please help fill these in..​

3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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Answer:

5 is the correct answer.............

Answer:

it would be the two on the right because they both pass the vertical line test

Step-by-step explanation:

The angle measure of the minor arc is 62°

A circle is the locus of a point such that its distance from a fixed point (center) is always constant.

The diameter is the length of the line that passes through the center circle touching two points on the circle's circumference.

The arc of a circle is the part or segment of the circumference of a circle.m∠EFG = minor arc EGminor arc EG = 62°

The measure of the arc is 62°

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Answer:

D. 41

Step-by-step explanation:

Use Pythagorean Theorem: a² + b² = c²

With that in mind, we already have a and b, so:

40² + 9² = c²

√(40² + 9²) = c

c = 41

And we have our final answer!

Answer: 43

Step-by-step explanation:

Let's start with what we know about triangles which is that the sum of the angles in a triangle = 180. So far, we have one angle at 79 and another at 58, when adding them up: 79 + 58 = 137.  Then we do 180 - 137 = 43.

So x = 43.

Answer:

Step-by-step explanation:

Increased price = 11% of   £ 13000

                          = 0.11 * 13000

                           = 1430

Price after increase = 13000 + 1430 =  £ 14,430

Answer:

A translation by 1 unit to the left and 7 units up.

Step-by-step explanation:

(3,-4) --> (2,3)

x-values decreased by 1.

y-values increased by 7.

Left 1.

Up 7.

Interest morgan will pay is $1560.

Compound interest, also known as interest on principle and interest, is the practice of adding interest to the principal amount of a loan or deposit.

Given, Morgan used a payment plan to purchase brand-new living room furnishings for $6,500. He put down $500, and over the following three years, he must pay a monthly payment of $210.00.

Hence he has to total pay = 500 + 210*12*3

The total money morgan has to pay is $8060.

Therefore total interest morgan has to pay is 8060-6500 = $1560.

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Answer:

A sample size of at least 531 is required.

Step-by-step explanation:

We are lacking the confidence level to solve this question, so i am going to use a 90% confidence level.

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1-0.9}{2} = 0.05\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).

So it is z with a pvalue of \(1-0.05 = 0.95\), so \(z = 1.645\)

Now, find the margin of error M as such

\(M = z*\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

Find the required sample size for the new study.

A sample size of at least n is required.

n is found when \(M = 0.05\)

We have that \(\sigma = 0.7\)

So

\(M = z*\frac{\sigma}{\sqrt{n}}\)

\(0.05 = 1.645*\frac{0.7}{\sqrt{n}}\)

\(0.05\sqrt{n} = 1.645*0.7\)

\(\sqrt{n} = \frac{1.645*0.7}{0.05}\)

\((\sqrt{n})^{2} = (\frac{1.645*0.7}{0.05})^{2}\)

\(n = 530.4\)

Rounding up

A sample size of at least 531 is required.

Answer:

Step-by-step explanation:

c + a = 342 ..................... (1)

5c + 12a = 2550 ........... (2)

- 5 × (1) + (2)

7a = 840

a = 120

c = 342 - 120 = 222

Given:

Number of reams of paper = 5

Number of sheets in one ream = 500 sheets

Let's explain how we could estimate the thickness of 2 sheets of paper.

To find the thickness of 2 sheets of paper, we are to first find the number of sheets in the box.

Where:

Number of sheets in the box = Number of reams x Number of sheets in one ream

= 5 x 500 = 2500 sheets.

Now, we know there are 2500 sheets in the box.

Here, we are to first determine the total height of the stacked ream.

To find the thickness of 2 sheets of paper, divide the height of the stacked ream by the total number of sheets then multiply by 2.

It can be expressed as:

Where:

• x represents the height of the stacked ream.

• y represents the total number of sheets

• ANSWER:

To estimate the thickness of 2 sheets of paper, divide the height of the 5 stacked reams of paper by the total number of sheets, then multiply by 2.

The correct answer is option b. When the homoskedasticity assumption is violated, The beta parameter estimates are biased while the rest of the OLS assumptions are correct.

When the homoskedasticity assumption is violated, the ordinary least squares (OLS) estimator is still consistent but no longer efficient. This means that the estimates of the regression coefficients (beta parameters) are still unbiased, but they have higher variances and covariances.

In other words, the OLS estimator is no longer the best linear unbiased estimator (BLUE) and it may be biased when the errors are heteroscedastic. Therefore, option b is correct.

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Answer:

a.x=39.2

b.Use whole  wire as a circle

Step-by-step explanation:

We are given that

Length of piece of wire=70  units

Let length of wire used to make a square =x units

Length of wire used in circle=70- x

Side of square=\(\frac{perimeter\;of\;square}{4}=\frac{x}{4}\)

Circumference of circle=\(2\pi r\)

\(70-x=2\pi r\)

\(r=\frac{70-x}{2\pi}\)

Combined area of circle and square,A=\((\frac{x}{4})^2+\pi(\frac{70-x}{2\pi})^2\)

Using the formula

Area of circle=\(\pi r^2\)

Area of square=\((side)^2\)

a.\(A=\frac{x^2}{16}+\frac{4900+x^2-140x}{4\pi}\)

Differentiate w.r.t x

\(\frac{dA}{dx}=\frac{x}{8}+\frac{2x-140}{4\pi}\)

\(\frac{dA}{dx}=0\)

\(\frac{x}{8}+\frac{2x-140}{4\pi}=0\)

\(\frac{\pi x+4x-280}{4\pi}=0\)

\(\pi x+4x-280=0\)

\(x(\pi+4)=280\)

\(x=\frac{280}{\pi+4}\)

x=39.2

Again differentiate w.r.t x

\(\frac{d^2A}{dx^2}=\frac{1}{8}+\frac{1}{2\pi}\)>0

Hence, the combined area of circle and the square is minimum at x=39.2

b.When the wire is not cut and whole wire used  as a circle . Then, combined area is maximum.

Answer:

yes

explanation:

a rectangle is a parallelogram because its pairs of opposite sides are parallel.

The solution to the system of equations is x = 18/11 and y = 56/11.

To solve the system of equations:

3x + y = 10   ...(1)

5x - 2y - 2 = 0   ...(2)

We can use the method of substitution or elimination to find the values of x and y that satisfy both equations.

Let's use the method of elimination:

Multiply equation (1) by 2 to make the coefficients of y in both equations opposite:

6x + 2y = 20   ...(3)

Now, add equations (2) and (3):

(5x - 2y - 2) + (6x + 2y) = 0 + 20

11x = 18

Divide both sides by 11:

x = 18/11

Substitute the value of x into equation (1):

3(18/11) + y = 10

54/11 + y = 10

y = 110/11 - 54/11

y = 56/11

Therefore, the solution to the system of equations is x = 18/11 and y = 56/11.

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Answer:

-32

Step-by-step explanation:

Let the number be x.

\(2(x+8)=-48 \\ \\ x+8=-24 \\ \\ x=-32\)

Answer:

AB =  4.9cm

Step-by-step explanation:

We know

AC is 9.1 centimeters, and BC is 4.2 centimeters.

Find AB

We take

9.1 - 4.2 = 4.9cm

So, AB = 4.9cm

Answer:

7x-4

Step-by-step explanation:

That is the answer

Answer:

I trying to solve this sorry

2.

In order to calculate how many seconds it took, we can use the free fall formula:

Where DeltaS is the displacement, g is gravity and t is the amount of time.

So, using DeltaS = 450 and g = 9.81, we have:

So it took 9.578 seconds for the cellphone to reach the ground.

Step-by-step explanation:

2.

In order to calculate how many seconds it took, we can use the free fall formula:

\Delta S=\frac{gt^2}{2}ΔS=

2

gt

2

Where DeltaS is the displacement, g is gravity and t is the amount of time.

So, using DeltaS = 450 and g = 9.81, we have:

\begin{gathered}\begin{gathered} 450=\frac{9.81\cdot t^2}{2} \\ 9.81t^2=900 \\ t^2=\frac{900}{9.81} \\ t^2=91.74312 \\ t=9.578\text{ s} \end{gathered}\end{gathered}

450=

2

9.81⋅t

2

9.81t

2

=900

t

2

=

9.81

900

t

2

=91.74312

t=9.578 s

So it took 9.578 seconds for the cellphone to reach the ground.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.

The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.

To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:

Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

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The mood depicted in the given passage is: Anger

Mood is defined as a feeling or emotion that is dominant at any given time, so the mood of a story is the overall feeling the reader gets that is projected by the story elements. The mood of a story can change depending on which part of the story is examined; however, the overall mood can be determined in spite of these changes.

There are a number of story elements and devices that writers can use to project mood. For example, stories have settings, characters, conflicts, themes, diction and tone that can lead to a conclusion about mood. In addition, writers use devices such as figurative language and sensory description to help set a mood.

In this case, when we look at the given story, it is clear that the mood here is one of anger.

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Answer:

the value of x that makes the equation true is x = 3.5.

Step-by-step explanation:

To find the value of x that makes the equation 18x + 5 - 3 = 65 true, we need to simplify the equation and solve for x.

Starting with the equation:

18x + 5 - 3 = 65

First, combine like terms:

18x + 2 = 65

Next, isolate the term with x by subtracting 2 from both sides:

18x = 65 - 2

18x = 63

Finally, divide both sides of the equation by 18 to solve for x:

x = 63 / 18

x = 3.5

Therefore, the value of x that makes the equation true is x = 3.5.

The answer is:

Steps & work :

First, I focus only on the left side.

Combine like terms:

\(\sf{18x+5-3=65}\)

\(\sf{18x+2=65}\)

Subtract 2 from each side:

\(\sf{18x=63}\)

Now, divide each side by 18:

\(\sf{x=\dfrac{63}{18}\)

Clearly, this fraction is not in its simplest terms, and we can divide the top and bottom by 9:

\(\sf{x=\dfrac{7}{2}}\)

\(\therefore\:\:\:\:\:\:\stackrel{\bf{answer}}{\boxed{\boxed{\tt{x=\frac{7}{2}}}}}}\)

We need to write an equation that relates x and y.

We know those values vary directly. And one pair of values are given. Thus, we have the following proportion:

values of x values of y

2 5

x y

Then, cross multiplying the above quantities, we obtain:

Now, we need to isolate y on the left side of the equation. We can do so by dividing both sides of the equation by 2. We obtain:

Answer

Answer:

60%

Step-by-step explanation:

6/10=60%

Answer:

If you mean 6/10 then the answer would be 60%

Step-by-step explanation:

% means 100

So the denominator is 10, and we need it to be 100

To get to 100 from 10, you need to multiply. ( 10 x 10 = 100 )

What you do to the bottom, you have to do to the top. ( 6 x 10 = 60 )

That would get you 60/100, which equals 60%

Have a nice day!

Answer:

B

Step-by-step explanation:

The points with these coordinates form a triangle with a side 5 units and height 4 units. It' area is equal to 5*4÷2=10units^2