What is the equation of the
line that goes through
(-1, 3) and is perpendicular
to y = 4x - 7?

A function is even if

A function is odd if

For the given question, we will test for both even and odd conditions

Step 1: Test for an even condition

Step 2: Test for an odd function

Quadrilateral ABCD has coordinate

A(-4, 3) , B(-3, 6) C(0,8) & D(-2,5)

so we will find the length of the sides

for CD

as we can see AB and CD is not equal to Quadrilateral is not equal.

now we compute the midpoint of the diagonals

midpoint of

The area of a square is equal to the squared of one side.

Using the given data, we can have the quadratic equation of

We can solve for x in 2 ways

Or by using the quadratic formula

Given:-

Given amount is $50.

Price of article is $24.

GST is 7%.

PST is 7%.

To find:-

The remaining amount.

The GST amount is,

The PST amount is,

So the total tax amount is,

Now the total amount of the article is,

So the remaining amount is,

So the remaining amount is $22.64

Answer:d is the correct answer.

Step-by-step explanation:

The solution to the inequality is m ≤ -14/11 which is the correct answer would be option (C).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

If it is "> or," the shaded arrow is drawn to the right of the inequality graph; if it is "or," it is drawn to the left.

Given the inequality, -1/2m ≥ 7/11,

Which represents the solution to one-half m is greater than or equal to negative seven elevenths

Solve for m:

⇒ -1/2m(-2) ≥ 7/11(-2)

m ≤ -14/11 [Because we are multiplying both sides by a negative value, the sign shifts]

The solution to the inequality is m ≤ -14/11 which the graph is attached below for m ≤ -14/11.

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3:4 ratio

height: 52 in

width: height * 4/3 = 52*4/3 = 208/3 in

Area of the TV: height*width = 52*208/3 = 3605 1/3 square inches

9:16 ratio

height: 52 in

width: height * 16/9 = 52*16/9 = 832/9 in

Area of the TV: height*width = 52*832/9 = 4807 1/9 square inches

Then, the difference in the areas is: 4807 1/9 - 3605 1/3 = 1201 7/9 square inches

The sum of the two numbers 1,235,721 and 9,576,345,123 is 9,577,580,844 after applying the arithmetic operation.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

It is given that:

= 1,235,721 + 9,576,345,123

The above number expression is representing the sum of two big numbers.

After applying the arithmetic operation on the number expression:

1,235,721 + 9,576,345,123 = 9,577,580,844

Thus, the sum of the two numbers 1,235,721 and 9,576,345,123 is 9,577,580,844 after applying the arithmetic operation.

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ANSWER

EXPLANATION

We have that Sarah got a $60 gift card to use in Walmart.

This means that everything she can buy cannot be worth more than $60 (i.e. less than or equal to $60).

She buys orange juice for $4.50 and she wants to buy shirts (which cost $2.29 each)

Let n be the number of shirts Sarah wants to buy.

This means that the cost of n shirts is $2.29n.

Recall that she can only spend less than or equal to $60. This means that the sum of the cost of the orange juice and n shirts is less than or equal to $60.

That is:

That is the inequality that represents the situation.

The total area of all exposed surfaces of a geometric solid is called surface area .

The area is the entire amount of space filled by flat or two-dimensional objects. In other words, the number of square units that cover the surface of a closed figure is used to represent its area.

It is quantified in square inches, or square units. The area only has length and width since 2-dimensional shapes can be measured using them.

The area is a two-dimensional measurement of the size of a flat surface, whereas surface area is a measurement of a solid shape's exposed surface (three-dimensional).

The main distinction between area and surface area is this. However, both amounts are expressed in square units, which is the same for both. Learn the distinction between area and volume as well.

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Given:

x > 3 and x < 5

The inequality compound is:

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following formula for the statement

They ask us to rewrite this formula solving for the total price of the computer, it would be like this:

A triangle, when rotated about one of its sides will generate a solid in a form of a Cone.

The cone could be a hollow one or a solid-filled one, depending on the properties of the triangle being rotated.

Therefore, the shape generated is a cone.

Answer: D.

Answer:

17 53/60

Step-by-step explanation:

Answer: x > -3 or x < -5

Step-by-step explanation:

The function is positive when y > 0.

So if we make this function into an inequality, we can solve for the values of x.

0 < |x + 4| -1

1 < | x + 4 |

Absolute values make the answer always positive despite the sign so now we have to solve for x when x + 4 > 1 and when x + 4 > -1.

x = 1 - 4 = -3

x = -1 -4 = -5

So for the function to be positive,

x > -3 or x < -5

If it is given  f(x) = 3x− 6 and g(x) = 2- x² then f(g(x)) = -6x².

To solve this problem we have to know more about mathematical functions.

What is a mathematical function?

A mathematical function is a such type of mathematical device as it establishes a special type of relation which provides an output concerning an input.

Example:  f(x) = x²+ 2 where f(x) is a function of x where x is the input. If x = 3 then the output value of f(x) = 3²- 2 = 9-2 = 7.

Here we have to calculate, f(g(x)) where f is a function of g(x) and g(x) is a function of x.

g(x) = 2- x².

f(x) = 3x - 6.

Therefore,

f(g(x)) = 3( 2- x² ) - 6.                 [where g(x) = 2- x²]

So,  f(g(x)) = 3( 2- x² ) - 6 = 6 -6x² -6 = -6x²

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The complete question:

Given that f(x) = 3x − 6 and g(x) = 2 - x² , calculate f(g(x))

Answer:

1 and 7 and 0

Step-by-step explanation:

Answer:

D. In the ordered pair (9,7), 7 is the x-coordinate

Explanation:

The ordered pairs have the form (x, y) where the first number is the x-coordinate and the second number is the y-coordinate. So, in the ordered pair (9, 7), 7 is the y-coordinate. This makes the last statement false and the answer is

D. In the ordered pair (9,7), 7 is the x-coordinate.

Answer

Rate = 800 copies per minute

Explanation

Work = rate x time

Work = 2400 copies

Time = 3 minutes

Rate = work / time

Rate = 2400 / 3

Rate = 800 copies per minute

Therefore, rate is 800 copies per minute

Answer: 55

Step-by-step explanation: It makes sense

a) We have to calculate the total reimbursement.

We can list the types of lunches and reimbursements for each:

0. Free lunches: the school served 29,000 free lulnches and will receive $2.68 for each one.

1. Reduced-price lunches: the school served 19,000 reduced-price lunchs and will receiv $2.28 for each one.

2. Full price lunches: the school seved 51,000 regular-price lunches and will receive $0.25 for each one.

Then, we can calculate the total reimbursement as:

The lunch reimbursement should be $133,790.

b) The milk reimbursement can be estimated as $0.035 per lunch, so it can be calculated as:

The milk reinbursement is $3,465.

c) We can calculate the total reinbursement as the sum of the lunch reinbursement and the milk reinbursement:

The total reinbursement is $137,255.

d) We can calculate the average reinbursement per lunch dividing the total reinbursement by the number of lunches:

The average reinbursement is $1.39 per lunch.

A rotation of 270 degrees counterclockwise is the same as a rotation 90 degrees clockwise.

This rotation will make a point from the first quadrant go to the fourth, from the second to the first, from third to second and from fourth to third.

If the point goes from the first quadrant to the fourth, we change the signal of the x-coordinate.

If the point goes from the second quadrant to the first, we change the signal of the y-coordinate.

If the point goes from the third quadrant to the second, we change the signal of the x-coordinate.

If the point goes from the fourth quadrant to the third, we change the signal of the y-coordinate.

Also, in all those rotations, we need to switch the x and y coordinates between themselves.

So we have that:

From the given equation 13x + 5y - 2 = 3, we can tell that;

Variables are; x and y

Coefficients are; 13 and 5

Constants are; -2 and 3

We are given the equation;

13x + 5y - 2 = 3

A variable is a term that is subject to change and is not fixed. Thus, in our expression, the variables are x and y.

Now, the constants are terms that a single without a variable attached to them. Thus, in our expression, the constants are -2 and 3

The coefficients are basically the numbers that are attached to the variables. Thus, the coefficient of x is 13 and the coefficient of y is 5.

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Congruent shapes are produced by combining the three different transformations—rotations, reflections, and translations. Actually, by combining one or more of these three transformations, any pair of congruent shapes can be matched to one another.

A point, line, or geometric figure can be transformed in four different ways, each of which alters the shape and/or placement of the object. While Image refers to the position and ultimate shape of the object, Pre-Image refers to the shape of the thing as it was before alteration.

Given Data

We now understand that the size and shape of the figures are preserved during stiff transformations (reflections, translations, and rotations). The pre-image and the actual image concur all the time.

The following Matt's transformational skills:

Reflection

Since the reflection maintains its original shape, The line of reflection remains the same distance away from comparable points from the pre-image to the image.

As a Congruence Transformation, rotations

Rotating a figure causes it to twist. Even though the figure is the same size and shape as before, it appears to have toppled over. A clock is a fantastic example of how the earth actually rotates. Every hour or every day, the clock's connecting arms revolve around their axis. A rotation's degree determines what it is, and common rotations include 90, 180, and 270 degrees. Before going back to its original position, the figure rotates a full 360 degrees. the direction of a rotation, whether it is counterclockwise or clockwise. It is possible to determine the degree, amount, and the revolution's direction.

Transformation based on translational congruence

When an object or shape is transported from one location to another without changing its size, shape, or orientation, the movement is referred to as a translation. During a translation, also known as a slide, every point on an object or shape is moved by the same amount and in the same direction.

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The expected value is given as:

then in this case we have:

therefore the expected payoff is $8.52

Answer:

Let [tex]g[/tex] equal the number of games.

Let [tex]r[/tex] equal the number of rides

System of Equations

[tex]2.50g+4r=52.50[/tex]

[tex]r=2g[/tex]

Step-by-step explanation:

One game costs $2.50, so [tex]g[/tex] games cost [tex]2.50g[/tex]. One ride costs $4.00, so [tex]r[/tex] rides cost [tex]4r[/tex]. The total [tex]2.50g+4r[/tex] equals $52.50: [tex]2.50g+4r=52.50[/tex]

Since Stella's number of rides she went on is twice the number of games she played, there are two times the number of games for her number of rides. [tex]r=2g[/tex]

The most appropriate choice for function can be given by

q[tex]o[/tex]p(3) =  [tex]\sqrt{15}+1[/tex]

p[tex]o[/tex]q(3) =  [tex]2\sqrt{3} + 10[/tex]

What is function?

A function from A to B is a rule that maps to each element of A a unique element of B.

A is called the domain of the function and B is called the co domain of the function.

We can do addition, subtraction, multiplication, division and composition on functions.

Let f and g be two functions

f[tex]o[/tex]g(x) = f(g(x)) and g[tex]o[/tex]f(x) = g(f(x))

This is known as composition of function.

Here,

[tex]p(x) = x^2 + 6\\q(x) = \sqrt{x} +1[/tex]

q[tex]o[/tex]p(x) = q(p(x))

          =[tex]q(x^2+6)[/tex]

          = [tex]\sqrt{x^2+6}+1[/tex]

q[tex]o[/tex]p(3) = [tex]\sqrt{3^2+6}+1[/tex]

          = [tex]\sqrt{15}+1[/tex]

p[tex]o[/tex]q(x) = p(q(x))

          = p([tex]\sqrt{x}+1[/tex])

          = [tex](\sqrt{x}+1)^2+6[/tex]

          = [tex]x + 1 + 2\sqrt{x} + 6[/tex]

          = [tex]x + 2\sqrt{x} +7[/tex]

p[tex]o[/tex]q(3) = [tex]3 + 2\sqrt{3} +7[/tex]

               [tex]2\sqrt{3} + 10[/tex]

               [tex]2\sqrt{3} + 10[/tex]

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Answer:

the answer is true

Step-by-step explanation:

Victor earns 19% commission

He sold a microscope that cost $368.84.

so, the commission = 19% of $368.84 = 0.19 * 368.84 = 70.0796

Rounding to the nearest cent

So,

the commission = $70.08