Use synthetic division to divide 2x^4 − 12x^3 + 18x^2 − 13x +20 ; x−4.

Applying the relations given, considering equivalent angles, the trigonometric measures for the angles are given as follows:

The sine of 240º can be written as follows:

sin(240º) = sin(180º + 60º).

Applying the first relation given on the second line, we have that:

sin(180º + 60º) = -sin(60º)

It is known that sin(60º) = sqrt(3)/2, hence the sine of 240º is given as follows:

sin(240º) = -sin(60º) = -sqrt(3)/2.

The cosine of 225º can be written as follows:

cos(225º) = cos(180º + 45º).

Applying the second relation given on the second line, we have that:

cos(180º + 45º) = -cos(45º)

It is known that cos(45º) = sqrt(2)/2, hence:

cos(225º) = -cos(45º) = -sqrt(2)/2.

The tangent of 225º can be written as follows:

tan(225º) = tan (180º + 45º).

Applying the third relation given on the second line, we have that:

tan(180º + 45º) = tan(45º)

It is known that tan(45º) = 1, hence:

tan(225º) = tan(45º) = 1.

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Step 1: Write the given expression

Step2: Expand the expression

Hence

hence the righ

Answer:

A

Step-by-step explanation:

I hope this is clear enough , although I did not arrive at the same answer using x in both equation .

The employer will charge $55 for 5 hours

The first step is to calculate the amount charged for an hour

22= 2

x= 1

cross multiply

2x= 22

x= 22/2

x= 11

The amount charged for 5 hours can be calculated as follows

11= 1

y= 5

cross multiply

y= 55

Hence $55 will be charged for 5 hours

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The ratio of 114 hours to 13 days is 19:52.

It should be noted that ratio is simply used to show the comparison between two things that are illustrated.

In this case, we want to calculate the ratio of 114 hours to 13 days. It should be noted that 24 hours make one day. Therefore, 13 days will be:

= 13 × 24 = 312 hours.

The ratio of 114 hours to 13 days will be:

= 114 / 312

= 19 / 52

The ratio is 19:52.

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the loan payment on a fixed term mortgage loan of $100,000 at 8% for 30 years will be $ 340,000.

Principal amount = $ 100,000

Interest rate = 8 %

Time period = 30 years.

Now, the interest is simple interest as it is a fixed rate/ fixed term mortgage.

So, the interest will be:

Simple interest = p r t / 100

SI = 100,000 × 8 × 30 / 100

SI = $ 240,000

Amount will be:

A = $100,000 + $ 240,000

A = $ 340,000

Therefore, we get that, the loan payment on a fixed term mortgage loan of $100,000 at 8% for 30 years will be $ 340,000.

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Answer

B n G = {2}

B u G = {-2, -1 , 0 , 2, 3, 4, 5, 7)

Step-by-step explanation:

Given the following two sets

B = { -2, 2, 3, 5}

G = { -1, 0, 2, 4, 7}

Part A

Find the intersection of B and G

The intersection of two sets is defined as the set of all the elements in set A that is also present in set G

Hence, the set of elements that is present in set B and set G is 2

Mathematically, B n G = {2}

Part B

Find the union of set B and set G

The union of two sets is a set containing all elements that are in both sets B and G

B u G = {-2, -1 , 0 , 2, 3, 4, 5, 7)

It is given that the product of 7 and a number, increased by 3, is equal to twice the number, subtracted from 39.

It is required to find the number.

To do this, write the statement as an algebraic statement.

Let the number be x.

The product of 7 and a number is:

The product of 7 and a number increased by 3 is:

Twice the number is:

Twice the number subtracted from 39 is:

Since it is given that these expressions are equal, it follows that:

Solve the resulting equation for x:

The number is 4.

Answer:

x=6

Step-by-step explanation:

[tex]9(x - 1) - 13x = - 3(x + 5)[/tex]

[tex]9x - 9 - 13x = - 3x - 15[/tex]

[tex]9x - 13x + 3x = - 15 + 9[/tex]

[tex] - x = - 6[/tex]

[tex] \frac{ - \times }{ -1 } = \frac{ - 6}{ - 1} [/tex]

[tex]x = 6[/tex]

We have the following:

We can see that time is located on the x axis and the price of gasoline is located on y, we can conclude that in both periods the price increases, but in the first it increases slowly and in the second it increases quickly

Therefore, the answer is:

First, the price of gasoline in New mexico increases slowly, and then it increases quickly

Answer:

The given function is a power function.

[tex]\textsf{The constant of variation is $\sqrt[3]{\dfrac{7}{5}}$}.[/tex]

[tex]\textsf{The power is $\dfrac{1}{3}$}.[/tex]

Step-by-step explanation:

Power function

Any function that can be written in the form:

[tex]\boxed{f(x)=k \cdot x^a}[/tex]

where:

Given function:

[tex]f(x)=\sqrt[3]{\dfrac{7x}{5}}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}:[/tex]

[tex]f(x)=\sqrt[3]{\dfrac{7}{5}\cdot x}[/tex]

[tex]\implies f(x)=\sqrt[3]{\dfrac{7}{5}} \cdot \sqrt[3]{x}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies f(x)=\sqrt[3]{\dfrac{7}{5}} \cdot x^{\frac{1}{3}}[/tex]

Therefore, the given function is a power function.

[tex]\textsf{The constant of variation is $\sqrt[3]{\dfrac{7}{5}}$}.[/tex]

[tex]\textsf{The power is $\dfrac{1}{3}$}.[/tex]

Using the normal distribution, it is found that the indicated z-score is Z = 1.08. A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution.

A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution. The standard normal distribution is centered at zero, and the standard deviation indicates how much a specific measurement deviates from the mean.

While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

The z-score of a measure X in a normal distribution with mean and standard deviation is given by:

z = (x-μ)/σ,

It counts the number of standard deviations the value deviates from the mean.

We look at the z-score table after determining the z-score to determine the p-value, which is the percentile of X.

We want Z in this problem to have a p-value of 0.8599, thus Z = 1.08.

The complete question is,

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.8599.

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Answer:

(0, 8) and (-4, 0)

Step-by-step explanation:

Equation is -2x + y = 8

Manipulate this equation so that it becomes a slope-intercept form of equation

To do this:

Add 2x on both sides

-2x + 2x + y = 2x + 8

y = 2x + 8

Once we have this, 2 points which definitely lie on the line are its x and y intercepts

This is the equation of a line with slope = 2 and x-intercept = 8

x-intercept is y-value when x = 0
We can check by plugging in 0 for x in y = 2x + 8

=> y = 2(0) + 8 = 8

=> Point(0, 8) is one of the ordered pairs

Similarly we can find the x-intercept by setting y = 0 and solving for x

Setting y = 0 in y = 2x + 8

=> 0 = 2x + 8

Switch sides

2x + 8 = 0

Subtract 8 from both sides

2x + 8 - 8 = 0 - 8

2x = -8

Divide both sides by 2

=> 2x/2 = -8/2

x = -4

So (-4, 0) is another point on the line

Two ordered pairs are therefore

(0, 8) and (-4, 0)

The attached graph shows you that it is indeed so

The change that Grant received to the nearest cent after giving the delivery driver with a $100 bill is $ 32.6.

This is a question of percentages.

Given that:-

Price of bouquet of flowers = $ 55

Sales tax % = 6.5 %

Tip % = 15 %

Delivery fee= $10

We have to find the change that Grant received to the nearest cent after giving the delivery driver with a $100 bill.

Sales tax = (6.5/100)*55 = $3.575

$55 + $3.575 = $58.575

Tip = (15/100)*58.575 = $ 8.78625

Total money paid by Grant = 55 + 3.575 + 8.78625 = $ 67.36125 ≈ $ 67.4

Hence,

Change received by Grant = 100 - 67.4 = $ 32.6

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The length of one side of the base is 7 inches.

The height of the box is 3.5 inches.

The minimum surface area of the box is 147 inch².

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Answer:

2702700

Step-by-step explanation:

Hi there ,

Given:

In a running competition, a bronze, silver and gold medal must be given to the top three girls and three boys. If 15 boys and 11 girls are competing.

To find:

How many different ways could the six medals possible be given out?

Explanation:

As given,

The number of boys competing in a competition = 15

The number of girls competing in a competition = 11

Three medals are given to top three girls and three medals are given to top three boys.

(I have given the rest of the answer in the images below :-)

If this helped you out do mark me as brainliest and stay positive :)

A fellow mate

Cheers !

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

To solve an inequality, we need to isolate the value of x, and to do so we will perform a series of calculations in such a way that it remains the inequality unchanged, or at least still true.

To do so, we will perform first a sum of 2x to both sides of it, as follows:

Now, we subtract 3 from both sides:

To finish it, we divide both sides by 2:

In another way, we can express the following:

It means that the solution is option B.

To solve the second part, we need a filled line that comes from the negative infinity and goes until 2, but it must be including the number 2, and for this reason, the correct answer in the second part is:

D.

We are asked to find the probability that it contains cookies given that it contains coffee.

This is called conditional probability and is given by

This means that the probability of event A given that event B has occurred.

For the given case, it becomes

The probability P(Cookies and Coffee) is the intersection of the column "Cookies" and the row "Coffee" divided by the grand total.

The probability P(Coffee) is the row total of the row "Coffee" divided by the grand total.

Finally, the conditional probability is

Therefore, the probability that it contains cookies given that it contains coffee is 0.25

there u gooooooooooooooooooooooooooooooooo

The equation that represent the situation of the quadrilateral is 40 = 3q + 7

A quadrilateral is a polygon with 4 sides.

Three sides of a quadrilateral are the same length, q.

The length of the fourth side is 7 inches.

The perimeter of the quadrilateral is 40 inches.

The equation to represent the situation is as follows:

perimeter of a figure is the sum of the whole sides.

Hence,

perimeter of the quadrilateral = q + q + q + 7

perimeter of the quadrilateral = 3q + 7

Therefore,

40 = 3q + 7

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Answer:

3q + 7 = 40

Step-by-step explanation:

I got this lesson

A two-variable linear equation is one with the formula ax + by + c = 0.

The solution of the system exists  (1, 1) and (2, 4).

Let the system of Equations be

y = 3x - 2 and y = x²

From these Equations:

x² = 3x - 2,

simplifying the above equation, we get

⇒ x² - 3x + 2 = 0

⇒ x = 1, 2.

Therefore, the value of x exists x = 1, 2.

Therefore, the solution of the system exists  (1, 1) and (2, 4).

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Okay so draw a diagram with a ladder leaning against a wall and draw the ground now label the diagram take the hypotenuse is ladder and the base is distance between the ladder and the wall while the perpendicular is the wall

As we know hypo=√perpendicular^2+base^2 if we want to finder the p(perpendicular) the formula changes to p=√hypo^2-base^2 put the no in the places of the equation It should look something like this p=√20^2-10^2 use calculate to solve the answer should be 17. 32

Data

Given;

Hypo(h)= 20

Base(b)= 10

Required;

Perpendicular (p)=

Solution

As we know

hypo=√perpendicular^2+base^2

by changing the formula to find p

p=√hypo^2-b^2 -----eqi

by putting the values in eq i

p=√20^2-10^2

p=17.32

Answer:balls

Step-by-step explanation:your mom

Answer:

0.1 gallons = 11.8 miles

10 gallons - 1,180 miles

Step-by-step explanation:

To solve this problem we will use the following property of triangles:

So if we are given the angles a and b of a triangle, the third side c, must be:1) The angles are a =

i. 70°

2) a = 48° and b = 62°, so we have:

h. 73°

3) a = 41° and b = 86°, so we have:

j. 53°

4) a = 61° and b = 88°, so we have:

d. 31°

5) a = 55° and b = 92°, so we have:

b. 33°

Answers

0. j. 70°

1. h. 73°

2. j. 53°

3. d. 31°

4. b. 33°

If on January 1, a company purchased new furniture at a cost of $26,000. The furniture is estimated to have a useful life of 5 years and a salvage value of $3200. The  book value of the furniture on December 31 of the first year is: $21,440.

Given data:

Cost = $26,000

Useful life  = 5 years

Salvage value = $3,200

First step is to calculate the  depreciation expenses:

Particular Amount

Cost $26,000

Less: Salvage value ($3,200)

Net cost (a) $22,800

Useful life (b) 5

Depreciation expenses (a/b) $4,560

($22,800 / 5 years)

Second step is to compute the  book value of furniture on 31 Dec of first year:

To determine the book value we would have to deduct the depreciation expenses from the cost.

Particular Amount

Cost of an furniture $26,000

Less: Depreciation ($4,560)

Book value $21,440

Therefore we can conclude that the book value is the amount of $21,440.

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The complete question is:

On January 1, a company purchased new furniture ata cost of $26,000. The furniture is estimated to have a useful life of 5 years and a salvage value of $3200The company uses the straight-line method of depreciation. What is the book value of the furniture on December 31 of the first year?

Answer:

A) 384, 216

b) 14575

Step-by-step explanation:

A) to find the missing values you do 3-1 which gives you 2.

here is a trick!

then you take your answer (in this case it is 216) and add it to your second row (168) to get the first row's answer (384). so you are basically going backward.

B) here you do the same thing go backward!

5967+8608 = 14575

then if you want you can double-check by subtracting them.

I hope this helps!

Total number of jerseys he have now is 32 jerseys.

A coach has 12 jerseys in beginning. Now, he buys 2 sets of jerseys.

Each set of jerseys have 10 jerseys.

2 set of jerseys have 20 jerseys.

Using unitary method this can also be written as,

1 set ---------------->  10 jerseys

2set ---------------->  20 jerseys

So, total of 20 jerseys are present in 2 sets of jerseys.

Total number of jerseys he have now = 12 jerseys + jerseys in two sets

Total number of jerseys he have now = 12 jerseys + 20 jerseys = 32 jerseys

So we can write, he have total of 32 jerseys now.

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