Choose the answer that best completes the sentence.

The inequality statement comparing m and n is m > n.

The inequality is true because m is further along the number line than n

It should be noted that an inequality is simply used to express the information given hat aren't equal.

Based on the number line that's drawn we came we that is close to 3 and n is close to 1.

Therefore, this shows that m is greater than n.

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The required solution of given polynomial equation is [tex]x+1-\frac{8}{2x+5}[/tex] .

Given polynomial equation is [tex]2x^{2}+7x-3[/tex] which is to be divided by [tex]2x+5[/tex]

In case of division of polynomials we Long division method to calculate final value of the given equation.

For solving given equation let us start from;

[tex]\frac{2x^{2} +7x-3}{2x+5}[/tex] = [tex]x+\frac{2x-3}{2x+5}[/tex]

[tex]x+\frac{2x-3}{2x+5}[/tex] = [tex]x+1 +\frac{-8}{2x+5}[/tex]

[tex]x+1-\frac{8}{2x+5}[/tex]

The final solution for given equation is [tex]x+1-\frac{8}{2x+5}[/tex]

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Answer:

Step 2

Step-by-step explanation:

In basic algebra, if one side is positive then you must subtract on both sides, and if one side is negative then you must add on both sides to isolate the x variable.

The area of rectangle B is 560 square inches.

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle.

Given that,

Scale factor = 4

Rectangle A has

length = 5 inches

breadth =  7 inches

Area of a rectangle A = length×breadth

                                    = 5×7

                                    = 35 square inches

Scale factor is 4 so length and width of a new rectangle is

length = 5×4 = 20 inches

breadth =  7×4 = 28 inches

Area of a rectangle B = length×breadth

                                    = 20×28

                                    = 560 square inches

Hence, The area of rectangle B is 560 square inches.

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Answer:

m = 14

Step-by-step explanation:

-(5m+11) = 3 (m - 41)

-5m -11 = 3m - 123

-5m -3m = -123+11

-8m = -112

m = -112/-8

m = 14

Answer:

Solutions Below.

Step-by-step explanation:

These questions test on the concept of Functions Substitution.

Function Substitution is about giving an input (domain) to a function to produce an output (range)

Example: f(x) = 9x , f(9) = 9(9) = 81

We are given the following function:

f(x) = 10x + 8, where we can express it as

y = 10x + 8

Now we can find the value of f(5) by substituting x = 5 into the function. (Meaning: Find the value of y when x = 5.)

f(5) = y = 10(5) + 8 = 50 + 8 = 58

Next, applying the same concept, we can find the value of f(-7) by substituting x = - 7 into the function. (Meaning: Find the value of y when x = -7.)

f(-7) = y = 10(-7) + 8 = -70 + 8 = - 62

This last question requires us to work in reverse, where we find the value of x when f(x) = y = 88.

f(x) = y = 10x + 8

10x + 8 = 88

10x = 88 - 8

10x = 80

x = 80 ÷ 10 = 8

The correct statement is  f minus 7 over 8 is greater than negative 2 over 3. Option C

Inequalities are defined as mathematical relation with an unequal comparison between two numbers, elements, quantities or mathematical expressions.

They are mostly used in the comparison of two numbers on the number line on the basis of their size of magnitude.

From the information given, we have that;

Let the number be f

This is expressed as;

f - 7/8 > -2/3

This is written in word form as;

f minus 7 over 8 is greater than negative 2 over 3

Hence, the expression is f - 7/8 > -2/3

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Answer:

Step-by-step explanation:

c i have spoken

A. The lines with equation 3x - 4y = 6 and 3y = -4x + 9 are perpendicular

B. The lines with equation y = 1⁄2x - 7 and 6x - 12y = 24 are parallel

From the equation of lines, we can detect if they are parallel or perpendicular as follow:

With the above information, we can obatin the answer to the questions. Details below

For question A.

We shall determine the slope of each line. This can be obtained as follow:

3x - 4y = 6

Rearrange

4y = 3x - 6

y = 3/4x - 6/4

Comparing y = 3/4x - 6/4 with y = mx + c, the slope is 3/4

3y = -4x + 9

y = -4/3x + 9/3

Comparing y = -4/3x + 9/3 with y = mx + c, the slope is -4/3

m₁ × m₂

3/4 × -4/3 = -1

Thus, we can say: 3x - 4y = 6 and 3y = -4x + 9 are perpendicular

For question B.

We shall determine the slope of each line. This can be obtained as follow:

y = 1/2x - 7

Comparing y = 1/2x - 7 with y = mx + c, the slope is 1/2

6x - 12y = 24

Rearrange

12y = 6x - 24

y = 6/12x - 24/2

y = 1/2x - 12

Comparing y = 1/2x - 12 with y = mx + c, the slope is 1/2

m₁ = m₂

Thus, we can say: y = 1/2x - 7 and 6x - 12y = 24 are parallel

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The solution of the inequality (x-3)(x-5) ≥ 0 is union of two intervals

 (-∞,3] or  [5,∞) that is x ≥5 or x≤3

An inequality is a statement that compares two expressions using ≤, ≥, <, > .

We can solve an inequality by adding same number to both sides or by subtracting same number from both side. While adding or subtracting the sign of the inequality will not change.

Given inequality (x-3)(x-5) ≥ 0

It generates two cases either case1 is true or case 2.

Case1.   (x-3)(x-5) ≥ 0 when (x-3) ≥0 and (x-5)≥0

       ⇒(x-3) ≥0 and (x-5)≥0

     ⇒ x ≥ 3 and x ≥ 5

     ⇒ x ∈ [3,∞) and x∈ [5,∞)

    ⇒  x ∈ [3,∞) ∩[5,∞)

    ⇒ x ∈ [5,∞)

∴ x is greater than or equal to 5

Case 2: (x-3)(x-5) ≥ 0 when (x-3) ≤0 and (x-5)≤0

      ⇒(x-3) ≤0 and (x-5)≤0

     ⇒ x ≤3 and x ≤ 5

     ⇒ x ∈ (-∞,3] and x∈ (-∞,5]

    ⇒  x ∈ (-∞,3] ∩ (-∞,5]

    ⇒ x ∈  (-∞,3]

∴ x is less than or equal to 3

Solution of the given inequality is case 1 or case 2

⇒  x ∈ [5,∞) or  x ∈  (-∞,3]

⇒ x  x ∈  (-∞,3] ∪ [5,∞)

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Answer:  

800,000

Step-by-step explanation:

Answer:

B. x = -3

Step-by-step explanation:

f(x) = y

or however the vertical axis is called.

that is just something you always have to consider.

so, for what value of x does the functional curve ever reach the result (y) value of 3 ?

imagine a horizontal line you put through y = 3.

at what points is the functional graph touching or intersecting this line ?

at exactly 1 point. and that is at x = -3.

Answer:

If you’re in the mood for a scary movie, you may want to check out one of the five most popular horror movies of all time—I am Legend, Hannibal, The Ring, The Grudge, and The Conjuring. Figure 1 shows the amount, in dollars, each of those movies grossed when they were released as well as the ticket sales for horror movies in general by year. Notice that we can use the data to create a function of the amount each movie earned or the total ticket sales for all horror movies by year. In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this section we will investigate methods for determining the domain and range of functions such as these.

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=30x+65

y=30(3)+65

y=90+65

y=155

The equivalent expression is (-2)^2. Option D

Index forms are simply defined as mathematical expressions with a number or element raised to a variable or number.

Example for index forms are;

2^7

5^2

6^x

2^y

Equivalent expressions are defined as algebraic expressions that are equal to each other but have different arrangement of its values or elements.

From the information given, we have that;

Now, substitute the values, we have;

(-2)^4/(-2)^2

Take inverse of the power

(-2)^4 - 2

Subtract the values

(-2)^2

Hence, the expression is (-2)^2

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The complete question:

Choose an expression that is equivalent to negative two raised to the fourth power divided by negative two raised to the second power.

a. 6

b. (-2)^4

c. 8

d. (-2)^2

Answer:

d

Step-by-step explanation:

Answer:

BC = 10

Step-by-step explanation:

given CD ≅ BC , then

BC = CD , that is

3x + 1 = 13 - x ( add x to both sides )

4x + 1 = 13 ( subtract 1 from both sides )

4x = 12 ( divide both sides by 4 )

x = 3

Then

BC = 3x + 1 = 3(3) + 1 = 9 + 1 = 10

The number of the total students that are at the school is 570 if the ratio of boys to girls in a school is nine: ten and there are 300 girls at the school.

The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.

Given that a and b are separate amounts for two quantities, the combined total quantity is denoted as (a + b).

Three steps are necessary to determine the ratio of three numbers:

Step 1: Add the ratio's numbers together to determine the total number of pieces.

Step 2: By dividing the given sum by the total number of parts, determine the value of each component in the ratio.

Step 3: Divide the original ratio by the sum of each component's values.

The ratio is given as 9:10 as boys to girls.

Number of girls = 300

Thus, girls will be 10x and boys will be 9x

then 10x = 300

⇒x = 30

Then we can calculate the number of boys as

9x = 9*30

=270

Thus, the total number of students in the school

= exact number of girls + exact number of boys

= 300 + 270

= 570

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The equation that passes through the given points is the 3 option which is y = -3/2 x + 5

A x + B y = C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x + 3y = 5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y). An algebraic equation with simply a constant and a first-order (linear) term, such as y = mx +b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Ax + b = 0, where a and b are two integers, and x is a variable, is an example of a linear equation with one variable. This equation has only one solution. 2x + 3 = 8, for instance.

According to the given points

x = -1

So

y = (-3/2)(-1) + 5

y = 6.5

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To solve the inequality given by -n/7 ≤ 14 , -7 should be multiplied to both sides of the inequality .

Any monotonically rising function can, by definition, be applied to both sides of an inequality without changing their connection to one another (provided that both expressions are in the domain of that function).

The inequality is -n/7 = 14

or, -n ≤ 14 × 7

or, -n ≤ 98

or, n ≥ -98

Therefore the first step is solve the inequality is to multiply both sides by 7.

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The difference between the numerator and denominator of the fraction parameters is 40

From the question, the fraction is given as

5/3

The above fraction can be represented as

5x/3x

This is so because of the following equation

5x/3x  = 5/3

The above is calculated by dividing the numerator and the denominator by the common factor x

Solving further, we have

Sum of the numerator and denominator = 160

This means that

5x + 3x = 160

Evaluate the sum in the above equation

So, we have

8x = 160

Divide both sides of the fraction by 8

So, we have

x = 20

The required difference is represented as

Difference = 5x - 3x

Evaluate

Difference = 2x

Substitute x = 20 in Difference = 2x

So, we have

Difference = 2 x 20

Evaluate

Difference = 40

Hence, the difference between the fraction parameters is 40

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Answer:

2/5

Step-by-step explanation:

8+12=20

8/20 12/20

8 ÷ 4= 2

20÷4= 5

2/5

Answer:

the anwser is 180

Step-by-step explanation:

Answer:

  a drop of 5 degree F, or -5 °F

Step-by-step explanation:

You want to know the total change in temperature after a drop of 2 degree F and a second temperature drop of 3 degree F.

The total change will be the sum of changes.

We can figure the total drop in temperature as the sum of drops:

  2 °F +3 °F = 5 °F . . . . the total drop in temperature

If we use negative values to represent temperature drops, then the total change can be written as ...

  (-2 °F) +(-3 °F) = -5 °F . . . . . the total change in temperature

__

Additional comment

We often find it convenient to use negative numbers to represent decreases, drops, amounts below some reference level, and so on. Positive numbers can be used for the same purpose if we define the meaning of a positive number in the context.

Here, we can identify a temperature drop by saying it is a drop of 5 degrees, where a positive temperature drop means a change to a lower value. Or, we can say it is a change of -5 degrees, where a positive change is defined as a change to a higher value.

Defining the meaning of positive and negative numbers is especially important when an "improvement" is a reduction in some value (cost, for example). A positive improvement may mean a negative change, and vice versa.

The value of y in the equation 1/2 = 1/4y + 1/8y when solved is y = 4/3 .

A linear equation in one variable is defined as an equality between two expression either or both containing the variable .

The given expression can be written a linear equation of the form :

1/2 = 1/4y + 1/8y

Simplifying the equation we get :

y = 4 / 3

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Answer:

x = 200

Step-by-step explanation:

a) Simplify both sides of the equation.

1/5x - 2/3(15) = 30

1/5x + -10 = 30

1/5x - 10 = 30

b) Add 10 to both sides.

1/5x - 10 + 10 = 30 + 10

1/5x = 40

c) Multiply both sides by 5.

5 * (1/5x) = (5) * (40)

x = 200

Answer:

a = 5

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

          = [tex]\frac{4+6+4+7+8+a+6+7+7}{9}[/tex] = 6 ( multiply both sides by 9 to clear fraction )

49 + a = 54 ( subtract 49 from both sides )

a = 5

Answer:

Step-by-step explanation:

it would be a 20% tip

Answer:

3.75

Step-by-step explanation:

5% of 75 is 3.75

Let's use the variable x to represent the length of the paper and y to represent the width of the paper.

If there are margins of 1 inch along the sides and 3 inches along the top and bottom, and the area with printer matter is 27 in², we can write the equation:

Solving for x, we have:

Then, the equation that we want to minimize is the area equation, so:

The critical points of this function are:

y = 0 (one of the roots)

y = -15/2 (one of the roots)

y = 6 (function is not defined)

Answer: look it up on calculator

Step-by-step explanation:

The distance between two points can be calculated using the formula;

For points;

Given the points;

The distance between the two points can be calculated using the above formula;

The distance between the two points is;

Answer:

(9, 1 )

Step-by-step explanation:

a translation 2 units right means add 2 to the x- coordinate

a translation of 1 unit up means add 1 to the y- coordinate.

(7, 0 ) → (7 + 2, 0 + 1 ) → (9, 1 )