[02.06]
Solve and graph the absolute value inequality: 12x + 4 > 8. (1 point)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
5 6 7 8 9
-9-8-7-6-5-4-3 -2 -1 0 1 2 3 4 5 7 8 g
-9-8-7 -6 -5 -4 -3 -2 -1 0 1
2
3
4
5 6
7
8 9

A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas.  

A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas. Every variable in the equation "literally" represents a crucial aspect of the overall relationship that the equation expresses. Multiple letters or variables make up a literal equation. Examples include the formula for calculating speed (v=Dt) and the area of a circle (A=r2). In this part, we resolve straightforward one-variable equations.

Alternatively,

Ax +By = C

Any sign that crosses over equal(=) signs always change

In this case, Ax crosses over to C

By = C - Ax

To eliminate y from By, then

By/y = (C - Ax) /y

y cancel out y on the left side

B  = (C - Ax) /y

The complete question is,

Solve for B in the literal equation Ax+By=C

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, The constant proportionality is 3

What is Proportionality Constant ?

The proportionality constant is the ratio between two variables that varies directly . For directly proportional variables, their ratio is always a constant and this constant is the proportionality constant.

Now, We have the equation is:

y = 3x

To get the constant of proportionality,

we will derive both sides of the equation by x.

y/x = 3x/x

y/x = 3

Hence, The constant proportionality is 3

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The area of rectangle in square inches is 8649 inches .

The subject of mathematics known as mensuration is concerned with measuring geometric shapes and their various characteristics, such as length, volume, shape, surface area, lateral surface area, etc. In fundamental mathematics, learn about mensuration.

Mensuration is the name given to the area, volume, and length of various geometric shapes in mathematics. These shapes can be found in either two or three dimensions.

Mensuration is the process of calculating various shape parameters, such as the perimeter, area, and volume, whereas geometry is the study of the characteristics and relationships between the points and lines that make up different shapes.

the area of rectangle will be =  length *  width

therefore just substituting the values given in the question

thus ,

area will be = 279 * 31

                    = 8649 square inches

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Answer:

i hope i can answer your question

Step-by-step explanation:

Amber wants to have $300,000 so i don't see another number that you can solve on maybe type that first so i can answer please

The pounds of the less expensive tea used in the mixture is 10 pounds.

The correct option is Option(1) 10.

Given:

Price of less expensive tea = $2.00

Price of expensive tea = $5.00

Price of custom-blended tea = $4.25

The total price of 40 pounds of custom blended tea = 40 × $4.25

                                                                                       = $170

Let the pounds of the less expensive tea used in the mixture be x pounds.

So, the pounds of expensive tea = 40-x

Now, the equation is

2x + 5(40 - x) = 170

2x + 200 - 5x = 170

3x = 30

x = 10 pounds

Therefore, there are 10 pounds of less expensive tea.

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Answer:

Yes the triangles are congruent.

Step-by-step explanation:

You are going to move all the points 2 units to the left and  4 units up.

Look at the vertices of the triangle.  The points are (0,1) and (-5,0) and (2,-5).  If we moved all three of these points to places to the left and 4 up, they would be at (-2,4), (-7,4) and (0,-1)  This would make a image that is a congruent triangle.  You have just translated the original triangle 2 places to the left and 4 places up.

Imagine putting a mirror on the page and adding a reflection. You must identify the line in which the shape is mirrored when describing a reflection. The sum of the transformations can be referred to as a single transformation.

Imagine putting a mirror on the page and adding a reflection. You must identify the line in which the shape is mirrored when describing a reflection. Every point of a shape will be separated from the line of reflection by the same amount as the reflected point is separated from the line.

There are occasions when a shape is altered in more than one step, such as when a rotation is followed by a reflection. Typically, the sum of the transformations can be referred to as a single transformation.

Enlargements are a particular kind of transformation where the original shape's size is altered by multiplying it by a scale factor to make it bigger or smaller. To employ a center of enlargement, lines must be drawn from the center via the original shape's vertices. They are known as ray lines.

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The equation of the line passes through (2, -10) and to parallel to 14x +2y =  6 is 7x + y = 4

In the above question,

The equation of the line = 14x + 2y = 6

2y = 6 - 14x

y = [tex]- \frac{14x - 6}{2}[/tex]

y = -(7x - 3)

y = -7x + 3

The inclination of a line with respect to the horizontal is measured numerically is called as Slope

Slope of the given line = -7

The slope of a line parallel to the given line would be the same as they both are parallel to each other, hence the needed line's slope is also -7

The point through which is passes = (2, -10)

We need to find the equation of the line which passes through (2, -10) and to parallel to 14x +2y =  6

The equation of a line parallel to the given 14 x + 2 y = 6, and passing through the point (2, -10) is

[y - (-10)] = (-7)[x - 2]

y + 10 = -7x + 14

7x + y = 14 - 10

7x + y = 4

Hence, the equation of the line passes through (2, -10) and to parallel to 14x +2y =  6 is 7x + y = 4

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The value of the function operation of each one is represented below.

To solve this problem, we have to perform the operation on each one.

1) (fg)(x)

[tex](fg)(x) = 2x^3 + 12x^2 + 24x + 16[/tex]

2) (hg)(x)

[tex](hg)(x) = x^4 + 4x3 -16x -16[/tex]

3)

(fh)(2)

[tex](fh)(2) = 0[/tex]

4) (gh)(x)

[tex](gh)(x) = x^4 + 4x^3 - 16x -16[/tex]

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Answer:The midsegment of a trapezoid is parallel to each base, and its length is one-half the sum of the lengths of the bases. If MN is the midsegment of trapezoid ABCD, then MN || AB, MN || DC, and MN = (AB + CD).

Step-by-step explanation:

Answer:

MN is 1/2 of DC

Step-by-step explanation:

DC= 44

MN= 22

The 'x' and 'y' variables and the 4 angles are highlighted in the boxes

Given:

The cost of belonging to a gym can be modelled by,

To find:

The slope and the y-intercept

Explanation:

The equation is of the slope-intercept form of the linear equation,

Where m is the slope and c is the y-intercept.

Comparing we get,

Here, the slope represents the cost per month of membership and the y-intercept represents the fixed initial fee to be given to the gym for joining.

Final answer:

• The slope is 50.

• The y-intercept is 79.50.

Answer:

B 36

Step-by-step explanation:

36 = 6×6 = 6^2

6^2 is a perfect square

The  inequality can be represented as 55 + 5x < 70

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

Mayerlin pays a flat cost of $55 per month and $5 per gigabyte.

She wants to keep her bill under $70 per month.

let  x be the number of gigabytes Mayerlin can use.

So, the inequality can be represented as

55 + 5x < 70

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ANSWER

No 3. x = 41 degrees

No 4. x = 6.5 degrees

EXPLANATION

Question 3

Note: One of the angles in a right triangle is 90 degrees. As a result, the sum of the other two angles is 90.

That is:

Question 4

Note: The sum of angles in a triangle is 180

That is:

Answer:

-2

Step-by-step explanation:

f(x) = 2x, g(x) = x - 4

f(g(3)) = f(-1) = 2(-1) = -2

Answer: [tex]y \geq 1[/tex]

Step-by-step explanation:

The range of a function is the set of y-values.

The explicit equation of the sequence is an = 3 + (n-1)*6

First term = 3

Second term = 9

A series of numbers in mathematics whose each term is always expressed as a, a+d, a+2d, or a+3d. An arithmetic progression is defined as a + (n-1)d, where a is the first term,d is the common difference of the series and n is the number of terms in the sequence

Any two continuous terms in the arithmetic sequence differ by the same number.

Arithmetic sequence is given by an = a + (n-1)d

So, the common difference = 9-3 = 6

a = 3

Substituting the values in the formula we get:

For nth term: an = 3 + (n-1)*6

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Answer:

B

Step-by-step explanation:

i had the thing 2 days ago lol

Answer:

Step-by-step explanation:

T = 0.27·c + 31

0.27·c = T - 31

c = (T - 31) / 0.27 = (77 - 31) / 0.27 ≈ 170

Answer:

170 times a minute a cricket chirps at 77° F

Answer:

It's (7, 13) not sure how to explain that

Answer:

sinθ-cosθ = 0

sinθ= cosθ

sinθ/cosθ = 1

tanθ = 1

Bu tan45 = 1

So,

tanθ=tan45

θ = 45°

sin45 = 1/√2  cos45 = 1/√2

sin⁴θ+cos⁴θ  = (1/√2)⁴+(1/√2)⁴

                     = 1/4+1/4 = 2/4 = 1/2 = 0.5

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hope this helped you..................

The principal amount was invested for 8 Years.

In the given question, it is stated that when $314 was invested as the Principal amount, it got an Interest of $175.84 at an interest rate of 7%. We have to find out the total period of time the principal amount was kept and got interested in in order to complete the interest amount of $175.84.

To calculate the Interest, we know that the formula for Simple Interest is:

=> S.I. = (P*R*T)/100, where P = Principal amount, R = Rate of Interest, and T is the Time period. Now, putting values in the formula we get:

=> S.I. = (P*R*T)/100

=> 175.84 = (314*7*T)/100

=> T = 17584/2198

=> T = 8

Hence, we get Invested Time for 8 years.

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Answer:

price ×time×rate/100 40000×6×14/100

33600

radius = 30 in

Area = 900 in^2

To calculate the area of a circle, use the equation A = pi r^2

His mistake was that he did not multiplicate by pi (3.1416)

The actual area = (3.1416)(30)^2

A = 2827.44 in^2

The given expression is equivalent to the third option -19.5b - 6.9. We get this on solving the algebraic expression.

The given expression in the question is

3(-4.5b-2.1) - (6b +0.6)

= -13.5b - 6.3 - 6b - 0.6         (multiplying 3 and -1 respectively with the elements in the bracket)

= -19.5b - 6.9

Therefore we can see that on solving the given algebraic expression we get that it is equivalent to -19.5b - 6.9

Hence the third option which is -19.5b -6.9 is the correct answer.

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The distance between J1 and J2 is 2.94 miles using cosine rule.

What is cosine rule?

Cosine rule relates to the lengths of the sides of a triangle with any of its angles being a cosine angle. With the help of this rule, we can calculate the length of the side of a triangle or can find the measure of the angle between the sides.

cos x = ([tex]b^{2} +c^{2} -a^{2}[/tex])/2bc

x = 45

b = 4

c = 2

to find a

cos 45 = 4(4) +2(2) - [tex]a^{2}[/tex]/2(4)(2)

1/[tex]\sqrt{2}[/tex] = 16 +4 - [tex]a^{2}[/tex]/16

16/[tex]\sqrt{2}[/tex] = 20 - [tex]a^{2}[/tex]

a = 2.94

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Step-by-step explanation:

1 + 1 + 1 - 1 - 5 - 5r - 3 - 3 --2 - 6 --4

3 - 1 - 5 - 5r - 3 - 3 -- 2 - 6 -- 4

2 - 5 - 5r - 3 - 3 -- 2 - 6 -- 4

-3 - 5r - 3 - 3 -- 2 - 6 -- 4

-5r - 6 - 3 + 2 - 6 + 4

-5r - 9 + 2 - 6 + 4

-5r - 7 - 6 + 4

-5r -13 + 4

-5r - 9

This is the furthest it can be reduced to if you're not trying to find the value of r.

Hope this helps! :)

The total amount accrued, principal plus interest, from simple interest on a principal of $1,500.00 at a rate of 3.5% per year for 30 years is $3,075.00. With a principal of £1,500.00 and an interest rate of 3.5% over a 30-year period, Sarah-Jane will save UK £1,575.00. It is undoubtedly a wise investment because the original UK £1,500 doubled.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest.

A = P(1 + RT)

A=Final Amount

P = Principal

R = Rate of Interest

T = Time period

Here,

A = $3,075.00

I = A - P = $1,575.00

A = P(1 + rt)

First, converting R percent to r a decimal

r = R/100 = 3.5%/100 = 0.035 per year.

Solving our equation:

A = 1500(1 + (0.035 × 30)) = 3075

A = $3,075.00

$3,075.00 is the total amount accrued from simple interest on a principal of $1,500.00 at a rate of 3.5% per year for 30 years (principal plus interest). In a 30-year loan with a £1,500.00 principal and a 3.5% interest rate, Sarah-Jane will save UK £1,575.00. The original UK £1,500 doubled, so it is unquestionably a smart investment.

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The sampling distributions reach a normal distribution as sample sizes increase.

For the given statement in the question-

As sample sizes grow larger, sampling distributions reach a normal distribution.

The mean of the sampling distribution equals the population mean (µ) (with "infinite" numbers of the successive random samples).

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Answer:

She earned $42,000 in the previous year

Step-by-step explanation:

9% can be rewritten as 0.09

0.09x is 4050

divide both sides by 0.09

0.09x becomes x

4050 becomes 45,000

then we subtract 3,000 from 45,000 to find the previous years salary