Use the grouping method to factor the polynomial below completely.
x3-5x2+3x-15
A. (x²+5)(x-3)
B. (x² - 3)(x + 5)
O C. (x² - 5)(x+3)
D. (x²+3)(x - 5)

The inverse function of f(x) is [tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]

The function is given as:

f(x) = (x + 3)^3 - 1

Rewrite as:

y = (x + 3)^3 - 1

Swap x and y

x = (y + 3)^3 - 1

Add 1 to both sides

(y + 3)^3 = x +  1

Take the cube root of both sides

[tex]y + 3 = \sqrt[3]{x + 1}[/tex]

Subtract 3 from both sides

[tex]y = \sqrt[3]{x + 1} - 3[/tex]

Rewrite as:

[tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]

Hence, the inverse function of f(x) is [tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]

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Answer:

373 feet

Step-by-step explanation:

Since the rate of the machine producing ribbon is proportional to time, we can determine the number of inches of ribbon in 8 hours by some quick operations.

There are 16 1/2 hours in 8 hours, so we can multiply 280 by 16.

[tex]280 *16=4480[/tex]

Now, we have the number of inches it can produce in an 8-hour work day. However, we must convert to feet since that is the form of measurement the question is asking for. We can do so by dividing by 12.

[tex]4480/12=373.33[/tex]

Therefore, the number of feet the machine can produce in an 8-hour work day is 373.

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Step-by-step explanation:

the other answer is correct.

a few add-ons :

1 ft = 12 in

30 minutes = 1/2 hour (as every hour has 60 minutes)

every hour has therefore 2 half hours.

1 hour = 2 × 1/2 hour

8 hours = 8 × 2 × 1/2 hours = 16 × 1/2 hour

so, in 16 times the amount of time (8 hours) the machine can produce 16 times the amount of ribbon (16 × 280 in).

16 × 280 = 4480 in

and because every 12 in is 1 ft, this is then

4480/12 = 373.3333333... ft

therefore, 373 is the right answer (rounded).

The linear model for the data is expressed as: R = 20p - 160.

Using two pairs of values from the table values, say, (32, 480) and (33, 500), find the unit rate (m).

Unit rate (m) = (500 - 480)/(33 - 32) = 20/1

Unit rate (m) = 20.

Substitute (p, R) = (32, 480) and m = 20 into R = mp + b to find b

480 = 20(32) + b

480 = 640 + b

480 - 640 = b

b = -160

To write the linear model, substitute m = 20 and b = -160 into R = mp + b:

R = 20p - 160

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Answe1/5 of r = 15

Step-by-step explanation:

1/5 r=

Answer:

$30

Step-by-step explanation:

Let,

  x - fiction book

  x + $6 - novel

EQUATION:

  4(x) + 2(x + $6) = $84

  6x + $12 = $84

  6x = $84 - $12

  6x = $72

  x = $12

SUBSTITUTE:

    novel = $12

    fiction = $18

TOTAL COST OF NOVEL AND FICTION

$18 + $12 = $30

The integer that represents Omar's score is -14.

Integers are whole numbers. It is a number without a fraction or decimal component. Integers can either be positive, negative or zero.

When Omar wins, the points are added and when he losses, the points are subtracted.

0 + 8 - (6 x 4) + 2

0 + 8 - 24 + 2 = -14

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Answer:

x = 4

Step-by-step explanation:

3(-3x -3) + 2x + 4 = -33

(3*-3x + 3*-3) + 2x + 4 = -33

(-9x - 9) - 2x + 4 = -33

-9x + 2x - 9 + 4 = -33

-7x -5 = -33

-7x = -33 + 5

-7x = -28

x = -28/-7

x = 4

Check:

3((-3*4)-3) + 2*4 + 4 = -33

3(-12-3) + 8 + 4 = -33

3(-15) + 12 = -33

-45 + 12 = -33

Answer:

B

Step-by-step explanation:

It has both point and line symmetry

Answer:

The relation {(2,1),(3,2),(-1,1),(0,-2)} is a function because the domain {2,3,-1,0} and range {1,2,1,-2} of the relation is paired exactly only once.

Step-by-step explanation:

The given relation is {(2,1),(3,2),(-1,1),(0,-2)}.

It is required to determine the relation is a function.

Step 1 of 1

The given relation is {(2,1),(3,2),(-1,1),(0,-2)}.

This relation shows that the domain of the relation {2,3,-1,0} is paired with one element of the range {1,2,1,-2}.

Hence, the relation is a function.

The probability that a student takes art, given that the student takes music is 10.8%

In probability, we say two events are independent if knowing one event occurred doesn't change the probability of the other event.

For example, the probability that a fair coin shows "heads" after being flipped is 1/21/21, slash, 2. What if we knew the day was Tuesday? Does this change the probability of getting "heads?" Of course not. The probability of getting "heads," given that it's a Tuesday, is still 1/21/21, slash, 2. So the result of a coin flip and the day being Tuesday are independent events; knowing it was a Tuesday didn't change the probability of getting "heads."

Two events, A and B, are independent if

P(A ∣ B)=P(A)

P(A).P(B) = P(A ∩ B)

In the given question there are independent events.

Given:-

P(A) = Student takes both art and music = 0.9

P(B) = Student takes music = 0.12

P(A ∩ B) = student takes art, given that the student takes music

Thus by using the formula we get,

P(A ∩ B) = 0.9 x 0.12 = 0.108 = 10.8%

The probability that a student takes art, given that the student takes music is 10.8%

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The area of the trapezoid is 87.5 square cm if the parallel side lengths are 10 and 15 cm, the height is 7 cm.

It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a trapezoid ABCD shown in the picture.

As we know the area of the trapezoid is given by:

= (a+b)h/2

= (10+15)(7/2)

= 87.5 square cm

Thus, the area of the trapezoid is 87.5 square cm if the parallel side lengths are 10 and 15 cm, the height is 7 cm.

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A)√500 is the correct answer.

It is an expression that has the same value but does not look the same. If you simplify an expression, you're  trying to write it in the simplest way possible.

According to the question,

The given expression is 10√5.

By computing the number out of the square root,

So,

[tex]=10 \sqrt{5} \\=\sqrt{10^2(5)} \\=\sqrt{100 (5)} \\=\sqrt{500}[/tex]

Therefore,

The equivalent expression for 10√5 is √500.

Complete question is attached below.

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The confidence interval for the true mean coefficient of restitution is (29.9911,30.0089).

Given sample mean coefficient of restitution 0.835,population standard deviation of 0.019 and the confidence level of 0.835.

We have to find the confidence interval for the true mean coefficient of restitution.

We can easily find the confidence interval through the formula of margin of error.

Margin of error is the difference between the calculated values and the real values.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where z is the z value of p value,

σ is population mean or sample mean,

n is the sample size.

In our problem the sample size is 30.

z value for the p value of 0.99 is 2.576.

Margin of error=2.576*0.019/[tex]\sqrt{30}[/tex]

=0.048944/5.4772

=0.0089

Upper level=mean +margin of error

=30+0.0089

=30.0089

Lower level=Mean-margin of error

=30-0.0089

=29.9911.

Hence the confidence interval for the true mean coefficient of restitution is (29.9911,30.0089).

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The system of linear inequalities which satisfy the region R in the graph above are:

Mathematically, the general equation of a straight line is given by y = mx + b.

In order to determine the system of linear inequalities that satisfy the region R, we would identify the points through which these straight lines passes through.

For the left line, we have:

y-intercept = 3.

x-intercept = -3/2.

Points (x, y) = (0, 3) and (-3/2, 0).

Thus, the inequality is given by:

(x/-3/2) + y/3 ≤ 1.

-2x + y ≤ 3

y ≤ 2x + 3

For the right line, we have:

y-intercept = 4.

x-intercept = 4.

Points (x, y) = (0, 4) and (4, 0).

Thus, the inequality is given by y ≥ -x + 4

For the lower line, we have:

y-intercept = 0.

x-intercept = 4.

Points (x, y) = (4, 0)

Thus, the inequality is given by y ≤ x + 4

In conclusion, the system of linear inequalities which satisfy the region R in the graph above are:

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Answer:

36 pieces of ribbon

Step-by-step explanation:

When Audrey cuts the ribbon into pieces that are each 1/3 yards long, she has 18 pieces (1/3 * 18 is 6, or the other way to think about it would be, 6 / (1/3) = 18). If she were to cut each of the pieces in half one more time, she would have 18 * 2 or 36 pieces of ribbon

Answer:

(2, - 2 )

Step-by-step explanation:

4x - y = 10 → (1)

x - 4 = y → (2)

substitute x - 4 = y into (1)

4x - (x - 4) = 10 ← distribute parenthesis on left side by - 1

4x - x + 4 = 10

3x + 4 = 10 ( subtract 4 from both sides )

3x = 6 ( divide both sides by 3 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (2)

2 - 4 = y

- 2 = y

solution is (2, - 2 )

Answer:

x = 2 , y = -2

Step-by-step explanation:

I will use the elimination method :

4x-y = 10 - Equation Number 1

x-4 = y  - Equation Number 2

For the second equation we add 4 to both sides and subtract y from both sides :

x = y + 4

x - y = 4 - Let's call this equation number 3 :

Now we can subtract the equation 1 with 3 to eliminate y :

3x = 6

x = 2

Now we substitute this value into equation 2 to solve for y :

(2)-4 = y

y = -2

Substitute these values into equation 1 to verify :

4(2) - (-2) = 10

8 + 2 = 10

10 = 10

So these values must be correct

Hope this helped and have a good day

Answer:

f(5)=17

Step-by-step explanation:

if,f(x)=3x+2

Then,f(5)=3*5+2

f(5)=17

1) [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect each other (given)

2) [tex]\overline{AE} \cong \overline{EC}[/tex] (a bisector splits a segment into two congruent parts)

3) [tex]\overline{BE} \cong \overline{ED}[/tex] (a bisector splits a segment into two congruent parts)

4) [tex]\angle BEA \cong \angle CED[/tex] (vertical angles are congruent)

5) [tex]\triangle BEA \cong \triangle DEC[/tex] (SAS)

6) [tex]\angle EBA \cong \angle EDC[/tex] (CPCTC)

7) [tex]\overline{AB} \parallel \overline{CD}[/tex] (converse of alternate interior angles theorem)

8) [tex]\angle DEA \cong \angle BEC[/tex] (vertical angles are congruent)

9) [tex]\triangle AED \cong \triangle BEC[/tex] (SAS)

10) [tex]\angle BCE \cong \angle EAD[/tex] (CPCTC)

11) [tex]\overline{BC} \parallel \overline{AD}[/tex] (converse of alternate interior angles theorem)

The reason why people sometimes assume that the calculation 9 + 10 = 21 is as explained below.

We want to find out the reason why people say that; 9 + 10 = 21

Now, the way you have explained it is one way to look at it by utilizing number bases to play around with the figures to arrive at 21.

However, another way is to use algebra trick pattern which is;

9 can be expressed as 3 * 3

Also, 10 can be expressed as 5 * 2. Thus, we now have;

(3 * 3) + (5 * 2)

The applying properties of algebra to cross multiply gives;

(3 * 2) + (5 * 3)

= 6 + 15

= 21

Now, though your explanation arrived at 21 and mine also 21, but those are not correct mathematical methods as 9 + 10 must be equal to 19 and not 21.

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The average rate of change from x=1 to x= 4 is -0.7

We have f(1) to be 3

while we have f(4) as 1

The average rate of change can be solved as

f(4) - (f(1) / 4 - 1

This is solved as

1 - 3 / 4 - 1

= -2 / 3

= -0.7

Hence the average rate of change for the graph that we have above is -0.7

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Answer:

2304 cm³

Step-by-step explanation:

To find the volume of a composite figure, it is easiest to break it down into smaller, more recognizable shapes.

here, we can break our shape into two sections: the green section and the blue section

then, we will add the volumes of these shapes together

green section's volume:

note: you could also calculate this as four separate cubes

to find the volume of a rectangle, we need to multiply

length × width × height

here, our length is 12 (6 + 6); our height is 12 (6 + 6); and our width is 6

let's multiply these together: (12)(12)(6) = 864

so, the volume of the green section is 864 cm³

now, let's work with the blue section:

once again, the volume for a rectangle is length × width × height

here, our length is 18, our height is 10, and our width is 8

let's multiply these together: (18)(10)(8) = 1440

so, the volume of the blue section is 1440cm³

now, we can add our sections together:

1440 + 864 = 2304

meaning that the volume of the composite figure is 2304 cm³

hope this helps!! have a lovely day :)

The range of the step function is all negative integers, thus, the correct option is A.

Domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

For the given function h(x)=-2|x|, any value of x will return a negative value, therefore, the range of the function is all negative numbers. This can be observed in the graph given below.

Hence, the range of the step function is all negative integers, thus, the correct option is A.

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Considering the given table, we have that:

A function has a relative maximum when it changes from increasing to decreasing.

Looking at the given table, it happens when x is near 3.

Also, looking at the table, for x > 3 the function is decreasing, hence as x approaches positive infinity, the value of the function approaches negative infinity.

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Answer:

74 yards squared

Step-by-step explanation:

Divide the shape up into 2 3x5 rectangles and one 11x4 rectangle

2(3x5)+11x4=30+44=74

74 yards squared

Answer:

84 mm (C)

Step-by-step explanation:

We are given the centimeter/millimeter side of the ruler. It is probably easier to first look at the centimeters since the lines are much bigger. We can see that the line goes from 0cm to around 8.4cm. Now, we can convert centimeters to millimeters because we know that there are 10 millimeters in one centimeter. 8.4cm * 10 gives us 84 millimeters (C)

Answer:

28 should do it

Step-by-step explanation:

35+35+82= 152

180-152=28

The thing that best describes the values of x and y is option B; they will be real numbers greater than or equal to 0.

The real number refers to the union of both rational and irrational numbers that can have negative or positive values.

From the given information:

Peaches are being bought and sold for $2 per pound.

There is no negative value used here if x represents the number of pounds of peaches bought and y represents the total cost of the peaches.

Thus, a conclusion that can be reached as to the values of x and y is that they contain real numbers greater than or equal to 0.

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Answer:

im pretty sure its d

Step-by-step explanation:

----- ______------

Answer:

they reached the shore they get 135 miles