Please help me with this question so I can better help my son to understand this better. I have attached the graph that were working from below? The graph shows f(x)and its transformation g(x).Enter the equation for g(x) in the box.g(x) =
Answers
Answer
g(x) = 2ˣ⁺² or 2^(x + 2)
[tex]g(x)=2^{x+2}[/tex]
Explanation
When a function f(x) is translated horizontally along the x-axis by a units, the new function is represented as
f(x + a) when the translation is by a units to the left.
f(x - a) when the translation is by a units to the right.
Looking at the coordinates of the points given on f(x) and g(x), we can see that g(x) is just f(x) translate 2 units to the left.
Hence, if f(x) = 2ˣ
g(x) = f(x + 2) = 2ˣ⁺² or 2^(x + 2)
Hope this Helps!!!
Related Questions
mariana races on a BMX bike with 12-in-radius wheels. when she is traveling at a speed of 24 ft/sec, how many revolutions per minute are her wheels making?
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First, we have to calculate the circumference of the wheels:
Circumference (c) = pi x 2radius
C = pi x 2(12)
C= 75.4 inches
Convert into feet:
Since 1 ft =12 inches
75.4 in / 12 in/ft = 6.28 ft
Multiply the speed by 60 to convert into ft/min
1minute =60 seconds
24 ft/sec x 60 sec = 1,440 ft/min
Divide the speed by the circumference:
1,440 / 6.28 = 229.3 revolutions per minute
I have a picture of the question
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Given in the question:
a.)
When summarizing the distribution of a data set with Strong outlier the what number summary is a better choice than the mean and standard deviation?
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Since the mean and the standard deviations are "sensible" to outliers, that is, t
Solve the equation using the quadratic formula.x² - 12x + 85 = 0Select one:O A. {6 ± 7i}O B. {12 + 14i}O C. {13, -1}O D. {-6 ± 7i}
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the sWe have the next quadratic formula:
[tex]x²-12x+85=0[/tex]Use the form x²+bx+c
Where:
a=1
b=-12
c=85
Then,
[tex]\begin{gathered} x=\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(85)}^{}}{2(1)} \\ \end{gathered}[/tex][tex]x=\frac{12\pm14i}{2}[/tex][tex]\begin{gathered} x=\frac{2(6+7i)}{2} \\ x=6+7i \end{gathered}[/tex]Hence, the correct answer is option A.
Convert 258.55° to radian measure. Round your answer to the nearest hundredth. ?
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Convert ange in radian.
[tex]\begin{gathered} 258.55^{\circ}\times\frac{\pi}{180^{\circ}}=4.512 \\ =4.51 \end{gathered}[/tex]So answer is 4.51 radians.
2 + 12p - 9p - x - 10x +10
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You have the following polynomial:
2 + 12p - 9p - x - 10x +10
In order to simplify the previous expression you proceed as follow:
2 + 12p - 9p - x - 10x +10
first, simplify similar term, terms with p, terms with x and independent terms, as follow:
(12p - 9p) + (- x - 10x) + (10 + 2)
In the previous line similar terms were grouped. You subtract 12 and 9 for variable p, sum 1 and 10 for variable x (by taking into account that is a sum of negativ numbers) and sum 10 and 2 for number without variables. Thus, you obtain:
3p - 11x + 12
Hence the simplified expression is 3p - 11x + 12
Find a formula for the nth term inthis arithmetic sequence:a1 = 28, a2 = 21, a314. a4an
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Given the following?
a1 = 28
a2 = 21
a3 = 14
a4 = 7
We are asked to find the formula for the nth term in above arthmetic sequence.
Generally the nth term of an arithmetic sequence is:
an = a1 + (n - 1)d
Where:
a1 is the first term
d is the common difference.
Lets find the common difference, d:
d = a2 - a1 = a3 - a2
d = 21 - 28 = 14 - 21
d = -7 = -7
d = -7
So,
an = a1 + (n - 1)d
an = 28 + (n - 1)-7
an = 28 -7n + 7
an = -7n + 28
The mean of 10 numbers is 14. Three of the numbers have a mean of 4. The remaining seven numbers are 15 18, 21, 5, m, 34 and 14. Find (i) the sum of the remaining seven numbers, (ii) the value of m
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Given the following question:
The mean of 10 numbers is 14
m = 14
The mean of three of those 10 numbers is 4
m = 4
The remaining seven are 15, 18, 21, 5, m, 34, and 14
Three of the numbers has a mean of 4
[tex]\begin{gathered} 15+18+21+5+34+14 \\ 15+18=33+21=54+5=59+34=93+14=107 \end{gathered}[/tex][tex]\begin{gathered} 3\times4=12 \\ 12+107=119 \\ 140-119=21 \\ m=21 \\ 10\times14=140 \end{gathered}[/tex][tex]15+18+21+21+5+34+14=128[/tex]The rat population in a major metropolitan city is given by the formula n(t)measured in years since 2001 and n(t) is measured in millions.66e0.015€ where t isWhat was the rat population in 2001 ?ratsWhat does the model predict the rat population was in the year 2020 ?rats
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The given formula is:
[tex]n(t)=66e^{0.015t}[/tex]Where t is measured in years since 2001 and n(t) is measured in millions.
a. What was the rat population in 2001?
Since t is measured in years since 2001, then we need to subtract 2001 from the year we want to analyze. So:
[tex]t=2001-2001=0[/tex]By replacing t=0 into the formula we obtain:
[tex]\begin{gathered} n(0)=66e^{0.015*0} \\ n(0)=66e^0 \\ n(0)=66*1 \\ n(0)=66\text{ millions} \end{gathered}[/tex]As n(t) is measured in millions, thus, the rat population in 2001 was 66000000 rats.
b. What does the model predict the rat population was in the year 2020?
t in the year 2020 is:
[tex]t=2020-2001=19[/tex]Then:
[tex]\begin{gathered} n(19)=66e^{0.015*19} \\ n(19)=66e^{0.285} \\ n(19)=66*1.33 \\ n(19)=87.764294\text{ millions} \end{gathered}[/tex]In the year 2020 the predicted rat population was 87764294 rats.
A scientist is interested in whether stretching before running 5 kilometers will improve a runner’s time. The scientist decides that an experimental study is the best method to use to answer the question. One group of runners will run a 5-kilometer race without stretching, and a second group of runners will follow a specific stretching routine before running the race. The finishing times will be recorded, along with the group type for each runner.The distribution of times for the group that followed a specific stretching routine before the race is shown. Why is it reasonable to model this distribution with a normal distribution?
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First, to understand the reason to use a normal distribuition, let's analyse some of it's properties.
The normal distribution is given by the following formula:
[tex]f(x)\text{ = }\frac{1}{\sigma\sqrt[]{2\pi}}\text{exp\lbrack}\frac{-1}{2}(\frac{x-\mu}{\sigma})^2\text{ \rbrack}[/tex]The normal distribuition is centered at the mean(given by 'mu' in the equation above) and its growth is controlled by its standard deviation(given by the 'sigma').
It is shaped like a bell(centered, with a gaussian decay, symetric). The data given by the question, have all of those properties. Is centered at the middle with a exponential decay in both 'directions'. Since the data agrees with the gaussian distribution properties, it makes sense to model this distribuition as a normal distribuition.
The students in Mr.Collins class used a surveyors measuring devices to find the angle from their location to the top of a building. The also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, find the height of the building. A.36ft B.137ft C.32ft D.154ft
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Given:
The angle from the location of surveyors is 63 degrees and the distance to the bottom of the building is 70 ft.
To find:
The height of the building
Solution:
We can solve the question, using the trigonometric function tangent.
From the figure, the tangent of the angle is:
[tex]\begin{gathered} \tan 63=\frac{x}{70} \\ 1.96=\frac{x}{70} \\ x=70\times1.96 \\ x=137.2 \end{gathered}[/tex]Thus, the height of the building is approximately 137 ft.
Thus. option B is correct.
function G is an exponential function passing through two points
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Hello, how do I solve these equations when the domain is restricted to 0 ≤ θ <2πa) 5cot(θ) -2 = 3cot(θ) - 2b) 2sinθ = tanθc) 3cos^2θ - sin^2θ = 2
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a)
The given equation is
[tex]5cot\theta-2=3cot\theta-2[/tex]Subtract 3cot(theta) from each side
[tex]\begin{gathered} 5cot\theta-3cot\theta-2=3cot\theta-3cot\theta-2 \\ 2cot\theta-2=-2 \end{gathered}[/tex]Add 2 to both sides
[tex]\begin{gathered} 2cot\theta-2+2=-2+2 \\ 2cot\theta=0 \end{gathered}[/tex]Divide both sides by 2
[tex]\begin{gathered} \frac{2cot\theta}{2}=\frac{0}{2} \\ \\ cot\theta=0 \end{gathered}[/tex]cot(theta) = 0 at theta = pi and theta = 3/2pi
[tex]\theta=\pi,\frac{3}{2}\pi[/tex]b)
[tex]2sin\theta=tan\theta[/tex]Change tan(theta) to sin(theta)/cos(theta)
[tex]\begin{gathered} tan\theta=\frac{sin\theta}{cos\theta} \\ \\ 2sin\theta=\frac{sin\theta}{cos\theta} \end{gathered}[/tex]Multiply both sides by cos(theta)
[tex]2sin\theta cos\theta=sin\theta[/tex]Subtract sin(theta) from both sides
[tex]2sin\theta cos\theta-sin\theta=0[/tex]Take sin(theta) as a common factor on the left side
[tex]sin\theta(2cos\theta-1)=0[/tex]Equate each factor by 0
[tex]\begin{gathered} sin\theta=0 \\ \theta=0,\pi \end{gathered}[/tex][tex]\begin{gathered} 2cos\theta-1=0 \\ 2cos\theta=1 \\ cos\theta=\frac{1}{2} \\ \theta=\frac{\pi}{3},\frac{5\pi}{3} \end{gathered}[/tex][tex]\theta=0,\frac{\pi}{3},\pi,\frac{5\pi}{3}[/tex]c)
[tex]3cos^2(\theta)-sin^2(\theta)=2[/tex]Change sin^2(theta) to 1 - cos^2(theta)
[tex]\begin{gathered} 3cos^2\theta-(1-cos^2\theta)=2 \\ 3cos^2\theta-1+cos^2\theta=2 \\ 4cos^2\theta-1=2 \\ 4cos^2\theta=3 \\ cos^2\theta=\frac{3}{4} \end{gathered}[/tex]Take a square root for each side
[tex]cos\theta=-\frac{\sqrt{3}}{2},cos\theta=\frac{\sqrt{3}}{2}[/tex]The values of theta are
[tex]\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}[/tex]problem here to solve
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Answer:
Step-by-step explanation:
-8.4=c/-2+-5.4
We subtract -5.4 from both sides.
3=c/-2
multiply both sides by -2
-6=c
Where would 1 2/3 be on a number line
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So we want to put the number:
[tex]1\frac{2}{3}[/tex]on a number line.
Remember that, this number can be expressed as:
-Taking values between 1 and 2 and divide this interval in three parts. The second part will be the location of the number. If we draw:
So the correct answer is A.
A magazine asks its readers to complete a brief survey and respond by mailing back their responses in an envelope. This survey may be biased because
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The magazine asks its readers to complete a survey and respond by mailing.
The fact that the survey could be biased can only be that occurs a problem with the delivery.
With this argument, we can discard the other options, having in mind the context.
Then, the correct answer is A.
I will provide another picture with the questions for this problem.Please note that this problem is quite lengthy!
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Albert) Let's define
[tex]\begin{cases}A=\text{ money earned from 1000 dollars and 1.2\% of annual interest compounded monthly,} \\ L=\text{ 2\% of 500 dollars, lost over the course of the ten years,} \\ B=\text{ money earned from 500 dollars growing compounded continuously at a rate of 0.8\% annually.}\end{cases}[/tex]Then,
[tex]M(\text{Albert})=A+(500-L)+B.[/tex]To calculate A, we have the following compound interest formula:
[tex]A=1000\cdot(1+\frac{0.012}{12})^{12\cdot10}\approx1127.43[/tex]L is easy to calculate:
[tex]L=0.02\cdot500=10.[/tex]To calculate B, we have a formula as well:
[tex]B=500\cdot e^{0.008\cdot10}\approx541.64.[/tex]Then,
[tex]M(\text{Albert})\approx1127.43+(500-10)+541.64=2159.07.[/tex]AnswerThe balance of Albert's $2000 after ten years is $2159.07.
Distance between P1 and P2
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Answer:
Can't solve
Step-by-step explanation:
Theres no image.
triangle ABC has the following verticles A (-4,6)B (6,6)C( 1,-3) is triangle ABC an equilateral traingle and why?
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we know that
An equilateral truangle has three equal length sides
so
If triangle ABC is an equilateral triangle
then
AB=BC=AC
so
step 1
Find out the distance AB
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^2+(x2-x1)^2}[/tex]we have
A (-4,6)
B (6,6)
substitue in the formula
[tex]\begin{gathered} d=\sqrt{(6-6)^2+(6+4)^2} \\ d=\sqrt{(0)^2+(10)^2} \\ dAB=10\text{ units} \end{gathered}[/tex]step 2
Find the distance BC
we have
B (6,6)
C( 1,-3)
substitute the values in the formula
[tex]\begin{gathered} d=\sqrt{(-3-6)^2+(1-6)^2} \\ d=\sqrt{(-9)^2+(-5)^2} \\ d=\sqrt{81+25} \\ dBC=\sqrt{106\text{ units}} \end{gathered}[/tex]we have that
AB is not equal to BC
therefore
Is not an equilateral triangle
Is not necessary calculate the distance AC
what is 620÷3? i keep getting 6.02 as the answer
explain with long division pleasee
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Answer:
206.67 round it
Step-by-step explanation:
11. Find the surface area of the rectangular prism with l = 15.5 m, w = 16.5 m, and h = 4.5 m.A.73 m2B.2,301.75 m2C.799.5 m2D.575.4 m2
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Solution:
Given:
[tex]\begin{gathered} l=15.5m \\ w=16.5m \\ h=4.5m \end{gathered}[/tex]To calculate the surface area of a rectangular prism, the formula below is used:
[tex]A=2(lw+lh+wh)[/tex]Substituting the given values into the formula:
[tex]\begin{gathered} A=2((15.5\times16.5)+(15.5\times4.5)+(16.5\times4.5)) \\ A=2(255.75+69.75+74.25) \\ A=2(399.75) \\ A=799.5m^2 \end{gathered}[/tex]Therefore, the correct answer is OPTION C.
identify the vertex the focus and the directrix of the parabola with the given equation: y=x2+4x-3
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To obtain the vertex of the parabola, we are going to re-write the given parabola equation into its vertex form.
The vertex form of a parabola is given as:
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where (h,k) is the vertex} \end{gathered}[/tex]Thus, by completing the square of the given parabola equation, we have:
[tex]\begin{gathered} y=x^2+4x-3 \\ y=x^2+4x+4-4-3 \\ y=(x+2)^2-7 \end{gathered}[/tex]Comapring this equation with the vertex form of a parabola;
Hence, the vertex of the parabola is:
[tex](h,k)=(-2,-7)[/tex]The focus of a parabola is at the point;
[tex]Focus=(h,k+\frac{1}{4a})[/tex]The parabola obtained opens up. An alternative equation for a parabola that opens up is:
[tex]y-k=4a(x-h)^2[/tex][tex]\begin{gathered} \text{ Rewriting }y=(x+2)^2-7\text{ to fit this form leads to} \\ y+7=4a(x+2)^2 \end{gathered}[/tex]We must find the value of a that makes the equation true at any point (x,y).
Suppose x=1;
[tex]\begin{gathered} y=x^2+4x-3 \\ y=1^2+4(1)-3 \\ y=1+4-3 \\ y=2 \end{gathered}[/tex][tex]\begin{gathered} y-k=4a(x-h)^2 \\ 2-(-7)=4a(1-(-2))^2 \\ 2+7=4a(1+2)^2 \\ 9=4a\times3^2 \\ 9=36a \\ a=\frac{9}{36} \\ a=\frac{1}{4} \end{gathered}[/tex]Hence, the focus of the parabola is:
[tex]\begin{gathered} F=(h,k+\frac{1}{4a}) \\ F=(-2,\text{ -7+}\frac{1}{4}) \\ F=(-2,-\frac{27}{4}) \end{gathered}[/tex]The directrix is:
[tex]y=-\frac{29}{4}[/tex]what does being independent or mutually exclusive do to the way we calculate the probability??
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If two events are independent, it means that the probability of one event happening does not depend on the probability of the other happening. If A and B are 2 independent events, the probability of them happening is the product of their seperate probabilities. P(A) x P(B)
If two events are mutually exclusive, it means that they cannot occur together. If A and B are 2 mutually exclusive events, the probability of them happening is together is 0
b) 10x-8 = 8x
e) 2x+3 = x-9
h) 5x+8 = 7x-32
Answers
Answer:
b) x = 4
e) x = -12
h) x = 20
Step-by-step explanation:
b) 10x - 8 = 8x
10x - 8 + 8 = 8x + 8
10x = 8x + 8
10x - 8x = 8x + 8 - 8x
2x = 8
[tex]\frac{2x}{2} = \frac{8}{2}[/tex]
x = 4
e) 2x +3 = x - 9
2x +3 -3 = x - 9 -3
2x = x - 12
2x -x = x -12 -x
x = -12
h) 5x + 8 = 7x - 32
5x + 8 - 8 = 7x -32 -8
5x = 7x - 40
5x - 7x = 7x - 40 -7x
-2x = -40
[tex]\frac{-2x}{-2} = \frac{-40}{-2}[/tex]
x = 20
g(1)=-19, g(n)= g(n-1)+6,find an explicit formula for g(n)=
Answers
Question:
g(1)=-19,
g(n)= g(n-1)+6,
find an explicit formula for g(n)
Answer:
g(n) = 6n - 25.
Step-by-step explanation:
We have an arithmetic sequence here.
The common difference (d) is g(n) - g(n - 1) = 6.
The first term a1 = -19 so the formula is:
a1 + (n - 1)d
-19 + (n - 1)6
= 6n - 19 - 6
= 6n - 25.
Answer:
6n-25
Step-by-step explanation:
sorry no step by step explanation because I am in a rush
and the answer is correct I did th quiz. Anyways I hope this helps bye. :D
Select the correct answer. Simplify (8x + 5) + (4x+6) A. 4x - 11 B. 12x-1 C. 12x + 11 D 4x + 1
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we are given the following expression:
[tex]\mleft(8x+5\mright)+(4x+6)[/tex]First, we will associate like terms, that is terms that have the same variable elevated to the same exponent:
[tex](8x+4x)+(5+6)[/tex]Adding like terms:
[tex]12x+11[/tex]Since we can't simplify any further, this is the final answer.
I nee someone to answer this and actually explain it to me please.
Answers
Given Data:
[tex]\begin{gathered} a=1.4 \\ b=-2.6 \\ c=5.2 \end{gathered}[/tex]Here the point d is the horizontal distance, it can be found by adding the distance 'a' and 'c', since 'a' and 'c' are horizontal measurements. Th distance 'b' is given in vertical measurements. Thus, the distance 'b' can be ignored while finding the value of d.
[tex]\begin{gathered} d=a+c \\ d=1.4+5.2 \\ d=6.6 \end{gathered}[/tex]Thus, the distant d is in 6.6 unit from the origin, or from the y-axis.
I already found the range of the logarithmic function, so if you could just help me find the domain.
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The domain of a logarithmic function:
[tex]f(x)=\log _ax[/tex]will always be all the positive numbers, that is the domain is:
[tex](0,\infty)[/tex]Juan made $1000 in taxable income last year.Suppose the income tax rate is 15% for the first $ 7000 plus 17% for the amount over $7000. How much must Juan pay in income tax for last year?
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step 1
$1,000 < $7,000
so
the tax rate is 15%
15%=15/100=0.15
0.15*1,000=$150
therefore
The answer is $150N 4. Select the correct answer. Function fis an increasing exponential function that is negative on the interval (-C, 2) and positive on the interval (2,). Which could graph of function f? O A. Х -2 -2 OB. All rights reserved
Answers
according to the graph
answer: D