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]
A farmhouse shelters 16 animals, some are pigs, and some are ducks. Altogether there are 42 legs. How many pigs are there?
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?
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!
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
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?
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
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
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.
Answer:
Show us the picture ijoejdjoemwpoe
Find the volume of the cone-
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
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
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
Answer: 10 I think not sure
Step-by-step explanation: 1/2 base times height-> 1/2(6•10)
Express 12 as a sum, a difference, a product, and a quotient.
Please help! Thank you! :))
what is 6.9 times 10^-2 in standard form? thanks :)
Answer:
0.069
Step-by-step explanation:
6.9 ×10^-2
69/1000
0.069
Rewrite using Radicals
Answer:
cannot be put into radical form, sorry!
Step-by-step explanation:
What is meant by the order of operations?
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
Answer:
yes,no, no, yes
Step-by-step explanation:
Which inequality represents all possible solutions of - 4n<16?
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
Answer:
Step-by-step explanation:
HERE ARE THE ANSWERS
What is 2x+7y=28 in slope intercept form
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.
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
Answer:
it is D) consecutive interior
Step-by-step explanation:
whats12 divided by 1/3 (infractions)
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?
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?
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?
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!
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
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
Solve for XSolve for X
Solve for X
Solve for X
Solve for X
Solve for X
Solve for X
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