What transformation takes
f(x)=15x+3 to g(x)=5x+3 ?
Question 1 options:
a horizontal compression by a factor 1/3
a translation 6 units right
a horizontal stretch by a factor of 3
a translation 6 units down
Answers
[tex]5x + 3 = 15( \frac{1}{3} x) + 3 = f( \frac{1}{3} x)[/tex]
So [tex]g(x) = f( \frac{1}{3} x)[/tex]
When a function f(x) is transformed into f(ax) where |a| > 1, it's a horizontal compression by a factor of 1/a. But when a function f(x) is transformed into f(ax) where |a| < 1, it's a horizontal stretch by a factor of 1/a.
In this case, a = 1/3. So that's a horizontal stretch by a factor of 1/(1/3) = 3. Thus the answer choice is C.
Related Questions
HELLLLLPPP PLLEASEEE
Answers
The answer is B
Eleven less than seven times a number is five more than six times the number.
Answers
The problem is a simple algebraic equation in the form 7x - 11 = 6x + 5. By rearranging and simplifying, we find the solution is x = 16.
Explanation:The question presents a mathematical statement that needs to be solved for the variable. Translating the words into an equation, we get: 7x - 11 = 6x + 5. This equation is saying seven times a number (we'll call it 'x') reduced by eleven is equal to six times that number increased by five.
To solve for 'x', first, rearrange the equation to get all 'x' terms on one side and constants on the other. By subtracting 6x from both sides, we get x - 11 = 5. Then, add 11 to both sides to isolate 'x': x = 16.
So, the number or 'x' that satisfies this equation is 16.
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x = 16.
To solve this, let the unknown number be represented by x.
We can set up the equation based on the given information:
7x - 11 = 6x + 5
Subtract 6x from both sides of the equation:
7x - 6x - 11 = 6x - 6x + 5
Simplify the equation:
x - 11 = 5
Add 11 to both sides:
x - 11 + 11 = 5 + 11
Simplify the equation:
x = 16
Thus, the number is 16.
JIMMMM! :)
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2^x and y = 4^x−2 intersect are the solutions of the equation 2^x = 4^x−2. (4 points)
Part B: Make tables to find the solution to 2^x = 4^x−2. Take the integer values of x between −4 and 4. (4 points)
Part C: How can you solve the equation 2^x = 4^x−2 graphically? (2 points)
Answers
The x coordinates are the inputs of the functions f(x) = 2^x and g(x) = 4^(x-2)
If we have some input x that leads to f(x) = g(x), then this x value is a solution. It makes the equation f(x) = g(x) true. This is why the x coordinate of the intersection point of y = 2^x and y = 4^(x-2) is the solution.
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Part B
See attached for the table. See figure 1.
This is how you get the results you see in the table
Plug x = -4 into f(x) to get:
f(x) = 2^x
f(-4) = 2^(-4)
f(-4) = 0.0625
Do the same for g(x):
g(x) = 4^(x-2)
g(-4) = 4^(-4-2)
g(-4) = 4^(-6)
g(-4) = 0.000244140625
-------------------
Plug x = -3 into f(x) to get:
f(x) = 2^x
f(-3) = 2^(-3)
f(-3) = 0.125
Do the same for g(x):
g(x) = 4^(x-2)
g(-3) = 4^(-3-2)
g(-3) = 4^(-5)
g(-3) = 0.0009765625
-------------------
Plug x = -2 into f(x) to get:
f(x) = 2^x
f(-2) = 2^(-2)
f(-2) = 0.25
Do the same for g(x):
g(x) = 4^(x-2)
g(-2) = 4^(-2-2)
g(-2) = 4^(-4)
g(-2) = 0.00390625
-------------------
Plug x = -1 into f(x) to get:
f(x) = 2^x
f(-1) = 2^(-1)
f(-1) = 0.5
Do the same for g(x):
g(x) = 4^(x-2)
g(-1) = 4^(-1-2)
g(-1) = 4^(-3)
g(-1) = 0.015625
-------------------
Plug x = 0 into f(x) to get:
f(x) = 2^x
f(0) = 2^(0)
f(0) = 1
Do the same for g(x):
g(x) = 4^(x-2)
g(0) = 4^(0-2)
g(0) = 4^(-2)
g(0) = 0.0625
-------------------
Plug x = 1 into f(x) to get:
f(x) = 2^x
f(1) = 2^(1)
f(1) = 2
Do the same for g(x):
g(x) = 4^(x-2)
g(1) = 4^(1-2)
g(1) = 4^(-1)
g(1) = 0.25
-------------------
Plug x = 2 into f(x) to get:
f(x) = 2^x
f(2) = 2^(2)
f(2) = 4
Do the same for g(x):
g(x) = 4^(x-2)
g(2) = 4^(2-2)
g(2) = 4^(0)
g(2) = 1
-------------------
Plug x = 3 into f(x) to get:
f(x) = 2^x
f(3) = 2^(3)
f(3) = 8
Do the same for g(x):
g(x) = 4^(x-2)
g(3) = 4^(3-2)
g(3) = 4^(1)
g(3) = 4
-------------------
Plug x = 4 into f(x) to get:
f(x) = 2^x
f(4) = 2^(4)
f(4) = 16
Do the same for g(x):
g(x) = 4^(x-2)
g(4) = 4^(4-2)
g(4) = 4^(2)
g(4) = 16
Note that since the input x = 4 leads to the same output (16) this makes x = 4 a solution.
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Part C
To solve graphically, you need to use the table in part B to draw a curve through the set of points. Then determine where the curves cross (if they cross at all). You may need to adjust the graph window if the intersection point is off the screen.
See figure 2 for the graph (attached as well). Point A in green is the intersection point.
A = (4,16)
so x = 4 is the solution to f(x) = g(x).
Part A: The point or points of intersection are the values of the variables which satisfy both equations at a particular point.
If [tex]y=2^x and y=4 ^{x-2} [/tex] and the solution of which will satisfy both equations. This idea of equating the two equations is something that you would have come across before, maybe without realizing it.
Consider this:
[tex]x^2 + 6x + 9=0 This can also be looked at as being the two equations: y=x^2 +6x+9 and y=0 [/tex]
So the points of intersection are the roots in this case and satisfy the equation:
[tex]x^2 + 6x +9=0 This explains why it will be the solution to: 2^x = 4 ^{x-2} , because this is the equation formed at the intersection.[/tex]
Part B:
You just put integer values between -4 and 4 in each equation and when the output is the same for both that is the solution.
[tex]2^ ^{-4} = 0.0625 , [/tex] and [tex]4 ^{-6} = 0.000244[/tex]
[tex]2 ^{-3} = 0.125, [/tex] [tex]4 ^{-5} =0.000977[/tex]
[tex]2 ^{-2} =0.25[/tex] and [tex]4 ^{-4} =0.003906[/tex]
[tex]2 ^{-1}= -0.5,[/tex] and [tex]4 ^{-3} =0.01563[/tex]
[tex]2^0 =1[/tex] , and [tex]4 ^{-2} =0.0625[/tex]
[tex]2^1 = 2 [/tex] and [tex]4 ^{-1} =0.25[/tex]
[tex]2^2 =4 [/tex] and [tex]4^0 =1[/tex]
[tex]2^3 =8[/tex] and [tex]4^1=4[/tex]
[tex]2^4 =16, [/tex] and [tex]4^2 = 16 [/tex] (This is the solution when x=4)
Part C:
To solve graphically you just plot the two equations [tex]=2^x[/tex] and [tex]y=4 ^{x-2} [/tex]
Together graph of [tex]y=2^x [/tex] and [tex]y=4 ^{x-2} [/tex]
The picture below is how the graph looks like.
Full Credit to my online calculator 'cause we don't have a graphing calculator here.
I hope I helped!
Can somebody please help me?
Answers
Goran runs 3 miles in 25 minutes. at the same rate, how many miles would he run in 20 minutes?
Answers
3 mi/25 min= x mi/20 min
Cross multiply:
3*20=60
60/25= 2.4=x
Final answer: 2.4 miles
if I work z hours overtime, and my overtime wage is $25 per hour, what's my overtime pay?
Answers
∠C and ∠D are vertical angles with m∠C=−x+26 and m∠D=2x−10 . What is m∠D ? Enter your answer in the box.
Answers
+x +10 +x +10
36+3x
divde by 3
12=x
m∠D=2(12)-10
=24-10
=14
Answer:
m∠D=14
Step-by-step explanation:
∠C and ∠D are vertical angles with m∠C=−x+26 and m∠D=2x−10
Vertical angles are equal. So equate the angles C and d . Solve for x
m∠C=m∠D
[tex]-x+26=2x-10[/tex]
Subtract 2x from both sides
[tex]-3x+26=-10[/tex]
Subtract 26 from both sides
[tex]-3x=-36[/tex]
Divide both sides by -3
x=12
m∠D=2x−10
Substitute 12 for x
m∠D=2(12)−10=24-10= 14
Find the parabola whose minimum is at (−12,−2)(−12,−2) rather than the point given in the book. the parabola's equation is y=x2+ax+by=x2+ax+b, where
Answers
[tex]y-k=a(x-h)^2[/tex]
where (h, k) is the vertex of the parabola.
Given that the vertex of the parabola is (-12, -2), the equation of the parabola is given by
[tex]y-(-2)=a(x-(-12))^2 \\ \\ y+2=a(x+12)^2=a(x^2+24x+144)=ax^2+24ax+144a \\ \\ y=ax^2+24ax+114a-2 \\ \\ y=x^2+24x+ \frac{114a-2}{a} [/tex]
For a = 1,
[tex]y=x^2+24x+112[/tex]
The parabola whose minimum is at (−12,−2) is given by the equation [tex]y=x^2+ax+b[/tex], where a = 24 and b = 112.
Which algebraic expression is a polynomial with a degree of 2?
a)4x3 − 2x
b10x2 −
c)8x3+ + 3
d)6x2 − 6x + 5
Answers
the one u have marked is not a polynomial because it has a variable in the square root...a polynomial cannot have that
Answer:
D) 6x² − 6x + 5 has degree 2.
Step-by-step explanation:
Given : Polynomial .
To find : Which algebraic expression is a polynomial with a degree of 2.
Solution: We have given polynomial
Degree : The highest power of the polynomial is called degree.
We can see from the given polynomials two polynomial have 2 power
first is [tex]10x^{2} -\sqrt{x}[/tex].
Second is 6x² − 6x + 5.
But the first term have root so, it is not a polynomial.
So 6x² − 6x + 5 has degree 2
Therefore, D) 6x² − 6x + 5 has degree 2.
hard question ! Jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her own expenses. After a month of driving from neighborhood to neighborhood and walking door-to-door, she figures out that her weekly earnings are approximately a linear function of the number of doors she knocks on. She writes the equation of the function like this: E(x) = 20x - 50, where x is the number of doors she knocks on during the week and E(x) is her earnings for the week in dollars. Which of the following are reasonable interpretations of the y-intercept of Jessica's function? Check all that apply.
A. Her expenses are $50 per week.
B. She can earn $20 per week even if she does not knock on any doors.
C. If she does not knock on any doors at all during the week, she will lose $50.
D. She will lose $20 per week if she does not knock on any doors.
Answers
Answer:
A and C
Step-by-step explanation:
Just answered on apex
Is -2 less than 0???????????????????????????
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Give an estimate for 42.8 x 13.6
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Final answer:
A reasonable estimate for the product of 42.8 x 13.6 is 602, achieved by rounding each number to the nearest whole number and then multiplying them together.
Explanation:
To estimate the product of 42.8 x 13.6, we can round each number to the nearest whole number and then multiply. So, 42.8 is approximately 43, and 13.6 is approximately 14. Now, multiply these estimated values.
Estimated Calculation:
43 x 14 = 602
Therefore, a reasonable estimate for the product of 42.8 and 13.6 is 602. Remember, in estimation, we aim to simplify the calculation while still arriving at a number that's close to what the actual answer would be if we calculated it exactly.
Help me please don’t know how to do this and I have psat in a week.
Answers
x = 3/2
x = -5
Since 3/2 = 1.5 is larger than -5, this means r = 3/2 = 1.5 and s = -5
Subtract r and s:
r - s = (3/2) - (-5)
r - s = (3/2) + (5)
r - s = (3/2) + (5/1)
r - s = (3/2) + (10/2)
r - s = (3+10)/2
r - s = 13/2
Therefore the final answer is B) 13/2
Max spent $53 and now has no money left. How much did he have before his purchase
Answers
An equation is formed when two equal expressions. The amount Max had before his purchase is $53.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that Max spent $53 and now has no money left. Therefore, we can write the details as,
The amount spent on the purchase = $53
The amount left after purchase = $0
Let the amount before purchase be represented by M. Therefore, we can write the amount remaining after purchase as,
Amount before purchase - Amount spent on purchase = Amount remaining after purchase
M - $53 = $0
Adding 53 on both sides.
M - 53 + 53 = 53
M = 53
M = $53
Thus, the amount Max had before his purchase is $53.
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Use the graphs of f and g. Which describes the transformation from the graph of f to the graph of g?
f(x)=−4x+8f(x)=−4x+8
g(x)=−f(x)g(x)=−f(x)
1.horizontal translation 1 units left
2.vertical translation 4 units down
3.reflection in the x-axis
4.reflection in the y-axis
5.horizontal shrink by a factor of 1/4
6.horizontal stretch by a factor of 4
7.vertical shrink by a factor of 1/4
8.vertical stretch by a factor of 4
Answers
The transformation from the graph of [tex]\( f(x) = -4x + 8 \)[/tex] to [tex]\( g(x) = -f(x) \)[/tex] is a reflection in the x-axis.
The [tex]- \( f(x) = -4x + 8 \)[/tex] is a linear function with a negative coefficient in front of [tex]\( x \)[/tex], indicating a reflection in the x-axis.
When you negate f(x) to get g(x) = -f(x), it reflects the graph of f(x) in the x-axis.
So, the correct answer is: 3. Reflection in the x-axis
The height of the closet is 96 inches, and aisha would like to have 4 rows of cube organizers. what is the most the height of each cube organizer can be
Answers
so the greatest height of each cube can be : 96/4 = 24 inches
Answer: the most the height of each cube organizer can be 24 inches
Step-by-step explanation:
Since we have given that
Height of the closet = 96 inches
Number of rows of cube organizers = 4
Greatest height of each cube organizer can be is given by
[tex]\frac{96}{4}=24[/tex]
Hence, the most the height of each cube organizer can be 24 inches.
find the coordinates of the midpoint of EF with endpoints E(-2,3) and F(5, -3)
Answers
The coordinates of the midpoint of line segment EF with endpoints E(-2,3) and F(5, -3) are (1.5, 0), calculated using the midpoint formula.
To find the coordinates of the midpoint of line segment EF with endpoints E(-2,3) and F(5, -3), you can use the midpoint formula which is:
( (x1 + x2)/2, (y1 + y2)/2 )
Let's apply the formula:
x-coordinate of midpoint = ( (-2) + 5 ) / 2 = 3 / 2 = 1.5
y-coordinate of midpoint = ( 3 + (-3) ) / 2 = 0 / 2 = 0
So the midpoint of EF is (1.5, 0).
find four consecutive even integers such that 2 times the sum of the first and second is 14 more than 3 times the fourth.
Answers
2 (x + x+ 2) = 3(x + 6) + 14
4x + 4 = 3x + 18 + 14
x = 18 + 14 - 4 = 28
the four integers are 28,30,32 and 34.
The required four consecutive even integers are given as 28, 30, 32, and 34.
Given that,
Four consecutive even integers such that 2 times the sum of the first and second is 14 more than 3 times the fourth.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Let, the first term be a, and the common difference be d,
And series 2n, 2n + 2, 2n +4, 2n + 6
According to the question,
2[2n + 2n + 2] = 14 + 3[2n + 6]
8n + 4 = 14 + 6n + 18
2n = 28
n = 14
Series can be given as,
28, 30, 32, 34
Thus, the required four consecutive even integers are given as 28, 30, 32, and 34.
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The larger of two numbers is 3 more than twice the smaller. if the twice the larger is decreased by 5 times the smaller the result is 0. find the two numbers
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Which graph below shows a system of equations with infinitely many solutions?
A)coordinate plane with two parallel lines
B)coordinate plane with two intersecting lines
C)coordinate plane with two coinciding lines
D)coordinate plane with two intersecting lines
Answers
Answer:
The correct option is C.
Step-by-step explanation:
Consider the provide information.
Now consider the provided options
Option A) If there is a coordinate plane with two parallel lines.
if the plane has two parallel line then, It has no solution because you can get the solution if lines intersect at a point. Thus, it is not the required option.
Option B) and D) If there are two intersecting lines then you can get only one solution. Thus, it is not the required option.
Option C) If there are two coinciding lines then you can find infinite intersecting points. Thus, it is the required option.
Therefore, the correct option is C.
1. What is the product of -2.5 and 8.77 ?
2. Alexander purchased a computer on sale. The original price was $1,200. The sale price was 5/6 of the original price. How much did Alexander pay for the computer?
3. Mara finished 1/5 of her assignment on Saturday and 3/8 of her assignment on Sunday. What Fraction of her assignment did she complete on Saturday and Sunday?
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2. 5/6 of 1,200 is 1000. 1,200÷6=200 200•5=1000.
3. 1/5+3/8. Find like denominators. (40) 8/40+15/40=23/40 or as a decimal, 0.575.
Hoped I helped!
2. $200
3. 23/40
PLEASE HELP!
Solve for t: A=P (1+rt)
Answers
A = P + Prt
A - P = Prt
(A - P)/Pr = t
Step 1) A = P*(1+rt)
Step 2) A = P*(1)+P*(rt)
Step 3) A = P+P*(rt)
Step 4) A-P = P+P*(rt)-P
Step 5) A-P = P*(rt)
Step 6) A-P = t*(Pr)
Step 7) (A-P)/(Pr) = (t*(Pr))/(Pr)
Step 8) (A-P)/(Pr) = t
Step 9) t = (A-P)/(Pr)
----------------------------------------------
and here are the explanations for each step
Step 1) Nothing to do here. This is the original equation
Step 2) Distribute the outer P term into each inner term (1 and rt)
Step 3) Multiply P and 1 to get P*(1) = P
Step 4) Subtract P from both sides
Step 5) Simplify. Note how the P-P on the right side becomes 0P = 0 which goes away on the right side
Step 6) Rearrange the terms on the right side to go from P*(rt) to t*(Pr).
Step 7) Divide both sides by Pr.
Step 8) Simplify. The Pr term on the right side divides with itself to get 1. Because 1 times anything is itself, we effectively have Pr cancel out and go away.
Step 9) Flip the equation so that the t is on the left side
----------------------------------------------
The answer is t = (A-P)/(Pr) which can be written as [tex]t = \frac{A-P}{Pr}[/tex]
The parenthesis in the equation t = (A-P)/(Pr) are important because we are specifying that we are dividing all of "A-P" all over all of "Pr"
Ron works 5 hours for a total of $300. He deposits all of his money in his account. He is trying to save a $500 for a new LED TV. How many hours must he work to ake home $500, if he saves all of his earnings
Answers
Ron's hourly wage is $60. To save $500 for a new LED TV, he needs to work approximately 8.3 hours. Rounding up, he should work 9 hours to earn the required amount.
Ron earns $300 for working 5 hours, which means his hourly wage is $300 / 5 hours = $60 per hour. To save up for a $500 LED TV, Ron needs to determine how many hours he must work to earn that amount.
To calculate the total hours Ron needs to work to save $500, we divide the total amount he wants to save by his hourly wage:
$500 ÷ $60 per hour = 8.3 hours
Therefore, Ron needs to work approximately 8.3 hours to earn $500, assuming he continues to save all of his earnings. In practice, since he cannot work a fraction of the hour, Ron would need to round up to the nearest whole hour, meaning he needs to work 9 hours to meet or exceed his savings goal.
On a baseball field, the infield is a square. the distance from home plate to first base is 90ft. what is the distance from home plate to second base?
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Simplify
8 - [- ( - 3 )]
A. 5
B. -5
C. 11
D. -11
Answers
Let me help you out...
First, keep in mind that they just put these negative signs to make the thing looks difficult to solve :)
Do you remember this:
[tex]Minus * Minus = Plus [/tex]
Well this the same thing. We gonna multiply the two negative signs that are behind the parentheses together and make it plus sign
Here is how it works
[tex]8-[-(-3)] =8 + (-3) =8 - 3 =5[/tex]
The correct answer is option A (5)
Good luck with your studies, Miranda.
What are the slope and the y-intercept of the line shown in the graph?
(A) y-intercept = 2 and slope = -3
(B) y-intercept = 2 and slope = 3
(C) y-intercept = 3 and slope = 2
(D) y-intercept = -3 and slope = 2
Answers
the slope is rise over run. Try to choose two points on the line that you can make out the location of like (0,2) and (1,-1) is close enough. Count rise down -3 over run right +1 = -3 slope
y-intercept = 2
slope = -3
let's take the 2 coordinates from the line.
(0, 2)(1, -1)
The y-intercept is when x = 0, When x = 0, y = 2 . This means the y-intercept is 2.
m = slope = -1 - 2 / 1 - 0 = -3 / 1 = -3
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Solve for y.
4y = 144
What is the answer?
Answers
/4 /4
4 is canceled out
y=144
/4
144/4 = 36
y = 36
The solution is y = 36. Divide both sides of the equation by 4 to isolate y. To isolate y, we want to get rid of the coefficient 4 that is multiplying y.
We do this by dividing both sides of the equation by 4:
4y / 4 = 144 / 4
On the left side, the 4 in the numerator and the 4 in the denominator cancel out, leaving us with just y:
y = 144 / 4
Now, Simplify the equation.
Now, we can perform the division to find the value of y:
y = 36
The solution is y = 36.
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What is the area of a rectangle with vertices at (−3, −1) , (1, 3) , (3, 1) , and (−1, −3) ? Enter your answer in the box. Do not round any side lengths.
Answers
[tex]d = \sqrt{{(y2 - y1)}^{2} + {(x2 - x1)}^{2} }[/tex]
[tex]w = \sqrt{{(1 - 3)}^{2} + {(3 - 1)}^{2} } \\ = \sqrt{( {( - 2)}^{2} + {(2)}^{2})} = \sqrt{4 + 4} \\ = \sqrt{8} \: = [/tex]
[tex]l = \sqrt{({(3 - - 1)}^{2} + {(1 - - 3)}^{2})} \\ = \sqrt{({(3 + 1)}^{2} + {(1 + 3)}^{2})} \\ = \sqrt{({(4)}^{2} + {(4)}^{2})} \\ = \sqrt{({16} + {16})} \: = \sqrt{32} [/tex]
[tex]a \: = l \times w = \sqrt{32} \times \sqrt{8} \\ = \sqrt{256} = 16 \: {units}^{2} [/tex]
How to do this ?? How
Answers
The two bars | | is used to indicate the function absolute value.
Remember this definition:
| x | = - x if x < 0 and x if x > 0
So, | x | > c =>
x > c or x > - c
Therefore:
|ax - b| > c => ax - b > c or ax - b > - c
That is the third option of the answer list.
Answer:
|ax - b| > c
The two bars | | is used to indicate the function absolute value.
Remember this definition:
| x | = - x if x < 0 and x if x > 0
So, | x | > c =>
x > c or x > - c
Therefore:
|ax - b| > c => ax - b > c or ax - b > - c
Step-by-step explanation:
Sarah is 50 years old. she is twice as old as her friend bill and bill is 5 times as old as his sister jane. jane's mom is 12 times older than jane. what is the age difference between jane's mom and sarah?
Answers
Sarah is twice as old as Bill so 2X=50 and X=25 so Bill is 25. Bill is 25 and bill is 5 times older than his sister Jane so 5n=25 N=5 so Jane is 5 years old. Jane's mom is 12 time older than Jane so 12x5=60 and so
60-50=10 so the answer is 10