# 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

QUESTION POSTED 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:

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:

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.

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:

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.

12 x 2 = (24 - 3) = 21

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

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

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

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

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! :-)

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

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

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

**Answer:**

**Step-by-step explanation:**

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

Apply exponential property

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

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

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!

Hope this helps!!! :) Pls mark me BRAINLIEST!

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

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

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

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

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

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

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

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

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

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**B**. **Statement B is not true.**

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

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

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

**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

Basically, we need to isolate y

Assuming 0 is unnecessary:

x + 19y = 38

19y = -x + 38

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**

Assuming 0 is unnecessary:

x + 19y = 38

19y = -x + 38

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

If the 0 is unnecessary, your answer is

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

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

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 and CY be

The radius of the outer circle can be written as or which we can equate to find the value of

Therefore, the radius of the circle is

And hence the area of the circle is =324

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

We know that YZ=YD=10 cm

Let DC be and CY be

The radius of the outer circle can be written as or which we can equate to find the value of

Therefore, the radius of the circle is

And hence the area of the circle is =324

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

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

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

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

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

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

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

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

Y=meters

x=centimeters

Y=100x

x=centimeters

Y=100x

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

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

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

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

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

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

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

x = -2/3 , 1/3

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

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

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

C is the correct answer

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

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

**Answer:**

45

**Step-by-step explanation:**

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

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

**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

Hope this helps you

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

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

It would be 6.95, (follow what you were doing, just do 6.95)

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

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

**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

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 = (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

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

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