With an example, how do I explain what the graph of a rational function looks like. Explain it in terms of it being a line and why the line is shaped the way it is on the graph.

Answer:

P(x) = x³ - 3x² - 5x + 15

Step-by-step explanation:

∵ The roots of the polynomial are -√5 , √5 , 3

∴ The polynomial has 3 factors:

  (x - √5) , (x + √5) , (x - 3)

∴ P(x) = (x - √5)(x + √5)(x - 3)

          = (x² + √5x - √5x - 5)(x - 3)

          = (x² - 5)(x - 3) = x³ - 3x² - 5x + 15

∴ P(x) = x³ - 3x² - 5x + 15

Answer:

See below

Step-by-step explanation:

Because her answer is greater than 2 (7/3 = 2 1/3)

We are multiplying a number less than 2 (1 2/3) by a number less than 1 (5/6), so we have less than one of the number 1 2/3, which has to be less than 1 2/3.

let's firstly convert the mixed fraction to improper fraction.

[tex]\bf \stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{6}\times \cfrac{5}{3}\implies \cfrac{25}{18}\implies 1\frac{7}{18}[/tex]

Answer:

f(x)/g(x) = x+6  

Step-by-step explanation:

f(x) = 3x^2 +16x -12

g(x) = 3x-2

f(x)       3x^2 +16x -12

---- =   -------------------

g(x)       3x-2

Factor

f(x)       (3 x - 2) (x + 6)

---- =   -------------------

g(x)       3x-2

Cancel the common terms

f(x)       (x + 6)

---- =   -------------------

g(x)       1

Answer:

Option A. [tex]SQ=7\ cm[/tex]

Step-by-step explanation:

we know that

In the figure

The triangles PTQ and RTS are similar by AA Similarity Theorem

so

Remember that

If two figure are similar, then the ratio of its corresponding sides is equal

so

[tex]\frac{PT}{RT}=\frac{QT}{ST}[/tex]

we have

[tex]PT=18\ cm[/tex]

[tex]RT=RP+PT=6+18=24\ cm[/tex]

[tex]QT=21\ cm[/tex]

[tex]SQ=ST-21\ cm[/tex] ------> equation A

substitute the values and solve for ST

[tex]\frac{18}{24}=\frac{21}{ST}[/tex]

[tex]ST=21*24/18[/tex]

[tex]ST=28\ cm[/tex]

substitute the value of ST in the equation A to find the value of SQ

[tex]SQ=28-21=7\ cm[/tex]

Answer: 77cm

Step-by-step explanation:

3^3 + 2^7

Step-by-step explanation:

There really is no other way that I can think of other than guessing and checking. 3^3 is 27, when subtracted from 155 gives you 128. 128 can be rewritten as 2^7, leaving your final answer as 3^3 +2^7.

"taken from MrScienceguy"

Answer:

3^3 + 2^7

Step-by-step explanation:

There really is no other way that I can think of other than guessing and checking. 3^3 is 27, when subtracted from 155 gives you 128. 128 can be rewritten as 2^7, leaving your final answer as 3^3 +2^7.

Answer:

x < [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

Given

x - 10 < 6 - 5x ( add 5x to both sides )

6x - 10 < 6 ( add 10 to both sides )

6x < 16 ( divide both sides by 6 )

x < [tex]\frac{16}{6}[/tex], that is

x < [tex]\frac{8}{3}[/tex]

The difference between fixed expenses and variable expenses is that fixed expenses do not change, regardless of how many items are produced. Variable expenses change based on the number of items produced.

An example of a fixed expense is the rent. The rent is always the same amount, regardless of production.

Materials would be a variable expense. You need enough material to make each item, so the more items you produce, the more material you need.

Answer:

the answer is c

Step-by-step explanation:

Final answer:

To subtract 6 ounces from 3 pounds, convert 3 pounds to ounces (3 x 16 = 48 ounces), subtract 6 ounces (48 - 6 = 42 ounces), then convert back to pounds and ounces (42 ounces = 2 pounds and 10 ounces). The answer is 2 pounds, 10 ounces.

Explanation:

Subtracting Ounces from Pounds

The question asks to subtract 6 ounces from 3 pounds. In order to compare or subtract different units of weight, it is essential to convert them to the same unit. Firstly, we must remember the unit equivalence where 1 pound = 16 ounces. Now, to start the conversion, we multiply the number of pounds by 16 to get the total number of ounces, which is a step in solving these types of conversion problems.

Therefore, for 3 pounds:

3 pounds × 16 ounces/pound = 48 ounces.

Now subtract the given ounces: 48 ounces - 6 ounces = 42 ounces.

Since we know there are 16 ounces in a pound, we divide the total ounces by 16 to convert back to pounds and ounces.
42 ounces ÷ 16 ounces/pound = 2 pounds with a remainder of 10 ounces.

Hence, subtracting 6 ounces from 3 pounds gives us 2 pounds, 10 ounces.

Answer:

The volume of a rectangular prism is [tex]28\frac{7}{8}\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

[tex]V=BHL[/tex]

Convert the given dimensions to an improper fractions

[tex]B=3\frac{1}{2}\ cm=\frac{3*2+1}{2}=\frac{7}{2}\ cm[/tex]

[tex]H=1\frac{1}{2}\ cm=\frac{1*2+1}{2}=\frac{3}{2}\ cm[/tex]

[tex]L=5\frac{1}{2}\ cm=\frac{5*2+1}{2}=\frac{11}{2}\ cm[/tex]

substitute in the formula

[tex]V=(\frac{7}{2})(\frac{3}{2})(\frac{11}{2})=\frac{231}{8}\ cm^{3}[/tex]

Convert to mixed number

[tex]\frac{231}{8}=\frac{224}{8}+\frac{7}{8}=28\frac{7}{8}\ cm^{3}[/tex]

Answer:

1693.88888889

Step-by-step explanation:

15,245 divided by 9 or 15,245/9

The correct answer is 1,693.88889

If you round this, the answer is 1,694

Hope this helps!

Answer:

B.  The relationship between the variables in the table is quadratic because the second differences are constant.

Step-by-step explanation:

We have to look for the differences in the y values of the given table.

The y values are:

0, 2, 6, 12, 20, 30, 42

The differences between the consecutive values are:

2, 4, 6, 8, 10, 12

These are the first differences and are not constant. This means the relationship is not linear. Now we again find the differences between the consecutive values:

2, 2, 2, 2, 2

These are the second differences. The second differences are constant. So this means the given relationship is quadratic.

Therefore, option B gives the correct answer. The relationship between the variables in the table is quadratic because the second differences are constant.

Answer: 1 out of 19

Step-by-step explanation:

add up all of the students, wes and maureen are two people, so it's two out of thrity eight, then just simplify it and you're done <3

The probability that both Wes and Maureen will be selected is 1/360.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, Wes is in a class of 18 students and Maureen is in a class of 20 students.

Now, this is an independent event, therefore, the probability that both Wes and Maureen will be selected will be,

= (1/18)×(1/20).

= 1/360.

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?? hold on I'ma work the problem out

Answer:

6/22

Step-by-step explanation:

Just add wanted  outcomes over all outcomes

Answer:

The fan should expect the red team to win 9 more games than the blue team.

Step-by-step explanation:

Using proportions, it is found that over the entire season, the fan should expect the red team to win 9 less games.

A proportion is a fraction of a total amount.

In this problem, considering the proportions of the red and of the blue teams, the number of games they are expected to win is given by:

108 - 99 = 9, hence the fan should expect the red team to win 9 less games.

More can be learned about proportions at https://brainly.com/question/24372153

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Answer:

[tex]\large\boxed{y=\dfrac{1}{4}x+2}[/tex]

Step-by-step explanation:

The slope-intercept form of the equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b)

The point-slope form of the equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

We have the equation of a line:

[tex]y-4=\dfrac{1}{4}(x-8)\to m=\dfrac{1}{4}[/tex]

and the point (0, 2) → b = 2.

Substitute:

[tex]y=\dfrac{1}{4}x+2[/tex]

Answer:

Step-by-step explanation:

DDD

Answer:

−2sin(2θ)cos(4θ)

Step-by-step explanation:

sin(2∅)-sin(6∅)

Sum product Identity

sinα  - sinβ  = 2cos((α+β)/2)sin((α-β)/2)

Putting α= 2∅ and β= 6∅ in the identity we get

sin(2∅)-sin(6∅) = 2cos((2∅+6∅)/2)sin((2∅-6∅)/2)

                        =2cos(8∅/2)sin(-4∅/2)

                        =2cos(4∅)sin(-2∅)

                         = -2sin(2∅)cos(4∅)

Answer:

C

Step-by-step explanation:

sqrt(200)

Find the highest square multiple.

200 = 100 * 2

sqrt(100) = 10

10 goes on the outside, and the one that is left, 2, goes on the inside.

Answer:

Your answer is C) [tex]10\sqrt{2}[/tex]

Step-by-step explanation:

This is because [tex]10\sqrt{2}[/tex] is [tex]\sqrt[4]{200}[/tex] simplified.

Confirming the answer above!

I hope this helps!~

Answer:

see explanation

Step-by-step explanation:

He cycles [tex]\frac{3}{4}[/tex] Km and jogs [tex]\frac{3}{4}[/tex] - [tex]\frac{1}{6}[/tex]

Adding the 2 together gives the total he cycled/ jogged

[tex]\frac{3}{4}[/tex] + [tex]\frac{3}{4}[/tex] - [tex]\frac{1}{6}[/tex]

We require the denominators to be common before adding/ subtracting

The lowest common denominator of 4 and 6 is 12, hence

= [tex]\frac{9}{12}[/tex] + [tex]\frac{9}{12}[/tex] - [tex]\frac{2}{12}[/tex]

= [tex]\frac{9+9-2}{12}[/tex]

= [tex]\frac{16}{12}[/tex] = [tex]\frac{4}{3}[/tex] = 1 [tex]\frac{1}{3}[/tex] Km

Do 3/4 x 3 = 9/12

Do 1/6 x 2 = 2/12

Then do 9/12 - 2/12 = 7/12

Next you do 7/12 + 9/12 = 16/12

Then simplify. 1 4/12

Simplify again. 1 1/3

Answer:

-0.14 * 0.12 = -0.0168

Step-by-step explanation:

You could multiply both numbers by 100 to make them whole integers.

-0.14 * 100 = -14

0.12 * 100 = 12

-14 * 12 = -168

Now divide by 100 twice.

-168 / 100 = -1.68 / 100 = -0.0168

Answer:

[tex] 3^3 = 27 \Longleftrightarrow \log_3 27 = 3 [/tex]

Step-by-step explanation:

[tex] b^y = x \Longleftrightarrow \log_b x = y [/tex]

A logarithm is an exponent. The base of the logarithm is the base of the power.

[tex] 3^3 = 27 \Longleftrightarrow \log_3 27 = 3 [/tex]

Answer:

[tex] log_3 2 7 = 3 [/tex]

Step-by-step explanation:

We are given the following equation and we are to write it in logarithmic form:

[tex] 3 ^ 3 = 27 [/tex]

We know that [tex] a ^ n = b [/tex] is written as [tex] log _ a b [/tex] when expressed in logarithmic form.

So here we have [tex] 3 ^ 3 = 27 [/tex], converting it logarithmic form we get:

[tex] log_3 2 7 = 3 [/tex]

Final answer:

To find out how many cups of orange juice Harry should use with 18 cups of soda water, set up a proportion and solve for x.

Explanation:

In this problem, we know that Harry uses 2 parts orange juice to 2 parts soda water for his fruit punch. This means that for every 2 cups of orange juice, he uses 2 cups of soda water. Since the amount of soda water is directly proportional to the amount of orange juice, we can set up a proportion to find out how many cups of orange juice Harry should use with 18 cups of soda water.

2 cups orange juice / 2 cups soda water = x cups orange juice / 18 cups soda water

To solve the proportion, we can cross multiply:

2 cups orange juice * 18 cups soda water = x cups orange juice * 2 cups soda water

36 cups orange juice = 2x cups soda water

By dividing both sides of the equation by 2, we find that Harry should use 18 cups of orange juice with 18 cups of soda water.

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-3, -1) and (-6, 8). Substitute:

[tex]m=\dfrac{8-(-1)}{-6-(-3)}=\dfrac{9}{-3}=-3\\\\y-8=-3(x-(-6))\\\\y-8=-3(x+6)[/tex]

Answer:

[tex]\$974.83[/tex]  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=10\ years\\ P=\$535\\ r=0.06[/tex]  

substitute in the formula above  

[tex]A=\$535(e)^{0.06*10}=\$974.83[/tex]  

Answer: 701953087225 is the answer

Answer:

csc θ = [tex]\sqrt{85}[/tex]/6

sec θ = [tex]\sqrt{85}[/tex]/7

tan θ = 6/7

Step-by-step explanation:

The first thing to do will be to compute the length of the hypotenuse using the Pythagoras theorem;

6^2 +7^2 = hypotenuse^2

hypotenuse = [tex]\sqrt{85}[/tex]

csc θ = 1/sinθ

sinθ = opposite side/hypotenuse

       = 6/[tex]\sqrt{85}[/tex]

csc θ = [tex]\sqrt{85}[/tex]/6

sec θ = 1/cosθ

cosθ = adjacent side/hypotenuse

sec θ = hypotenuse/adjacent side

         = [tex]\sqrt{85}[/tex]/7

tan θ = Opposite side/adjacent side

         = 6/7

Whenever you have a decision tree like this, the probability of reaching a specific leaf is the multiplication of the probabilities of each step you have to reach the leaf.

So, in order to reach the "hardcover and nonfiction" leaf, we have to take the "buys hardcover" branch (probability 0.35), and then the "buys nonfiction" branch (probability 0.55).

Given what we said above, the probability for "hardcover and nonfiction" is

[tex]0.35\cdot 0.55=0.1925[/tex]

The probability of buying a hardcover and non-fiction book is 0.1925

We have the below parameters for our Calculation;

The probability that someone buys a hardcover and non- fiction book ;

Now we have;

P(hard cover n Non-fiction) = 0.35 × 0.55 = 0.1925

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Answer:

STEP ONE: 2x

STEP TWO: 5=X (should be the final answer)

Step-by-step explanation:

Hi Lasagna!

So basically, this is extremely simple. In order to "solve" that equation, the x has to be on one side. The easiest way to do this would be to take the 2x to the other side. If you want the 2x to go to the other side, you need to subtract it (since it is already positive, therefore it needs to cancel out). Once you do that, you must always do the same thing to the other side: subtract 2x from 3x. That should get you one x there, which you can just write as x if it's just one. Then you're all set! :D

Answer: step 1. 2 from both sides

Step-by-step explanation:

just take away the = number by doing the opposite action for ex. if it it 2x then divide both sides by 2.

Answer:

B=65 degrees, c=65 degrees

Step-by-step explanation:

Opposite angle in a parallelogram are equal. 3n+20 = 6n-25. n=15. You then plug n in into the equations. B=65 and D=65

Answer:

the answer to this question is B. Trust me I'm not wrong.

Answer:

B

Step-by-step explanation:

D: You will not get a cubic function. Nothing adds to give a term with x^3 in it.

C: A rational function is of the form (x^2 + 3x + 2) / (x^2). In other words it has a numerator and a denominator that are polynomials. Unless one or both started out like that, the answer is not a rations function.

A: It can't be linear. The x^2 term will carry over after addition.

The answer is B. One of the polynomials started out as a quadratic. It will remain that way.