construct the exponential function that contains the points (0,2) and (3,54)

Answers

Answer 1

The exponential function that passes through (0,2) and (3,54) is a growth function

The exponetial function is y = 2 * 3^x

How to construct the exponential function?

The points are given as:

(x,y) = (0,2) and (3,54)

An exponential function is represented as:

y = ab^x

Substitute the points in the equation

2 = ab^0 and 54 = ab^3

Solve 2 = ab^0

a = 2

Substitute 2 for a in 54 = ab^3

54 = 2b^3

Divide by 2

27 = b^3

Take the cube roots of both sides

b = 3

So, we have:

y = ab^x

This becomes

y = 2 * 3^x

Hence, the exponetial function is y = 2 * 3^x

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Related Questions

how do I write this out? Expand to write an equivalent expression…
1/2(-4x + 2y)

Answers

Answer:

-2x + y

Step-by-step explanation:

This is distributive property, so multiply the terms inside the parentheses by 1/2.

1/2 (-4x) = -2x

1/2(2y) = y

-2x + y


Derek bought a pair of pants for $35 and 3 shirts. He spent a total of $62.50. How much did each shirt cost? What is the equation for X?

Answers

Answer:

62.25=35+3x

62.25-35=27.25

27.25=3x

divide both sides by 3

x=9.08 or just 9

Jeremiah answered 20 out of 25 questions correctly on the math test. What percent of the questions did Jeremiah answer correctly?

Answer, explain and setup problem.

Answers

=20/25*100%
=2000/25%
=80%
Therefore she answered 80% answer correctly

I need help. Work has to be shown but i don’t know how to do them

Answers

Step-by-step explanation:

1.

1% of 500 is 5 so multiply 5 by 8 for one year. which is 40 so multiply that by 2.

1% of 500 = 5

5 × 8 = 40

40 × 2 = 80

2.

1% of 1000 = 10

10 × 5 = 50

50 × 3 = 150

3.

12 months = 6%

6/12 = 1 month

0.5 = 1 month

0.5 × 9 = 4.5 (the amount of interest for 9 months.)

800 × 4.5% = 36

4.

12 months = 7%

7/12 = 1 month ( i'll leave this in fraction form because of the decimal points.)

7/12 x 8 = 4.666667 or 4.7 rounded.

1200 × 4.7% = 56.40

Find the average of this set of numbers.2, 5, 6, 14, 83
A) 22
B) 20
C) 19
D) none of the above

Answers

the answer is D i added then subtracted

Two equivalent ratios are shown on the graph. How can you plot more equivalent ratios, starting at one of the plotted points? Select all that apply.

A. Move up 2 and right 1.
B. Move up 1 and right 2.
C. Move up 4 and right 2.
D. Move down 2 and left 1.
E. Move down 1 and left 2.

Answers

Answer:

A, move up 2 and right 1

Step-by-step explanation:

If you follow this rule, you can see that all those consistent dotted points will simplify to the same ratios.

Answer:

A, C, D

Step-by-step explanation:

First, we have to create a line based on the data.

Now, we know that the equation of the line is as follows

y = 2x

meaning that whenever we go a certain amount of units to the right or left, we move double that amount up or down

Now, A is equivalent to the Slope, so nthat is automatically equivalent.

C and D are both placed on the line, so they are correct

Another way to think about this is using fractions

x = 1/2 y

For A,

1 = 1/2(2)

For C,

2 = 1/2(4)

For D,

-1 = 1/2(-2)

Evaluate 9 divided by 3 [(18-6)-2 to the second power]

Answers

Answer: 24

I hope this helped

According to the line plot how many apples weigh 5/8 of a pound

Answers

Answer:

Answer:4 apples weigh 5/8 pound.

Step-by-step explanation:

Answer:

2(−5) − 10 = 2(0)

Step-by-step explanation:

If you substitute the values x = 0 and y = −5 into the second equation, you get a false statement

the sum of 3x and 1 is greater than-5 and less than or equal to 10

Answers

Answer:

x is greater than -2 and less than or equal to 3

Step-by-step explanation:

so the 3x + 1 is greater than -5

so 3x is greater than -6

we divide both sides by 3

then we find out that x is greater than -2

we also know that 3x + 1 is less than or equal to 10

so 3x is less than or equal to 9

we divide both sides by 3

then we find out that x is less or equal to 3

so we can say that x is greater than -2 and less than or equal to 3

After a 25% reduction, a sweater is on sale for $41.25.
What was the original price?

Answers

Let the original price be x.

x * (1 - 0.25) = $41.25

0.75x = $41.25

x = $41.25 / 0.75 = $55

Answer:

$55

Step-by-step explanation:

____ decrease by 25%= $41.25, which the unknown number is $55.

* WILL MARK BRAINIEST*
PLEASE HELP
7.03 Understanding Compound Events -

Record your results here:

Landing: Frequency:
heads, heads ____________
heads, tails ______________
tails, heads ______________
tails, tails ________________
TOTAL: 50
please help :))

Answers

Answer:

Tails, tail: 26

Heads: 9

Heads Tails: 26

Tails: 15


Step-by-step explanation:
(credit to the person who answered your question before me)

Have a great rest of your day
#TheWizzer

how many positive integers are between 28/3 and 83/5

Answers

Answer: ur dad

Step-by-step explanation:

lol

There are 7 positive integers in between 28/3 and 83/5.

What is an integer?

An integer is a whole number (not a fractional number) that can be positive, negative or zero.

Given that;

Two fractions are;

28/3 and 83/5.

Now, Write fraction into decimal form as;

28/3 = 9.33

83/5 = 16.6

So, All Integers in between 9.33 and 16.6 are;

⇒ 10, 11, 12, 13, 14, 15, 16

Thus, There are 7 positive integers in between 28/3 and 83/5.

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Need help with math probelm if do 5 stars and brainly points

Answers

Set up:-

Find volume of closet storageFind volume of each cubeDivide and get no of cubes

Solution:-

Here it's a cuboid

Length=L=6.5ftBreadth=B=4ftHeight=H=12.5ft

Volume:-

[tex]\\ \rm\rightarrowtail V=LBH[/tex]

[tex]\\ \rm\rightarrowtail V=6.5(4)(12.5)[/tex]

[tex]\\ \rm\rightarrowtail V=325ft^3[/tex]

For cubes

sides=0.25ft

Volume:-

[tex]\\ \rm\rightarrowtail V=side^3[/tex]

[tex]\\ \rm\rightarrowtail V=(0.25)^3[/tex]

[tex]\\ \rm\rightarrowtail V=0.015625ft^3[/tex]

Now

Total cubes:-

[tex]\\ \rm\rightarrowtail \dfrac{325}{0.015625}[/tex]

[tex]\\ \rm\rightarrowtail 20800cubes[/tex]

Arun and Benny started saving at the same time. Each day, Arun
saved $1.20 and Benny saved $0.30 more than Arun. How much would
Arun have saved if Benny saved $11.40 more than Arun?

Answers

Answer:

$45.60 would be what Arun would have saved.

help me please. either one is fine.

Answers

7)
95+(3x+23)+(7x-4)+(9x-6)+90 = (5-2) x 180
x = 18

9)
41+(3x+6)+(7x-11)+62+(4x+7)+(6x-5) = 360
x = 13


which is a better value? 1 pound of apples for 2.15 or 3 pounds of apples for 5.76

Answers

Answer:

From what i've gotten on another answer on brainl It might be 3 pounds of apples for 5.76. On another question i've resarched i've also gotten $7.91.

Step-by-step explanation:

Sorry if none of these answers have helped you.

Answer:

The 2nd offer - 3 pounds of apples for 5.76

Step-by-step explanation:

1. Find the unit price for the 1st offer.

The unit price is 1 pound of apples for $2.15.  <-- given information

2. Find the unit price for the 2nd offer.

We can set up a proportion to find the unit price.

3 pounds / $5.76 = 1 pound / $x

Let x = how much 1 pound of apples are for the 2nd offer

Cross multiply

3 · x = 5.76 · 1

Simplify

3x = 5.76

Divide both sides by 3 to isolate x

x = 1.92 = $1.92 for a pound of apples (2nd offer)

3. Compare the two offers' unit prices.

$2.15   <-- 1st offer

$1.92   <-- 2nd offer

The second offer is the better value because it costs less for each pound of apple.

I hope this helps and please mark me as brainliest!

20.
19. Make Sense and Persevere Use the Distributive
Property to expand 7(7x - 3y) - 6.
HELP PLEASE

Answers

Answer:

49x-21y-6

Step-by-step explanation:

7(7x) 7(-3y) -6

49x-21y-6=0

enter the value for x

Answers

12 times 7 equals 84 so the answer is 84

What is the sum of 1/4 and 5/12 ?

Answers

Answer: 8/12

Step-by-step explanation:

1/4 times 3 will give you 3/12 and add 5/12


Find the range, mean, and standard deviation of the data set
{8, 9, 8, 4, 4, 7, 18, 14}
The range is

(Type a whole number.)

The mean is

(Type an integer or a decimal.)

The standard deviation is

(Round the final answer to two decimal places as needed Round all intermediate values to three decimal places as needed.)

Answers

Answer:

mean: 8

medium:7

min: 4

max: 18

hope that helps

The perimeter of the rectangle below is 168 units. Find the length of side AB.
Write your answer without variables.
D
С
AB
0
4z + 1
SZ+2

Answers

Answer:

47

Step-by-step explanation:

10z + 4 + 8z + 2 = 168

first we find z

z = 9

5×9 +2 is 47

ANSWER IS 47

___________________cm

Answers

Answer:

10 cm

Step-by-step explanation:

mostly guess and check, 15 is 5 more than 10, and both added together is 25.

I REALLY NEED HELP MY GRADES GO IN TONIGHT AND I CANT SOLVE THIS I NEED A REAL ANSWER I WILL CHECK BEFORE GIVING POINTS!!!!!!!!!!!!!!!!!

Answers

Answer:

it's "whats shaking"

Step-by-step explanation:

Answer:

k=8.

n=12

a=29

h=5

i=297

g=89

Here are two fractions.
3/10 5/7

Work out which of the fractions is closer to 1/2

You must show your working.

Answers

Answer:

5/7

Step-by-step explanation:

Umm because the denominator 7 is less than 10 and 7 is the nearest number to 1/2

I hope it helps

1ST TO ANSWER GETS BRAINLIEST
What is the total area of the patio, walkway, and garden?

Answers

Answer:

82 ft²

Step-by-step explanation:

Help help help help help

Answers

Answer:

A' = (- 3, 0)

Step-by-step explanation:

[tex]A' = (x + 3, \: y - 2) \\ \\ \implies \: A' = ( - 6+ 3, \: 2 - 2) \\ \\ \implies \: A' = ( - 3, \: 0) [/tex]

Answer:

A' = (-3, 0)

Step-by-step explanation:

Pre-Image coordinate:

A (-6, 2)

Translation: (x, y) --> (x + 3, y - 2)

(-6 + 3, 2 - 2)

(-3 0)

Image coordinate:

A' = (-3, 0)

hope this helps!! p.s. i really need brainliest :)

A point located at (1, 8) is reflected over the x-axis. What are the coordinates of the image?

(-1, 8)
(8, 1)
(-1, -8)
(1, -8)

Answers

Answer:

(1, -8)

Step-by-step explanation:

In this case, we are reflecting. Since we are reflecting over the x axis, the only thing that will change will be the y.

----------------------------------------------------------------------------------------------------------

The x is staying the same because it is not moving. The y, however, is changing sides.

----------------------------------------------------------------------------------------------------------

Since the y is positive in its original spot, when you reflect over the x axis, you will have a negative y value, which is why it is a -8.

----------------------------------------------------------------------------------------------------------

I hope this helps!

-No one

Which describes the combined variation in the formula h=2a/b?
h varies jointly with 2 and A and inversely with b.
h varies directly with A and inversely with b.
h varies jointly with A and b.
h varies inversely with A and b.

Answers

Step-by-step explanation:

h varies directly with a and inversely with b.

2 is the constant of variation.

What is the equation of the parabola with focus (0, 1/2) and directrix y= -1/2

Answers

keeping in mind that the vertex is half-way between the focus point and the directrix, and since the focus point is above the directrix, meaning the parabola is a vertical parabola opening upwards, the parabola will more or less look like the one in the picture below, with a distance from the vertex of "p" being positive since it's opening upwards.

[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\begin{cases} h=0\\ k=0\\ p=\frac{1}{2} \end{cases}\implies 4(\frac{1}{2})(y-0)~~ = ~~(x-0)^2\implies 2y=x^2\implies y=\cfrac{1}{2}x^2[/tex]

A silo of a barn consists of a cylinder capped by a hemisphere. The
height of a cylinder is 60 feet and its diameter is 30 feet. What is the approximate volume of the entire silo

Answers

The approximate volume of the entire silo which consists of a cylinder capped by a hemisphere is 42,390 cubic feet

Volume of the silo

Volume of a cylinder = πr²h

where,

π = 3.14

Radius, r = diameter / 2

= 30 ft / 2

= 15 ft

Height, h = 60 ft

Volume of a cylinder = πr²h

= 3.14 × 15 × 15 × 60

= 42,390 cubic feet

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