Find a formula for the exponential function passing through the points (-2, 4/9) and (3,108)

The proportional relationship can be represented by using an equation y = kx

Proportional relationship defined as the relationships between two variables where their ratios are equivalent. We can say that , in a proportional relationship, one variable is always a constant value times the other. That constant is called as the "constant of proportionality"

Consider y and x are in direct proportional relationship

y ∝ x

We can write this proportional relationship as

y = kx

Where y and x are the two variables

K is the constant of proportionality

In this equation we can see that the variable y is a constant value times the other variable x

Hence, the proportional relationship can be represented by using an equation y = kx

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Step-by-step explanation:

850÷100=17/2=8.5

8.5×24=204

850-204=646

646÷100=6.46

6.46×13=83.98 1st

646-83.98=562.02

562.02÷100=5.6202 2nd

5.6202×13=73.0626

562.02-73.0626=488.9574

488.9574÷100=4.889574 3rd

4.889574×13=63.564462

4.889574×13=63.564462

488.9574-63.564462=425.392938

425.392938÷100=4.25392938 4th

4.25392938×13=55.30108194

425.392938-55.30108194=370.0918561

370.0918561÷100=3.700918561 5th

3.700918561×13=48.11194129

370.0918561-48.11194129=321.9799148

321.9799148÷100=3.219799148 6th

3.219799148×13=41.85738893

321.9799148-41.85738893=280.1225259

280.1225259÷100=2.801225259 7th

2.801225259×13=36.41592836

280.1225259-36.41592836=243.7065975

I spent waaaaay to much time typing this

answer out I swear if it is incorrect I am done

£243.71

Answer: True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer: a= 3b + 4c -8

Step-by-step explanation:

a= 3b + 4c -8

-2a + 6b = -8c + 16

-6b from the left the isolate a

-2a = -6b - 8c + 16

then divide by -2 to cancel it out

a = 3b + 4c -8

The equation is equivalent to -2a + 6b = -8c + 16 will be a= 3b + 4c -8

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given the linear equation;

a= 3b + 4c -8

-2a + 6b = -8c + 16

-6b from the left the isolate a

-2a = -6b - 8c + 16

Then divide by -2 to cancel it out;

a = 3b + 4c -8

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The mean score in the fifth game that will allow you to advance is 73.

The mean score in the fifth game that will allow you to advance can be gotten this way:

Assign the mean score, the variable, and x.

Compute the scores with remarks as follows:

95 + 91 + 77 + 89 + x  ≥ 85

              5

352 + x ≥ 85

      5

85 × 5 = 425

352 + x ≥ 425

x = 425 - 352

x = 73.

So, the score in the fifth game that will allow you to advance will be 73.

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Answer:

Linear Function

Step-by-step explanation:

A linear function has constant slope

That means the ratio of y differences to x differences must be the same throughout the function. In other words the rate of change of the function y value is the same throughout the function

IF we look at the table we see that as x increases by 1, y decreases by 15

For example at x = 0, y = 20 and at x = 1, y = 5

So change in y/change in x = 0  = (5-20)/(1-0) = -15/1 = -15

If we look at another pair of points, say x = 1, y=5 and x = 2, y = -10

we get the rate of change = (-10 - 5)/(2-1) = -15/1 = -15

This is the same for any two x, y pair of values

So it is a linear function

1800 lawns were mowed. 800 driveways were shoveled.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Given Data

Let mowed grass be x

Let shoveled snow be y

Last year you mowed grass and shoveled snow for 12 houses

x + y = 12

y = 12 -x

You earned $225 for each lawn you mowed and $200 for each house you shoveled for a total of $2600.

225x + 200y = 2600

Equating value of y

225x + 200(12-x) = 2600

225x + 2400 - 200x = 2600

225x - 200x = 2600 - 2400

25x = 200

x = 8

For value of y,

y= 12 -x

y = 12 - 8

y = 4

Lawn mowed = 225(8)

Lawn mowed = 1800

Shoveled snow = 200(4)

Shoveled snow = 800

1800 lawns were mowed. 800 driveways were shoveled.

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Answer:

[tex]m_1=\frac{Fd^2}{Gm_2}[/tex]

Step-by-step explanation:

[tex]F=G \left(\frac{m_1 m_2}{d^2} \right) \\ \\ \frac{F}{G}=\frac{m_1 m_2}{d^2} \\ \\ \frac{Fd^2}{G}=m_1 m_2 \\ \\ m_1=\frac{Fd^2}{Gm_2}[/tex]

The equation of the linear graph is expressed in slope intercept form as; y = 20x

The equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept (which is the point where the line crosses the y-axis)

From the graph given we can see that the line crosses the y-axis at 0. Thus; c = 0

Now, we can pick two coordinates to find the slope;

Slope = (y2 - y1)/(x2 - x1)

Slope = (40 - 20)/(2 - 1)

Slope = 20

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Since the microwave raises the temperature of water by about 80°F in 5 minutes, the graph that has the slope that represents this rate of increase is option A.

Temperature is seen as a given unit used to stand for hotness as well as the coolness  of a given object or thing, it is said to be mostly  in Fahrenheit as well as Celsius.

Based on temperature, heat energy is one that tends to shift from a hotter  part of a body  to a colder part of the same body.

Note that:

Temperature = 80

Minutes = 5

Y = m

5m  = 80

m = 80/5

m = 16

So y  = 16x

Therefore, the graph that can give you the value above is graph A.

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The student that is correct with regards to the prime factorization of 956 is student B.

A factor is a number that divides another number without leaving any remainder. For example, 10 is a factor of 100. A prime number is a number that is perfectly divisible by 1 and that number only.

For example, a prime number is 7. A prime factor is the factor of a number that is a prime number. For example, a prime factor of 28 is 2.

In order to determine the prime factorization of a number, express the number as its prime factors.

Prime factors of 92 = 2 x 2 x 2 x 2 x 2 x 3

Thus, it is only student B that is correct. 5 is not a factor of 96.

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Answer:

x = -11

Step-by-step explanation:

           JL + LM = JK + KM

x + 2 + 2x + 27 = 9 + 7

x + 2x + 22 + 27 = 9 + 7

Combine like terms,

             3x + 49 = 16

Subtract 49 from both sides,

                      3x = 16 - 49

                     3x  = -33

Divide both sides by 3,

                      x = -33/3

                     x = -11

Based on the points given for the line in the table, the equation in slope intercept form is y = -1/2 + 1

To find the equation of a line, you first need to find the slope of the line as:

= Change in y / Change in x

= (0 - 1) / (2 - 0)

= -1 / 2

= - 1/2

Using the slope, find the y-intercept:

y = slope(x) + y-intercept

0 = -1/2(2) + y-intercept

y-intercept = 0 + 1

y-intercept = 1

The equation in slope-intercept form is:

y = -1/2 + 1

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Answer: la respuesta es 5.25

Step-by-step explanation: 0.75 x 7 = 5.25

Answer:

D

Step-by-step explanation:

Answer/Step-by-step explanation:

y = -x - 3

m = slope = (-1/1)

b = y-intercept = -3 or (0, -3)

Point 1: (0, -3)

Point 2: (-1, -2)

Point 3: (1, -4)

I hope this helps!

Answer:

Step-by-step explanation:

  y=-x-3

x | -3 | 0 |

y |  0 | -3|

1) x=-3

y=-(-3)-3

y=3-3

y=0

Thus, (-3,0)

2) x=0

y=-0-3

y=-3

Thus, (0,-3)

Answer:

30

Step-by-step explanation:

Answer:

y = -3(x + 2)^2 + 10.

Step-by-step explanation:

y = –3x2 – 12x – 2

Divide first 2 terms by -3:

y = -3(x^2 + 4x) - 2            Now complete the square on x^2 + 4x:-

y = -3(x^2 + 4x + 4 - 4) - 2

y = -3[(x + 2)^2 - 4] - 2

y = -3(x + 2)^2 + 12 - 2

y = -3(x + 2)^2 + 10.

Answer:

5:2

5x-30 = 2x+30

3x = 60

x = 20

total cars:

5(20)+2(20)

=100+40

=140cars

The value of the inequality expression given as –3(2x – 5) < 5(2 – x) are x < 5 and number line (4)

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The inequality expression is given as

–3(2x – 5) < 5(2 – x)

Open the brackets

So, we have

-6x + 15 > 10 - 5x

Collect the like terms

So, we have

5x -6x > 10- 15

Evaluate the like terms

So, we have

-x > -5

This gives

x < 5

When represented on a number line, it can be represented as the number line in option (4)

Hence, the equivalents of the inequality are x < 5 and number line (4)

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Answer:

the relation in the table is a function

the relation in the set of points is not a function

Step-by-step explanation:

the definition of a function is that one input (x) can only have one output (y). In the set of points, the input 4 appears twice, which means it is not a function.

6.85 miles is how deep it is. Under water, sound may travel 4700 feet in a second. The Time takes to travel the sound is 7.69.

Given that,

The deepest area in the ocean is the Marianas Trench in the Pacific Ocean. 6.85 miles is how deep it is. Under water, sound may travel 4700 feet in a second.

We have to calculate the time it takes for sound to travel from the ocean's surface to the Marianas Trench's depths and back, to the nearest tenth of a second.

We know the Distance formula is

Distance =rate×times

Time=Distance/rate

We convert 4700 feet to miles

We get,

4700 feet =0.89 miles

Now,

Time=6.85/0.89

Time=7.69

Therefore, the Time takes to travel the sound is 7.69.

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Answer: 40

Step-by-step explanation:

There are 9 cogs on the outside, and the circumference of a circle is 360 degrees. Dividing 360 by 9 yields 40 degrees.

The expected number of points as a function of a and b is C = b+a.

In this questions what we are been asked is for the expected value C, to solve the problem we need to recognize the random variables and their respective probability.

x1 = roll a 1 -> P1 = 1/6

x2 = roll a 2 -> P2 = 1/6

x3 = roll a 6 -> P3 = 1/6

x4 = roll a 1, 4 or 5 -> P4 = 1/2

E = P1*x1 + P2*x2 + P3*x2 + P4*x4

x1 is equal to zero (no points and the game stop), x2 is equal to C+b (win a points, affecting the expected value), x3 is equal to C-a (win b points, affecting the expected value) and x4 is equal B (no points are lost and the game continues, therefore the expected value is not affected)

C = 1/6*0 + 1/6*(C+b) + 1/6*(C-a) + 1/2*(C)

1/6*C = 1/6*b + 1/6a

Solving for C

C = b+a

Conclusion: If you get a "2, 4 or 5, this means the game will be unaffected (in terms of points), you need to pay special attention to x1 and x2 (all with the same probability)  that are the results that are going to affect your game.  

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The number of centers that will be needed to contain the guests is 5.

It should be noted that the question isn't well written but will be answered based on the information given.

From the information, a space center can have at most 7 guests and there are 31 guests. In this case, the number of space centers needed will be calculated by dividing the number of guests by the numbers that are contained in each center.

This will be:

= Number of guests / Number contained by each center

= 31 / 7

= 4 3/7

In this case, since there's a remainder of 3, this implies that we will need an extra space center. Therefore,the total space centre will be:

= 4 + 1

= 5

In this case, the value of 5 that's gotten simply shows the number of space centers that will be needed.

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No the value of functions are not same .

What is function in math?

  - 5 × ( -5)⁻⁹  =  -5 ×  1/-5⁹  ⇒ 1/5⁸  = 1/390625

[ -5 × (-5)]⁻⁹ = [25]⁻⁹  = 1/25⁹ = 1/3814697265625

No the value of functions are not same .

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Answer: the slope is 1

Step-by-step explanation: