Anybody can help with these 2 I would really appreciate it for my last grade

Answer:

The polynomial is:

[tex]p(x) = x^3 + 2x^2 - 3x + 20[/tex]

Step-by-step explanation:

A third degree polynomial can be written in function of it's zeros [tex]x_1, x_2, x_3[/tex] the following way:

[tex]p(x) = a(x - x_1)(x - x_2)(x - x_3)[/tex]

In which a is the leading coefficient.

Integer coefficient that have zeros: 1+2i, 1-2i, -4

Leading coefficient: 1

So

[tex]p(x) = 1(x - (1+2i))(x - (1-2i))(x - (-4))[/tex]

[tex]p(x) = (x - 1 -2i)(x - 1 + 2i)(x + 4)[/tex]

[tex]p(x) = ((x-1)^2 - (2i)^2)(x + 4)[/tex]

[tex]p(x) = (x^2 - 2x + 1 - 4i^2)(x + 4)[/tex]

Since [tex]i^2 = -1[/tex]

[tex]p(x) = (x^2 - 2x + 1 + 4)(x + 4)[/tex]

[tex]p(x) = (x^2 - 2x + 5)(x + 4)[/tex]

[tex]p(x) = x^3 + 4x^2 - 2x^2 - 8x + 5x + 20[/tex]

[tex]p(x) = x^3 + 2x^2 - 3x + 20[/tex]

Answer:

36

Step-by-step explanation:

Break it into parts to make it easier. The equation would become 16+12+8 which is 36

Brainliest is highly appreciated and goodluck!

Answer:

Use the formula

Step-by-step explanation:

c2=a2−b2...The formula generally associated with the focus of an ellipse is c2=a2−b2 where c is the distance from the focus to center , a is the distance from the center to a vertex and b is the distance from the center to a co-vetex .

Answer: -8x^6

Step-by-step explanation:

-32x^8/4x^2=

-32x^6/4=

so the answer is -8x^6

Answer:

[tex]f\left(x\right)=\cos\left(x\right)\: and\:\: g\left(x\right)=\left(2x^2-1\right)[/tex]

Step-by-step explanation:

We have, [tex]H\left(x\right)=\cos\left(2x^2-1\right)H ( x )[/tex]

                          [tex]=\cos\left(2x^2-1\right)[/tex]

And   [tex]H\left(x\right)=\left(f\:\circ\:g\right)\left(x\right)H ( x ) = \left(f\:\circ\:g\right)( x )[/tex]

        [tex]\Rightarrow \left(f\:\circ\:g\right)(x)=\cos\left(2x^2-1\right)[/tex]

Now, [tex]f\left(x\right)=\cos\left(x\right)[/tex]   and [tex]g\left(x\right)=\left(2x^2-1\right)[/tex]

Answer:

(1, -2)

Easy Question for me

Answer:

A sample of 11352 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

For this problem, we have that:

400 cards, 120 cases were correct. So

[tex]p = \frac{120}{400} = 0.3[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

How large a sample n would you need to estimate p with margin of error 0.01 and 95% confidence

We would need a sample of size n, and n is found when [tex]M = 0.01[/tex]. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.01 = 2.325\sqrt{\frac{0.3*0.7}{n}}[/tex]

[tex]0.01\sqrt{n} = 2.325\sqrt{0.3*0.7}[/tex]

[tex]\sqrt{n} = \frac{2.325\sqrt{0.3*0.7}}{0.01}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.325\sqrt{0.3*0.7}}{0.01})^2[/tex]

[tex]n = 11351.8[/tex]

Rounding up

A sample of 11352 is needed.

Answer:

=0.5(1.1) - 0.5(2x)+2.4x-2.10

=0.55-x+2.4x-2.10

=1.4x-1.55

Ans A

Answer:

The sample is the 150 randomly selected customers.

Step-by-step explanation:

When you survey a group of people, to gauge whaever you are interested, these people are what makes your sample.

In this question:

Nick surveys 150 randomly selected customers to determine whether or not they were satisfied.

So the sample is the 150 randomly selected customers.

Answer:

15= -3m-9

15+9 = -3m

24 = -3m

-8= m

Therefore the m value is -8

Answer:

7x+8+8x+7+45=180

15x+15+45=180

15x+60=180

15x=120

x=8

7×8+8= 64

Answer:

a) equilateral

b) Isosceles

c) scalene

d) right angle

e) acute angle

f) obtuse angle

It is correct answer

Answer:

x = 68

Step-by-step explanation:

[tex]3x-18=186\\\\3x=186+18\\\\3x=204\\\\x= \frac{204}{3}\\\\x=68[/tex]

Answer: 1) on the x axis.

Step-by-step explanation:

Every coordinate ,where y is 0, lies on the x axis.

Answer:

0.3 or in fraction form 3/10

Step-by-step explanation:

3/4    =   3/10

2.5             1

add like terms. y's and x's go with other y's and x's

Answer:

83, 94, 105

Step-by-step explanation:

it's going up by 11

Answer:

83

Step-by-step explanation:

Its adding 11 each time

Answer:

Step-by-step explanation:

Help me

Answer:

y=15+x

Step-by-step explanation:

A PARALLEL line has the same angular coeficient, so:

[tex]f(x) = 2x+b[/tex]

[tex]f(4) = 5[/tex]

[tex]5 = 2\cdot 4 +b[/tex]

[tex]b = 5-8[/tex]

[tex]b = -3[/tex]

The line asked is:

[tex]f(x) = 2x-3[/tex]

Answer:

-2x+y=-3

Step-by-step explanation:

Choose a point (4,5) that the parallel line will pass through.

Find the slope m=2

To find an equation that is parallel to   y=2x-4 the slopes must be equal. Using the slope of the equation, find the parallel line using the point-slope formula.

y-y1=m(x-x1) if m=2 and x1=4 and y1=5

y-5=2(x-4)

y-5=2x-8

Solve for  y --- > y=2x-3

-2x+y=-3

(-2x+y=-3)*-1

2x-y=3

Answer:

yes it would go down a little bit but not much, so it nothing to worry about to much

Step-by-step explanation:

Answer:

You should use Brainly so that we can help.

Step-by-step explanation:

Answer:

Do it.

Step-by-step explanation:

Answer:

625

Step-by-step explanation:

(-5)(-5)(-5)(-5) = 625

Here,

The midpoint of segment QR is M

m(-2,9) x3=-2,y3=9

Q=(-8,12)x1=-8,y1=12

R=x2,y2

we know that,

[tex]\tt{ m=\dfrac{Q+R}{2} }[/tex] ⠀

So,

x3=[tex]\tt{\dfrac{x1+x2}{2} }[/tex] ⠀

[tex]\tt{-2=\dfrac{-8+x2}{2} }[/tex] ⠀

[tex]\tt{-2×2=-8+x2 }[/tex] ⠀

[tex]\tt{x2=8-4 }[/tex] ⠀

[tex]\tt{x2=4 }[/tex] ⠀

x2=4

now we find the y coordinate y2.

y3=[tex]\tt{\dfrac{y1+y2}{2} }[/tex] ⠀

[tex]\tt{9=\dfrac{12+y2}{2} }[/tex] ⠀

[tex]\tt{9×2=12+y2 }[/tex] ⠀

[tex]\tt{y2=18-12 }[/tex] ⠀

[tex]\tt{y2=6 }[/tex] ⠀

y2=6

Now we get the two coordinate of R

so,

R=(x2,y2)=(4,6)

Answer: -30

Step-by-step explanation: