Sam wants to create a linear function and an exponential function, both of which have a y-intercept
of (0,8) and pass through the point (9,512). Help Sam create his functions.

Answers

Answer 1

Step-by-step explanation:

Exponential function is

[tex]y = a \times {b}^{x} [/tex]

where a is the y intercept, or the initial value.

b is the constant rate.

Since a is the y intercept, this means a is 8. So we have

[tex]y = 8 \times {b}^{x} [/tex]

Now, plug in 9 for x. 512 for y to find b.

[tex]512 = 8 \times {b}^{9} [/tex]

[tex]64 = {b}^{9} [/tex]

[tex] \sqrt[9]{64} = b[/tex]

[tex]64 {}^{ \frac{1}{9} } = b[/tex]

[tex]4 {}^{ \frac{1}{3} } = b[/tex]

[tex] \sqrt[3]{4} = b[/tex]

So the equation is

[tex]y = 8( \sqrt[3]{4} ) {}^{x} [/tex]


Related Questions

find the area of the shaded region. please show your work​

Answers

Answer:

≈184.25

Step-by-step explanation:

1) if r=10 and 'a' is the length of the side of the triangle, then the ratio

a=r√3;

2) the required area can be calculated as

A=πr²-√3/4*a²; ⇔ A=πr²-3√3/4 r²;

3) according to the formula above, the required area:

[tex]A=r^2(\pi -\frac{3\sqrt{3} }{4} ); \ = > \ A=100*(3.1415-\frac{3*1.7321}{4})=184.2462[/tex]

What is the slope for the graph shown? Leave he answer as a fraction and simplify if necessary

Answers

Answer:

Slope 1/3

Step-by-step explanation:

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!

Answer:

slope = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (3, - 1) and (x₂, y₂ ) = (9, 1) ← 2 points on the line

m = [tex]\frac{1-(-1)}{9-3}[/tex] = [tex]\frac{1+1}{6}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

Help I don't knoz if this is right but I think the answer is d​

Answers

-10k + 15
15 -4k-6k
Yes! The answer would be D.

Why would you want a small remote valve and a large valve close to the cylinder?

Answers

An individual will want small remote valve and a large valve close to the cylinder in order to build the pressure.

What is pressure?

It should be noted that pressure simply means the measure of the force that's applied over a unit area.

In this case, an individual will want small remote valve and a large valve close to the cylinder in order to build the pressure between each valve and also create more pressure for the cylinder.

Learn more about pressure on:

https://brainly.com/question/25736513

Can u do these for me

Answers

Answer:

Step-by-step explanation:

Compare the decimals using >, <, or =

2.95 > 2.949 (2.95 can be written as 2.950, which is > 2.949)3.75 < 3.8 (3.8 can be written as 3.80, which is > 3.75)0.98 = 0.980 (0.98 can be written as 0.980, which is = 0.980)0.86 < 0.861 (0.86 can be written as 0.860, which is < 0.861)1.76 < 2 (2 can be written as 2.00, which is > 1.76)3.15 < 3.2 ( 3.2 can be written as 3.20, which is > 3.15)

Name two equivalent fractions for each fraction listed below.

2/4 = 1/2 = 4/81/3 = 2/6 = 3/91/10 = 2/20 = 3/30

If there are 16 cups in one gallon, how many cups are in 3 gallons?

16 cups = 1 gal.

? cups = 3 gals.

3 * 16 = 48 cups

How many cups are in 5 gallons?

5 * 16 = 80 cups

Compare and contrast squares are rectangles

Squares: have four sides and four equal sides

Rectangles: have four sides and have 2 parallel sides, meaning that they have 2 opposite sides that are equal.

Hope this helps!

The volume of this right prism is 266.5 ft³.

What is the height, x, of the prism?

Enter your answer as a decimal in the box.

x =
ft

Answers

Hey there!

1/2 lwh = v

lwh = 2v

h = 2v/lw

Formula:

H = 2v / l w

H = 2(266.5ft³)/lw

H = 533/lw

Other length are Missing like length and width

Incomplete question

Answer:

The answer is 8.2, I took the test.

Which statement is correct?

Answers

Answer:

C because the answer is right

grade 6 math 1. Mr. Carlos bought a T-shirt for ₱ 254.95. Round this off to the nearest peso.

Answers

Answer:

255

Step-by-step explanation:

254.95

.95 is closest to 255.

254.95...255.

solve for x and please roundddd

Answers

Should be 37 degrees

We know the lengths of the adjacent and opposite sides when looking at the angle x, so we use those two sides to find the trig ratio.

So we use Opposite/adjacent (Tangent) Which is 54/72=0.75

Now we get out the trig ratio table. Because we used the tangent ratio (O/A) , we use that column to look for the closest number to 0.75.
The closest is 0.754, and the degree for it is 37 degrees

Rlly hope this helps :)))

Writing Equations of Parallel Lines
y
5
What is the equation of the line parallel to the given line
with an x-intercept of 4?
y =
4
V
3
2
-5 4 3 2 1
2
5
-1
-2
-3
-5
Intro
Done

Answers

Answer:

  y = 4x -16

Step-by-step explanation:

The equation of the parallel line can be written from the given x-intercept when we know its slope. The slope will be the same as that of the graphed line. It can be found using the slope formula with the marked points (-3, -3) and (-1, 5).

  m = (y2 -y1)/(x2 -x1)

  m = (5 -(-3))/(-1 -(-3)) = 8/2 = 4 . . . . . slope of the lines

The point-slope equation for the line with slope 4 through point (4, 0) will be ...

  y -k = m(x -h) . . . . line with slope m through point (h, k)

  y -0 = 4(x -4) . . . . line with slope 4 through the given x-intercept

  y = 4x -16 . . . . . . expanded to slope-intercept form

32. Michelle invested $10,000 in an account that earns 8.5% interest that is compounded monthly. Write an exponential model for the balance of the account, then determine the amount of money in the account in 15 years. Answer: Equation:​

Answers

Answer:

$25,626.53

Step-by-step explanation:

You are going to want to use the compound interest formula, which is shown below.

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 8.5% into a decimal:

8.5% ->  -> 0.085

Now lets plug in the values into the equation

Lastly, subtract the total from the initial balance:

Michelle earned $25,626.53 in interest.

If f(x) = x + 1, and g[f(x)] = x, what is g(x)?

Answers

Answer:

x-1

Step-by-step explanation:

f(x) = x+1

g[f(x)] = x

g[x+1]=x

g(x)=x-1

how many 1/4 foot cubes would fill the inside of a rectangular prism

Answers

Answer: 192 cubes.

Step-by-step explanation:  Each cube with side lengths of 1/4 have a volume of (1/4)3 which means each cube’s volume is 0.015625 cubic units. To find how many cubes are needed to fill the prism, divide 3 cubic units by 0.015625 cubic units. Your answer will be 192 cubes.

Tim wants to buy soda. He can choose a 6-pack of 0.355-liter cans or a 2-liter bottle. Which statement is true?
The 6-pack contains 0.130 liters more soda.
The 2-liter bottle contains 0.130 liters more soda.
The 2-liter bottle contains 0.645 liters more soda.
The 6-pack contains 0.645 liters more soda.

Answers

Answer:

The 6-pack contains 0.130 liters more soda.

What would be the formula if the farm agency could only use the letters A, B, C, and blank spaces?

Answers

The formula of the farm agency illustrates a geometric progression

The formula the farm agency could use is y = 3^n

How to determine the formula?

The number of characters is given as:

n(A,B,C) = 3

Represent the number of tags to create with y.

So, we have:

y = 3×3×3×3×..........×3( in n places)

Express as exponent

y = 3^n

Hence, the formula the farm agency could use is y = 3^n

Read more about formulas at:

https://brainly.com/question/2500080

Answer: y=4^n

Step-by-step explanation: I got the question right and this was the answer, I believe its because the company uses A,B,C and blank spaces so that adds one.

The price of a ring was increased by 9% to £1800. What was the price before the increase? Give your answer to the nearest penny.

Answers

Price after 9% increased 1800
Price before increase 1800-9%*1800
=1638

From the coordinate 8,12 to 10 and 15 what was the scale factor

Answers

Answer:

Scale factor is 5/4

Step-by-step explanation:

To find scale factor make a fraction. New coordinates/old coordinates

Make the fractions and reduce.

10/8  and 15/12

5/4 and 5/4

The scale factor is 5/4

-2 (3x -5) -2= 22 - 68

Answers

Answer:

9

Step-by-step explanation:

Answer:

i belive the awnser is 9

Step-by-step explanation:

help 1 hour left please

Answers

Answer: 110 degrees

Step-by-step explanation:

Find the volume of the prism.

Answers

Answer:

the volume is 210

Step-by-step explanation:

length x width x height

length=6

width=5

height=7

6 x 5 = 30

30 x 7 = 210

ABC is a straight line. BD=BC Angle ADB=80° Angle BDC=20° Work out the size of the angle marked x. Give reason for your answer. ​

Answers

Answer:

hai

Step-by-step explanation:

Pak Awi mau beli jam tangan Rolex hulk submarine dengan harga 300jt. Dia mau beli 2 tahun lagi

dengan asumsi harga jam naik 2% / tahun. Future Value

Uang pak awi sekarang hanya 100jt, berapa yang harus pak awi tabung tiap bulan nya agar 2 tahun lagi

dia bisa beli jam tangan tersebut, jika bunga tahunan adalah 15% / tahun (pajak = 10%) ??? Present

value. Future value. Present value annuity.

Bunga di terima per bulan, dan tetap di gulung.

Ya Berapa yang dia tabung tiap bulan

-pakai tabel

Can someone help me with these questions

Answers

Answer:

Step-by-step explanation:

When you take the n-th root of a number, you can rewrite the expression by taking it to the 1/n-th power. For example:

[tex]\sqrt[n]{x} =x^\frac{1}{n}[/tex]

For the first expression, we can use this proprtery to get:

[tex]\sqrt[5]{a^x} =(a^x)^\frac{1}{5}[/tex]

Using exponent rules, you can combine the exponents by simply multiplying them to get:

[tex]a^\frac{x}{5}[/tex]

Moving on to the second expression. It is now the square root, or equivalently a 1/2 power. If we break up the terms under the radical into powers of 2, we can cancel a lot of the terms:

[tex]\frac{\sqrt{81a^3b^1^0} }{\sqrt{3}a } =\frac{\sqrt{81a^2*a*b^1^0} }{\sqrt{3}a }[/tex]

The a^2 and b^10 can be taken out of the radical because they have perfect roots:

[tex]\frac{\sqrt{81a^2*a*b^1^0} }{\sqrt{3}a }=ab^5\frac{\sqrt{81a} }{\sqrt{3}a }[/tex]

The square root of 81 has a perfect root of 9. We have:

[tex]ab^5\frac{\sqrt{81a} }{\sqrt{3}a }=9ab^5\frac{\sqrt{a} }{\sqrt{3}a }[/tex]

You can divide 9 and the square root of 3 by breaking up 9 into a product:

[tex]\frac{(3*3)ab^5}{\sqrt{3} } \frac{\sqrt{a} }{a }=3\sqrt{3} ab^5\frac{\sqrt{a} }{a }[/tex]

Simply by cancelling the 'a' terms to get:

[tex]3\sqrt{3} ab^5\frac{\sqrt{a} }{a }={3\sqrt{3}}\sqrt{a}b^5=3b^5\sqrt{3a}[/tex]

by finding tan θ in 2 different triangles find the value of m

Answers

Answer:

m = 3.75

Step-by-step explanation:

tanθ = 3/4θ = 37°

⇒ Angle opposing 3 in the left triangle is 53°

sin53° ⇒ 4/5 = 3/m4m = 15m = 15/4m = 3.75

A circle has a radius of 9 cm and a sector of the circle has an arc length of 9. 7cm

Answers

Answer:

S = R θ      where θ is in radians

If θ  = 2 pi then S = 2 pi R       the circumference of the circle

θ = S / R = 9.7 / 9 = 1.08 rad

Since 1 rad = 360 / (2 pi) = 57.3 deg

the angle included = 1.08 rad * 57.3 deg/rad = 61.9 deg

3 3/5 + 1 1/6 answer as a fraction

Answers

Answer:

[tex]\boxed{\sf{4\dfrac{23}{30} }}[/tex]

Step-by-step explanation:

It is necessary to add the whole numbers of fractions from left to right in order to solve this problem.

3 3/5+1 1/6

First, you have to add the whole numbers.

3+1=4

After that, you can combine by a fraction.

6*3=18

18/5+ 1 1/6

1+6=7

7/6

Rewrite the problem down.

18/5+7/6

Solve.

5*6=30

143/30

=23/30

[tex]\boxed{\sf{4\dfrac{23}{30} }}[/tex]

Therefore, the final answer is 4 23/30.

I hope this helps you! Let me know if my answer is wrong or not.

express 59/2^4×5^4 in decimal form.
answer asap. Ill mark brainliest​

Answers

Answer:

~Male Y/n here~ I think this would be your question in decimal form,

2304.6875

(Hope this helps!)

Let x, y, and z represent three rational numbers, such that y is 512 times x and z is 50.25 more than x. If y=15.5, what is the value of z?
Enter your answer in the grid.
WHAT IS Z?

Answers

Answer:

z = 50.2802734375

Step-by-step explanation:

y = 15.5

y is 512 times x

z is 50.25 more than x

15.5/512 = 0.0302734375

x = 0.0302734375

0.0302734375 + 50.25 = 50.2802734375

z = 50.2802734375

Thank you please help if you can

Answers

Answer:

The answer is -

15.5^2 Mi

Give brainliest if it helps you

solve for the missing side

Answers

Answer: D

Step-by-step explanation:

Trigonometry, how would I find the area of this triangle?

Answers

Answer:

Step-by-step explanation:

Area of triangle = 1/2 * base * height

Use the side of length 5.6cm as base, the height will be a perpendicular line from the base to the tip of the triangle.

From the right-angle triangle formed by the height and the side of length 3.9cm,

sin(56°45') = height / 3.9

height = 3.9*sin(56°45')

Substituting back into the area equation:

Area = 1/2*5.6*3.9*sin(56°45')

= 9.0cm^2

= 9cm^2

Use sine rule for Area

[tex]\\ \rm\rightarrowtail Area=\dfrac{1}{2}absinC[/tex]

[tex]\\ \rm\rightarrowtail Area=\dfrac{1}{2}(3.9)(5.6)sin56°45'[/tex]

[tex]\\ \rm\rightarrowtail Area=10.92(0.836)[/tex]

[tex]\\ \rm\rightarrowtail Area=10.22cm^2[/tex]

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