Which comparison symbol makes each inequality statement true?
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Basic

The quadratic equation with the given x-intercepts and that passes through the point (1, 192) is the one in option D.

y = -8x^2 -64x + 264

If a quadratic equation has x-intercepts x₁ and x₂ and a leading coefficient a, we can write the quadratic equation as:

y = a*(x - x₁)*(x - x₂)

Here we know that the x-intercepts are -11 and 3, replacing that in the equation above we will get:

y = a*(x + 11)*(x - 3)

We also know that the line passes through the point (1, 192), replacing the values in the quadratic equation we will get:

192 = a*(1 + 11)*(1 - 3)

192 = a*12*-2

192 = -24*a

192/-24 = a

-8 = a

So the quadratic equation is:

y = -8*(x + 11)*(x - 3)

Expanding this, we will get:

y = -8x^2 -64x + 264

So the correct option is D.

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The relation (10, 8), (7, 9), (9, 13), (8, 5) is representing a function. (option B)

A function defines relations between input and output, where all input has a distinct output.

Given are the relations,

A) (14, 12), (10, 12), (-13, 7), (11, 15)

In this, two inputs 14 and 10 have same output 12, so it can not be a function.

B) (10, 8), (7, 9), (9, 13), (8,5)

In this, we can see, every input have distinct outputs, so it can be considered as a function.

Hence, (10, 8), (7, 9), (9, 13), (8,5) is a function.

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Answer:

-m + 13

Step-by-step explanation:

The radii of the cylinders found using the formular for the volume of a cylinder, and the 2009.6 cubic centimeter and 196.25 cubic centimeter volumes of the cylinders, indicates;

The radius of the 2009.6 cm³ cylinder is 8 centimeters

The radius of the 196.25 cm³ cylinder is 2.5 centimeters

A cylinder is a solid that has three dimensions, consisting of two circular, parallel bases that enclose a curved pipe like surface in between.

The volume of one cylinder = 2009.6 cubic centimeters

The volume of the other cylinder = 196.25 cubic centimeters

The height of each cylinder, h = 10 centimeters

The formula for finding the volume of a cylinder is; V = π·r²·h

Where;

r = The radius of the cylinder

h = The height of the cylinder

The formula for finding the volume of a cylinder indicates;

r² = V/(π·h)

r = √(V/(π·h))

The radius of the cylinder of volume 2009.6 cubic centimeters, r₁ is therefore;

r = √(2009.6/(3.14 × 10) = 8

The radius of the 2009.6 cubic centimeters volume cylinder is r₁ = 8 cm

The radius, of the 196.25 cubic centimeters cylinder, r₂, is therefore;

r₂ = √(196.25/(3.14×10)) = 2.5

The radius of the 196.25 cubic centimeter volume cylinder, r₂ = 2.5 cm

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Emma needs 8 seed packets to grow 16 plants.

What is unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. Finding the value of a single unit using the unitary technique, then extrapolating from this value.

Given that,

Emma grew 6 plants with 3 seed packets.

To grow 6 plants Emma needs 3 seed packets.

Applying unitary method:

To grow 1 plants Emma needs 3/6 seed packets.

To grow 16plants Emma needs (3 × 16)/6 seed packets.

                                                   = 8 seed packets.

The unitary method is used to unite rate.

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Answer:

  $360

Step-by-step explanation:

You want the amount of simple interest earned by $6000 in 3 years at the rate of 2%.

The simple interest formula is ...

  I = Prt

where P is the principal invested at rate r for t years.

$6000 invested at 2% for 3 years earns ...

  I = $6000·0.02·3 = $360

Chris will be paid $360 in interest in the first 3 years.

Answer:

y = 9

Step-by-step explanation:

The line that has a slope of 0: y = 0*x + ?

pass through the point (9,-4): 9 =0*(-4) + ?, we can get 9.

So the answer is y = 9.

Answer: y=0x-4

Step-by-step explanation:

y=mx+b

-4 = (0)(9)+b

b = -4

y = -4

The total cost of the meal plus tip and tax was more than 122% of the cost of the bill.

What is percent?

A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.

Indigo goes out to lunch.

The bill, before tax and tip, was $10.85.

A sales tax of 3% was added on.

Indigo tipped 18% on the amount after the sales tax was added.

The amount after adding sales tax is,

$10.85 x 3% = 0.3255

⇒ $10.85 + 0.3255 = $11.1755

Now to find the amount after tipped 18% on the amount after the sales tax was added.

$11.1755 x 18% = 2.01159

⇒ $11.1755 + 2.01159 = $13.18709

Hence, the amount  after tipped 18% on the amount after the sales tax was added is $13.18709.

Let x be the percent of more than the cost of the bill of $13.18709.

⇒

[tex]\frac{10.85(x)}{100} = 13.18709\\ x = \frac{100 (13.18709)}{10.85}\\ x = 121.54[/tex]

Hence, the total cost of the meal plus tip and tax was more than 122% of the cost of the bill.

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The value of x and y at which function P = 3x+2y becomes maximum are

(9,0), data from given graph.

What is the graph?

Graph is the pictorial representation of given data.

Graph is defined as to create a diagram that shows a relationship between two or more things. An example of graph is to create a series of bars on graphing paper.

The four most common are

1. Probably line graphs,

2. Bar graphs and histograms,

3. Pie charts, and

4. Cartesian graphs

To find the maximum, input the vertices (0,8), (5,4) and (9,0) into the objective function (P = 3x + 2y) to determine which vertex obtains the maximum value.

Note: (5,4) is not a vertex.

(0,8) :

P = 3*0 + 2*8

  = 16

(5,4):
P = 3*5 + 2*4

  = 23

(9,0):

P = 3*9 + 2*0

  = 27.

So, the maximum value = 27 at (9,0).

So, the x value = 9 and

      the y value = 0.

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The equation of the line, in slope-intercept form,  that passes through the given points, (6,-4) and (6,5) is: x = 6.

An vertical line can be written in slope-intercept form as x = a, because the line has no y-intercept and the change in x values in the slope formula is equal to zero.

The value of a in the equation is the point on the x-axis where the vertical line intercept, irrespective of the change in y-values up the line.

Given the line goes through the points, (6, -4) and (6, 5), it means the line is a horizontal line because they both have the same x-value, 6.

Therefore, the value of a is 6. The equation of the line would be x = 6.

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The scale factor from B to A is 5/8. Since the scale-up and scale-down of A and B are reciprocal to each other. I.e, scaling of geometry can be reversed by the reciprocal of its scale factor.

The scale factor for the given shape to transform from A to B is 8/5.

So, the original shape is A and it is scaled up by the factor 8/5 and named B.

(Scaled up since scale factor (8/5 = 1.6) > 1)

So, the scaling from B to A is the reverse process of scale-up. That means scale-down. For this, the scale factor is reduced by taking its reciprocal. So, that the shape gets reversed.

The scale factor for scaling down from B to A is 1/(8/5) ⇒ 5/8.

Therefore, the scale factor from B to A is 5/8.

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Answer:

x^2 + y^2 = 400

Step-by-step explanation:

the general equation of a circle is,

x^2 +y^2 = r^2

where x, y are the coordinates of the circle

r is the radius

The constant amount that Carson makes every hour is $16.25.

It is important to note that this question has to do with a proportional relationship. Since Carson earns $113.75 for 7 hours of work and he makes a constant hourly wage.

The amount that he makes per hour will be:

= Amount / Number of hours

= $113.75 / 7

= $16.25

Therefore the constant amount he makes every hour is $16.25.

Note that the options weren't given but the question has been solved accordingly.

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Step-by-step explanation:

3x + 1 < 2x - 4

3x-2x <-4-1

x<-5

The graphed two lines will have one solution.

Any line that isn't twisted or bent is said to be straight.

Intersecting lines are two or more lines that have exactly one point in common. The point of junction is this central location that connects all of these lines.

A system of Intersecting Lines will have one unique solution

Lines that are parallel to one another on a plane do not overlap or meet at any point. They are always parallel and equally spaced from one another.

A system of Parallel Lines will have no solution

Here we have

System of equations

Given that the two lines are not parallel line

As we can see that both lines meet at a point

So here we can conclude that both lines are Intersecting Lines

Therefore,

The graphed two lines will have one solution.

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The value of a comic book in dollars has been found to be 0.20y + 1.50, where y is the number of years since it was released. is  

(a)  [tex]0.2$[/tex]

(b) [tex]1.5$[/tex]

[tex]0.2 y+1.5 \longleftarrow \text { initial value }[/tex]

[tex]when $y$ increase one. the value increase $\$ 0.2$[/tex]

Travelling to movies and television programmes. An element of a comic book being in a popular film or television programme is a major factor in its value rising. Characters' comic book appearances have become far more valuable as they are integrated into the Marvel Cinematic Universe.

Marvel's first comic book just sold for $1.26m. Movies have contributed to the enduring popularity of superheroes, bringing in new audiences. The printed comic is still big business, worth over $1bn in North America alone.

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Answer:

The last answer is correct

Step-by-step explanation:

3x = 24  Divide both sides by 3

x = 8

A pair of shoes cost $8

The solution for the angle x in the figure is 130 degrees

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

The transversal and the parallel line

By the theorem of vertical angles, we have the following equation

x = 5y

Also, we have the following equation

x = 2y - 78 --- by the theorem of corresponding angles

Substitute x = 2y - 78  in x = 5y

So, we have the following representation

5y = 2y - 78

Evaluate the like terms

3y = 78

Divide both sides by 3

y = 26

Substitute y = 26 in x = 5y

x = 5 * 26

Evaluate

x = 130

Hence, the value of x is 130

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The time for each of them to cover 1 mile is; Evian = 10 min, Toby = 9 min and Jillian = 12 min. The fastest is Toby and No, Jillian can't make the team.

A unit rate means a rate for one of something.

Given that, Students at Polk Middle School are given a fitness test.

The fitness test result is;

Evian can run [tex]1\frac{1}{2}[/tex] miles in 15 minutes, Toby can run 2/3 miles in 6 minutes and Jillian can run 3/4 miles in 9 minutes

a) The rate of running in 1 mile = (total miles covered)/(total time taken)

Evian =

3/2 miles in 15 minutes

1 mile = 15x2/3

1 mile = 10 minutes

Toby =

2/3 mile in 6 minutes

1 mile = 6x3/2

1 mile = 9 minutes

Jillian =

3/4 miles in 9 minutes

1 mile = 9x4/3

1 mile = 12 minutes.

b) Since, Toby is covering 1 mile in the least minutes in comparison with other two, therefore Toby is fastest among them.

c) Jillian's rate = 1 mile in 12 minutes

Speed = 1/9 miles per minute

Therefore, she will cover 7/2 miles in = 12x7/2 = 42 minutes

That means, she can't make the team.

Hence, the answers are a) Evian = 10 min, b) Toby = 9 min and Jillian = 12 min, the fastest one is Toby and Jillian can't make the team.

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Approximate percent increase in how much the student pays with Optin 2 versus Option is 20%

$540 plus 15% sales tax now.=$515

Pay exactly $120 now and then $58 each month for 9 months=$642

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Answer:

The perimeter is approximately 6.40.

Step-by-step explanation:

To find the perimeter of a triangle with vertices X (1, 3), Y (-4, -1), and Z (4, -1), we can first find the distance between each pair of points using the distance formula.The distance between points X and Y is:

$d(X,Y) = \sqrt{((1 - (-4))^2 + (3 - (-1))^2)} = \sqrt{25 + 16} = \sqrt{41}$

The distance between points Y and Z is:$d(Y,Z) =

\sqrt{((-4 - 4)^2 + ((-1) - (-1))^2)} = \sqrt{0 + 0} = 0$

The distance between points X and Z is:

$d(X,Z) = \sqrt{((1 - 4)^2 + (3 - (-1))^2)} = \sqrt{9 + 16} = \sqrt{25}$

We can then find the perimeter of the triangle by adding up the lengths of the sides. In this case, the perimeter is $d(X,Y) + d(Y,Z) + d(X,Z) = \sqrt{41} + 0 + \sqrt{25} = \sqrt{41} + \sqrt{25} = 6.40\ldots$.

Rounded to two decimal places, the perimeter is approximately 6.40.

The expression which represents the composite function (f - g) (x) as required in the task content is; 11x - 10.

It follows from the task content that the expression which represents the composite function (f - g) (x) as required in the task content be determined.

Since the given functions are;

f(x) = 6x − 8 and g(x) = −5x + 2

The composite function; (f - g) (g) is equivalent to;

f (x) - g (x)

Therefore, we have;

(f - g) (x) = 6x - 8 - (-5x + 2)

(f - g) (x) = 6x + 5x - 8 -2

(f - g) (x) = 11x - 10.

On this note, the required expression which represents (f - g) (x) is; 11x - 10.

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The constraints to represent the incoming students at the college is B. 0 < x ≤ 100 and 0 < y ≤ 400

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this situation, the college is currently accepting students that are both in-state and out-of-state. They plan to accept four times as many in-state students as out-of-state, and they only have space to accept 100 out-of-state students.

Let x = the number of out-of-state students and

y = the number in-state students.

The constraints is 0 < x ≤ 100 and 0 < y ≤ 400.The correct option is B.

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There are 12 different positive two digit integers can be formed using these digits if a digit can be repeated in an integer.

Integer:

An integer is zero (0), a positive integer (1, 2, 3, etc.), or a negative integer with a minus sign (-1, -2, -3, etc.). A negative number is the additive reciprocal of the corresponding positive number. In mathematics languages, sets of integers are often denoted by a bold Z or a bold {Z}.

Given the question :

The number of different positive two integer number can be obtained by:

P(4, 2) = 4P2

We know that:

[tex]^nP_r[/tex] = n! / (n - r)!

⁴P₂ = 4! / (4 - 2)!

⁴P₂ = 4! / 2!

⁴P₂ = (4 * 3 * 2 * 1) / ( 2 * 1)

⁴P₂ = 24 / 2

⁴P₂ = 12

Hence, 12 different positive two-digit integers can be formed using these digits if a digit may not be repeated in an integer.

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The probability that we will draw 4 kings from the 52-card deck be 1/270725.

Given, we draw 4 cards from a standard 52-card deck

we have to find the probability that we draw 4 kings

As, we know that the deck of cards contain 4 kings of two red and two black.

we have to choose 4 kings from 4 kings in the deck

Number of ways to choose 4 kings from the deck of cards =  C(4 , 4)

Now, total number of ways in which 4 cards can be chosen be,

C(52 , 4)

So, the probability of drawing 4 kings from the deck of cards be,

P(E) = C(4 , 4)/C(52 , 4)

P(E) = 4×3×2 / 52×51×50×49

P(E) = 1 / 13×17×25×49

P(E) = 1/270725

Hence, the required probability be 1/270725

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Answer:

5/9 In fraction form. In decimal form 0.51 and in percentage form %51

Step-by-step explanation:

To find the ratio of the number of female runners to the total number of runners, we can divide the number of female runners by the total number of runners and express the result as a fraction. There are 25 female runners, and there are a total of 24 men + 25 women = 49 runners. Therefore, the ratio of the number of female runners to the total number of runners is 25/49. This fraction can be reduced to 5/9.

Answer:

q= 1.09

Step-by-step explanation:

the works there its a little messy tho

Answer: 27, 65, 29, 77, 37

Step-by-step explanation:

The number of diagonals of an [tex]n[/tex]-gon is [tex]\frac{n(n-3)}{2}[/tex].

The number of apothems of an [tex]n[/tex]-gon is [tex]n[/tex].

Answer:

Step-by-step explanation:

The salvage value of the PS 5 system after 6 years will be $640.

The formula for the depreciation;

Depreciation per year = (cost of asset - salvage value)/ (useful life of assets)

For the stated question-

12 = (712 - salvage value)/ (6)

salvage value = 712 - 12x6

salvage value = $640.

Thus, the salvage value of the PS 5 system after 6 years will be $640.

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