The number of students in attendance since 2000 at Lamar Community College can be represented by the equation below, where x equals the time in years after 2000. S(x) = (x - 50)² + 19 The college creates a graph to better view the decreases and increases in attendance. Which of the following describes the end behavior of their graph? O A. As x approaches positive infinity, S(x) remains constant. OB. As x approaches positive infinity, S(x) approaches positive infinity. OC. As x approaches positive infinity, S(x) approaches zero. OD. As x approaches positive infinity, S(x) approaches negative infinity.​

Answer:

Step-by-step explanation:

The answer is 12

Answer:

x=12

Step-by-step explanation:

[tex]\frac{5}{6}x+3=13\\\frac{5}{6}x+3-3=13-3\\\frac{5}{6}x=10\\6(\frac{5}{6}x)=10(6)\\5x=60\\(\frac{1}{5})5x=60(\frac{1}{5})\\x=12[/tex]

Answer: 40%

Step-by-step explanation:

Take 10 divided by 25; then times 100 = 40%

Answer:

1. y = 5

2. y = 2x - 1

3. x = -1

Answer:

8, 0

Step-by-step explanation:

For figure 2) the value of the 'x' would be x = 14.

and for figure 3) the value of the 'x' would be x = 17 or x = 1 .

What is the Basic Proportionality Theorem?

The Basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle that intersects the other sides into two distinct points, then the line divides those sides in proportion.

Figure 2)

By using the Basic Proportionality Theorem, we can write

                        [tex]\frac{11}{22}=\frac{x}{42-x}\\\\\frac{1}{2}=\frac{x}{42-x}\\\\42-x=2x\\\\3x=42\\\\x=14[/tex]

Now for figure 3)

            By using Pythagoras' theorem, we can write

                        [tex]24^2+(x+7)^2=(2x-10)^2\\\\576+x^2+14x+49=4x^2-40x+100\\\\3x^2-54x+51=0\\\\x^2-18x+17=0\\\\x^2-17x-x+17=0\\\\(x-17)(x-1)=0\\\\x=17 $ or $ x=1[/tex]

Hence, for figure 2) the value of the 'x' would be x = 14.

and for figure 3) the value of the 'x' would be x = 17 or x = 1 .

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Answer:

5

Step-by-step explanation:

[tex] {x}^{3} - {2xy}^{2} + {y}^{3} \\ {( - 2)}^{3} - 2( - 2)(3) {}^{2} + {3}^{3} \\ - 8 + 4 - 18 + 27 \\ 31 - 26 = 5[/tex]

Answer:

55

Step-by-step explanation:

1. Substitute in the values

  -2^3 - ( 2 * -2 * 3^2 ) + 3^3

2. Simplify the powers

  -8 - ( 2 * -2 * 9 ) + 27

3. Solve the brackets

  -8 - ( -4 * 9 ) + 27

  -8 - ( -36 ) + 27

  -8 + 36 + 27

4. Solve

  -8 + 63

  55

Answer:

Step-by-step explanation:

-6y = -5x + 36

y = 5/6x - 6

Answer:

[tex]\frac{85}{17}[/tex]

Step-by-step explanation:

[tex]\frac{8.5}{1.7}[/tex] multiply the top and bottom by 10

[tex]\frac{85}{17}[/tex]

Answer:

u > -11/10

Step-by-step explanation:

The diagram 2 represents the model that depicts the ratio given in the story.

Ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

Given is that Peace Park sets up an outdoor ice-skating rink each winter. Yesterday afternoon, there were 5 skaters who brought their own skates for every 3 skaters who rented skates.

The given ration of 5 skaters for every 3 skaters is shown in the

diagram 2. In the first column, five blocks are colored and in the second

column, three boxes are colored.

Therefore, the diagram 2 correctly represents the model in the story.

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Th value of the equation f ( x ) is given as

when x = 0 , f ( 0 ) = 5

when x = 1 , f ( 1 ) = 7

when x = 5 , f ( 5 ) = 15

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given as

f ( x ) = 2x + 5

Now , the values of the function f ( x ) can be determined when we substitute for the values for x in the equation

So , in order to find f ( 0 ) , substituting the value for x as x = 0, we will get the value for the function

a)

when x = 0

The equation is f ( x ) = 2x + 5

f ( 0 ) = 2 x 0 + 5

f ( 0 ) = 5

So , the value of f ( 0 ) = 5

b)

when x = 1

The equation is f ( x ) = 2x + 5

f ( 0 ) = 2 x 1 + 5

f ( 0 ) = 7

So , the value of f ( 0 ) = 7

c)

when x = 5

The equation is f ( x ) = 2x + 5

f ( 0 ) = 2 x 5 + 5

f ( 0 ) = 15

So , the value of f ( 0 ) = 15

Therefore , the values of the equations are f ( 0 ) = 5 , f ( 1 ) = 7 , f ( 5 ) = 15

Hence ,

Th value of the equation f ( x ) is given as

when x = 0 , f ( 0 ) = 5

when x = 1 , f ( 1 ) = 7

when x = 5 , f ( 5 ) = 15

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Rate at which 88 copies will get printed is 44 dollars

By using the unitary method to find the value of a single unit, we may use that value to calculate the values of the required number of units.

According to the given information :

Applying the unitary method

we get,

Rate at which 16 copies get printed = 8 dollars

Rate at which one copy gets printed = [tex]\frac{8}{16}[/tex]

Rate at which 88 copies get printed =  [tex]\frac{8}{16}[/tex]×88

                                                            = 44 dollars

Rate at which 88 copies will get printed is 44 dollars.

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Answer:

C. 45,257

Step-by-step explanation:

5280 * 60 = 316,800

316,800 ÷ 7 = 45,257

The distance between two consecutive rest stops is 45257 feet.

Division is the process of dividing a number by a given number.

Given that, the 60-mile road is divided into 7 equal parts.

The length of each part is:

60/7 mile

Given that;

1 mile = 5280 feet

Therefore;

60/7 mile = (60/7)5280 feet

60/7 mile ≈ 45257 feet

Hence, the distance between two consecutive rest stops is 45257 feet.

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The fourth degree polynomial function with zeros 5, -5, 5i, and -5i. written  in factored form is

The zeros of a polynomial function is the the value of x when the function is equal to zero

The zero is also called the root of the polynomial

To find the polynomial we equate to the zeros

the first

x = 5

x - 5 = 0

the second

x = -5

x + 5 = 0

the third

x = 5i

x - 5i = 0

the fourth

x = -5i

x + 5i = 0

Bringing the terms together

(x - 5) (x + 5) (x - 5i) (x + 5i)

Therefore the polynomial of zeros 5, -5, 5i, and -5i is gotten in factored form in the form (x - 5) (x + 5) (x - 5i) (x + 5i)

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The height of the soil in the new planter is 4/3 feet

Consider the old planter

The height of the prism = [tex]1\frac{1}{2}[/tex] feet = 3/2 feet

The length of the prism = [tex]3\frac{2}{3}[/tex] feet = 11/3 feet

The width of the prism = 2 feet

The volume of the rectangular prism = Length × width × height

= 11/3 × 2 × 3/2

= 11 cubic feet

The area of the base of the new planter = [tex]8\frac{1}{4}[/tex] square feet = 33/4 square feet

The volume of both planter will be equal

The base area × height = volume

33/4 × h = 11

h = 11 / (33/4)

h = 11 × 4/11

h = 4/3 feet

Therefore, the height of the new planter is 4/3 feet

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Answer:

The selected answer should be correct!

Step-by-step explanation:

I did the problem step by step and got 1 5/7 which is the simplified version of 1 15/21.

I hope this helped somewhat!!

The swimming pool was on sale for $1206.2, which is 18.5% less than its initial $1429.35 cost.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

Here,

Sale price after discount=$1206.2

Discount percent=18.5%

Original price=1206.2+18.5%*1206.2

=$1429.35

The original price of the swimming pool was $1429.35 as It was at sale price of $1206.2 with the discount of 18.5%.

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Answer:

x = 30 degrees

Step-by-step explanation:

By Parts-Whole Postulate, x + 100 = 130, meaning that x = 30 degrees.

Answer: 30

Step-by-step explanation: 130-100=30

a) The probability of rolling a total of 5 is 1/9.

b) If a pair of fair dice 360 times, then 40 times you will get a total of 5.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The number of 5 in the table is 4.

The total number of outcomes is 6 × 6 = 36

The number of outcomes of favorable event is 4.

Total number of outcomes is 36.

The probability getting total of 5 after rolling the pair of dice is

=4/36

Divide the denominator and numerator by 4:

= 1/9

If 360 time the pair of dice rolled, the number of times to get total 5 is

360 × (1/9)

= 40.

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The function f(x) is 4x5 – 3x has exactly 5 roots according to the Fundamental Theorem of Algebra.

The correct answer is therefore d) 5 roots.

Complete question :

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?

f(x) = 4x5 – 3x

1 root

2 roots

4 roots

5 roots

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The midpoint of the line segment is (1, 2). Then the correct option is B.

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoints of the line segment are (-1, 7) and (3, -3). Then the mid-point of the line segment will be given as,

(x, y) = [(-1 + 3) / 2, (7 - 3) / 2]

(x, y) = (2/2, 4/2)

(x, y) = (1, 2)

The midpoint of the line portion is (1, 2). Then the right choice is B.

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The equation for the given linear function is y = 12m + 20.

A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.

It can be represented as a straight line on a graph.

The given points for the linear function are (2, 44) and (5, 80) respectively.

The slope can be obtained as,

m = (80 - 44)/(5 - 2)

   = 36/3

   = 12

Substitute the value of m in the general form y = mx + c to obtain,

y = 12x + c

Now, substitute x = 2 and y= 44 in the above expression as,

44 = 12 × 2 + c

=> c = 44 -24

=> c = 20

Thus the linear function can be written in the form of equation as,

y = 12m +  20

Hence, the equation of the function for the given case is y = 12m + 20.

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Answer:

<

A

Step-by-step explanation:

9 is the mean of clusters

What are equivalent equations?

Equivalent equations are algebraic equations that are having identical roots or solutions. By adding or subtracting the same number or expression to both side of an equation we get an equivalent equation. Also by multiplying or dividing both sides of an equation by the same non zero number we get equivalent equation.

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Answer:

7 cm ; 10 cm ; 14 cm

Step-by-step explanation:

x = y + 3

z = 2y

x + y + z = 31

y + 3 + y + 2y = 31

4y = 31 -3

4y = 28

4/4 y = 28/4

y = 7

z = 7(2) = 14

x = 7 + 3 = 10

Jeff bicycles 144 miles at the rate of r mph. The same trip would have taken 3 hours longer if he had decreased his speed by 4 mph. The value of r is 16.

What is speed ?

The speed at which an object's position changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it only has a direction and no magnitude, speed is a scalar quantity.

144/r= t

144/(r-4)-144/r = 3

LCM r(r-4)

144r-144(r-4)/r(r-4)=3

Simplify [tex]$\frac{144 r-144(r-4)}{r(r-4)}: \frac{576}{r(r-4)}$[/tex]

[tex]\frac{576}{r(r-4)}=3[/tex]

Multiply both sides by r(r-4)

[tex]\frac{576}{r(r-4)} r(r-4)=3 r(r-4)[/tex]

Simplify

576=3 r(r-4)

Solve [tex]$576=3 r(r-4): \quad r=16, r=-12$[/tex]

r=16, r=-12

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32 more blue marbles need to be added to the bag so that the probability of randomly drawing a blue marble is 3/4

A bag contains 10 red marbles, 7 blue marbles, and 3 green marbles.

we need to find the numbar of blue marbles need to be added to the bag so that the probability of randomly drawing a blue marble is 3/4

Let the number of blue marbles added be n,

required probability P = 3/4

Total marbles = 10 + 7 + 3

                      = 20

Number of blue marbles=7

Using definition of probability,

(7 + n)/(20+n) = 3/4

4(7+n)=3(20+n)

28+4n=60+3n

n = 32

Therefore, we need to add 32 more blue marbles to make the probability of randomly drawing a blue marble be 3/4.

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The inequality that can be used to determine the number of books, b, Erin must sell in order to meet her goal of making more than $180 in book sales is 12b ≥ 180.

2. The solution to the inequality 12b ≥ 180 is that b ≥ 15.

Inequality is a mathematical statement that two or more mathematical expressions are unequal because their solutions are not equivalent in value.

Inequalities are depicted as less than (<), more than (>), not equal to (≠), less than or equal to (≤), and more than or equal to (≥).

The selling price per book = $12

The total sales revenue expected is ≥ $180

The number of books = b

Inequality describing the situation = 12b ≥ 180

b ≥ 180 ÷ 12

b ≥ 15

Thus, we can conclude that Erin needs to sell 15 or more books to earn $180 or more from the book sales.

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The expression that shows how many sweatshirts were not adult sizes is  s - 19 .

Given :

the lacrosse team sold s team booster sweatshirts, and 19 of them were adult sizes.

Expression :

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Expression = number of sold sweatshirts - number of adult sizes.

= s - 19.

This gives the number of sweatshirts that are not adult sizes

if s = 25

then not adult sizes sweatshirts = s - 19

= 25 - 19

= 6

Hence the expression is s - 19.

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