The graph below represents the function f(x) and the translated function g(x) .
If f(x) = x ^ 2 , which of the following functions could be an algebraic representation of g(x) ?
Answers
Answer: D. [tex]g(x) = (x-b)^2[/tex]
Explanation:
If we want to shift the curve some distance b to the right, then we'll need to replace x with x-b. What this effectively does is shift the xy axis itself b units to the left while the curve is fixed in place. This gives the illusion of the curve moving b units to the right.
Put another way: the old input x is updated to the new input x-b which is smaller by b units. This helps explain why the xy axis is shifted to the left this amount.
So that's how we go from [tex]f(x) = x^2[/tex] to [tex]g(x) = (x-b)^2[/tex]. You can think of it as [tex]g(x) = f(x-b) = (x-b)^2[/tex]
Related Questions
f(x) = 3x + 1 and f-1 = f-1 = x-1 / 3
then f -'(7) =
Answers
Answer:
2
Step-by-step explanation:
f^-1 (7) = [tex]\frac{x-1}{3}[/tex] = [tex]\frac{7-1}{3}[/tex] = [tex]\frac{6}{3}[/tex] = 2
Line a passes through points (3, 1) and (5, 10). Line b is parallel to line a. What is the slope of line b?
Answers
Answer:
9/2
Step-by-step explanation:
Answer:2.8
Step-by-step explanation: casue yeas.
HELP ME OUT PLEASE
A die was rolled six times. The polls were 1,2,3,3,4 and 5. What is the mean deviation for this data!
A) 3/5
B) 1
C) 2
D) 6
Answers
Answer:The mean deviation of the given data is;
Option B: 1
Step-by-step explanation:
Σ(x - x¯)/n
Now, x¯ is the mean = (1 + 2 + 3 + 3 + 4 + 5)/5
x¯ = 3
Thus;
1 - 3 = -2
2 - 3 = -1
3 - 3 = 0
3 - 3 = 0
4 - 3 = 1
5 - 3 = 2
Mean deviation is usually a positive value. Thus;
Σ(x - x¯) = 2 + 1 + 0 + 0 + 1 + 2
Σ(x - x¯) = 6
Thus;
Σ(x - x¯)/n = 6/6
Σ(x - x¯)/n = 1
Second Graph problem! Can anybody please help me out with this? (Almost done for today) (Algebra graph problem)
Answers
Answer:
x = -2
Step-by-step explanation:
The expression f(x) = 1 corresponds to the point on the graph that is 1 unit above the x-axis. You can locate that horizontal line and see where it intersects the graph. That point of intersection is 2 grid squares to the left of the y-axis, where x = -2.
f(-2) = 1
x = -2
A rectangular field is 350 meters long and 200 meters wide. What is the area of the field in square kilometers? Do not round your answer. Be sure to include
the correct unit in your answer.
0
km
km2
km
Answers
The area of the rectangular field is 0.07 square kilometers (km²).To find the area of the rectangular field in square kilometers, we need to convert the given dimensions from meters to kilometers.
To find the area of the rectangular field in square kilometers, we need to convert the given dimensions from meters to kilometers and then calculate the area.
Given:
Length of the field = 350 meters
Width of the field = 200 meters
To convert from meters to kilometers, we divide the measurements by 1000, since there are 1000 meters in a kilometer.
Length in kilometers = 350 meters / 1000 = 0.35 kilometers
Width in kilometers = 200 meters / 1000 = 0.2 kilometers
Now that we have the dimensions of the field in kilometers, we can calculate the area.
Area of the field = Length in kilometers * Width in kilometers
Area of the field = 0.35 kilometers * 0.2 kilometers
Multiplying the values, we get:
Area of the field = 0.07 square kilometers
Therefore, the area of the rectangular field is 0.07 square kilometers.
It's important to include the correct unit in the answer, which is "square kilometers" (km²). This represents the unit for measuring the two-dimensional area. In this case, the area of the field is 0.07 km².
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What is the answer to
2 3/8 - 1 5/8 =
Answers
Answer:
6/8
Step-by-step explanation:
you have to convert each fraction into an improper. because the denominators are already the same, you dont have to worry. once you have it as an impropper, you can now subtract it. 19/8 - 13/8 = 6/8
reduce if you can
Find the equation of the line passing through the points 7,2 and 9,1
Answers
9514 1404 393
Answer:
y = -1/2x +11/2
Step-by-step explanation:
The slope of the line is ...
m = (y2 -y1)/(x2 -x1)
m = (1 -2)/(9 -7) = -1/2
The y-intercept is ...
b = y -mx
b = 2 -(-1/2)(7) = 11/2
Then the slope-intercept equation is ...
y = -1/2x +11/2
_____
Alternative solution
A general form equation for the line can be ...
(y1 -y2)(x -x1) -(x1 -x2)(y -y1) = 0
(2 -1)(x -7) -(7 -9)(y -2) = 0
x-7 +2y -4 = 0
x +2y -11 = 0 . . . . . general form equation
x +2y = 11 . . . . . . . standard form equation
Note that we want the x-coefficient to be positive, so we chose the order of the points to make that be the case.
Last year, Dante had $10,000 to invest. He invested some of it in an account that paid 7% simple interest per year, and he invested the rest in an account
that paid 8% simple interest per year. After one year, he received a total of $730 in interest. How much did he invest in each account?
Answers
a = amount invested at 7%
b = amount invested at 8%
we know that total that he invested was 10000, therefore a + b = 10000.
hmmm how muich is 7% of "a"? well (7/100) * a => 0.07a.
how much is 8% of "b"? well (8/100) * b => 0.08b.
After a year he received in interest $730, so we know that at simple interest rate, 0.07a + 0.08b = 730.
[tex]\begin{cases} a+b=10000\\ 0.07a+0.08b=730\\[-0.5em] \hrulefill\\ b = 10000 - a \end{cases}\qquad \stackrel{\textit{substituting on the 2nd equation}}{0.07a+0.08(10000-a) = 730} \\\\\\ 0.07a+800-0.08a=730\implies 0.07a-0.08a=-70\implies -0.01a=-70 \\\\\\ a=\cfrac{-70}{-0.01}\implies \boxed{a = 7000} ~\hfill \stackrel{\textit{we know that}}{b = 10000 -a}\implies \boxed{b = 3000}[/tex]
The sum of two numbers is 65. The larger number is 5 more than the smaller number. What are the numbers?
Answers
Answer:
30 and 35
Step-by-step explanation:
Put this question into equation form:
Let x be the smaller number, if the larger number is 5 more and the total is 65:
x + 5 + x = 65
2x + 5 = 65
Subtract 5 from both sides
2x + 5 - 5 = 65 - 5
2x = 60
Divide both sides by 2:
2x ÷ 2 = 60 ÷ 2
x = 30
As the larger number is 5 bigger:
30 + 5 = 35
So the two numbers are 30 and 35.
Hope this helps!
Answer:
Small number 30
Large Number 35
Step-by-step explanation:
The sum of x and y is 65. In other words, x plus y equals 65 and can be written as equation A:
x + y = 65
The difference between x and y is 5. In other words, x minus y equals 5 and can be written as equation B:
x - y = 5
Now solve equation B for x to get the revised equation B:
x - y = 5
x = 5 + y
Then substitute x in equation A from the revised equation B and then solve for y:
x + y = 65
5 + y + y = 65
5 + 2y = 65
2y = 60
y = 30
Now we know y is 30. Which means that we can substitute y for 30 in equation A and solve for x:
x + y = 65
x + 30 = 65
X = 35
Therefore the large and small number us 35 and 30 respectively.
(b) Express the number 17
(i) in base 2
(ii) in base 5
Answers
Answer:
Step-by-step explanation:
IF 17 is in base 10
THEN
17₁₀ = 1 x 10¹ + 7 x 10⁰
10001₂ = 1 x 2⁴ + 0 x 2³ + 0 x 2² + 0 x 2¹ + 1 x 2⁰
32₅ = 3 x 5¹ + 2 x 5⁰
What is 2+100009 it for my homework and I need it done today
Answers
Answer:
100011
Step-by-step explanation:
what is 3/4 divided by 11/20
Answers
Answer:
11/15
Step-by-step explanation:
11/20 / 3/4
11/20*4/3
44/60
22/30
11/15
Answer:
15/11
Step-by-step explanation:
3/4 divided by 11/20?
Reduce the expression, if possible, by canceling the common factors.
Exact Form: 15/11
decimal form: 1.36
mixed number form: 1 4/11
plsssss helpppppp i’ll give brainliest
Answers
Answer:
[tex]-6\leq x\leq 6[/tex]
Step-by-step explanation:
This is answer for the last question.
A scale model of a bicycle has a scale of 1 : 25. The real bicycle has a length of 1.75 m. What is the length of the model in cm?
Answers
Answer:
It's 7 I just did this question today and got it right
WHAT is the next sequence
Answers
Answer: its 21
Step-by-step explanation:
the sequence goes up by 1 each time
Answer:
21
Step-by-step explanation:
a1=1
a2=a1+2
a3=a2+3
a4=a3+4
...
a(n)=a(n-1)+n
Hey everybody! Can anybody help me out with this algebra problem? I would really appreciate it if you can!
The following relation is a variation. Which description best represents the relation?
Answers
Answer:
x and y are directly related because y = -3x
Step-by-step explanation:
Simplify 10^9 ÷ 10^7
Answers
Answer:
10^2
Step-by-step explanation:
10^9/10^7 is the same as 10^9*10^-7 if you multiply two same bases you can add there exponents. So, 9+(-7)=2. So, it’s 10^2
Answer:
100
Step-by-step explanation:
Hope it helps
In a math class, the teacher asked the students to find the approximate value of one of the x-coordinates of a point of intersection of two functions: f(x) = 2x2 − 3x + 4 g(x) = 5x − 1 Her students gave her different answers. Which answer is the most accurate?
A.
0.8
B.
0.9
C.
1.9
D.
1.1
Answers
Answer:
A. 0.8Step-by-step explanation:
An easy way is to substitute values into both equations and compare:
A. x = 0.8
f(x) = 2(0.8)² - 3(0.8) + 4 = 2.88g(x) = 5(0.8) - 1 = 3B. x = 0.9
f(x) = 2(0.9)² - 3(0.9) + 4 = 2.92g(x) = 5(0.9) - 1 = 3.5C. x = 1.9
f(x) = 2(1.9)² - 3(1.9) + 4 = 5.52g(x) = 5(1.9) - 1 = 8.5D. x = 1.1
f(x) = 2(1.1)² - 3(1.1) + 4 = 3.12g(x) = 5(1.1) - 1 = 4.5As we see the most accurate one is A
Let's graph both function(Attached)
Let's round 0.775
[tex]\\ \sf\longmapsto 0.775[/tex]
[tex]\\ \sf\longmapsto 0.77[/tex]
[tex]\\ \sf\longmapsto 0.8[/tex]
Option A is correct
Task 1:
Taxi Cab Company A: $8 per ride and $0.35 per mile
• Write an equation in slope intercept form to represent the cost of a
taxi ride using company A.
Hint: use y=mx+b
OY =
• What does the y-intercept mean in the context of this problem?
Hint: What do you pay to step into the cab?
Answers
Using the slope - intercept form to represent the scenario described, the equation obtained would be y = 0.35x + 8
The cost per ride represents the intercept = $8
The cost per mile represents the slope = $0.35
The slope - intercept form of a linear equation is expressed as :
y = bx + c b = slope ; c = interceptTherefore, the slope intercept form for the cost of taxi ride is y = 0.35x + 8
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Rewrite 2/3 and 1/15 as a unit rate
Answers
Answer:
10:1
Step-by-step explanation:
Answer:
Step-by-step explanation:
The unit rate is found by dividing.
2/3 = 0.(6)
1/15 = 0.(6)
The student government snack shop sold 64 snacks this week. 8 of the snacks sold were fruit cups. What percentage of all snacks sold were fruit cups?
Rewrite the equation as a division equation.
Answers
Answer:
8/64 = 0.125 = 12.5%
Step-by-step explanation:
8/64 = 0.125 = 12.5%
write an indirect proof that a triangle cannot have 2 right angles
Answers
Solve the following equation for x: 5x-3 1/2 = 9x+4 Enter answers as a decimal with no variable, no spaces, and no equal sign. DO NOT ROUND.
Answers
Answer:
− 1.875
Step-by-step explanation:
Do you want an explanation?
phone company offers to monthly plans. Plan a cost $11 plus an additional $.19 for each minute of calls. Plan B cost $16 plus an additional $.15 for each minute of calls
Answers
Answer:
whats the question I can't help without a question
The half-life of caffeine in a healthy adult is 4.8 hours. Jeremiah drinks 18 ounces of caffeinated
coffee in the morning. How long will it take for only 60% of the caffeine to remain in his body?
Answers
We want to see how long will take a healthy adult to reduce the caffeine in his body to a 60%. We will find that the answer is 3.55 hours.
We know that the half-life of caffeine is 4.8 hours, this means that for a given initial quantity of coffee A, after 4.8 hours that quantity reduces to A/2.
So we can define the proportion of coffee that Jeremiah has in his body as:
P(t) = 1*e^{k*t}
Such that:
P(4.8 h) = 0.5 = 1*e^{k*4.8}
Then, if we apply the natural logarithm we get:
Ln(0.5) = Ln(e^{k*4.8})
Ln(0.5) = k*4.8
Ln(0.5)/4.8 = k = -0.144
Then the equation is:
P(t) = 1*e^{-0.144*t}
Now we want to find the time such that the caffeine in his body is the 60% of what he drank that morning, then we must solve:
P(t) = 0.6 = 1*e^{-0.144*t}
Again, we use the natural logarithm:
Ln(0.6) = Ln(e^{-0.144*t})
Ln(0.6) = -0.144*t
Ln(0.6)/-0.144 = t = 3.55
So after 3.55 hours only the 60% of the coffee that he drank that morning will still be in his body.
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Exercise #14: The mile and the kilometer are relatively close in size. Can you convert 1 mile into an equivalent
in kilometers? Here's what I'll give you. There are 2.54 centimeters in an inch, 5,280 feet in a mile, 100
centimeters in a meter, and 1000 meters in a kilometer. All else you should be able to do for yourself. Round
your answer to the nearest tenth of a kilometer. This takes quite a string of multiplications, but you can do it!
Answers
The equivalent of 1 mile to kilometres is approximately 1.6 km.
2.54 cm = 1 inch
5280 ft = 1 mile
100 cm = 1 m
1000 m = 1 km
Using the information let's convert 1 mile to kilometre.
1000 m = 1 km
Therefore,
1 m = 0.000621371 miles
1000 m(1 km) = ?
cross multiply
length = 1000 × 0.000621371 = 0.621371 miles
Therefore,
0.621371 miles = 1 km(1000 m)
1 miles = ?
length in km = 1.60934449789 km
Therefore,
1 miles = 1.6 km
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Emily took an airplane trip. Her plane flew an equal number of miles each hour. Write an equation to represent one way you can find how many miles Emily's plane flew each hour.
Use this to help you:
Air travel time: 12 hours
Destination: 2,184 miles
Answers
182.00 miles per hour
y = 182x will be the equation to represent one way you can find how many miles Emily's plane flew each hour.
What is the equation?A formula that expresses the connection between two words on each side of an indication. A calculation with an integer multiple is referred to as an equation. Algebra is widely used in equations. In performing calculations but unsure of the precise amount, algebra is utilized.
The information that is provided is
the air travel time is 12 hours
The destination miles will include 2,184 miles
Assuming the values of x and y
x = number of hours n
y = distance covered
The equation that will be made will be:
y = (2184 / 12)x
y = 182x
Therefore, the equation will be y = 182x.
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At football practice on Monday, Brandon threw a football into the target 5 times. The next Monday, he tripled the number of targets he hit. On the following Monday, his hits double that of the week before. Write and evaluate a numerical expression to find how many times he hit the target during those three weeks.
Enter the correct answers in the boxes.
Expression:
Answers
Answer:
try using a different app, it helps with all types of mathematical equations
Circle the multiplication problem that does not belong with the other three. explain 12×8=,22×4=,42×2=,33×3=
Answers
Answer: 12 x 8
Step-by-step explanation: The other three are not the basic multiplication facts from 0 - 12.
if 6sinx=3cosx the value of tanx is
Answers
Step-by-step explanation:
tanx=sinx/cosx=3/6=1/2