twice the sum of 9 and y is less than or equal to 5y

It can be determined that a relation represented as an equation is a function if and only if for each value on x-axis, there is a corresponding value on Y-axis.

which also signifies that for each value of x , there is a value of y which exists and is real.

A function is a mapping from one set to another such that nothing in the first set is mapped to more than one thing in the second set.

Or in simple words if there is no corresponding value of y for any x, then that is not a function.

For example,

[tex]x^{2} +y^{2}[/tex]=1

when the value of x is 0 , then value of y is 1 or -1, Thus, it will not be a function.

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When it skins photos at a consistent rate, the number of photos in 21 minutes will be 1323 photos.

From the information, it should be noted that the skin on skin 63 photos in a minute.

Therefore, the number of photos that can be skinned at a particular minutes will be illustrated as:

p = 63m

where p = number of photos

m = number of minutes

Therefore, it should be noted that using p = 63m. The appropriate number of photos will be:

p = 63m

p = 63 × 21

p = 1323 photos

Therefore, when it skins photos at a consistent rate, the number of photos in 21 minutes will be 1323 photos.

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An integer to represent the change in the worker position is -78

Hence, An integer to represent the change in the worker position is -78

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Amount of sugar eaten in the US in 2010 = 4.95 x 10¹⁰ lb

Approximate number of people in the United States of America in 2010 = 3.3 x 10⁸

Amount of sugar ate by an average person in US = 1.5 x 10² lb

We have to find an approximate amount of sugar eaten in US in 2010.

It will be the product of the number of people in US and the sugar ate by a person in US.

So, Amount of sugar eaten in the US in 2010 approximately = 3.3 x 10⁸ x1.5 x 10²

                                                                           = 4.95 x 10¹⁰ lb

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The number of minutes after liftoff of the plane at an altitude of 21,000 feet is 6 minutes

A function can be defined as an expression or law that shows the relationship between a dependent and independent variable.

Given the function;

a= 3400 t + 600

Where;

If the altitude is 21000 feet, let's determine the time

Substitute the value into the function

21000 = 3400t + 600

collect like terms

21000 - 600 = 3400t

20400 = 3400t

Make 't' the subject

t = 20400/ 3400

t = 6 minutes

Thus, the number of minutes after liftoff of the plane at an altitude of 21,000 feet is 6 minutes

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Answer:

12

Step-by-step explanation:

You have a right triangle, so use the Pythagorean theorem.

a² + b² = c²

5² + b² = 13²

25 + b² = 169

b² = 144

b = 12

An equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples is,

⇒ b = 2a + 30

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Cost of one pound of grapes = g

Cost of one pound of apples = a

Cost of one pound of banana = b

Since, The cost of one pound of grapes is 15 cents more than one pound of apples.

It can be written as;

g = a + 15   .... (i)

And, The cost of one pound of bananas is twice as much as one pound of grapes.

It can be written as;

b = 2g  ..... (ii)

To find an equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples as,

Put the value of g from (i) in (ii) we get,

b = 2 ( a + 15 )

b = 2a + 30

Hence, An equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples is,

⇒ b = 2a + 30

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Answer: the first option i believe

Step-by-step explanation:

Answer:4x + 8 y -12

Step-by-step explanation:

The age of Walter at the end of year 1999 will be equal to 55 years.

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.

Let's assume respective age of Walter and Walter's grandmother is x and y years respectively.

In 1994 , age of Walter was  :

x = y / 2

or y = 2x

It is also given that the sum of years they were born is 3838.

The year Walter was born = (1994 - x)

The year Walter's grandmother was born :

= (1994 - y)

= 1994 - 2x                                  (∵ y = 2x)

So , we can write an equation to find out Walter's age which is :

1994 - x + 1994 - 2x = 3838

3988 - 3x = 3838

3x = 3988 - 3838

x = 150 / 3

x = 50 years

or the age of Walter in 1994 is 50 years.

At end of 1999 Walter's age will be:

= 50 + 5.

= 55 years

Therefore , the age of Walter at the end of year 1999 will be equal to 55 years.

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The perimeter of the triangle is 4.5inches.

Equilateral Triangle : can be defined as a triangle having all three sides equal.

Perimeter of triangle is defined as the sum of the lengths of the three side.

Perimeter of triangle is denoted by 3x(side).

Given that the side of the triangle is 1.5 inches

Perimeter = 3x(1.5)

Perimeter=4.5 inches

Therefore , The Perimeter of the triangle is 4.5 inches .

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The given conditions to write an equation for the line passing through (−9,2) and parallel to the line whose equation is y = −3x+ 2.

There are many different methods to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically include one or more variables.

More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

[tex]$$We have the equation of a parallel line and a point which it passes through. To write the equation of the line in point-slope form, we will use the following formula:y−y1=m(x−x1)We know that the slope of parallel lines are same and we are given the equation for parallel line, y=−3x+2$$[/tex]

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Answer:

$675.75

Step-by-step explanation:

To find the sale price of the recliner, we can multiply 15% by the regular price.

15% = 0.15

(0.15)(795.00) = $119.25

This gives us the amount that the sale takes off from the regular price. We can subtract that from the regular price to find the sale price.

795.00 - 119.25 = $675.75

A bonus shortcut way to get our answer would be to subtract 15% from 100%.

100% = 1.00

1.00 - 0.15 = 0.85

This tells us that the sale price is 85% of the regular price. Using this information, we can multiply 85% by the regular price to also get our sale price.

85% = 0.85

(0.85)(795.00) = $675.75

y = -3/2x - 20.5 is the line crossing through (-7,10) perpendicular to 2x - 3y= -3

In an equation, parallel lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.

Here given that  2x - 3y= -3

can also be written as

y = 2/3x + 1

Here 2/3 is the slope and 1 is the y-intercept

To find a parallel line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.

y - y₁ = m(x - x₁)

We have, m = -3/2,  x₁ = -7 and y₁ = 10

y - 10 = -3/2(x - (-7))

y - 10 = -3/2(x + 7)

y - 10 = -3/2x - 21/2

y = -3/2x - 21/2 + 10

y = -3/2x - 20.5

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The answer to this question is 14

In the survey study, the explanatory variable is: number of complaints .

An explanatory variable can be described as a type of independent variable that is manipulated by the researcher which explains the or predict the differences that occurs in a response variable.

For example, number of complaints is the independent variable that the dependent variable, "accidents that occurs in an area" depends on. That is, it explains or predicts the accidents that occurs in an area.

Therefore, we can conclude that, in the survey study, the explanatory variable is: number of complaints .

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The statement is true that the domain of f(x)/g(x) consists of numbers "x" that are in the domains of both f(x) and g(x) for which g(x) is not equal to 0.

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Literal equations are equations containing two or more variables. Our goal is to solve for just one variable with respect to others. If it is known to us that  how to solve regular equations, then literal equations are very easy to solve.

Literal equation is also termed as simultaneous equation ,

where more than 1 variable is present and can be solved by inputting value entirely into 1 variable form

For example,

x+ y=6

x-y=2

now putting x=y+2 from  the second equation,

y+2+y=6

2y+2=6

y+1=3

y=2

x=y+2=2+2=4

To solve a literal equation means to express one variable with respect to the other variables in the equation.

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Equations that have two or more variables are considered literal equations. Our aim is to solve for a single variable in relation to other variables. Literal equations are fairly simple to solve if we know how to solve regular equations.

Simultaneous equation is another name for a literal equation.

where a problem with more than one variable can be handled by entering all of the values into a single variable form.

For Example :

                          x + y = 6

                          x - y = 2

Now putting x = y + 2 from the equation

                              y + 2 +y = 6

                                  2y + 2 = 6

                                  2y = 6-2

                                   2y = 4

                                    y = 2

  Hence,

                        x = y + 2 = 2 + 2 = 4

To express one variable in relation to the other variables in an equation is to solve it literally.

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The lengths 9, 9 / 2 and 9√3 are not part of a 30 - 60 - 90 right triangles. (Correct choice: A)

Herein we must find what set of lengths are part of a 30 - 60 - 90 right triangle. In accordance with the Euclidean geometry, there are the following relationships for the sides of the 30 - 60 - 90 right triangle:

Now we proceed to check if each set of sides belongs to a 30 - 60 - 90 right triangle:

Case 1

The length of the shortest leg of the triangle is 9 / 2, then the lengths of the longest leg and the hypotenuse are 9√3 / 2 and 9, respectively. (False)

Case 2

The length of the shortest leg of the triangle is 4, then the lengths of the longest leg and the hypotenuse are 4√3 and 8, respectively. (True)

Case 3

The length of the shortest leg of the triangle is 7, then the lengths of the longest leg and the hypotenuse are 7√3 and 14, respectively. (True)

Case 4

The length of the shortest leg of the triangle is 5 / 3, then the lengths of the longest leg and the hypotenuse are 5√3 / 3 and 10 / 3, respectively. (True)

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The measure of the supplementary angles are 48° and 132°.

Let the measure angle be x.

Its supplementary angle will be x + 84

We know that the sum of supplementary angles is 180°.

So, we get the equation as:

x + x + 84 = 180

Combining the like terms, we get that:

2 x + 84 = 180

Subtract 84 from both sides, we get that:

2 x = 180 - 84

2 x = 96

Divide both sides by 2, we get that:

x = 96 / 2

x = 48°

x + 84 = 48+ 84 = 132°

Therefore, we get that, the measure of the supplementary angles are 48° and 132°.

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Answer:

Option B: 6342

Step-by-step explanation:

Answer: 6342

Step-by-step explanation:

906 x 7 = 6342

Answer: 5.5 inches

Step-by-step explanation:

       Using the formula for the area of a square, we can plug the known values in and solve.

a = x²

30 = x²

[tex]\sqrt{30 } =\sqrt{x^2}[/tex]

[tex]\sqrt{30 }[/tex] = x

5.477 ≈ x

       Now, we will round to the nearest tenth.

5.477 ≈ 5.5 inches

Answer:

C Between 4 and 5, but closer to 4

Step-by-step explanation:

cube root of 70 is 4.1212

The Expression for the Area a of the rectangle as a function of length L is given by A(L) = 12L - L^2 .

Let,

length, L, and the width, W, are components that help determine the area, A, and the perimeter, P of the rectangle. These are given by the following equations

 A=LW

 P=2L+2W

Given,

Perimeter of the Rectangle = 24m.

We are asked to express the perimeter of the rectangle as a function of the length, L, of one of its sides.

We will first set up the equation of the Perimeter of the rectangle. We can let the width of the rectangle be W.

P = 2L+2W

24 = 2L+2W

12 = L+W

W = 12-L

Since we want to express the Area as a function of L, we have to find the value of W in terms of L. This is so we can eliminate the width in the equation for the Area. The Area as a function of L is as follows.

A(L, W) = LW

A(L) = L(12-L)

A(L) = 12L-L^2

Therefore, the Area as a function of L is given by A(L) = 12L-L^2.

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Answer:

1

Step-by-step explanation:

3^-4 x 3^5

3 - 2

=1