Which descriptions and equations could be the function rule? Select all that apply.
The table in the attached image shows some of the input and output values for a function rule.

The expression represents the area of the room not covered by the rug is A(x) = 2x² - 22x + 144.

Area of room = 3x² + 2x

Area of rug = x² + 24x - 144

We have to find the area of the room not covered by the rug.

Area of the room not covered by the rug = Area of the room - Area of rug

= (3x² + 2x) - (x² + 24x - 144)

= 3x² + 2x - x² - 24x + 144

= (3x² - x²) + (2x - 24x) + 144

= 2x² - 22x + 144

Hence, 2x² - 22x + 144 is the required expression for the area of the floor not covered by the rug.

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A rectangular prism has a volume of  2x ^ 3 + 19x ^ 2 + 24x

the volume of the rectangular prism is

The area contained by an object's limits in three-dimensional space is referred to as its volume.

Thus, a rectangular prism having the following dimensions: 2x length, (x2) width, and (x + 2) height

L x B x H = volume

= x× (x +8 )(2x + 3)

= x(x + 8)(2x + 3)

(2x + 3) * x ^ 2 + 8x(2x + 3)

2x ^ 3 + 19x ^ 2 + 24x

The area contained by an object's limits in three-dimensional space is referred to as its volume.

A rectangular prism's volume is thus 2x ^ 3 + 19x ^ 2 + 24x

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Answer:

A. 500 people will go out to the park when its 100F is incorrect.

Answer: 7x - 140

The expression 7(x-20) is a product of 7 and a grouping of x-20. To simplify this expression, we use the distributive property, which states that we can multiply the 7 by each term inside the grouping. So, 7(x-20) becomes 7x - 140. This is because 7x is the product of 7 and x, and 140 is the product of 7 and 20.

Step-by-step explanation:

From the trigonometric function sec θ = 13/12, two more functions are derived -

Option C: cos θ = 12/13

Option D: tan θ = 5/12

What is trigonometric function?

Simply put, trigonometric functions also referred to as circular functions are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle.

The given trigonometric function is -

sec θ = 13/12

Sec function is written as the ratio of hypotenuse to adjacent.

sec θ = 1/cos θ

Cos function is written as the ratio of adjacent to hypotenuse.

cos θ = 12/13

To find the opposite, apply the Pythagoras theorem -

(Opposite)² = (Hypotenuse)² - (Adjacent)²

(Opposite)² = (13)² - (12)²

(Opposite)² = 169 - 144

Opposite = √25

Opposite = 5

Tan function is written as the ratio of opposite to adjacent.

tan θ = 5/12

Therefore, from sec function, cos and tan function are obtained.

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The range of the ticket prices after the discount is used is 1.

The difference between the lowest and highest values, is considered as range.

Given that, groups of 25 and more receive a 20% discount to the zoo. tickets range in price from $10.00 to $15.00 depending on your age.

The range of a data is given by, difference of lowest element and largest element.

Here, 20% discount is to be given, and ticket price ranges from $10 to $15

20% of 10 = 2

And

20% of 15 = 3

Therefore, range = 3-2

= 1

Hence, the range of the ticket prices after the discount is used is 1.

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The equation of a circle with center located at (5,2) and that is tangent to the y-axis is given as follows:

C. x² + y² - 10x - 4y + 4 = 0.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

Considering the center, we have that:

(x - 5)² + (y - 2)² = r².

The circle is tangent to the y-axis, meaning that it passes through the point (0, 2), thus the radius is obtained as follows:

r² = 25.

Then the equation in standard form is given as follows:

x² - 10x + 25 + y² - 4y + 4 - 25 = 0.

x² + y² - 10x - 4y + 4 = 0.

Meaning that option C is correct.

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Answer: a-4b

Step-by-step explanation:

Combine like terms

4a-6b-3a+2b

1a-6b+2b

a-6b+2b

a-4b

The value of d in the given angles using the concept of complementary angles is; d = 13

Complementary angles are defined as angles that add up to 90 degrees.

Now, we are told that one angle measures 18°, and another angle measures (6d − 6)°. This tells us that;

(6d - 6) + 18 = 90

Expanding the bracket gives us;

6d - 6 + 18 = 90

6d + 12 = 90

6d = 90 - 12

6d = 78

Use division property of equality to divide both sides by 6 to get;

6d/6 = 78/6

d = 13

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Answer:

C) 11

Step-by-step explanation:

Exterior angles in a triangle = the sum of the interior angles of the triangle

Here, the exterior angle is ∠BCT while the interior angles are ∠CAB and ∠ABC

Using the above theorem we can say that ∠BCT = ∠CAB + ∠ABC

Plugging in the given expressions and values of the angles we acquire

9x + 6 = 3x + 2 + 70

==> combine like terms

9x + 6 = 3x + 72

==> subtract 3x from both sides

6x + 6 = 72

==> subtract 6 from both sides

6x = 66

==> divide both sides by 6

x = 11

The fourth option represents the reflection over the x-axis of f(x)=√x. The graph has been attached below. The solution has been obtained by the concept of reflections.

What is reflection?

A flip is the term for a reflection in geometry. The shape is mirrored in a reflection. The line of reflection is a line across which an image will reflect. A reflection is the shape's mirror image. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way.

We are given the function f(x)=√x.

When we replace x with -x, then the graph of the resulting equation i.e.

f(x)=√-x is captured by reflecting the graph of f(x)=√x vertically across the x-axis.

Thus, the reflection of the function f(x)=√x is a vertical reflection across the x-axis.

Hence, the graph below represents the reflection of the function f(x)=√x which is the fourth option.

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Answer:

A. C(x) = 495,000 (1.0325)^ x

Step-by-step explanation:

c(x) = 495,000 x (1+3.25%)^x

= 495,000(1.0325)

In the given parallelogram, the value of g is 116 degrees and that of h is 64 degrees.

A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure. A parallelogram is a type of quadrilateral with opposite pairs of sides that are parallel and equal. The diagram depicts a parallelogram ABCD with AB II CD and AD II BC. In addition, AD = BC and AB = CD. Non-Example: A trapezium is a parallelogram's non-example.

Here,

Since the given figure is parallelogram. Opposite angles are equal.

g=116 degree

h=64 degree

The value of g is 116 degrees and that of h is 64 degrees in the given parallelogram.

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Answer: 0.35x + 12.00 = 14.35

Explanation: You would make sure to include the x since we are unsure of how many apples to bought, we know the total it will be at the other side of the equal sign, she spent 12 on her groceries so we would add that to the number of apples she got.

Simon's target number of laps will be 80.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this case, his coach tells him to swim a target number of laps and Simon swims 45 laps before practice is canceled due to a thunderstorm. Simon still has 35 laps left to reach his target number

Let the target number be x. This will be:

x - 45 = 35

x = 45 + 35

x = 80.

The Target number is 80

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Answer:d

Step-by-step explanation:

The value of the variables 'x' and 'y' will be 47° and 27°, respectively.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.

The equations are given below.

2y = 180° - 126°

2y = 54°

y = 27°

2x + 1 = 180° - 85°

2x + 1 = 95°

2x = 94°

x = 47°

The value of the variables 'x' and 'y' will be 47° and 27°, respectively.

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By distributive property (5k + 2m)(3p + 4s) this we get   15kp + 20 ks + 6mp +8ms.

It is possible to multiply a single value by two or more values enclosed in a set of parenthesis using the distributive property, an algebraic property.

According to the distributive property, it is necessary to multiply each of the two terms by the factor when adding two terms to a factor. Only then may the addition operation be done. The following is a symbol for this property:

A (B+ C)=AB + AC

When there are three distinct values for A, B, and C.

Example : (5k + 2m)(3p + 4s)

Apply FOIL method:

(a + b) (c + d) = ac + ad + bc + bd

(5k + 2m)(3p + 4s) = 5k . 3p + 5k. 4s + 2m. 3p + 2m . 4s

5k . 3p + 5k. 4s + 2m. 3p + 2m . 4s

Simplify 5k . 3p + 5k . 4s + 2m .3p + 2m .4s : 15kp + 20 ks + 6mp +8ms

= 15kp + 20 ks + 6mp +8ms.

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a) Equation would be 5x + (x - 6) + (x - 6) = 180°

b) m∠1 = 180° and  m∠2 = 30°

What is the measure of angle?

The term "degree measure" refers to the measurement of an angle in degrees. Because one entire revolution equals 360°, it is divided into 360 parts. Each stage of the revolution represents a degree.

a) The angle measures in a triangle must add up to 180°.

Therefore, the equation to find x is:

        5x + (x - 6) + (x - 6) = 180°

b) Solving for x, we get:

x = 36

Therefore, angle m∠1 = (5x) = (5 * 36) = 180° (major angle)

angle m∠2 = (x - 6) = (36 - 6) = 30° (minor angle)

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Answer: 30$

Step-by-step explanation:

To find the slope of the equation, you can use the formula (y2-y1)/(x2-x1). Plugging the points the question gives us we can get:

(205-100)/(5-2)

= 105 / 3

= 35

Plugging this information along with a point into the formula y = mx + b:

100 = 35*2 + b

100 = 70 + b

b = 30

y = 35x + 30

To double check this is correct:

y = 35 * 5 + 30

y = 175 + 30

y = 205

(5,205) is a point therefore y = 35x + 30 is the equation

Because the x of the graph represents the number of months, the initial membership fee would be when x = 0.

y = 35*0 + 30

y = 30$

The required money will the businessperson have when they convert the money to U.S. dollars is 5220.96 dollar.

Commodities and services can be exchanged using money. Currency is defined as a unit of account that is issued by a government and is accepted at face value. When bartering, products and services were directly exchanged for one another.

We know that

1 US dollar = 6.4651 yuan

To find US dollar value of given yuan

1 yuan = 1/6.4651 US dollar

337 54 yuan = 337 54/6.4651  = 5220.96 dollar

Thus, required dollars are 5220.96.

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Answer:

the answer is 52.21 all u gotta do is divide 337.54 by 6.4651 and u get 52.20955592334225 and just round it and u get the answer which is 52.21

Step-by-step explanation:

Answer:

X < 250

Step-by-step explanation:

Inequalities:

> Greater/More than

< Less/Fewer than

= Equal to

>= Greater than/More than OR equal to

<= Less than/Fewer than OR equal to

Since it says fewer than, we'll use <

X in this case will be the actual number of people.

We know fewer than 250 will attend, making the inequality

X < 250

45 percent of the 8th graders estimated they spend less than an hour a day on social media. The solution has been obtained by using concept of frequency.

What is frequency?

The frequency of a specific value in a set of data is how frequently it appears. Typically, we would keep track of data frequency in a frequency table.

We are given that 17 8th graders spent more than an hour a day on social media and 14 8th graders spent less than an hour a day on social media.

The total 8th graders who spent time on social media is 14 + 17 = 31

The percentage of the 8th graders estimated they spend less than an hour a day on social media is

= 14*100/31

= 45.16%

= 45%

Hence, 45 percent of the 8th graders estimated they spend less than an hour a day on social media.

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The distance between G and H on the number line  -12 and -2 is -10.

What is Distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language .

The phrase is widely used metaphorically to refer to a measurement of the degree of difference between two similar objects since spatial cognition is a rich source of conceptual metaphors in human thought.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.  

What is number line?

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that each real number and each point on a number line relate to one another.

We are given two point G and H which are represented on number line;

The value G = -12 and H = -2

We have to find the distance between them;

So , we can simply subtract these two values of  G and H to get the distance between them;

distance = -12-(-2)

             = -12 + 2

             = -10

Therefore, the distance between G and H on the number line  -12 and -2 is -10.

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Answer:-√ 5

Step-by-step explanation:

4√ 20 = 8√ 5
3√ 45 = 9√ 5
8√ 5 - 9√ 5 = -√ 5

The initial fee charged to customers for using the gym, given the graph showing the charges to customers is $ 20.

To find the initial membership fee, you should look at the y - intercept of the graph.

The y - intercept is the point where the x vale is 0 and this case this point shows the cost when the customers have not worked out in the gym for any hour yet.

This y - intercept is therefore $ 20 as this is the point on the graph where the value of x is 0.

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The question is:

What is the initial fee charged to customers for using the gym?

The area, in square inches, will be 156.25π

You would require the radius in order to get the circle's area. You would enter the circumference (25) into the equation for the circle's circumference, which looks like this:

C = 2πr

25π = 2πr

Then you would figure out how to solve for r. (the radius)

25π = 2πr

12.5π = πr

12.5 = r  

After that, you would enter the radius into the equation for a circle's area.

A = π(r^2)

A = 12.5^2π

A = 156.25π

Due to the fact that meters were used as the unit of measurement, your response would be 156.25 meters.

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The new pair of basketball shoes become a "desire" because Frankie already owns a pair that he can use for the tryout. Frankie's new basketball shoes would be viewed as a "need" if he didn't already have a pair for the tryout.

When referring to possessing or acquiring specific commodities, people frequently use the terms "want" and "need" interchangeably. In terms of economics, a need is what a person needs in order to survive. If a certain need is not met, a person may get sick or perhaps pass away. On the other hand, a desire is something that a person hopes to achieve in the near or distant future. In the first instance, Frankie is able to attend the tryout in a pair of basketball shoes that he already has. He could wear the shoes he already owns, thus the new pair of shoes would be his desire. In contrast, Frankie needs a new pair of sneakers in the second scenario because he doesn't have any basketball shoes for the tryout.

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