Answers
Answer:
[tex]\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x[/tex]
Step-by-step explanation:
Exponential Function
The exponential function can be written with the general equation:
[tex]f(x)=A\cdot r^x[/tex]
Where A is the value when x=0 and r>0 is the ratio. If r is greater than 1, the function is increasing, if r is less than 1, the function is decreasing.
The table shows the relation between values of x and values of the function y. Note that as x increases (one by one), y decreases with a ratio of 1/2. Only the last two choices have ratios of r=1/2. We only have to test which one of them has the correct value of y=4 when x=0.
Substituting in the third function:
[tex]\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x[/tex]
[tex]\displaystyle f(0)=4\cdot\left(\frac{1}{2}\right)^0[/tex]
[tex]f(0) = 4[/tex]
This gives the correct value of f(0)=4.
Substituting in the fourth function:
[tex]\displaystyle f(x)=\frac{1}{2}\cdot\left(\frac{1}{2}\right)^x[/tex]
[tex]\displaystyle f(0)=\frac{1}{2}\cdot\left(\frac{1}{2}\right)^0[/tex]
[tex]f(0) = \frac{1}{2}[/tex]
This choice is wrong
Correct choice:
[tex]\boxed{\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x}[/tex]
Related Questions
Math equation with its graph
a) y=3x+2
b) y= -x+5
c) y= 2x-1
d) y= -4x
See picture attached
Please help
Answers
Answer:
y=3x+2 to B
y=-x+5 to D
y=2x-1 to C
y=-4x to A
Find the area of a rectangle whose length is 5 ½ feet long and 1 3/4 feet wide.
Answers
Answer:
11/2 x 7/4 = 77/8 = 9 5/8
Step-by-step explanation:
25. Explain the Error Jeremy factored 144x? – 100 as follows:
144x2 100 = (12x + 10)(12x – 10)
= 2(6x + 5)(6x – 5)
What was his error? Correct his work.
Answers
Given:
Consider the expression is
[tex]144x^2-100[/tex]
Jeremy factored the given expression and his steps are given.
To find:
The error in his solution.
Solution:
We have,
[tex]144x^2-100[/tex]
It can be written as
[tex]=12^2x^2-10^2[/tex]
[tex]=(12x)^2-10^2[/tex]
[tex]=(12x+10)(12x-10)[/tex] [tex][\because a^2-b^2=(a+b)(a-b)][/tex]
Taking out common factors from each parenthesis.
[tex]=2(6x+5)2(6x-5)[/tex]
[tex]=4(6x+5)(6x-5)[/tex]
So, Jeremy was incorrect because the common factor is [tex]2\times 2=4[/tex] instead of 2.
Therefore, Jeremy made his mistake in his last step.
A light bulb is designed by revolving the graph of:
[tex]y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}[/tex]
Over the interval 0 ≤ x ≤ 1/3 about the x-axis, where x and y are measured in feet. Find the surface area of the bulb and use the result to approximate the amount of glass needed to make the bulb. (Glass is 0.015 inch thick).
Answers
Answer:
[tex]\displaystyle 0.251327 \ in. \ of \ glass[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsExpand by FOIL (First Outside Inside Last)FactoringCalculus
Differentiation
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
Integration Property: [tex]\displaystyle \int\limits^a_b {cf(x)} \, dx = c \int\limits^a_b {f(x)} \, dx[/tex]Fundamental Theorem of Calculus: [tex]\displaystyle \int\limits^a_b {f(x)} \, dx = F(b) - F(a)[/tex]Area between Two CurvesVolumes of RevolutionArc Length Formula: [tex]\displaystyle AL = \int\limits^a_b {\sqrt{1+ [f'(x)]^2}} \, dx[/tex]Surface Area Formula: [tex]\displaystyle SA = 2\pi \int\limits^a_b {f(x) \sqrt{1+ [f'(x)]^2}} \, dx[/tex]Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}\\Interval: [0, \frac{1}{3}][/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle y' = \frac{1}{2} \cdot \frac{1}{3}x^{\frac{1}{2} - 1} - \frac{3}{2} \cdot x^{\frac{3}{2} - 1}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{1}{6}x^{\frac{-1}{2}} - \frac{3}{2}x^{\frac{1}{2}}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}[/tex]Step 3: Integrate Pt. 1
Substitute [Surface Area]: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{1+ [\frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}]^2}} \, dx[/tex][Integral - √Radical] Expand/Add: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{81x^2+18x+1}{36x}} \, dx[/tex][Integral - √Radical] Factor: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{(9x + 1)^2}{36x}} \, dx[/tex][Integral - Simplify]: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {-\frac{|9x + 1|(3x - 1)}{18}} \, dx[/tex][Integral] Integration Property: [tex]\displaystyle SA = \frac{- \pi}{9} \int\limits^{\frac{1}{3}}_0 {|9x + 1|(3x - 1)} \, dx[/tex]Step 4: Integrate Pt. 2
[Integral] Define: [tex]\displaystyle \int {|9x + 1|(3x - 1)} \, dx[/tex][Integral] Assumption of Positive/Correction Factors: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} \int {(9x + 1)(3x - 1)} \, dx[/tex][Integral] Expand - FOIL: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} \int {27x^2 - 6x - 1} \, dx[/tex][Integral] Integrate - Basic Power Rule: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} (9x^3 - 3x^2 - x)[/tex][Expression] Multiply: [tex]\displaystyle \frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|}[/tex]Step 5: Integrate Pt. 3
[Integral] Substitute/Integral - FTC: [tex]\displaystyle SA = \frac{- \pi}{9} (\frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|})|\limits_{0}^{\frac{1}{3}}[/tex][Integrate] Evaluate FTC: [tex]\displaystyle SA = \frac{- \pi}{9} (\frac{-1}{3})[/tex][Expression] Multiply: [tex]\displaystyle SA = \frac{\pi}{27} \ ft^2[/tex]It is in ft² because it is given that our axis are in ft.
Step 6: Find Amount of Glass
Convert ft² to in² and multiply by 0.015 in (given) to find amount of glass.
Convert ft² to in²: [tex]\displaystyle \frac{\pi}{27} \ ft^2 \ \div 144 \ in^2/ft^2 = \frac{16 \pi}{3} \ in^2[/tex]Multiply: [tex]\displaystyle \frac{16 \pi}{3} \ in^2 \cdot 0.015 \ in = 0.251327 \ in. \ of \ glass[/tex]And we have our final answer! Hope this helped on your Calc BC journey!
You want to add lace around the outside of your circular kitchen table cloth. If the diameter of the table cloth is 16 cm, then which of the following measurements would represent how much lace you need?
Answers
The length of lace would be the circumference of the circle.
Circumference = diameter x Pi
Circumference = 16pi cm
Circumference = 50.24 cm ( approximately)
Answer:
The circumference of the circle.
Step-by-step explanation:
b2-5c
b=15 & c=9
if you can show the work it would be really helpful:)
Answers
This table represents the relationship between m, the amount of
money an employee has in the morning, and p, the amount of
money an employee has later in the day after they receive their
paycheck.
Which equation represents the relationship in the table?
a) p=m-160.25
b) p=160.25-m
c)p=m+160.25
d)p=200.25m+160.25
Answers
Answer:
bB
Step-by-step explanation:
The correct equation which represents the relationship in the table is,
⇒ p = m + 160.25
Where, m, the amount of money an employee has in the morning, and p, the amount of money an employee has later in the day after they receive their paycheck.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
This table represents the relationship between m, the amount of money an employee has in the morning, and p, the amount of money an employee has later in the day after they receive their paycheck.
Hence, By all options, we can check by substitute the given values.
So, By option 3;
The equation is,
⇒ p = m + 160.25
Substitute m = 200.25,
⇒ p = 200.25 + 160.25
⇒ p = 360.50
Thus, The correct equation which represents the relationship in the table is,
⇒ p = m + 160.25
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
Solve the system of equations by Linear Combination (Elimination)
6x - 2y = 16
x + 2y = 5
a) (3,1)
b) (1,3)
c) Infinite Many Solutions
d) No Solution
PLEASE PLEASE PLEASE HELPPP MEEE
Answers
The two triangles shown are similar. Find the value of b.
Answers
Answer:
Since the corresponding sides of similar triangles are proportional,
[tex]\frac{a}{b}= \frac{2.1}{1.4} =\frac{3}{2}[/tex]
Kate has 48 softballs. She wants to divide them evenly among b softball bags. Which expression represents how many softballs she should put into each bag?
Answers
Answer:
Softballs = (48/b)
Step-by-step explanation:
Given that,
Total number of softballs = 48
She wants to divide them evenly among b softball bags.
We need to find an expression that represents how many softballs she should put into each bag.
As it is dividing among b softball, it means we divide 48 and b. So,
[tex]s=\dfrac{48}{b}[/tex]
Hence, the required expression is (48/b).
Division as Fractions - Word
Name
cach problem. Make sure to write your answer as a fraction.
Henry wanted to collect 65 pounds of cans in 7 days. How much should he
collect each day to reach his goal? Which two whole numbers does your
answer lie between?
Answers
Answer:
65/7
=9.28..lies btwn 9 and 10
Step-by-step explanation:
A store sells a pound of bananas for $0.40 and a pound of cabbage for $0.56. Can you buy more pounds of bananas or cabbage with $7? How many more pounds?
Answers
Answer:
The bananas will cost $1.38.
Step-by-step explanation:
Explanation:
Multiply the number of pounds by the price per pound.
2.51lb×$0.55lb=$1.38
A group of friends wants to go to the amusement park. They have no more than $275 to spend on parking and admission. Parking is $5, and tickets cost $27 per person, including tax. Write and solve an inequality which can be used to determine r, the number of people who can go to the amusement park.
Answers
Answer:
275=27x+5
Step-by-step explanation:
10 people can go to the park
27(10)+5=275
Please I need help this is already late
Answers
the first would be A and hopes this helps
5/8^3+9-1/4^3= I really need help!!!
Answers
Answer: 3/8q^3 + 9
Step-by-step explanation:
1. combine like terms 5/8q^3 - 1/4q^3, need to make denominator the same to subtract so multiply 2/2 by 1/4q^3, 5/8q^3 - 2/8q^3 = 3/8q^3
2. final answer is : 3/8q^3 + 9
The volume of a golf ball is approximately 4in.3 what is the diameter round you answer to the nearest whole number
A 4 in
B 6 in
C 1 in
D 2 in
Answers
Answer:
D. 2 inches.
Step-by-step explanation:
Given the following data;
Volume of golf (sphere) = 4 in³
A golf ball is spherical in shape. Thus, to find its volume we would use the formula for the volume of a sphere.
[tex] Volume \; of \; a \; sphere = \frac {4}{3} \pi r^{3} [/tex]
Substituting into the equation, we have;
[tex] 4 = \frac {4}{3} * 3.142* r^{3} [/tex]
Cross-multiplying, we have;
[tex] 12 = 4 * 3.142* r^{3} [/tex]
[tex] 12 = 12.568 * r^{3} [/tex]
[tex] r^{3} = \frac {12.568}{12} [/tex]
[tex] r^{3} = 1.0473 [/tex]
Taking the cube root of both sides, we have;
Radius, r = 1.016 inches.
To find the diameter;
Diameter = radius * 2
Diameter = 1.016 * 2
Diameter = 2.03 ≈ 2 inches.
Answer:
the answer is 2.
Step-by-step explanation:
i just did this question on the exam
Calculate or Simplify the value of each expression a {-8} . 2/3
Answers
Answer:
Step-by-step explanation:
[tex](-8)*\frac{2}{3}=\frrac{(-8)*2}{3}= \frac{-16}{3}[/tex]
PLZ ANSWER QUICK IT WILL HELP A LOT!
Answers
Answer:
A
Step-by-step explanation:
i need help plssssssssssssss
Answers
Answer:
It doesn't show what the drop down is. However, both of those are linear expressions.
Sergio's expressionn siplifies to: 9+3x (because two minuses cancel each other).
Leon's expression cancels to 12+6x (because 9+3=12)
Step-by-step explanation:
You have to show the dropdown to be able to answer exactly what they are looking for as an answer.
n the rectangle P Q R S , the side P Q is of length 2 and the side Q R is of length 4
Please i need the answer ASAP
Answers
here u go
In the rectangle PQRS , the side PQ is of length 2CM and the side QR is of length 4CM Points T and U lie inside the rectangle so that Triangle PQT and TRIANGLE RSU are equilateral triangles.PLS MARK ME AS BRAINLIST!!!!!
Use synthetic division
1.
(2x3 - 5x2 + 3x + 7) = (x - 2)
Answers
Answer:
Step-by-step explanation: that should help
what is the answer to 4x+10=26
Answers
Answer:
x=4
Step-by-step explanation:
4x+10=26
Subtract 10 from both sides
4x=16
Divide by 4
x=4
A mechanic charges $20.00 an hour, h for labor plus parts. If the parts cost $217.00, write a linear equation that will find the total cost, c.
Answers
Answer:
y=20x+217
Step-by-step explanation:
PLEASE DUE IN 20 MINUTES!!!!!!
Write the quadratic function in standard form.
f(x) = (x + 14)2
Answers
Answer:
Step-by-step explanation:
It's essential that you use the symbol " ^ " to indicate exponentiation.
Expanding f(x) = (x + 14)^2 results in x^2 + 28x + 196 (which is in standard form)
What is the image of the point (8,-6)(8,−6) after a rotation of 180 counterclockwise about the origin?
Answers
Answer:
(-8, 6)(-8, 6)
Step-by-step explanation:
The formula for 180 degree rotation is (-x, -y)
ANSWER FOR BRAINLIEST
Answers
Answer:
x = 10
Step-by-step explanation:
( 6x - 6 ) + ( 7x + 1 ) + 55 = 180
6x + 7x = 180 + 6 - 1 - 55
13x = 130
x = 10
Check:
6(10) - 6 = 56
7(10) - 1 = 69
55 + 56 + 69 = 180 ✔️
Hey Everyone I was asking anyone can help with this problem it would really appreciated.
Answers
Answer:
angle G = angle I
HGI=HIJ by RHS fact
HGI=HIJ corresponding angles are alwyas congurrent
15 POINTS HURRY
Write an expression that is equivalent to 5
3
r - 8
2
Answers
Add 3 + 2
5 = r - 8
Add 8 to 5 while canceling it out
13 = r
3 + 2 = 5
R =13
13 - 8 = 5
That is a true statement so an expression would be
3 + 2 = r - 8
A line passes through the point (-8, -9) and has a slope of 5/4
Write an equation in slope-intercept form for this line.
Answers
Answer:
y = 5/4x + 1
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
Answer:
y=(5/4)x(-8)+3
Step-by-step explanation:
EZ
what does 40 centimeters equals in meters
Answers
Answer:
Its 0.4 meters!
Step-by-step explanation:
