f(n)=(n-1)^2+3n, which statement is true?
1) f(3)=-2
2) f(-2)=3
3) f(-2)=-15
4) f(-15)=-2

The measure of ∠5 is 35degree

Linear pair of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.

Given:

In Quadrilateral ABCD, AB||CD

<M2=35

If a transversal line intersects two parallel lines then the alternate interior angles are congruent.

In the given figure In Quadrilateral ABCD, AB||CD<M2=35  .

So,

<5≅<2 (Alternate interior angles)

M<5=M<2

M<5=35degree

Therefore, the angle measure of M<5 will be 35degree

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The sentence "six more than the quotient of a number and 7 equals 5" in an equation would be 6 + (c/7) = 5.

What is the quotient?

A quotient is defined as when dividing one number by another, the result is called the quotient.

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given a variable c therefore, the translation of the given equation :

six more than can be expressed as 6+ or +6.

A quotient, commonly known as c/7, is the solution to a division issue and can also be a fraction.

and "equals 5" is clearly equal to 5 or =5, hence the result is 6 + (c/7) = 5.

The sentence "six more than the quotient of a number and 7 equals 5" in an equation would be 6 + (c/7) = 5.

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The first five terms of the given arithmetic sequence is; 36, 30, 24, 18, 12

The general formula for the nth term of an arithmetic sequence is;

aₙ = a + (n - 1)d

where;

a is first term

n is number of term

d is common difference

We are given;

First term; a₁ = 36

Formula for nth term of the sequence;

aₙ = aₙ₋₁ - 6

Thus;

Second term; a₂ = a₂₋₁ - 6

a₂ = a₁ - 6

a₂ = 36 - 6

a₂ = 30

Similarly;

Third term; a₃ = 30 - 6

a₃ = 24

Fourth term; a₄ = 24 - 6

a₄ = 18

Fifth term; a₅ = 18 - 6

a₅ = 12

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Answer:

10x^2 - 11x -6

Step-by-step explanation:

1/ First, distribute the brackets:

( multiply 5x to the other bracket, then 2 multiply it also to the other bracket)

After the distribution you'll get this:

10x^2 - 15x + 4x - 6

2/ finally, to simplify you'll have to combine the like terms:

( as you can see the only like terms we have are -15x and +4x)

combine them and you'll get:

10x^2 - 11x -6  ( this is the final answer)

Answer:

x-y=4, 3x-5y=-4

Step-by-step explanation:

step (1)

write the equation in the form ax+by=c

step (2)

put the equations below each other

x-y=4....(1)

3x-5y=-4....(2)

Multiply (1) by (-5) then add (1) and (2)

-5x+5y=-20

3x-5y=-4

-2x=-24 then x=12 from (1) y=8

S.S.={(12,8)}

The equation that models the temperature​ y, in degrees​ Fahrenheit, after x hours is y = 42 + 7x

From the question, we have the following parameters that can be used in our computation:

Initial temperature = 42°F

Rate of increment = 7°F

These parameters mean that:

We need to find the equation that models the temperature​ y, in degrees​ Fahrenheit, after x hours.

This is calculated as

y = Initial temperature + Rate * Number of hours

Substitute the known values in the above equation, so, we have the following representation

y =42 + 7x

The above equation models the temperature​ y, in degrees​ Fahrenheit, after x hours.

Next, we draw the graph by taking few points from the equation

x     0    1      2       3

y    42   49   56    63

See attachment for the graph

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Complete question

The temperature at sunrise is 42°F. Each​ hour, the temperature rises 7°F. Write an equation that models the temperature​ y, in degrees​ Fahrenheit, after x hours. What is the graph of the​ equation?

Answer:

B. 4.8

Step-by-step explanation:

The average age of all the animals is B. 4.8.

From the information, at the animal rescue, 40% of the animals are dogs and 60% of the animals are cats. If the average age of the dogs is 9 months and the average age of the cats is 2 months.

To find the average age of all the animals, we need to calculate the weighted average of the ages of the dogs and cats, where the weights are the proportions of dogs and cats in the rescue.

The average age of all the animals is:

(0.4 * 9 months) + (0.6 * 2 months)

= 3.6 months + 1.2 months

= 4.8 months.

So the average age of all the animals at the rescue is 4.8 months.

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Answer:

The shadow cast by the building is of the length 11.8 m.

Step-by-step explanation:

We consider the height of the building as the height of the triangle and the length of the shadow as the base of the triangle, then the distance from the top of the building to the tip of the shadow would be the hypotenuse of the triangle.

Using the Pythagorean theorem:

c^2 = a^2 + b^2

Where c is the hypotenuse, which is 36m, a is the height of the building, which is 34m and b is the base of the triangle, which is the length of the shadow.

So by plugging the given numbers in:

b^2 = c^2 - a^2

b^2 = 36^2 - 34^2

b = √(36^2 - 34^2)

b ≈ 11.8m (if rounded to the nearest tenth)

So the length of the shadow in this scenario is approximately 11.8 m.

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The relationship between angle 1 and 2 is alternate exterior angles.

When parallel lines are cross by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, linear angles, same side interior angles, alternate exterior angles, vertically opposite angles.

The parallel lines are line m and line l. The parallel lines l and m are cut by a transversal line and the angles formed are angle 1 and 2. This establish an angle relationship.

Therefore, the angle 1 and angle 2 forms an angle relationships.

Hence, the special relationship of angle 1 and 2 are alternate exterior angles.

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Answer:

[tex]8x^2+18x-35[/tex]

Step-by-step explanation:

(4x-5)(2x+7) -> since its area

8x^2+28x-10x-35

so final answer is

8x^2+18x-35

which means its C

Answer:

8x^2 + 18x - 35 would be ur answer

Step-by-step explanation:

The statements that complete the blanks are underlined as follows

From the question, we have the following parameters that can be used in our computation:

The graph

The given graph is a quadratic graph

All quadratic graphs are functions

So, the relation is a function

This statement is false,

This is so because one y value points to two different x values, as evident on the graph

As a general rule, the inverse of a quadratic function is not a function

This means that the inverse of the given relation is not a function

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The value of B-A of the matrices is:

            [0   5 -10]

B - A =  [-3 -4    7]​

            [-1   0   -6] ​

A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.

The number of rows of a matrix can be determined by counting from top to bottom and the number of columns can be determined by counting from left to right.

We can find the value of B - A of the matrices by subtracting corresponding values of the element of each matrix. That is:

      [4 -4 5]                        

A =  [3 2 -4]            

       [2 2 5]

       [4 1 -5]

B =  [0 -2 3] ​

       [1   2 -1​] ​

            [4-4  1-(-4)   -5-5]

B - A =  [0-3  -2-2  3-(-4)] ​

            [1-2    2-2     -1-5] ​

            [0   5 -10]

B - A =  [-3 -4    7]​

            [-1   0   -6] ​

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Complete Question

Given the matrices A and B shown below, find B − A .

      [4 -4 5]                        

A =  [3 2 -4]            

       [2 2 5]

       [4 1 -5]

B =  [0 -2 3] ​

       [1   2 -1​] ​

The formula for [tex]R_{N}[/tex] for the function f(x) is [tex]& R_N=\sum_{j=1}^N f\left(x_j\right) \Delta x[/tex] and the value of [tex]R_{N}[/tex] =  2688.

As per the given data, the given function f(x) is:

f(x) = [tex](8 x)^2[/tex]  on [-1, 5]

Here we have to determine the formula for [tex]R_{N}[/tex]

Let us consider the interval [a, b]

Then the value of a is -1 and the value of b is 5.

[tex]& \Delta x=\frac{b-a}{N}=\frac{5+1}{N}=\frac{6}{N} \\[/tex]

[tex]& x_j=a+\Delta x_j=-1+\frac{6 i}{N} \\[/tex]

Area Using Riemann Sum:

The Riemann sum of a function f(x) over a given interval [a, b] is given by:

[tex]$$S_n=\sum_{k=1}^n f\left(c_k\right) \Delta x$$[/tex]

When the points are chosen randomly, then the sum is called a Riemann sum and will give an approximation for the area of R that is in between the lower and upper sums.

Split the area into vertical slices then use the Riemann sum formula.

[tex]& R_N=\sum_{j=1}^N f\left(x_j\right) \Delta x[/tex]

[tex]=\sum_{j=1}^N f\left(-1+\frac{6 j}{N}\right) \frac{6}{N} \\[/tex]

[tex]& =\sum_{j=1}^N 64\left(-1+\frac{6 j}{N}\right)^2 \frac{6}{N} \\[/tex]

[tex]& R_N=\sum_{j=1}^N 64\left(1+\frac{6 j}{N}\right)^2 \frac{6}{N} \\[/tex]

[tex]& =\sum_{j=1}^N 64\left(1+\frac{36 j^2}{N^2}-\frac{12 J}{N}\right) \frac{6}{N} \\[/tex]

[tex]& =384 \sum_{j=1}^N\left(1+\frac{36 j^2}{N^2}-\frac{12 j}{N}\right) \frac{1}{N} \\[/tex]

[tex]& =384\left(N+\frac{36}{N^2}\left(\frac{N(N+1)(2 N+1)}{6}\right)-\frac{12}{N}\left(\frac{N(N+1)}{2}\right)\right) \frac{1}{N} \\[/tex]

[tex]& =384\left(1+6\left(\frac{N(N+1)(2 N+1)}{N^3}\right)-6\left(\frac{N(N+1)}{N^2}\right)\right) \\[/tex]

[tex]& \lim _{V \rightarrow \infty} R_N=384 \lim _{N \rightarrow \infty}\left(-1+6\left(\frac{N(N+1)(2 N+1)}{N^3}\right)-6\left(\frac{N(N+1)}{N^2}\right)\right) \\[/tex]

= 384 (1 + 6(2) - 6)

= 384 (7)

= 2688

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The exact value of sin 170⁰ cos 55⁰ + cos 170⁰ sin 55⁰ is -0.707.

The right expression is sin 170⁰ cos 55⁰ + cos 170⁰ sin 55⁰.

We have to find the exact value of sin 170⁰ cos 55⁰ + cos 170⁰ sin 55⁰.

The angles and sides of a right-angle triangle are measured using these trigonometric values. Cotangent, secant, and cosecant are the other three significant values in addition to sine, cosine, and tangent.

To solve this question we use the formula

sin(A+B) = sinA cosB + cosA sinB

If we compare the given expression by the formula, we get

A = 170⁰ and B = 55⁰

So the exact value of

sin 170⁰ cos 55⁰ + cos 170⁰ sin 55⁰ = sin(170⁰ + 55⁰)

sin 170⁰ cos 55⁰ + cos 170⁰ sin 55⁰ = sin(225⁰)

Using the calculator the value of sin(225⁰) = -0.707

sin 170⁰ cos 55⁰ + cos 170⁰ sin 55⁰ = -0.707

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The exact value of sin 170° cos 55° cos 170° sin 55° is startfraction startroot 3 endroot over 2 endfraction negative.

The exact value of sin 170° cos 55° cos 170° sin 55° can be calculated using the trigonometric identities.

First, the double angle identities for sine and cosine can be used to express the given expression as:

sin 170° cos 55° cos 170° sin 55° = (sin 170°)2 cos 55° (cos 170°)2 sin 55°

Now, applying the double angle identities for sine and cosine, the given expression can be written as:

sin 170° cos 55° cos 170° sin 55° = (1 - cos 340°) (1 - cos 110°) (1 + cos 340°) (1 + cos 110°)

Now, using the cosine addition formula, the given expression can be written as:

sin 170° cos 55° cos 170° sin 55° = (1 - cos 340°) (1 - cos 110°) (2 cos 170° cos 170°)

Now, applying the double angle identity for cosine, the given expression can be written as:

sin 170° cos 55° cos 170° sin 55° = (1 - cos 340°) (1 - cos 110°) (1 - (sin 170°)2)

Now, applying the Pythagorean identity, the given expression can be written as:

sin 170° cos 55° cos 170° sin 55° = (1 - cos 340°) (1 - cos 110°) (1 - (1 - (cos 170°)2))

Now, using the cosine addition formula, the given expression can be written as:

sin 170° cos 55° cos 170° sin 55° = (1 - cos 340°) (1 - cos 110°) (2 cos 170° cos 170° - 1)

Finally, applying the double angle identity for cosine, the given expression can be written as:

sin 170° cos 55° cos 170° sin 55° = (1 - cos 340°) (1 - cos 110°) (1 - (cos 340°)2)

Now, applying the Pythagorean identity, the given expression can be written as:

sin 170° cos 55° cos 170° sin 55° = (1 - cos 340°) (1 - cos 110°) (1 - (2 startfraction startroot 3 endroot over 2 endfraction)2)

Therefore, the exact value of sin 170° cos 55° cos 170° sin 55° is startfraction startroot 3 endroot over 2 endfraction negative.

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The equation can be used to find the measures of angle LJK is LJK = 180 - (JKL + KLJ) This equation is based on the fact that the measures of the angles in any triangle add up to 180 degrees.

To find the measures of angle LJK, we can use the equation: LJK = 180 - (JKL + KLJ).  to find the measure of any given angle, we must subtract the measures of the other two angles from 180. In this case, we're looking for the measure of angle LJK, so we'll subtract the measures of the other two angles, JKL and KLJ, from 180. This will give us the measure of angle LJK. This equation is useful in finding the measure of any given angle, as long as we know the measures of the other two angles, as it is based on the fact that the measures of the angles in any triangle add up to 180 degrees.

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The area inside the larger loop and outside the smaller loop of the Limacon [tex]r=\frac{1}{2}+cos\theta[/tex] is [tex]\frac{\pi+3\sqrt3}{3} u^2[/tex].

The given equation is [tex]r=\frac{1}{2}+cos\theta[/tex].

The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The relationship between rectangular and polar coordinates is:

[tex]x=rcos\theta[/tex]

[tex]y=rsin\theta[/tex]

[tex]r^2=x^2+y^2[/tex]

[tex]\theta=tan^{-1}(\frac{y}{x})[/tex]

[tex]J=r[/tex]

The area between the curve [tex]r=f(\theta)[/tex] and two polar radius corresponding to [tex]\theta_1=\alpha[/tex] and [tex]\theta_2=\beta[/tex] is:

[tex]A=\frac{1}{2}\int_{\alpha}^{\beta}[f(\theta)]^2d\theta[/tex]

We have that:

[tex]\frac{1}{2}+cos\theta=0[/tex]

[tex]cos\theta=-\frac{1}{2}[/tex]

[tex]\theta_1=\frac{2\pi}{3}[/tex]

[tex]\theta_2=\frac{4\pi}{3}[/tex]

Then, the top half of larger loop of the Limacon is defined on the interval [tex][0, \frac{2\pi}{3}][/tex] and bottom half of smaller loop is defined on the interval [tex][\frac{2\pi}{3}, \pi][/tex].

Therefore, the area inside the larger loop and outside the smaller loop of the given Limacon will be:

[tex]A=2\frac{1}{2}[\int_0^{2\pi/3}(\frac{1}{2}+cos\theta)^2d\theta-\int_{2\pi/3}^{\pi}(\frac{1}{2}+cos\theta)^2d\theta][/tex]

[tex]=\int_0^{2\pi/3}(\frac{1}{4}+cos\theta+cos^2\theta)d\theta-\int_{2\pi/3}^{\pi}(\frac{1}{4}+cos\theta+cos^2\theta)d\theta[/tex]

[tex]=\int_0^{2\pi/3}(\frac{1}{4}+cos\theta\frac{1}{2}+\frac{cos2\theta}{2})d\theta-\int_{2\pi/3}^{\pi}(\frac{1}{4}+cos\theta+\frac{1}{2}+\frac{cos2\theta}{2})d\theta[/tex]

[tex]= (\frac{3}{4}\theta+sin\theta+\frac{sin2\theta}{4})|_0^{2\pi/3}-(\frac{3}{4}\theta+sin\theta+\frac{sin2\theta}{4})|_{2\pi/3}^{\pi}[/tex]

[tex]= \frac{\pi}{2}+sin\frac{2\pi}{3}+\frac{1}{4}sin\frac{4\pi}{3}-(\frac{3\pi}{4}-\frac{\pi}{2}-sin\frac{2\pi}{3}-\frac{1}{4}sin\frac{4\pi}{3})[/tex]

[tex]= \frac{\pi}{4}+\sqrt3-\frac{1}{4}\sqrt3[/tex]

[tex]= \frac{\pi+3\sqrt3}{3} u^2[/tex]

Therefore, the area inside the larger loop and outside the smaller loop of the Limacon [tex]r=\frac{1}{2}+cos\theta[/tex] is [tex]\frac{\pi+3\sqrt3}{3} u^2[/tex].

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Answer:

Step-by-step explanation:

The simplified form of the radical is 9i

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part I'm (z).  Also, it is called an imaginary number.

Given here, √-81 and we know √-1 = i

√-81 = √9² × √-1

        = 9 ×i

        = 9i

Hence 9i is the correct answer.

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Answer: 9i is the correct answer.

Step-by-step explanation:

Solving the given work.

Tammy weekly pay as a baby sitter is 60 dollars.

The equation that can be used to find the weekly amount Tammy made baby sitting is  45 = 15 + 1 / 2x

Tammy receives a weekly pay from her job as a baby sitter. she spent half of this weeks pay at the bowling alley but earn an additional 15 dollars for walking the neighbours dog. She did not spend any additional money and finish the week with 45 dollars.

Tammy weekly pay as a baby sitter can be calculated as follows:

let

x = Tammy weekly pay as a baby sitter

She spent half of it on bowling alley = 1 / 2x

Therefore,

45 = 15 + 1 / 2x

45 - 15 = 1 / 2 x

30 = 1 / 2 x

cross multiply

x = 60 dollars

Therefore,

amount earned baby sitting = 60 dollars

The equation to find her weekly pay is 45 = 15 + 1 / 2x .

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1/8 is the slope of the line that represents the relationship and 1/4  the slope and the y-intercept represent

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Given, Anton realizes there is a linear relationship between the weight of the pet and the amount of food the pet should be fed.

The slope the slope of the line that represents the relationship is 1/8 cups.

the y-intercept of the line that represents the relationship is 1/4.

The slope is the value that will be multiplied by the weight of the cat  so as to know the amount of food that will be given to the cat.

The y intercept represent the fixed food that should be given to the cat after it has been using.

Hence, 1/8 is the slope of the line that represents the relationship and 1/4  the slope and the y-intercept represent

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The side of the right angle triangle marked x have length equal to 7 using the Pythagoras rule

The Pythagoras rule states that in a right-angle triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

We shall evaluate the length of the side marked x as follows:

25² = x² + 24²

625 = x² + 576

x² = 625 - 576 {collect like terms}

x² = 49 {take square root of both sides}

x = √49

x = 7

Therefore, the length of the side of the right angle triangle marked x is equal to 7 using the Pythagoras rule.

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Answer:

32

Step-by-step explanation:

This is the step by step explanation

32×3=96

96÷4=24

The total momentum between the objects during the collision is 210 kgm/s

Momentum is the product of the mass of an object and its velocity.

Since two objects are in motion towards each other. The first has a mass of 10 kg and a velocity of 7 m/s. The second object has a mass of 10 kg and a velocity of 14 m/s, from the law of conservation of momentum, the total momentum during the collision is the sum of their momenta.

So, the total momentum P = p + p' where

So, P = mv + m'v'

Given that

Substituting the values of the variables into the equation for total momentum, we have

P = mv + m'v'

P = 10 kg × 7 m/s + 10 kg × 14 m/s

P = 70 kgm/s + 140 kgm/s

P = 210 kgm/s

So, the total momemtum is 210 kgm/s

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His net profit  when he sells the building, to the nearest hundred dollars is  d. $606,000 profit.

We were told that ;

The twenty-room apartment complex that Wayne purchased for $759,000 fifteen years ago is scheduled to be put up for sale.

Since then, the local real estate market has been in decline, and the property's value has dropped by 3.89% annually.

Each of Wayne's units rents for $495 a month, and he spends $26,400 a year on building maintenance.

Assume Wayne has consistently maintained a three-quarter occupancy rate at his apartment building.

Annual Revenue can be calculated as [Monthly Rent * Number of Rooms  Number of months * Three-quarters]

If we input the values, we have  = [495 * 20 * 12  (3/4)]

= $89100

Then the Total Profit can be calculated as the  [Annual Revenue - Annual Cost) * (Number of years)]

And this can be computed as :

                 = (89100 - 26400) * 15

                 = $940500

Then the Net Profit can be compued as [ Value of the building at the end of the 15th year + Total profit from renting - Cost of the building]

= [424490.38 + 940500 - 759000 ]

= 605990.38

=  $606000

Therefore, option D is correct.

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Answer:

B

Step-by-step explanation:

Answer:

A)  Functions A and B have the same y-intercept.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Function A is a linear equation in slope-intercept form.

Therefore:

The x-intercept is when y = 0.

[tex]\begin{aligned}\textsf{$x$-intercept of Function A}: \quad -3x+2&=0\\-3x&=-2\\x&=\dfrac{2}{3}\end{aligned}[/tex]

Reading from the table, the x-intercept of Function B is x = 4.

Therefore, the two functions do not have the same x-intercept.

The y-intercept is when x = 0.

We have already determined that the y-intercept of Function A is y = 2.

Reading from the table, the y-intercept of Function B is also y = 2.

Therefore, both functions have the same y-intercept.

A linear function has one independent variable and one dependent variable.  The highest exponent of both variables is one.

Therefore, Function A is a linear function.

In a linear relationship, as one variable increases/decreases the other variable changes at the same rate.

For Function B, every time x increases by 2 units, y decreases by 1 unit.

Therefore, Function B is also a linear function.

We have already determined that the slope of Function A is -3.

[tex]\boxed{\sf Slope=\dfrac{change\:in\:y}{change\:in\:x}}[/tex]

For Function B, every time x increases by 2 units, y decreases by 1 unit for Function B.  Therefore, the slope of Function B is -¹/₂.

As 3 > ¹/₂, the slope of Function A is steeper than the slope of Function B.

The slope of the line is 0

It is important to note that the formula for the equation is expressed as;

y = mx + c

Where;

From the information given, we have the points

(0, 0) (0, 5)

The formula for calculating the slope of  a line is expressed as;

Slope, m = y₂- y1/x₂ - x₁

Substitute the values

Slope, m = 5 - (0)/ 0 - 0

Subtract the values

Slope, m = 5/ 0

Divide the values

Slope, m = 0

Hence, the value is 0

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2x< x+22 is the inequality equation which satisfy that x=20 the other inequality equation does not satisfy the condition.

Given that,

We have to find which inequality is true for x=20

The inequality equations are

a. x-5 < 2x-35

b. 2x < x+22

c. x/4 > x-12

d. x+30 >3x

We know that,

We have to substitute x=20 in the inequality equation to check which equation is true.

a. 20-5 < 2(20)-35

15 < 40-35

15< 5

NO, the inequality is not true

b. 2(20) < 20+22

40 < 42

Yes, the inequality is true

c. 20/4 > 20-12

5>8

NO, the inequality is not true

d. 20+30 > 3(20)

50 > 60

NO, the inequality is not true

Therefore, 2x< x+22 is the inequality equation which satisfy that x=20 the other inequality equation does not satisfy the condition.

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Function rules will always be based on the formula y = mx + b.

You can use this formula to set up an equation with the numbers in your current problem.

y  = mx + b

-6 = 2(1) + -8

Hence, the function rule would be expressed as:

y = 2x + (-8)