problem, you can go ahead and split up your equation to replicate the format that you've been provided in your first two equations.

–4a + 6x – 4c + 6y – 4b

a + b + c = (–9)
–4a – 4b – 4c = –4(–9)
–4a – 4b – 4c = 36

x + y = 8
6x + 6y = 6(8)
6x + 6y = 48

If you don't understand what I just did, consider what I have below (this is not part of your problem, this is just so you can understand how I got the answers for the individual equations above):

x = 6
2x = 2(6) = 12
3x = 3(6) = 18, etc...

So, your big equation should be equal to 48 + 36, which is 84. 

–4a + 6x – 4c + 6y – 4b = 84

Hope this helped you out! :-)

ANSWERED AT 17/10/2019 - 09:18 AM


QUESTION POSTED AT 17/10/2019 - 09:18 AM

Find the distance between these points.W(-6, -8), X(6, 8) 20 10 √8

\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
W&({{ -6}}\quad ,&{{ -8}})\quad 
%  (c,d)
X&({{ 6}}\quad ,&{{ 8}})
\end{array}\quad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
d=\sqrt{[6-(-6)]^2+[8-(-8)]^2}\implies d=\sqrt{(6+6)^2+(8+8)^2}

ANSWERED AT 17/10/2019 - 09:15 AM


QUESTION POSTED AT 17/10/2019 - 09:15 AM

What is the simplified form of the cube root of x squared times the third root of x squared

Answer:

x\sqrt[3]{x}

Step-by-step explanation:

\sqrt[3]{x^2} *\sqrt[3]{x^2}

Both terms have same cube root so we multiply the terms and put it inside the cube root

Apply exponential property

a^m * a^n = a^{m+n}

x^2* x^2 = x^4

\sqrt[3]{x^2} *\sqrt[3]{x^2}=\sqrt[3]{x^4}

\sqrt[3]{x^4}=\sqrt[3]{x^3*x^1}=x\sqrt[3]{x}

ANSWERED AT 17/10/2019 - 09:15 AM


QUESTION POSTED AT 17/10/2019 - 09:15 AM

HELP PLEASE!! Determine whether the statement is true or false then EXPLAIN: Line Plots display individual data.

TRUE. I'm going to be using a picture from Google to help me out. In the graph below the line plots are telling how much Sarah's is as the years past. Each line plot tell the data of how much her car cost in whatever year the plot is in. For example, in 2006 her car cost $10,000. How do we know? We know this because the line plot is point towards 10,000 and downwards to 2006. This is data that the line plots are displaying fro us.So yes, line plots do display individual data.
Hope this helps!!! :) Pls mark me BRAINLIEST!  

ANSWERED AT 17/10/2019 - 09:15 AM


QUESTION POSTED AT 17/10/2019 - 09:15 AM

What is the simplified form of the cube root of x squared times the third root of x squared

The cubic root of x, by itself, would simply be 1/3 x. but, when you have an exponent in the radicand as an unknown, it gets more complicated. first, you have to solve what is inside the radicand first, following order of operations. so, first you solve x squared. x is your unknown, so you would need to determine the value of x and then square it. after that, you cube your answer. if we place 2 as x, for an example, you would find 2 squared to be 4, then cube that for your answer.

ANSWERED AT 17/10/2019 - 09:13 AM


QUESTION POSTED AT 17/10/2019 - 09:13 AM

Find the lowest common denominator of 3/x^3y and 7/xy^4 A. x^3y^4 B. x^4y^5 C. y^4 D. x^2y^3

The answer I came up with is A)

ANSWERED AT 17/10/2019 - 09:11 AM


QUESTION POSTED AT 17/10/2019 - 09:11 AM

What is the surface area of 120 x 110 x 4

The surface area of a rectangular prism is:

A=2(xy+xz+yz), where x,y, and z are its dimensions...in this case:

A=2(120*110+120*4+110*4)

A=2(13200+480+440)

A=2(14120)

A=28240 mm^2

ANSWERED AT 17/10/2019 - 09:11 AM


QUESTION POSTED AT 17/10/2019 - 09:11 AM

What is the surface area of 120 x 110 x 4

surface area is the area of all the faces on a shape so to speak.

2(120 x 110)=26,400

2(120 x 4)=960

2(110 x 4)=880

880+960+26,400=28,240

Surface area = 28,240

ANSWERED AT 17/10/2019 - 09:11 AM


QUESTION POSTED AT 17/10/2019 - 09:11 AM

2(2x - 4) + x = 7 solve by combining like terms show all steps plz

2(2x - 4) + x = 7
Distribute the 2
4x - 8 + x = 7
combine like terms
5x - 8 = 7
add 8 to both sides
5x = 15
divide both sides by 5
x =3

CHECK
2(2*3-4) + 3  ?=? 7
2(6-4) + 3  ?=? 7
2(2) + 3 ?=? 7
7 = 7 CHECKS

ANSWERED AT 17/10/2019 - 09:11 AM


QUESTION POSTED AT 17/10/2019 - 09:11 AM

A - It is not misleading B - The x-axis does not have a consistent scale . C - The axes are both labeled

Well, we can clearly see that both axises are labeled. The left axis (often called the y-axis) is labeled Scores and the bottom axis (often called the x-axis) is labeled Students.

The graph doesn't look to be misleading either.

As for the middle statement:
The x-axis doesn't need a scale.
The y-axis is clearly increasing in 5-point intervals.

So, the answer is BStatement B is not true.

ANSWERED AT 17/10/2019 - 09:10 AM


QUESTION POSTED AT 17/10/2019 - 09:10 AM

Simplify (5x3− x + 14) − (3x2− 9x + 4)

Answer:

5x³− 3x²+ 8x + 10.

Step-by-step explanation:

Given : (5x³− x + 14) − (3x²− 9x + 4).

To find : Simplify.

Solution : We have given

(5x³− x + 14) − (3x²− 9x + 4).

On remove parenthesis

5x³− x + 14 − 3x²+ 9x - 4.

Combine like terms

5x³− 3x²+ 9x -x + 14 - 4.

5x³− 3x²+ 8x + 10.

Therefore, 5x³− 3x²+ 8x + 10.

ANSWERED AT 17/10/2019 - 09:09 AM


QUESTION POSTED AT 17/10/2019 - 09:09 AM

How would you write 0x+19y=38 in slope-intercept form?

Basically, we need to isolate y

Assuming 0 is unnecessary:

x + 19y = 38
19y = -x + 38
y= \frac{-x+38}{19}
y= -\frac{x}{19} +  \frac{38}{19}
y= -\frac{x}{19} +2



Assuming that 0 is necessary:

0x+19y = 38

0•x is equivalent to 0 so that cancels out x leaving us with

19y = 38

y = 38/19

y = 2


If the 0 is necessary, your answer is y = 2.
If the 0 is unnecessary, your answer is y = -(x/19)+2

ANSWERED AT 17/10/2019 - 09:08 AM


QUESTION POSTED AT 17/10/2019 - 09:08 AM

Line segment WX is the radius of circle X, and line segment ZY is the radius of circle Y. Points W, X, C, Y, and Z are all on line segment WZ. What is the area of circle C, which passes though points W and Z? 81 164 324 1296

Point D is the midpoint of the outer circle that we aim to find the area of

The circle has a diameter of WZ and radii of WC and CZ

We know that YZ=YD=10 cm

Let DC be x and CY be 10-x

The radius of the outer circle can be written as 8+8+x or 10+10-x which we can equate to find the value of x

8+8+x=10+10-x
16+x=20-x
2x=4
x=2

Therefore, the radius of the circle is 8+8+2=18

And hence the area of the circle is   \pi (18^{2})=324 \pi

ANSWERED AT 17/10/2019 - 09:07 AM


QUESTION POSTED AT 17/10/2019 - 09:07 AM

Please find the volume of each figure . Please show and explain all work or you will be reported do all and not some . 40) A 5m×3m×4m rectangular prism 41) A cube with edge of 6 ft 42) A cylinder with a height of 14 cm and base Diameter of 10 cm 43) A triangular prism with a base area of 15 square inches and height of 12 inches . 44) A cylinder with a base circumference of 8pi and height 7 45) A box has a volume of 24 ft^3 and base of 2 ft by 3 ft, what is the height ?

Volume formulas:
rectangle prism: l×w×h
cube: s^3
cylinder:(pi)r^2×h
triangle prism: (a×b/2)×h
cylinder:(pi)r^2×h
box:l×w×h

40) 5m×3m×4m =15m×4m= 60m^3

41) 6 ft × 6 ft ×6 ft = 36 ft × 6 ft = 216 ft^3

42) d=2r 10/2=5 r=5
3.14×5^2×14=78.5×14= 1099cm^3


43) 15=a×b/2 (area of trianlge)
15×12= 180in^3

44) c=2 (pi)r 8pi=2r (pi)
r=4
3.14×4^2×7=50.24×7=351.68

45) 24 ft^3 =2 ft × 3 ft × height
24=6×h
÷6 both sides
h=4ft

ANSWERED AT 17/10/2019 - 09:06 AM


QUESTION POSTED AT 17/10/2019 - 09:06 AM

Freddie is at chess practice waiting on his opponent's next move. He notices that the 4-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle. Part 1: How many radians does the minute hand move from 3:35 to 3:55? (Hint: Find the number of degrees per minute first.) Part 2: How far does the tip of the minute hand travel during that time?

Part1

there are 360° in a circle (clock), and thus if we check how many degrees in a clock with 60minutes, then it'd be 360/60, or 6° per minute

now, the clock went from 3:35 to 3:55, 20 minutes, how many degree is that? 6*20

part2

\bf \textit{length of an arc}\\\\
s=\cfrac{r\theta\pi }{180}\qquad 
\begin{cases}
r=radius\\
\theta=\textit{angle in degrees}\\
----------\\
r=4\\
\theta=6\cdot 20
\end{cases}\implies s=\cfrac{4\cdot 6\cdot 20\cdot \pi }{180}

ANSWERED AT 17/10/2019 - 09:06 AM


QUESTION POSTED AT 17/10/2019 - 09:06 AM

Write an expression to show how many meters are equivalent to x centimeters

Y=meters
x=centimeters

Y=100x

ANSWERED AT 17/10/2019 - 09:05 AM


QUESTION POSTED AT 17/10/2019 - 09:05 AM

Show how many meters are equivalent to x centimeters

There are 0.01 meters per centimeter. This means if you have a problem like, "Tony measured his pencil and found it to be 37 centimeters; how many meters long is the pencil?" you can plug 0.01 into the equation. (0.01 * 37= 0.37). Thus, the pencil is 0.37meters. You can also do it backward if you need too; "Tony measured his pencil as saw it was 0.37 meters, how many centimeters long is the pencil?" ( 0.37 / 0.01= 37cm). I know this is a long explanation, does it help?

ANSWERED AT 17/10/2019 - 09:04 AM


QUESTION POSTED AT 17/10/2019 - 09:04 AM

A 12 ​-foot piece of string is cut into two pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is x feet​ long, find the lengths of both pieces.

The shorter piece would be 3 feet long and the longer piece would be 9 feet long.

ANSWERED AT 17/10/2019 - 09:04 AM


QUESTION POSTED AT 17/10/2019 - 09:04 AM

Can someone help me find the area of the shaded region? is it just the area of the circle?

The shaded region is the area of the circle minus the area
of the pentagon.
A circle = pi * r^2
A circle = pi * 15^2
A circle = 706.5 cm^2

A regular pentagon = (a * p)/2 where a is the apothem, p is the perimeter.
The apothem id the perpendicular height from the midpoint of a side to the center of the pentagon.
To find the apothem you have to use a trig ratio.
A pent = (8.3 * 12*5)/2
A pent = 249 cm^2

Shaded region: circle - pentagon 706.5 - 249 = 457.5

ANSWERED AT 17/10/2019 - 09:04 AM


QUESTION POSTED AT 17/10/2019 - 09:04 AM

A quadratic equation is shown below: 3x2 − 16x + 2 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. Part B: Solve 9x2 + 3x − 2 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used.

NightowlPart A)The discriminant of 3x2 − 16x + 2 is 232. That tells us there are 2 real solutionsPart B) solve by factoring9x2 + 3x − 2 = 0(3x+2)(3x-1)=03x+2 = 0    or   3x-1 = 0
x = -2/3   ,  1/3

ANSWERED AT 17/10/2019 - 09:03 AM


QUESTION POSTED AT 17/10/2019 - 09:03 AM

What best describes the range of function

The range of a function is the set of all possible output values.

ANSWERED AT 17/10/2019 - 09:03 AM


QUESTION POSTED AT 17/10/2019 - 09:03 AM

What expresion shows 15 more than 5 15 / 5 a 15 - 5 b 15 + 5 c 15 x 5 d

C is the correct answer

ANSWERED AT 17/10/2019 - 09:02 AM


QUESTION POSTED AT 17/10/2019 - 09:02 AM

A parallelogram with sides of 6 and 10 has an area of 30. Find the measure of the small angle of the parallelogram.

Answer:

45

Step-by-step explanation:


ANSWERED AT 17/10/2019 - 09:02 AM


QUESTION POSTED AT 17/10/2019 - 09:02 AM

The angle measures of quadrilateral RSTU are shown. m∠R = (2x)° m∠S = (3x – 35)° m∠T = (x + 35)° The measure of angle U is unknown. Can quadrilateral RSTU be a parallelogram?

Answer:

No, RSTU can not be a parallelogram.

Step-by-step explanation:

Given,

The angles measures of quadrilateral RSTU are,

m∠R = (2x)°

m∠S = (3x – 35)°

m∠T = (x + 35)°

Since, the sum of all interior angles of a quadrilateral is 360°.

m∠R +  m∠S +  m∠T +  m∠U = 360°

⇒ (2x)°  + (3x – 35)°  + (x + 35)° + m∠U = 360°

⇒ 6x + m∠U = 360°     ( By operating like terms )

m∠U = 360° - 6x      ( Subtracting 6x on both sides )

Now, we know that, the opposite angles of parallelogram are congruent or equal,

If RSTU is a parallelogram,

Then, m∠R =  m∠T and  m∠T = m∠U,

When, m∠R =  m∠T ⇒ (2x)° = (x + 35)° ⇒ x = 35°,

But, for x = 35°, 35+ 35 ≠ 360° - 6 × 35

m∠T ≠ m∠U

Hence, RSTU can not be a parallelogram.

ANSWERED AT 17/10/2019 - 09:01 AM


QUESTION POSTED AT 17/10/2019 - 09:01 AM

. Find the volume of the composite space figure to the nearest whole number. 210cm^3 180cm^3 120cm^3 60cm^3

 n           i              g             g                   a   :)

Hope this helps you

ANSWERED AT 17/10/2019 - 09:01 AM


QUESTION POSTED AT 17/10/2019 - 09:01 AM

Quadrilateral EFGH has coordinates E(a, a), F(3a, a), G(2a, 0), and H(0, 0). Find the midpoint of EF? Please show how the problem is done.

Answer:

The midpoints of the EF is (2a,a) .

Step-by-step explanation:

Definition of midpoints.

The midpoint is the point lie in middle of a line segment. It is equidistant from both endpoints .

Formula

Midpoints = (\frac{x_{2}+x_{1})}{2} ,\frac{(y_{2}+y_{1}}{2})

Quadrilateral EFGH has coordinates E(a, a), F(3a, a), G(2a, 0), and H(0, 0).

Now find out the midpoints of the  E(a, a) and F(3a, a) .

Midpoints\ of\ EF = (\frac{(3a+a)}{2} ,\frac{(a+a)}{2})

Midpoints\ of\ EF = (\frac{4a}{2} ,\frac{2a}{2})

Midpoints of EF = (2a,a)

Therefore the midpoints of the EF is (2a,a) .



ANSWERED AT 17/10/2019 - 09:01 AM


QUESTION POSTED AT 17/10/2019 - 09:01 AM

A bowl contains 3 red, 8 blue, and 7 black beads. Margaret randomly selects 3 beads one after the other without replacement. Find the probability of getting a red, blue, and black bead, in that order. a. dependent; 204/7 b. independent; 7/243 c. independent; 1/68 d. dependent; 7/204

This is the concept of probability and statistics, we are required to calculate the probability of getting a red, blue and black respectively, given that there are 3 red, 8 blue and 7 black beads;
Probability of an event occurring=(Number of ways it can occur)/(Total number of outcomes )
The total number of outcome in our situation is:
3+8+7=18
P(Red)=3/18=1/6
P(Blue)=8/17
P(Black)=7/16
since these occurrence are such that the selection is without replacement, that means they are dependent. The probability of them occurring in that order will be:
P(x)=1/6*8/17*7/16=7/204
The answer is d. dependent; 7/204 

ANSWERED AT 17/10/2019 - 09:01 AM


QUESTION POSTED AT 17/10/2019 - 09:01 AM