Given that 4 - 3i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x) = r4 - 2x3 - 50x2 + 366x - 675

Answer:

36

Explanation:

Given the vertices of the triangle as A(-7, -4), B(1, 11), and C(-7, 5).

To be able to determine the perimeter of the triangle, we have to first find the distance between the vertices using the distance formula.

Let's determine the distance between A(-7, -4) and B(1, 11) as seen below;

Let's also determine the distance between B(1, 11) and C(-7, 5);

Let's determine the distance between C(-7, 5) and A(-7, -4);

To find the perimeter of the triangle, we'll add the distance between each vertex together;

EXPLANATION

We can get the total change in yards by multiplying the number of plays by the number of lost yards in a play.

The number of losses is negative.

-8 x 4 = -32

Taking the absolute value for both numbers:

|4| = |4|

|-8| = 8

Since -8 has the greater value, the answer is negative.

C) y=-2x

1)Perpendicular lines have the slope equal to the reciprocal multiplied by -1 of the original line.

2) As the given line is y = 1/2x + 1 and the point that is intercepted by (1,-2) we can state the following

Original line:

Slope m = 1/2

Point

Perpendicular line

slope = -2

Let's plug into the slope-intercept formula the given point, to find b the linear coefficient

y=mx +b

-2=-2(1) +b

-2 =-2 +b

-2+2=b

b=0

So the function is, y=-2x

Given:

To find:

the numerator of the rational expression on the right

To determine the numerator, we need to factorise the denominator:

Expanding the numerator on the right:

we have

Applying property of exponents

Adds the terms

we have a rational function

the two polynomials are

numerator ------> 3t^5+9 (binomial of degree 5)

denominator ----> t^3 (monomial of degree 3)

Given:

Sales = 768

Commission rate = 4%

To be able to get the commission, we multiply the sales by the commission rate in decimal form.

We get,

Therefore, the commission is 30.72.

Given:-

To graph the image.

So now we find the values of y when the value of x is -3,-2,-1,0,1,2,3.

When x is -3. we get,

So the required value is 27.

when x is -2. we get,

So the required value is 9.

When x is -1. we get,

So the required value is 3.

When x is 0. we get,

So the required value is 0.

When x is 1. we get,

So the required value is 1/3.

When x is 2. we get,

So the required value is 1/9.

When x is 3. we get,

So the required value is 1/27.

So the graph looks like,

This is the graph and it decreases from left to right.

Answer:

128, 64, 32, 16, 8, 4,2​

Explanation:

Each next term in the sequence is half of the previous term.

For example,

In a similar fashion, the a_3 term is 1/2 the previous term:

And similarly, a_6 is

Hence, the complete sequence with a_3 = 32 and a_6 = 4 is 128, 64, 32, 16, 8, 4,2​

Use equation in the form:

Where C is the cost, m is the monthly charge, x is the number of months and b is the joining fee:

Gym A:

Gym B:

Find the number of months (x) that it rill take for CA and CB to be equal:

Equal CA and CB:

Use the equation above to find the value of x:

32 pictures were painted with light colors

Here, we are interested in calculating the number of pictures that were painted with light colours

From the question, we can see that the ratio of pictures painted with light colours to that painted with dark colours is;

8 : 2

In the simplest form, this is the ratio 4 to 1

So, we can divide the total number of 40 pictures based on this ratio

We add up the ratios which is total 5

Then we place the number representing the number of light colours on it and multiply the fraction by 40

We have this as;

If DBC = 90° what is the relationship between AD and CD?​

_____________________________________

Answer

AD=CD

_____________________________________

The sum of supplementary angles is 180º

If ∠ DBC = 90°

∠ DBC = 90° so then ∠ DBA = 90º

DB is the same for the two triangles

and AB = BC

By the side angle side congruence theorem, we can conclude AD=CD

We will graph the solution set of the first linear inequality.

The related equation is

Now we take any two values of x, plug them into the equation, and solve for their respective y-coordinates.

Since the inequality is <, a strict one, the borderline is dashed.

Now, we consider a point that is not on the line, for example (0,0), and substitute in the inequality:

This is false. So, the solution does not contain the point (0,0). Therefore, we shade the lower half of the line.

We will graph the solution set of the second linear inequality.

To find the slope-intercept form, you need to isolate y, as follows:

-5x = 2y

2 is multiplying on the right, then it will divide on the left

-5x/2 = y

-5/2x = y

According to the trigonometrics they are defined as

identify the opposite side, the adjacent side and the hypotenesu according to the angle Y

Replace the sides to find the trigonometrics

Answer:

P(A∩B)= P(A/B)P(B)

Explanation:

A relationship for a conditional probability of two events A and B is:

Therefore, if we multiply both sides by P(B), we get:

So, the answer is:

P(A∩B)= P(A/B)P(B)

The probability of anyoutcome should always be between 0 and 1, if there is a value above 1 or below 0 that cannot be a probability.

⇒This problem is an absolute value problem where in we know that whatever is in the absolute signs always will come out positive

⇒If we are to check carefully 10 is the product of -5 and a positive number |x+1| so it is NOT possible anywhere in MATHEMATICS that when you multiply a negative number by a positive number it is going to give you a positive number, There is no solution for this question since the product of a negative number and a positive number is negative the given equation cannot be solved.

GOODLUCK!!!!

angle SPQ =90°

Becuase it is a right triangle

angle RPQ=62°

angle SPR= ?

the sum of angle RPQ and angle SPR must sum 90°

62+ angle SPR=90°

angle SPR=90-62=28°

the answer is

angle SPR= 28°

EXPLANATION

Given the function:

Factor out common term -3:

-3(x^3 -5x^2 -4x -20)

Factor x^3 -5x^2-4x-20:

Factor out -4 from -4x - 20:

-4x - 20

Rewrite 20 as 4*5:

=-4x - 4*5

Factor out common term -4:

=-4(x+5)

Factor out x^2 from x^3 + 5x^2:

Apply exponent rule: a^(b+c)= a^b*a^c

x^3=xx^2

=xx^2 + 5x^2

Factor out common term x^2:

=x^2(x+5)

=-4(x+5) + x^2(x+5)

Factor out common term x+5

=(x+5)(x^2-4)

Factor x^2-4:

Rewrite 4 as 2^2:

=x^2-2^2

Apply difference of two squares formula:

The resultant expression is:

So, the zeros are:

(-5,0) (-2,0) (2,0)

STEP - BY - STEP EXPLANATION

What to do?

Simplify the given expression.

Given:

-7w-6(2z-2w)+7z

To solve, we will follow the steps below:

Step 1

Open the parenthesis.

Step 2

Re-arrange the above.

ANSWER

5w - 5z

We have a rectangular coordinate system, we can represent x with blue color and y with red color in order to indentify better the points

For the point A, we can see that the value of x (blue color) is 0 and the value of y (red color) is 2.

So, the point A is A(0,2)

For the point B, we can see that the value of x is 5 and the value of y is -1.

So, the point B is B(5,-1)

For the point C, we can see that the value of x is 1 and the value of y is -1.

So, the point C is C(1,-1)

ANSWER:

A(0,2)

B(5,-1)

C(1,-1)

The value of the annuity at the end of 17 years is $22561.17.

Use a formula to determine the annuity in case of periodic deposit as

[tex]A = \dfrac{P[(1+r/n)^{nt}-1]}{\frac{r}{n} }[/tex]

Where P is periodic deposit amount interests,

r is rate annually is the number of times compounded annually and

t is time in a year.

Given that,

P = $195, r = 5.9% = 0.059,

t = 17 years, n = 4(quarterly)

[tex]A = \dfrac{P[(1+r/n)^{nt}-1]}{\frac{r}{n} }[/tex]

Substitute the values in the above formula,

[tex]A = \dfrac{195[(1+0.059/4)^{(4)(17)}-1]}{\dfrac{0.0059}{4} }[/tex]

A = $22561.17

Thus, the total value of the annuity is $22561.17.

Learn more about the formula of the annuity here:

brainly.com/question/13247656

#SPJ1

Let n be the number of Granola bars purchased with the $5 bill:

C(n) = 0.5n, where C = cost of n Granola bars.

With a $5 bill, one can purchase:

C(n) = 0.5n

5 = 0.5n

Divide both sides by 0.5:

So the linear function is function C(n) = 0.5n and a $5 bill can purchase 10 Granola bars.

Explanation:

To know what is the cost to travel 380 miles, we need to know the cost of one gallon of fuel. So, let's assume that this cost is $3.8 per gallon.

Since 380 miles spent 20 gallons of fuel, the cost is

C = 20 gallons x $3.8 = $76

Answers:

Therefore, the answers are:

How much would that cost: $76

What did you have to assume to get the answer: The cost of one gallon of fuel

Type the number you assumed here: 3.8

The total money was divided in two parts to be invested. Let's call the first part as 'x', and the other part 'y'. We know that the total amount sums up to $9500, then, we have the following equation:

We also know that the first part is invested at 12% yearly, and the second one at 7% rate. The total yield is $960. Converting this into a mathematical equation, we have:

Now, we have a system with two equations and two variables.

Rewriting the first equation to be x as a function of y, we have

Now, making a substitution(the x in the first equation for the x in the second equation)

Now, using our y value in any of our previous equations we get the value for x.

This means we invested $5900 at 12% and $3600 at 7%.

16 - 7k ≥ 8 + 3(-5k+8)

Distributing,

16 - 7k ≥ 8 + 3(-5k) + 3(8)

16 - 7k ≥ 8 - 15k + 24

16 - 7k ≥ (8 + 24) - 15k

16 - 7k ≥ 32 - 15k

15 is subtracting on the right, then it will add on the left

16 is adding on the left, then it will subtract on the right

-7k + 15k ≥ 32 - 16

8k ≥ 16

8 is multiplying on the left, then it will divide o the right

k ≥ 16/8

k ≥ 2

Area of the plane figure = 4 unit squares

Since the area of any shape is always in unit squares

Number of squares in the plane figure = 4

Area of the plane figure = 4 unit squares

Given:

Angles E and F are given supplementary angles.

The supplementary angles are the angles whose measures add upto 180 degrees.

Hence,

Substituting the values,

Hence,

Answer:

Explanation:

The probability we want to calculate is:

Now, we use the normal approximation of the binomial distribution

That would be:

p = 0.8 (probability of germination) given as 80%

q = 1 - p = 0.2 (probability of no germination)

We have the mean as:

We have the standard deviation as:

Now, let us get the value of z;

Now, we use the standard normal distribution table

n

Explanation

we have a right triangle,we need to know what it means:

The hypotenuse is the longest leg and is always the side opposite the 90-degree angle. The short leg is the one opposite the smallest angle, and the last leg is the long leg

so,the answer is

I hope this helps you