Simplify by finding the product of the polynomials below. Then Identify the degree of your answer. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. (2x^2+2x+1)(4x-1) This simplifies to: AnswerThe degree of our simplified answer is: Answer

The end of the spring is below equilibrium in terms of seconds, t, since the spring was released is D(t) = 17([tex]0.957^{t}[/tex])cos(28πt)

A state of balance between opposing forces or actions that is either static (as in a body acted on by forces whose resultant is zero) or dynamic (as in a reversible chemical reaction when the rates of reaction in both directions are equal).

Given that, a spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 3 seconds, the amplitude has decreased to 13 cm. The spring oscillates 14 times each second.

Amplitude begins at 17 cm, [tex]A_{0}[/tex] = 17 cm

The amplitude decreases by 13/3 = 4.33 per second = 0.043%

The amplitude function can be then modelled as =

A(t) = [tex]A_{0}[/tex][tex](1-0.043)^{t}[/tex]

A(t) = [tex]A_{0}[/tex][tex]0.957^{t}[/tex]

The spring oscillates 14 times each second, therefore,

T = 1/14

2π/B = 1/14

B = 28π

The graphical equation is;

D(t) = [tex]A_{cos}[/tex](Bt-C)+D

Horizontal shift = 0

Vertical shift = 0

Hence, The end of the spring is below equilibrium in terms of seconds, t, since the spring was released is D(t) = 17([tex]0.957^{t}[/tex])cos(28πt)

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The formula of the area of a circle is

where r is the radius

in this case, we have the length of the diameter, the diameter is twice the radius

d= diameter

d=2r

therefore

r=d/2

r=8/2

r=4

we substitute the value of the radius in the formula

the area of a circle with a diameter of 8km is 16pi km^2 or 50.27km^2

The Solution:

Given:

Required:

Determine the function of the given graph.

The required equation is:

Answer:

[option 2]

From the question we are given

Annual total cost in $ is given by

And an Annual total revenue in $ is given as

Where x is the number of pairs of boots sold

We are to find the profit function

Using the detains given we have

Profit function P(x) is

Therefore,

Therefore, the profit function is

Next we are to find determine the number of pair of boots that will maximize annual profit

Plotting the graph of the Profit function we have

Hence, at maximum we have the points (50, 6400)

Therefore, x = 50

This implies that the number of boots that will maximize the annual profit is 500

To find the angle, we will simply divide 360 by the number of sides

Number of sides = 8

That is;

Angle = 360 / 8 = 45 degree

The mean (μ) of a discrete random variable (z) is calculated as follows:

Substituting with data:

3/12 is 1/4 in its simplest form

The lines that are perpendicular to 3x – y = 10. is option C (x+3y= 27).

Line equation:

3x - y = 10

y = 3x - 10

here slope m = 3.

perpendicular line slope = -1/m = -1/3

so the perpendicular line must have slope m = -1/3

A.  

y = 3x + 5

here slope m = 3

This line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.

B.

y = -13x + 17

here slope m = -13

This line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.

C.

x + 3y = 27

3y = -x + 27

y = -1/3(x) + 27/3

y = -1/3(x) + 9

here slope m = -1/3

This line is perpendicular to the 3x - y = 10 because here slope is equal to -1/3.

D.

y - 2 = 13(3x+36)

y = 39x + 468 - 2

y = 39x + 466.

here slope m = 39.

So this line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.

Therefore the lines that are perpendicular to 3x – y = 10. is option C (x+3y= 27).

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SOLUTION:

Step 1:

In this question, we are given the following:

If two planes leave an airport at the same time with one flying west at 520 miles per hour and the other flying east at 540 miles per hour,

how long will it take them to be 3180 miles apart?

Step 2:

Let the distance of one of the planes flying west at 520 miles per hour be:

And let the distance of the other plane flying east at 540 miles per hour be:

where x , represents the time of flight in hours, such that:

CONCLUSION:

The time it will take them to be 3180 miles apart will be in 3 hours' time.

Answer:

The graph of the line shows that the value of k is the y-coordinate of the point where the x-coordinate is equal to 1.

k = 2.5

1 seagull eats 2.5 pounds of garbage.

Explanation:

First, we need to draw the point (4, 10) on the graph because 4 seagulls eat 10 pounds of garbage. Then, we need to draw a line that passes through this point, and through (0, 0). Finally, we need to identify the number of pounds of garbage when the number of seagulls is 1 or identify the point (1, k). So, we get:

Therefore, the value of k = 2.5 is the constant of proportionality and tell us the number of pounds of garbage that each seagull eat.

So, the graph of the line shows that the value of k is the y-coordinate of the point where the x-coordinate is equal to 1. Also, k represents the slope of the line.

So we will like to compare the three numbers -5, -4 and -3. We will like to compare the three temperatures. To know wich numbers is less than the other we can draw the real line

The more to the left the number are the lesser it is therefore

7x + 2y = -8 Equation 1.

8y = 4x​ Equation 2.

We solve for y in eq. 2; as follows:

y = 4x/8.

Now we replace y on eq. 1:

7x + 2(4x/8) = -8

7x + x = -8

8x = -8

x = -8/8

x = -1

Finally we replace x on eq 2:

8y = 4(-1)

8y = -4

y = -4/8

y = -1/2

Given:

Coordinates (-3 , 2), (6 , 2), (6 , -4), (-3 , -4)

Required:

Area and Parameter

Explanation:

Formula to find the distance between two points

Distance between (-3 , 2), (6 , 2) and (6 , 2), (6 , -4)

Final Answer:

f(x) = 5x²+10

Given the function g(x) expressed as:

If the function g(x) is translated vertically upward by 3 units to produce f(x), the resulting translation used will be given as:

Substitute the function g(x) into the translation rule to have:

Therefore the expression for f(x) is 5x²+10

Remember that

A relationship between two variables, x, and y, represent a proportional variation (direct variation) if it can be expressed in the form y=Kx

An equation of the line that passes through the origin

A relationship between two variables, x, and y, represents an inverse variation if it can be expressed in the form y=1/x

There is a vertical asymptote at x=0

therefore

Looking at the graph

The selling price of this hair clip will be $ 1.50.

Cost price of the clip is = $ 0.50

Markup price = 200 percent

Mark up price = 200 % of 0.5

Mark up price = 200 / 100 × 0.50

Mark up price = 2 × 0.50

Mark up price = $ 1

Selling price of the product will be:

SP = $ 0.50 + $ 1

SP = $ 1.50

Therefore, we get that, the selling price of this hair clip will be $ 1.50.

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Your question was incomplete. Please refer the content below:

The cost to manufacture a hair clip is $0.50. With a markup of 200 percent, what is the selling price of this hair clip?

We would find the volume of the ice cream contained in the cone by applying the formula for determining the voume of a cone which is expressed as

Volume = 1/3 x pi x radius^2 x height

From the information given,

height = 10

radius = 4

pi is a constant whose value is 3.142

Thus,

Volume = 1/3 x 3.142 x 4^2 x 10

Volume = 167.57

rounding to the nearest whole number,

Volume = 168 cubic cm

For this problem we have the following expression given:

Since any number multiplied by 0 is 0 then our expression becomes:

And since we have two terms we can categorize the expression as a binomial.

Answer:

13

Explanation:

The explicit formula of a sequence is given below:

When n=3

The 3rd term of the sequence is 13.

We will solve as follows:

So, the solution is 7b + 86.

ANSWER:

A) He will receive a refund of $435.

STEP-BY-STEP EXPLANATION:

According to the table for your income and marital status you must pay a total of $4091

If you already paid a total of $4,526, then:

Which means, they owe you a total of $435 back.

Therefore, the correct answer is A) He will receive a refund of $435.

a piecewise function​

x+ 4 , if -4 ≤x <3

. 3 ≤ x < 6

Then ,answer is [ -4,6)

Increasin function:

f(x) = a^x

Where a must be greater than 1:

A. 1/15 = 0.06 NO

B. 5 YES

C. 1/5 NO

D. 0.5 NO

Correct option B.5

5>1

Let's take this, step by step.

First step:

Rotate the coordinate 180 degrees about the origin.

When a 180 degrees rotation about the origin is performed the coordinates (x, y) changes to (-x, -y)

Thus, P(3, -4) changes to P'(-3, 4)

Second Step:

Perform a translation of (x, y+2)

P'(-3,4) = P''(-3, 4+2) = P''(-3, 6)

Third step:

Perform a dilation of 2.

P''(-3, 6) = P'''(-3*2, 6*2) = P'''(-6, 12)

We can see that,

P(3, -4) while P'''(-6, 12)

Therefore, P and P''' do not have the same coordinates

You have the following function:

f(x) = (x + 1)²

In order to determine the value of f(2) you replace the value x = 2 in the given function and make the operations, just as follow:

f(2) = (2 + 1)² simplify inside parenthesis

f(2) = (3)² 3² is the same as 3x3=9

f(2) = 9

Hence, the value of the function when x = 2 is f(2) = 9

We will use the equivalency:

Then, if we have an area of 32 m^2, we can multiply this value by the equivalency factor we wrote (as it is equal to 1) as:

Answer: the area is 344.48 sq ft.

Answer:

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Let the first term be a and common difference be d.

The explicit rule is a(n) = - 95 + 5 · (n - 1), whose recursive rule is [tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 5. The 30th element of the arithmetic sequence is 50.

Arithmetic sequences are sets of elements generated by a formula of the form:

a(n) = a + r · (n - 1), for n ≥ 1

Where:

Please notice that the common rate is the difference between any two consecutive elements of the sequence. The recursive form is described by the following form:

[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + r

Now we should determine the elements of the explicit rule by solving the following system of linear equations:

n = 18

- 10 = a + r · (18 - 1)

a + 17 · r = - 10

n = 40

100 = a + r · (40 - 1)

a + 39 · r = 100

Then, we solve the system of linear equations by numerical methods:

(a, r) = (- 95, 5)

And the 30th element of the arithmetic series:

a(n) = - 95 + 5 · (n - 1)

a(30) = - 95 + 5 · (30 - 1)

a(30) = 50

And the recursive form is [tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 5.

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the equation will be

-x - y = 7

"You are solving a system of equations of two linear equations in two variables, and you discover that there are no solutions to the system"​

So, it will mean the lines are parallel

so, the graph which describe the system is pink

The answer is option D

We have to apply the change of base formula:

We can apply this to our expression as:

Answer: -4.6