Given p(x) = x4 – 13x2 – 25x – 12.

A) Use long division to determine the remainder when p(x) is divided by (x2 – 4)? Show all of your work for full credit.

B) Use mathematical methods to prove that your quotient and remainder are correct. Show all of your work for full credit.

Answer:

D is a function.

Step-by-step explanation:

cause the line is related to both x and y

The relation that represents a function is the relation (d)

From the question, we have the following parameters that can be used in our computation:

The relations (1) to (4) represent the given parameter

Next, we test the options

Relation (1)

This relation is not a function

This is because it fails the vertical line test i.e. some output values all point to the same input value,

Relation (2)

This relation is not a function

This is because it fails the vertical line test i.e. some output values all point to the same input value,

Relation (3)

This relation is not a function

This is because it fails the vertical line test i.e. some output values all point to the same input value,

Relation (4)

This relation is a function

This is because the inputs all point to different output values

Hence, the relation that is a function is graph (d)

Read more about functions at

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Answer:

-3x+12

Since we are adding like terms you add everything that has an "x" after it [(3.4x) + (-5.4x) + (-x)] it all that adds up to -3x and the you add the 12 to it. It could also be written 12-3x

[tex]\huge\underline\mathtt\colorbox{cyan}{3/8}[/tex]

[tex]\huge\mathsf\colorbox{white}{}[/tex]

Total shared part:

1/4 + 1/8

Taking LCM and adding:

2/8+1/8

Adding gives:

3/8

Answer:

7

Step-by-step explanation:

42/6= 7

---

its a sort of memorization thing youll know when you do enough of them.

if not, you can divide by smaller parts.

3*2=6 so you can divide 42 by 2, and then 3 if that is easier

42/2

=21

then divide by 3 =7

Answer: 7

Step-by-step explanation: If you simplified 42/6 you would get 7 and 42/6 is basically 42 ÷ 6 which equals 7.

Answer:

35+43 = 78 so then E is 78 for both sides. then do 78+18 which is 96. so A is 96. I think

Answer:

help

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

An exponential function has the form

y = a[tex](b)^{x}[/tex]

Use the given solutions to find a and b

Using (0, 3 ) , then

3 = a[tex]b^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , so

a = 3

y = 3[tex](b)^{x}[/tex]

Using (1, 12 ) , then

12 = 3[tex]b^{1}[/tex] = 3b ( divide both sides by 3 )

4 = b , then

h(x) = 3[tex](4)^{x}[/tex] → A

Answer:

86 m, 59 cm

Step-by-step explanation:

a. perimeter is 2L + 2W

320 = 2L + 2(74)

320 = 2L + 148

172 = 2L

86 m is length

b. area = L x w

5723 = 97 x w

5723/97 = 2

59 cm is width

Answer:

f(0) = 3

f(-2) = -15

Step-by-step explanation:

You just have to plug in the value in f(b) into the b of the equation.

So for f(0) --> 2(0)^3 - |0-4| + 7

2(0) - |-4| + 7

0 - 4 + 7 = 3

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

for f(-2)

2(-2)^3 -|-2-4| + 7

2(-8) - 6 + 7

-16 -6 + 7 = -15

Answer:

(any real number, 5)

Step-by-step explanation:

Well given that y=7-2 and that y=5, we do not know the value of x, therefore x could be any real number with y being 5. I'm pretty sure that answered your question. So, a example of an ordered pair that would fit this rule would be say (5,5) or (7,5)

a) Evaluate the given function at each value of x. We have f(x) = 2x + 3.

• If x = -2, then

f(-2) = 2 (-2) + 3 = -4 + 3 = -1

• If x = -1, then

f(-1) = 2 (-1) + 3 = -2 + 3 = 1

• If x = 0, then

f(0) = 2 (0) + 3 = 0 + 3 = 3

and so on.

b) Kind of a silly question. Of course f(x) is a function, the instructions for part (a) say so!

But the real reason f(x) is indeed a function is that no single value of x returns more than one value of f(x).

Answer

First one is A

Second one is B

Third one is D

Problem 1

Answer: Choice A

(30, 225); Rocket reaches max height of 225 ft after 30 seconds.

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

Explanation:

Distribute the 0.25 through to get

y = 0.25(60x-x^2)

y = 15x - 0.25x^2

y = -0.25x^2 + 15x

This is in standard form y = ax^2+bx+c with a = -0.25, b = 15 and c = 0.

The first two values mentioned lead to this x coordinate of the vertex.

h = -b/(2a)

h = -15/(2*(-0.25))

h = -15/(-0.5)

h = 30

This tells us the answer is between A and C.

If you were to plug x = 30 into the original equation, you'll get y = 225. It means that after x = 30 seconds, the rocket has reached its max height of 225 feet. Therefore, the answer must be choice A.

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

Problem 2

Answer:  Choice B

(x-3)^2 = -8(y-6)

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

Explanation:

vertex = base of the bulb = (3,6)

focus = top of the bulb = (3,4)

This flashlight is pointed downward, which forms a downward opening parabola.

The distance from the vertex to the focus is p = 2 units. This is known as the focal distance.

We'll plug that in along with the vertex (h,k) = (3,6) in the formula below

4p(y-k) = (x-h)^2

4*2(y-6) = (x-3)^2

8(y-6) = (x-3)^2

Unfortunately that equation above produces a parabola that opens upward. To fix things, we stick a negative out front on either side, which will reflect the parabola over the x axis to make the parabola open downward. That leads us to choice B.

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

Problem 3

Answer:  D) square

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

Explanation:

We can form a point by intersecting the plane through the point where the two cones meet. The plane needs to be parallel to the base of each cone.

We can also form a line. To do so, we intersect the plane at exactly  along the edge of the cone. Make the plane tangent to the cone.

Lastly, we can form a circle by intersecting any plane parallel to the cone's base. This plane cannot pass through the meeting point of the two cones. Rather, the plane passes through one of the cones.

Those three previous paragraphs mean that we can rule out choices A,B,C. The only thing we can't form is a square. We can form straight lines, but we cannot form perpendicular lines needed to get a square. Nice work on selecting the correct answer.

Answer:

The explicit formula for the nth term of the sequence is [tex]a_n=9+8(n-1)[/tex]

Step-by-step explanation:

Recall:

The explicit formula for a sequence is [tex]a_n=a_1+(n-1)d[/tex] where [tex]a_n[/tex] is the [tex]n[/tex]th term, [tex]a_1[/tex] is the first term, and [tex]d[/tex] is the common difference

Given:

First term --> [tex]a_1=9[/tex]

Common Difference --> [tex]d=8[/tex]

Substitute:

[tex]a_n=9+(n-1)(8)[/tex]

[tex]a_n=9+8(n-1)[/tex]

Answer:

Each chicken wing costs $1.80.

Explanation:

To find the cost for each wings, you need to split the money by 7 which is: 12.60/ 7

this gives us:

1.80

Answer:

the answer is  2,500

Step-by-step explanation:

any number higher than 5 you round up but any number lower than 5 you round down.

4 is lower than 5 so you round it down and the 5 stays the same, and replace it with 0's.

Answer:

4800

3. Alexander is taking 15 credit-hours this semester at college. The

relationship between tuition and credit hours is shown by the graph below.

What is the constant of proportionality?

A. 15

B. 400

C. 800

D. 6000

4400

4000

3600

3200

2800

2400

2000

Tuition

1600

1200

800

400

2

3

S

4

Credit Hours

7

&

9

Step-by-step explanation:

Answer:

This answer would be c

Step-by-step explanation:

Answer:

[tex]f(1) = {(1)}^{3} + 3 {(1)}^{2} - 9(1) + 5 \\ (x - 1) = 0 \rightarrow \: x = 1 \\\frac{{x}^{3 } + {3x}^{2} - 9x + 5}{x - 1} = {x}^{2} + 4x - 5 \\ (x + 5)(x - 1) = 0 \\ x = - 5 \: or \: x = 1 \\ \color{red}\boxed{x_{1} = 1} \\\color{yellow} \boxed {x_{2} = 1} \\ \color{green}\boxed{x_{3} = - 5} [/tex]

The answer would be C and F

Answer: 1 & -5

Step-by-step explanation

Answer:

0.59 and 41%

Step-by-step explanation:

Plato/Edmentum

The approximate sample proportion is o.59, which means that 41% of the subscribers surveyed most often listen to music somewhere other than in a vehicle.

For this situation, the number of positive responses is 1486 out of a total sample size of 2500.

Substitute these values into the formula for sample proportion, where x is the number of positive responses and n is the sample size.

[tex]\hat p = \frac{x}{n}[/tex]

= [tex]\frac{1468}{2500}[/tex]

= 0.59

So, the approximate sample proportion is 0.59.

Since 0.59 represents the proportion who responded favorably, 1-0.59=0.41, represents the proportion which responded unfavorably.

This value of the same as 41%.

So, 41% of the subscribers surveyed most often listen to music somewhere other than in a vehicle.

Therefore, the approximate sample proportion is o.59, which means that 41% of the subscribers surveyed most often listen to music somewhere other than in a vehicle.

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Answer: x= 1.9

Step-by-step explanation:

Answer:

4.25 as decimal and 4 1/4 as a fraction

Step-by-step explanation:

Answer:

112cm^3

Step-by-step explanation:

Formula for volume of a cone is:

[tex] \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]

r = radius and h = height

To find the radius you divide the diameter by 2:

12.9 ÷ 2 = 6.45

Now substitute values into the formula:

[tex] \frac{1}{3} \times \pi \times {6.45}^{2} \times 16.6[/tex]

Which equals 112cm^3

Answer:

y/x^2=-2x+3

Step-by-step explanation: