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The function graphed shows the total cost of a gym membership for x months.

Select from the drop-down menus to correctly identify the gym membership information provided by the graph.

The Slope is
The Slope Represents

P(x) is a polynomial function having rational coefficients that has given roots is: P(x) = x³ + 2x² + 4x + 8.

P(x) has given roots: -4 and 2i. ​

A radical is always preceded by a pair of plus & minus signs.

As a result, there would be another root -2i.

All of the roots are -4, -2i, + 2i.

As, the number of roots given are 3, thus the polynomial formed ill be cubic.

The roots in terms of the polynomial can be written as-

P(x) = (x - (-2))(x - 2i)(x + 2i)

P(x) = (x + 2)(x - 2i)(x + 2i)

Simplifying,

P(x) = x³ + 2x² + 4x + 8

Thus, P(x) is a polynomial function having rational coefficients that has given roots is P(x) = x³ + 2x² + 4x + 8.

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The range of values that satisfy the given inequalities, 8x - 11 > 5 and 15(6x+2) > -150, is x > -2 OR x > 2

From the question, we are to determine the range of values which satisfy the given inequalities.

The given inequalities are

8x - 11 > 5 and 15(6x+2) > -150

To determine the range of values that satisfy the inequalities, we will solve each of the inequalities separately

Solving 8x - 11 > 5

Add 11 to both sides

8x - 11 + 11 > 5 + 11

8x > 16

Divide both sides by 8

8x/8 > 16/8

x > 2

Solving 15(6x+2) > -150

Divide both sides by 15

15(6x+2)/15 > -150/15

6x + 2 > -10

Subtract 2 from both sides

6x + 2 - 2 > -10 - 2

6x > -12

Divide both sides by 6

6x/6 > -12/6

x > -2

Putting the two solutions together,

x > -2 OR x > 2

Hence, the solution is x > -2 OR x > 2

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Given the slope of the line and the pair of points, the missing y - value can be found to be - 17

The slope formula is:

y = Slope(x) + y - intercept

Using the point (4, 8), the y - intercept can be found by the formula:
8 = 5/2 (4) + y - intercept

y - intercept = 8 - 10

y - intercept = -2

The missing y value is therefore:

y = Slope(x) + y - intercept

= -6 (5/2) - 2

= -15 - 2

= - 17

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In accordance with algebra properties and relationship between logarithms and powers, the logarithm ㏒ₐ (108 / a³) is equal to the pseudolinear expression 2 · b + 3 · c - 3.

In this problem we must determine the base of a given set of logarithms by using algebra properties and relationships between powers and logarithms. Now we proceed to solve:

Step 1 - We get the following equations:

㏒ₐ 2 = b, ㏒ₐ 3 = c  

Step 2 - Now we add the other logarithm:

㏒ₐ (108 / a³)

Step 3 - By logarithm properties:

㏒ₐ 108 - ㏒ₐ a³

㏒ₐ (2² · 3³) - 3 · ㏒ₐ a

㏒ₐ 2² + ㏒ₐ 3³ - 3 · 1

2 · ㏒ₐ 2 + 3 · ㏒ₐ 3 - 3

Step 4 - By Step 1:

2 · b + 3 · c - 3

The logarithm ㏒ₐ (108 / a³) is equivalent to 2 · b + 3 · c - 3.

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Answer:

 D    is the answer I thinnk

Step-by-step explanation:

There is no vertex in the graph and the transformations from are

By definition, a graph that has a vertex would have an obvious maximum or minimum point on it

In this case, there is no point that can be regarded as the minimum or the maximum in this graph

This means that the graph has no maximum or minimum; in other words, there is no vertex

The parent function of the above graph is a cubic function

A cubic function passes through the origin

However in this graph, we can see that the graph is 4 units to the left of the origin and 2 units below the origin

This means that the transformation is (x - 4, y - 2)

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Answer: b= (0,4)

Step-by-step explanation:

The 'b' value in a line is the y-int. of a linear equation. That means you need to determine where the linear equation intersects with the y-axis. In this scenario it intersects at the point (0,4)

The possible amount of time for which they could rent the meeting room is 1, 2, and 3 hours.

In the question,

It is given that,

Reservation fee is $49.

Additional fee is $5.80 per hour.

The math club can spend maximum of $72.20.

The inequality will be:

49 + 5.8*t < 72.20

5.8*t < 23.2

t < 4

Hence, the possible amount of time for which they could rent the meeting room is 1, 2, and 3 hrs.

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Answer:

  x = 3

Step-by-step explanation:

You want the equation of the line through points (3, -3) and (3, -6).

The two points have the same x-value, indicating the line through them is a vertical line. That will have an equation of the form x = c.

The x-value of the given points is 3, so the equation is ...

  x = 3

__

Additional comment

We note that the answer box is pre-filled with "y =". There is no "y =" equation that will go through these points. The slope is undefined, so the slope-intercept form of the equation cannot be used.

The probability that fewer than 60 adults will work from home will be 2%.    

we have to use the Normal probability distribution to find the probability

In a normal distribution with mean μ, SD σ, z-score Z of a measure X  is given by

Z = (X-μ)/ σ

here,

15% adults work from home , So  p= 0.15

                                                       n = 500

∴  μ = np = 500(0.15) = 75

σ  = [tex]\sqrt{np(1-p)}[/tex]

σ = 7.98

Now we have  selected adults(60) less than n (500)

So using the continuity correction , the probability is P(X< 60 - 0.5)

                                                                            = P( X< 59.5)

which is the p-value of Z when X = 59.5

∴ Z = (X-μ)/ σ

Z  =  (59.5 - 75)/7.98

Z =   - 1.98

so the p-value is 0.02

0.02 = 2% probability that fewer than 60 adults will work from home.

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I eat pizza or drink bottled water, for example, is a symbolic representation of the following statement.

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y-intercept: (0,60)

This is given in the table.

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

Using (1,50) and (2,40):

   [tex]m = \dfrac{40 - 50}{2-1} = \dfrac{-10}{1} = -10[/tex]

The slope is -10.

Using the slope-intercept form (y=mx+b) and the fact that we found m=-10 and b=60 from the table, the equation is:

   y = -10x + 60

The probability that the squad will have exactly three women members is 0.389

Total number of people in CU Boulder triathlon = 21

Number of Men = 9

Number of Women = 12

We are told that a 5-member squad is selected and now we want to find the probability that the squad will have exactly 3 women members.

Thus;

P(exactly 3 womens) = (12C3 * 9C2)/(21C5)

P(exactly 3 womens) =7920/1716

P(exactly 3 womens) = 0.389

Hence, the probability that the squad will have exactly three women members is 0.389

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The correct statements are,

(1) The equation 2n = p should be 2p = n.

(2) The actual cost of the onions is $3.00 per pound.

(3) Potatoes cost $1.50 per pound.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Mr. Yi buys vegetables at a market. He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18. Onions cost twice as much as potatoes.

The equation will be formed as,

6p + 3n = 18

n = 2p

Substitute the value of n = 2p in the equation,

6p + 3(2p) = 18

6p + 6p = 18

12p = 18

p = $1.5

The cost of an onion is,

n = 2p

n = 1.5 x 2

n = $3

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Answer: The answer is Fact Family

Step-by-step explanation:

The width of the rectangle is 12 feet and the length is 30 feet.

The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.

Given that, The perimeter of a rectangle is 84 feet. The ratio of the width to the length is 2:5.

Let the width be 2x and length be 5x,

Perimeter = 2(l+w)

2(2x+5x) = 84

2x+5x = 84/2

2x+5x = 42

7x = 42

x = 42/7

x = 6

Therefore, width = 6x2 = 12

Length = 5x6 = 30

Hence, The width of the rectangle is 12 feet and the length is 30 feet.

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The evaluation of the expression (2.4) · (1.3) gives 3.12

From the question, we have the following expression that can be used in our computation:

(2.4) · (1.3)

Express as products

This gives

(2.4) * (1.3)

Remove the brackets

So, we have the following representation

2.4 * 1.3

Evaluate the product

3.12

Hence, the solution is 3.12

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The change that Tamir would have to receive would be: $5.75

We would first have to solve for the total amount of the tickets that Tamir has received

This would be given as

32.5 + 26.5 dollars

= 59 dollars

Given that he has a 1/4 off in both of the tickets the amount that he would have to pay would be

59 - 1/4 * 59

59 - 14.75

= $44.25

This is the amount that he would have to pay for the coupons.

Given that he used a $50 bill, we would have to solve for his change.

This would be solved as $50 - $44.25

= 5.75

Hence his change is going to be $5.75

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The value of the shorter base which is x is 8 feet.

A trapezium is a quadrilateral with exactly one pair of opposite sides parallel to each other. The trapezium is a two-dimensional shape that appears as a table when drawn on a sheet of paper.

It has four sides and four vertices.

The trapezium is made of a rectangle and triangles.

Area of a trapezium = 1/2 (a + b ) h

where a = small base, b = big base and h = height.

from the above, b = 24 feet, h = 6 feet, a = x and area = 96 square feet

substituting the above into the equation

1/2 ( 24 + x) x 6 = 96

6(24 + x) = 96 x 2

6(24 + x ) = 192

multiplying the terms by 6

144 + 6x = 192

6x = 192 - 144

6x = 48

x = 48/6

x = 8 feet

In conclusion, the value of x is 8 feet

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The time taken to label 750 books if Clare labels books at 15 books per minute is 50 minutes.

In this situation, Clare volunteers at a library during the summer and has to label 750 books and she labels books at 15 books per minute and she takes no breaks.

Let the time taken to label the 750 books be represented by x.

This will be illustrated as:

1/x = 15/750

Cross multiply

(15 × x) = (750 × 1)

15x = 750

Divide

x = 750 / 15

x = 50

The time is 50 minutes.

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Complete question

Clare volunteers at a library during the summer and has to label 750 books. Clare labels books at 15 books per minute and she takes no breaks, then it would take her minutes to finish labeling all the books.

The dimensions that represent a similar triangle to triangle QRS are given as follows:

B. 10 cm, 20 cm, 25 cm.

Similar triangles are two triangles that have the same angle measures.

These triangles will also have proportional side lengths, because of the sine/cosine/tangent relations in a right triangle and the law of sines for non-right triangles.

In this problem, we want a triangle that is similar to a triangle with the dimensions presented as follows:

s,. 6 centimeters,. 12 centimeters,. q,. 15 centimeters,. r,.

Hence all these dimensions have to be multiplied by the same scale factor.

Then, option B is correct, as the ratios between the lengths are given as follows:

10/6 = 20/12 = 25/15 = 5/3.

Meaning that all sides were multiplied by 5/3.

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Answer Answer is B, thank you, I just love to help.

Step-by-step explanation:

Answer:

Step-by-step explanation:

If its a 28 day month then 671088640

29 days 1342177280

30 days 2684354560

and 31 days 5368709120

Answer:

64/125 > 150/512

Step-by-step explanation:

4/5 *4/5 *4/5 = 64/125 (also equals 0.512)

5/8 * 6/8 * 5/8 = 150/512 (also equals 0.293)

Therefore: 0.512 > 0.293

The angle that is same side exterior angle to ∠ABC is ∠EFH.

When parallel line are cut by a transversal line, angle relationships are formed such as corresponding angles, vertically opposite angles, alternate angles, same interior angles, etc.

AD and EG are parallel to each other.

CH is a transversal line to the parallel lines.

Therefore, let's find the angle that has the same relationship as same side exterior angles as angle ABC.

Two angles that are exterior to the parallel lines and on the same side of the transversal line are called same-side exterior angles.

Same side exterior angles are supplementary.

Therefore,

∠ABC and ∠EFH are same side exterior angles.

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Answer:

Example 1 : Convert 2 feet into inches. Solution : Here, we convert bigger unit into smaller unit. So we have to multiply. 2 feet = 2 x 12 inches = 24 inches Example 2 : Convert 3.5 yards into inches. Solution : Here, we convert bigger unit into smaller unit…

Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Divide the top and bottom on the fraction by 4

The train's speed was= 56.7 miles per hour

acc to our question-

Hence, The train's speed was= 56.7 miles per hour

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2x^2+6x

2(-5)^2+6(-5)

2(25)+6(-5)

50+6(-5)

50+(-30)

50-30

20