Write an equation using the explicit formula to represent each graph or scenario then rewrite the formula in function form

Answer:

rate of change = 5

Step-by-step explanation:

the slope m gives the measure of the rate of change of the function

calculate the slope m using the slope formula

m = [tex]\frac{y_{2-y_{1} } }{x_{2-x_{1} } }[/tex]

with (x₁, y₁ ) = (3, 38) and (x₂, y₂ ) = (1, 18) ← 2 ordered pairs from the table

m = [tex]\frac{18-38}{1-3}[/tex] = [tex]\frac{-20}{-2}[/tex] = 5

then rate of change = 5

Answer:

x ≥ 2

Step-by-step explanation:

the solid circle at 2 indicates that x can equal 2

the arrow points to the right indicating values of x greater than 2 , then the inequality being represented by the number line is

x ≥ 2

Answer:

12 possible outcomes

Step-by-step explanation:

The equation to find the possible outcomes is:

possible outcomes  x  total

We know she picks 1, so we have

1 x 12 = 12 possible outcomes

So, there are 12 possible outcomes

Answer:

24d^5

Step-by-step explanation:

Answer: C

Step-by-step explanation:

You would work backwards. So it would be 1:00-2 hours so the answer would be 11:00 A.M

The six-foot long ladder is 3√5 feet high up the wall having 3 feet distance from bottom of the ladder.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the ladder is the hypotenuse, and the wall and the ground make up the other two sides.

The ladder is 6 feet long, and the bottom of the ladder is 3 feet away from the wall, so the triangle is a 3-4-5 right triangle, which means the wall is 3 feet high.

So, if we square the length of the ladder (6^2 = 36)

The length of the base (3^2 = 9),

and add them together, then take the square root of that, we get the height of the wall.

sqrt(36+9) = sqrt(45) = 3*sqrt(5)

so the ladder is 3√5 feet high up the wall.

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Answer:

6 Students stayed in class

30 Students in Total

Step-by-step explanation:

Since there are 8/10 people on the trip, you divide the numerator(8) by 24

24 divided by 8 is 3. Also 3 x 8 is 24 so its proper

3 x 2 is 6 and 6 + 24 is 30

30 is 10/10 in this question so 6 is the answer for those who stayed in class and there is 30 in total

Answer:

18 and 21

Step-by-step explanation:

Let the smaller number = 3x

Let the larger number =  3x + 3

The three and the plus 3 insure that the numbers are multiples of 3 and are consecutive.

3* (3x + 3) = 7/10 * 5 (3x)       Multiply both sides by 10

30*(3x + 3) = 7 * 5 * 3x          Remove the brackets

90x + 90 = 7 * 5 * 3x             Combine the right

90x + 90 = 105x                    Subtract 90x from both sides.

-90x             -90x

           90 = 15x                     Divide by 15

x = 90/15

x = 6

Let's see if it works.

3*(3x + 3) = 3*(18 + 3) = 3 * 21 = 63

7/10 * 5 *3x = 7/10 * 5 * 3*6 = 630 / 10 = 63

Answer:

14km

Step-by-step explanation:

An expression to represent the sum of their ages is as follows.

g = 14 + L

If the ratio of the ages of X and Y is p:q and their sum is X, then the following formula can be used to calculate Y's age: Age of Y = Y/Total Ages x Total Ratios. Age of Y = (p+q) q x A.

Assume that L is Louannel's sister's age, m is Mark's age, and g is Gregory's age.

Gregory's age difference with his cousin Mark, who is 20 years older (m).

∴ g = 20 + m            .............(1)

Also given that Mark is 6 years younger than his sister Louanne(L)

∴ m = L - 6                ............(2)

Now, substituting m = L - 6 from (2) in (1),

∴ g = 20 + L - 6

∴ g = 14 + L

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Answer:

B

Step-by-step explanation:

We have to look at the full dot

Answer:

400= 2 x 2 x 2 x 2 x 5 x 5 = 2/4 x 5/2

Answer:

$1779.896

Step-by-step explanation:

From the above question

1 liter = $143.54

12.4 liters = $x

Cross Multiple

1 liter × $x = 12.4 liters × $143.54

$x = 12.4 liters × $143.54/1 liter

$x = $1779.896

Therefore, the total cost for Stacy gas in dollars and cents is $1779.896

Answer:

17

Step-by-step explanation:

8²+15²=289

√289=17

Remember,  Pythagorean theorem

Answer:

Simplified = 1.7×109

1.7×109 = 185.3

The degree of the polynomial as calculated from the given data7x³ + 5x + 4x⁵ + 2x² is 5 .

The given polynomial is  7x³ + 5x + 4x⁵ + 2x²

To find the degree of the polynomial we will write the equation down in the descending power of x

which is ,

4x⁵ + 7x³ + 2x² + 5x

Here , the highest power of the variable that appears with nonzero coefficient is 5.

So ,degree of the polynomial is said to be 5.

The hightest power of the variable in a polynomial is known as the degree of the polynomial. A polynomial expression is made up of constants and variables.

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Answer:

Third one

−10×3−4

Step-by-step explanation:

-30-4

-34

Answer:

-10 · 3 - 4

Step-by-step explanation:

20 - (-3) + 51 ÷ (-3) = 20 + 3 + 51 ÷ (-3) = 20 + 3 - 17 = 6 no

-2 - (-8) + 7 + (-11) = -2 + 8 + 7 - 11 = 2 no

-10 · 3 - 4 = -30 - 4 = -34 yes!

-4 · (-3) + 22 = 12 + 22 = 34 no

Answer:

rreflextion across x the reflection across y

Side D and B are both congruent

Step-by-step explanation:

The length of the shortest piece is 5, and the longest piece is 13 feet by solving the equations.

The length of the shortest piece is 5, and the longest piece is 13 feet.

the solution is as follows,

Greg has a piece of rope that is 18 ft long.

He wants to cut it into two pieces so that the longer piece is 2 ft less than three times the length of the.

Let the length of the shorter piece be x.

And the length of the longer piece is 3x -2.

Greg has a piece of rope that is 18 ft long.

Then,

longest piece+ shorter piece = 18

x + 3x -2 = 18

4x - 2 =18

4x = 18+2

4x = 20

x= 20/4

x = 5.

Therefore,

The length of the shorter piece is x =5.

And the length of the longer piece = 3x -2 = 3(5)-2 = 15-2 = 13

Hence, the length of the shortest piece is 5, and the longest piece is 13 feet.

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Yes, if the value of y = 0 then it makes the horizontal line.

The term horizontal line is defined as one that goes from left to right.

And here we also know that they are parallel to the x –axis in the coordinate plane.

And the horizontal line has a slope of zero.

While we looking into the move along the right of the line, then it does not rise or fall at all.

Here we have to the that the following factors are also included in feature:

In as the horizontal line is parallel to the x-axis and it is parallel to the horizon.

Where as the horizontal line is a sleeping line and it is also defined as can be a sleeping, standing, or a slanting line.

Where the horizontal line is perpendicular to the y-axis.

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Answer:

see explanation

Step-by-step explanation:

under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ) , then

C (1, 9 ) → C' (- 9, 1 )

D (4, 9 ) → D' (- 9, 4 )

E (0, 3 ) → E' (- 3, 0 )

The admission fee for the zoo and for the state park is given as follows:

For the zoo, the costs are divided as follows:

20 students are going to the zoo, hence the total cost spent at the zoo is given as follows:

20(2x + 3.25) = 40x + 65.

For the state park, the costs are divided as follows:

25 students are going to the state park, hence the total cost spent at the state park is given as follows:

25(x + 6.50) = 25x + 162.50.

The costs spent at both parks are the same, hence the value of x can be obtained as follows:

40x + 65 = 25x + 162.5

15x = 97.5

x = 97.5/15

x = 6.5.

Hence the admission fees are given as follows:

The table is given by the image presented at the end of the answer.

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Reading a math word problem through to the end will help you comprehend what you need to do in order to solve it. After reading it, you may determine which components of the issue that need to be resolved are the most important and which are not.

There are few basic steps to be followed while solving any mathematics problem:

1. Read and understand the problem.

2. Identify what is given and what is needed to solve the problem.

3. Choose an appropriate strategy to solve the problem.

4. Carry out the strategy.

5. Check your answer to make sure it is correct.

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Answer:

X of M is 6, Y of M is 4, Pair is (6,4)

Step-by-step explanation:

M = 6

M = 4

M (6,4)

Answer:

the answer is n ≥ -49

here are the steps for solving-

the problem Is like  n/7+3 ≥ -4

1. First subtract 3 from both sides. After doing that, the inequation should be Like This:

n/7 ≥ -7

2. since 7 is in Division form, when it goes to RHS, You multiply.

So -7 times 7 Is -49

so the answer is n≥ -49

When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent.

Equivalent ratios are two ratios with the same value. By multiplying or dividing the two amounts by the same number, you can determine the equivalent ratio. Finding equivalent fractions follows the same procedure.

The ratio formula can be used to represent a ratio as a fraction. The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.

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