The product of two positive integers is always

Answer: x = pm - n

Step-by-step explantake every value on the right to the left ( this also changes the action for that specific value)

Answer: p x m-n = x

Step-by-step explanation: First, minus n on both sides. This will give you m-n =x/p. Then, multiply P on both sides. This will give you p x m-n =x

Answer:

2.5

Step-by-step explanation:

15/6 (3p + 3s) = 2.5
18/7 (4p + 3s) = 2.5

The integer fraction of the expression 14x⁻², for x = 7 is 2 / 7.

The expression is expressed as follows:

14x⁻², for x = 7

This simply implies we have to simplify the expression when x = 7.

Therefore, we have to substitute the value of x in the expression. The value of x is 7.

Hence,

using indices law,

x⁻¹ = 1 / x

Therefore,

14x⁻² = 14 / x²

Hence,

14 / x² = 14 / 7²

14 / 7² = 14 / 49

14 / 49 ÷ 7 / 7 = 2 / 7

Therefore, the integer fraction of the expression 14x⁻², for x = 7 is 2 / 7.

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The inverse function is given by f⁻¹(x)=∛x+2 and the inverse is a function.

The opposite function is referred to as the inverse of a function. To map the dependent variable y based on the independent variable x, we should ideally utilize a function. The relationship that determines the value of x based on a certain value of y is known as an inverse function.

The domain of a function shifts to the range for an inverse function, and vice versa.

For a function that is mathematically denoted by the formula y=g(x), where g(x) is a polynomial of x. We use y to solve the equation for x.

Given function is in the form  f(x)=(x-2)³

It can be written as

y=(x-2)³

Then we take the cube root on either sides of the equation.

∛y=x-2

or, x=∛y+2

So the inverse function is:

f⁻¹(x)=∛x+2

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36 students will be in each buses for the trip.

The total number of empty seat in the buses is 32

The school ordered 16 buses that each have 40 seats for a school trip.

There are 32 teachers and 576 students.

Each bus must have 2 teachers and the rest students.

The students were distributed evenly amongst the buses.

Therefore,

number of student in each buses = total number of student / number of buses

number of student in each buses =  576 / 16

number of student in each buses = 36

Therefore, 36 students will be in each buses for the trip.

Each buses has 40 seats.

Recall, 2 teachers are even distributed in each buses.

Therefore

number of empty seat in total = 16 × (40 - 36 - 2)

number of empty seat in total = 16 × 2

number of empty seat in total = 32

Therefore, the total number of empty seats in the buses is 32.

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Your question was incomplete. Please refer below to find the table in the image.

We need to know about powers and indices to solve the problem. The value of nonzero number raised to the power of 0 is 1.

When a number is raised to a certain power, it can be simplified as the number is multiplied to itself the number of times as the power. For example if we write [tex]2^{3}[/tex] we mean 2x2x2 which is 8. Similarly in this question we have to find the various powers of 9, the answer to [tex]9^{4}[/tex] is given, we need to find for the powers 3,2,1, and finally 0.

[tex]9^{3}[/tex]=9x9x9=729

[tex]9^{2}[/tex]=9x9=81

[tex]9^{1}[/tex]=9

[tex]9^{0}[/tex]=1

When any nonzero number is raised to the power of zero the result is one.

Therefore we found out using the concept of powers and indices that the value of a nonzero number raised to the power of 0 is 1.

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Answer:

$-49

Step-by-step explanation:

If he has $42 in his savings account and he takes $7 a week for 13 weeks, we have to multiply 7x13 to find out how much money he takes out of the account.

7x13=91, 91 is more then how much he has in his account so he will be in debt?
42-91=-49

The multiplication equations are :

a. 10 ÷ 5 =  2 × 5 = 10 and  5 × 2 = 10

b. 4.5 ÷ 3 = 3 × 1.5 = 4.5 and1.5 × 3 = 4.5

A complete multiplication equation will have the numbers that are being multiplied together on one side of the equal sign, and what they are equal to on the other side of the equal sign.

a. 10 ÷ 5 = ?

First we will solve the given equation

so, 10 ÷ 5 = 2

In simple way we can write the multiplication equation of above equation in two ways :

First we can write it as 2 × 5 = 10

And second is as         5 × 2 = 10

These two don't have different conclusion but they have just different written pattern.

Same as we will do the other equations.

b. 4.5 ÷ 3 = ?

Let's solve the equation first

4.5 ÷ 3 = 1.5

Multiplication equation :

3 × 1.5 = 4.5

1.5 × 3 = 4.5

c. 1/2 + 4 = ?

Solution of the above equation is :

1/2 + 4 = 9/2 = 4.5

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The equation of the graph that is obtained by translating the parent function is as follows:

g(x) = |x + 2| + 1

The parent function is given as

f(x)= |x|

The following is a translation of the parent function f(x), which may be derived from the graph as follows:

2 units left translation

1 unit up translation

The translation of the sequence mentioned above is expressed as

(x, y) = (x + 2, y + 1)

So, we have

g(x) = |x + 2| + 1

Therefore, the equation of the graph that has been translated is g(x) = |x + 2| + 1

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Answer:

7(n+8)

Step-by-step explanation:

It says 7 times the SUM of a number, n, and 8. According to the order of operations or PEMDAS, you would find the sum first, which would be in parenthesis, and then multiply by the 7.

Hope this helps! :)

The value of the term 9w using the slope of the line is found as 54.

As per the given question;

The slope of the line is given as;

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = m = -1/9

The two coordinates from where the line is passing is (w, -2) and (3, -3).

Thus,

(x₁, y₁) = (w, -2)

(x₂, y₂) = (3, -3)

Put the values in the slope equation;

m = (y₂ - y₁)/(x₂ - x₁) = -1/9

(-3 + 2)/(3 - w) = -1/9

Cross- multiplying the terms;

9(-3 + 2) = -(3 - w)

Simplifying;

-9 = -3 + w

w = 6

The value of 9w = 9×6

9w = 54.

Therefore, the value of 9w is found as 54.

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√6 is greater than √2+1.

Suppose that √6 is greater than √2+1. Then we check if our assumption is correct.

So √6 > √2+1

Squaring both sides and using the identity [tex](a+b)^2=a^2+b^2+2ab[/tex],

⇒ 6 > 3 + 2√2

Subtracting 3 from both sides,

⇒ 3 > 2√2

Again squaring on both sides,

⇒ 9 > 8

This is true. So our assumption is right.

Therefore,  √6 > √2+1

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Jordin after working for 23 hours and 15 minutes would be paid $302. 25

From the information given, we have that;

Let's convert the minutes to hour

60 minutes is equivalent to 1 hour

Then 15 minutes is equivalent = x hour

cross multiply

x = 15/ 60

x= 0. 25 hour

He worked = 23 + 0. 25 = 23.25 hours

Then,

$13. 00 = 1 hour

$x = 23. 25

cross multiply

x = 13 × 23. 25

x = $302. 25

Thus, Jordin after working for 23 hours and 15 minutes would be paid $302. 25

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Answer:

(-2, -2)

Step-by-step explanation:

The point U, when rotated 270 degrees, will end up at the point (-2, -2) on the graph.

Answer: Solution is where the x intercepts on the graph

Step-by-step explanation:

Answer:

Step-by-step explanation:

11. Areas as Sum: 7d+28

   Areas as Product: 7(d+4)

12. Areas as Sum: [tex]y^{2}[/tex]+3y

    Areas as Product: y (y+3)

Answer:

Step-by-step explanation:

Using the distributive property, you would multiply 7(d+4) for the question after the example. The side length is your root, and you are multiplying the numbers after it by that root.

Answer:

[tex]4\frac{1}{2} [/tex]

Step-by-step explanation:

To make the division easier, we will convert them to improper fraction first.

[tex]12 \frac{3}{8} \div 2 \frac{3}{4} \\ = \frac{99}{8} \div \frac{11}{4} [/tex]

Now we will change the sign to multiply and swap the numerator and denominator of the divisor fraction.

[tex] \frac{99}{8} \div \frac{11}{4} \\ = \frac{99}{8} \times \frac{4}{11} \\ = \frac{396}{88} \\ = \frac{9}{2} = 4 \frac{1}{2} [/tex]

Answer: 72 degrees

Step-by-step explanation:

ok, so the interior angles of a pentagon are 108 degrees, and the line that the two angles are on is equal to 180 degrees, so 180-108 is 72 degrees

The situation is a function; the independent variable is the number of lines and the dependent variables is the total cost

The domain is 0 <= x <= 4 and the range is 0 <= y <= 120

The statement is given as

A cell phone plan costs $30 for each line

Let the number of lines be x and the total cost be y

So, we have

y = cost per line * x

This gives

y = 30x

The above equation represents a linear function

This means that the situation is a function; the independent variable is the number of lines and the dependent variables is the total cost

From the question, we have

You can have a maximum of four lines on a plan.

This means that the possible values of x are

x = 0, 1, ... 4

When these values are substituted in y = 30x, we have

y = 30 * 0 = 0

y = 30 * 4 = 120

Hence, the domain is 0 <= x <= 4 and the range is 0 <= y <= 120

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Answer:

Step-by-step explanation:

I’m pretty sure x= 10

Answer:

x=6

Step-by-step explanation:

Answer:

63/2

Step-by-step explanation:

Multiply the fraction.

[tex]\frac{9}{4}\cdot \:14\\=\frac{9}{4}\cdot \frac{14}{1}\\=\frac{9\cdot \:14}{4\cdot \:1}\\=\frac{9\cdot \:14}{4}\\=\frac{9\cdot \:2\cdot \:7}{4}\\=\frac{9\cdot \:2\cdot \:7}{2\cdot \:2}\\=\frac{9\cdot \:7}{2}\\=\frac{63}{2}[/tex]

Answer:

63/2

Step-by-step explanation:

[tex]\frac{9}{4}[/tex] [tex](\frac{14}{1})[/tex]  You can write 14 as a fraction by putting it over 1.

Now, multiple across

[tex]\frac{126}{4}[/tex]

Now divide the top and the bottom by 2

[tex]\frac{63}{2}[/tex]

The thing that intuition says about the degree measures of these angles is that ABC and DEF are supplementary angles.

It should be noted that the given measures are ABC = 70° and DEF = 110°

it should be noted that supplementary angles are the angles that have the addition as 180°.

In this case,

ABC + DEF

= 70° + 110°

= 180°

Therefore, the thing that intuition says about the degree measures of these angles is that ABC and DEF are supplementary angles.

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Answer:

line segment

Step-by-step explanation:

I'm no Einstein, but that looks like a line segement

ngl

The rationalization of the  denominator is  4√3 / 6 .

We have given a fraction √8/√6 .          ...(1)

The denominator of the fraction is √6.

Multiplying and dividing by √6 in equation (1), we get

√8/√6 = √8 × √6 /√6 × √6

           = √48 /6

          = 4√3 / 6

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After factorizing the expression we get: (2x ₋ 1) (2x ₋ 3) as factors of the expression.

Given the expression is 4x² ₋ 8x ₊ 3 = 0

factorize the expression.

The word "factor" is used to describe a number as the result of any two other numbers. Any mathematical object, including numbers, polynomials, and algebraic expressions, can have factors by using the factorization method. Finding the factors of a given algebraic expression is referred to as factorization of an algebraic expression.

4x² ₋ 8x ₊ 3 = 0

4x² ₋ 2x ₋ 6x ₊ 3 = 0

2x(2x ₋ 1) ₋ 3(2x ₋ 1) = 0

(2x ₋ 1) (2x ₋ 3)

Hence we get the factors of the expression as (2x ₋ 1) (2x ₋ 3)

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The area of the whole figure includes the areas of the rectangle and the two triangles and the value is 60 square units

The area of a shape is the amount of space on the shape.

For most regular shapes, the area is the product of their width and the length

Rectangle A

The dimensions of this rectangle are

Length = 8

Width = 10 - 5 = 5

The area of the rectangle is

Area = Length * Width

This gives

Area = 8 * 5

Evaluate the product

Area = 40

Triangle B

The dimensions of this rectangle are

Base = 6

Height = 10 - 5 = 5

The area of the triangle is

Area = 0.5 * Base * Height

This gives

Area = 0.5 * 6 * 5

Evaluate the product

Area = 15

Whole figure

The area of the whole figure is

Area = Rectangle A + Triangle B + Triangle C

This gives

Area =

Evaluate the product

Area = 40 + 15 + 5

Evaluate

Area = 60

Hence, the area of the whole figure is 60 square units

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The form of the linear equation y = -5x/4 + 5/4 is 0 = 5x + 4y - 5

The linear equation is given as

y = -5x/4 + 5/4

Multiply through the equation by 4

So, we have

4 * y = -5x/4 * 4 + 5/4 * 4

Evaluate the product in the above equation

So, we have

4y = -5x + 5

Collect the like terms in the above equation

So, we have

5x + 4y - 5 = 0

Rewrite as

0 = 5x + 4y - 5

Hence, the form of the linear equation y = -5x/4 + 5/4 is 0 = 5x + 4y - 5

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