Enter an equation for the function that includes the points.Give your answer in a(b)x. In the event that a=1 , give your answer in form (b)x. (2,2/3) and 3,5/9 The equation is f(x)=

Answers

Answer 1

Answer:

[tex]f(x) = \frac{24}{25} * \frac{5}{6}^x[/tex]

Step-by-step explanation:

Given

[tex](x_1,y_1) = (2,\frac{2}{3})[/tex]

[tex](x_2,y_2) = (3,\frac{5}{9})[/tex]

Required

Write the equation of the function [tex]f(x) = ab^x[/tex]

Express the function as:

[tex]y = ab^x[/tex]

In: [tex](x_1,y_1) = (2,\frac{2}{3})[/tex]

[tex]y = ab^x[/tex]

[tex]\frac{2}{3} = a * b^2[/tex] --- (1)

In [tex](x_2,y_2) = (3,\frac{5}{9})[/tex]

[tex]y = ab^x[/tex]

[tex]\frac{5}{9} = a * b^3[/tex] --- (2)

Divide (2) by (1)

[tex]\frac{5}{9}/\frac{2}{3} = \frac{a*b^3}{a*b^2}[/tex]

[tex]\frac{5}{9}/\frac{2}{3} = b[/tex]

[tex]\frac{5}{9}*\frac{3}{2} = b[/tex]

[tex]\frac{5}{3}*\frac{1}{2} = b[/tex]

[tex]\frac{5}{6} = b[/tex]

[tex]b = \frac{5}{6}[/tex]

Substitute 5/6 for b in (1)

[tex]\frac{2}{3} = a * b^2[/tex]

[tex]\frac{2}{3} = a * \frac{5}{6}^2[/tex]

[tex]\frac{2}{3} = a * \frac{25}{36}[/tex]

[tex]a = \frac{2}{3} * \frac{36}{25}[/tex]

[tex]a = \frac{2}{1} * \frac{12}{25}[/tex]

[tex]a = \frac{24}{25}[/tex]

The function: [tex]f(x) = ab^x[/tex]

[tex]f(x) = \frac{24}{25} * \frac{5}{6}^x[/tex]


Related Questions

A farmhouse shelters 16 animals, some are pigs, and some are ducks. Altogether there are 42 legs. How many pigs are there?

Answers

Answer:

5 pigs

Step-by-step explanation:

A farmhouse shelters 16 animals, some are pigs, and some are ducks. Altogether there are 42 legs. How many pigs are there?

Let us represent:

Number of pigs = x

Number of ducks = y

Our system of equations is given as:

A farmhouse shelters 16 animals, some are pigs, and some are ducks.

x + y = 16...... Equation 1

x = 16 - y

Altogether there are 42 legs.

Ducks have 2 legs(feet) , pigs have 4 legs,

4x + 2y = 42..... Equation 2

We substitute

16 - y for x in Equation 2

Hence:

4(16 - y) + 2y = 42

64 - 4y + 2y = 42

Collect like terms

- 4y + 2y = 42 - 64

-2y =- 22

y = -22/-2

y = 11 ducks

Solving for x.

x = 16 - y

x = 16 - 11

x = 5 pigs

Therefore, we have 5 pigs

A quartic polynomial P(x) has rational coefficients. If 2 − i and-√5 are roots of P(x) = 0, what are the other 2 roots?

Answers

Answer:

2 + i and + √5

Step-by-step explanation:

Since P(x) is a quartic equation, it has 4 roots.

Since 2 - i and -√5 are two of its roots, then its conjugate pairs of 2 + i and + √5 are its other two roots.

So, its other two roots are 2 + i and + √5

PLEASE HELP! Explanation and answer please!!!! :(

Thanks!

Answers

9514 1404 393

Answer:

  x = 19.25

Step-by-step explanation:

Each half of the rhombus is an isosceles triangle. The two "base" angles are the same measure, and the sum of all angles is 180°:

  (2x -1)° +(2x -1)° +(4x+28)° = 180°

  8x = 154 . . . . . . . . . . divide by °, collect terms, subtract 26

  x = 154/8

  x = 19.25

__

Check

The angle measures are ...

  (2x -1)° = (2(19.25) -1)° = 37.5°

  (4x +28)° = (4(19.25) +28)° = 105°

Then the angle sum is 37.5 +37.5 +105 = 180, as it should be.

what is 3 (2х-5) 2х+3=1

Answers

3(2x-5)+2x+3=1

6x-15+2x+3=1

8x-12=1

    +12 +12

8x=13

/8   /8

x=1.625

---

sorry if this doesn't help

What would be the best estimate for the height of a front door?

Answers

Answer: The height of a standard door is about 2 m. The length of an adult pace is about 1 m. The length of a size 8 shoe is about 30 cm. Most adults are between 1.5 m and 1.8 m in height.

Step-by-step explanation:

Answer the question pls

Answers

Answer:

f=54

Step-by-step explanation:

ma is m times a 3x18= 54

Answer:

F = -54

Step-by-step explanation:

You plug in the numbers that you can

so.. F = ma     -ma= m * a

M= 3

a = -18

F = 3* (-18)

because there is one (-) number and you are multiplying your answer is going to be (-)

F= -54

The diameter of a circle is 4 units.
What is the radius of the circle?
units

Answers

Answer:

radius = D/2

Step-by-step explanation:

radius= 4unit/2

=2unit

The diagram shows a square ABDE and an isosceles triangle BCD.
Angle C = 40°

Work out the size of angle EBC.


Answers

Answer:

Show us the picture ijoejdjoemwpoe

Find the volume of the cone-

Answers

Answer:

12.6ft³

Step-by-step explanation:

Hey There!

So the first thing we need to do is find the formula for volume of a cone

[tex]V=\pi r^{2} \frac{h}{3}[/tex]

r = radius

h = hypotenuse

Now all we have to do is plug in the hypotenuse and the radius

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

2²=4

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

4xπ=12.5663706144

And now we just round to the nearest tenth

so we can conclude that the volume of the cone is 12.6ft³

Which equation has exactly ONE solution?
A) 3 + 10x / 2 = 4x + 2
B) 15x − 5 / 3 = 5x + 4
C) 2 + 6x / 2 = 3x + 1
D) 4x − 10 / 2 = 2x − 5

Answers

Answer:

the answer is d.

Step-by-step explanation:

please mark brainliest

Answer:

I don't know  because

Step-by-step explanation:

A= -1

B)= 17/30

C)= has no solutions

D)= 0

A square has a radius of 10 ft. Find the area of the square

Answers

Answer:

Hello hello

Step-by-step explanation:

Answer:

a square does not have a radius

Step-by-step explanation:

but you can find the area by squaring one side

What is the base of the triangle? Pls I need it ASAP

Answers

Answer: 10 I think not sure

Step-by-step explanation: 1/2 base times height-> 1/2(6•10)

A triangle is B x H divided by 2. If the area is 30, then to work backwards we multiply it by 2. That gets us 60, and if one of the sides is 6, that can only mean it’s 10

Express 12 as a sum, a difference, a product, and a quotient.

Answers

6+6, 13-1, 6x2, 24/2
5+ 7 =12
100- 88 =12
3x 4 = 12
24 divided by 2 =12

Please help! Thank you! :))

Answers

The percent increase is a 30% increase.
Explaination: if you take 195-150 and get 45, you get close to 30% so it’s pretty close to the answer.

what is 6.9 times 10^-2 in standard form? thanks :)

Answers

Answer:

0.069

Step-by-step explanation:

6.9 ×10^-2

69/1000

0.069

Rewrite using Radicals

Answers

Answer:

cannot be put into radical form, sorry!

Step-by-step explanation:

What is meant by the order of operations?

Answers

Answer:

Step-by-step explanation: The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Choose Yes or No to tell whether the Addition Property of Inequality can be used to solve each statement.
1. w – 4 > –10
2. 12 ≥ 20x
3. 7y10 ≤ 5.5
4. –3.25 < x – 9.75

Answers

Answer:

yes,no, no, yes

Step-by-step explanation:

Which inequality represents all possible solutions of - 4n<16?

Answers

4n is the soultioncAnswer:

Step-by-step explanation:

Write the inequality represented by each graph..
Graph one : (0,-1) (6,3)

Graph two : (0,3) (4,-5)


Help

Answers

Answer:

Step-by-step explanation:

HERE ARE THE ANSWERS

What is 2x+7y=28 in slope intercept form

Answers

Answer:

y = -2/7x + 4

A right rectangular prism has a square base and a volume of 225 cubic centimeters. The height, h, of the prism is 9 centimeters. Find the area of the base, B. A. B. C. D.

Answers

Answer:

Area of base = 25cm

Step-by-step explanation:

The formula for the volume of a rectangular prism is:

Volume = length × width × height = lwh

for a square base, length = width

∴ volume = l × l × h = l²h

where:

l = length

h = height = 9cm

volume = 225 cm³

∴ 225 = l² × 9

l² = 225 ÷ 9

l² =  25

∴ length = √ 25 = 5cm

Area of base = Length × Length = 5 × 5 = 25cm

Anybody know ? Need help

Answers

Answer:

it is D) consecutive interior

Step-by-step explanation:

whats12 divided by 1/3 (infractions)

Answers

12 divided by 1/3 is also equal to 12 times 3.

12x3=36

To double check, you could use a calculator, but the answer would still be 36.

sorry if this doesn't help

Answer:

36/1

36

Step-by-step explanation:

What is the slope-intercept equation for the line below?

Answers

Answer:

Answer is C

Step-by-step explanation:

You are walking to the park and see several children and dogs running around. You count 19
heads and 52 legs. How many children did you see? How many dogs did you see?

Answers

MINECRAFT > FORTNITE

Answer:

13 dog's and 6 children

Step-by-step explanation:

karen is building a house in Norfolk, Virginia. She would like a bedroom that is 12 feet in length by 10 feet in width. What is the area of the bedroom?

Answers

Answer:

POINTFARMER.EXE=EZ

Step-by-step explanation:

Answer:

120 feet^2

Step-by-step explanation:

PLEASE HELPPP! I have to solve for X, this was my warmup but I'm not smart and I need to turn it in today!

Answers

Answer:

X=8

Step-by-step explanation:

48+22=70

4×8=48

so X is 8

Evaluate using P E M D A S 2 x 3 + 4

Answers

Step-by-step explanation:

We would do multiplication first, because of order of operations.

2x3=6

Now we add.

6+4=10

hope it helps! :3

First (2•3)+4
Then 6+4
Equals =10

Solve for XSolve for X
Solve for X
Solve for X
Solve for X
Solve for X
Solve for X

Answers

Answer:

Step-by-step explanation:

Because the angles are opposite each other they are equal so we can say

4x-25=75

4x=100

x=25

x= 25

4x -25 = 75 ( vertically opposit angle)

4x = 100

x = 100/4

x= 25

angle = 75

hope it helps

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