Answers
Answer:
[tex]k = 5[/tex]
Step-by-step explanation:
Given
[tex]g(x) = f(x) + k[/tex]
Required
Determine the value of k
First, we need to determine the equation of g(x)
Start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where x and y are two corresponding values:
[tex](x_1,y_1) = (1,1)[/tex]
[tex](x_2,y_2) = (0,-3)[/tex]
The slope (m) is:
[tex]m = \frac{-3- 1}{0 - 1}[/tex]
[tex]m = \frac{-4}{- 1}[/tex]
[tex]m = 4[/tex]
The equation is calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = 4[/tex] and [tex](x_1,y_1) = (1,1)[/tex]
[tex]y - 1 = 4(x - 1)[/tex]
[tex]y - 1 = 4x - 4[/tex]
Make y the subject of formula
[tex]y = 4x - 4 + 1[/tex]
[tex]y = 4x - 3[/tex]
So:
[tex]f(x) = 4x - 3[/tex]
Next, we determine the equation of f(x)
Start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where x and y are two corresponding values:
[tex](x_1,y_1) = (-1,-2)[/tex]
[tex](x_2,y_2) = (0,2)[/tex]
The slope (m) is:
[tex]m = \frac{2- (-2)}{0 - (-1)}[/tex]
[tex]m = \frac{2+2}{0+1}[/tex]
[tex]m = \frac{4}{1}[/tex]
[tex]m = 4[/tex]
The equation is calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = 4[/tex] and [tex](x_1,y_1) = (-1,-2)[/tex]
[tex]y - (-2) = 4(x - (-1))[/tex]
[tex]y + 2 = 4(x +1)[/tex]
[tex]y + 2 = 4x +4[/tex]
Make y the subject of formula
[tex]y = 4x + 4 - 2[/tex]
[tex]y = 4x + 2[/tex]
So:
[tex]g(x) = 4x + 2[/tex]
Recall that
[tex]g(x) = f(x) + k[/tex]
Make k the subject
[tex]k = g(x) - f(x)[/tex]
Substitute values for g(x) and f(x)
[tex]k = 4x + 2 - (4x - 3)[/tex]
[tex]k = 4x + 2 - 4x + 3[/tex]
[tex]k = 4x - 4x+ 2 + 3[/tex]
[tex]k = 5[/tex]
The transformation that maps f into g is a translation transformation,
involving the addition of k to the value of f(x).
The value of k that transforms f into g is; k = -5Reasons:
Points on the graph of g(x) are; (0, -3) and (0, 1)
[tex]\mathrm{The \ slope \ of \ the \ graph \ of \ g(x)} =\dfrac{-3 - 1}{0 - 1} = 4[/tex]
The equation of g(x) is; y - (-3) = 4·x, which gives;
y = 4·x - 3
The y-intercept = -3
Points on the graph of f(x) are; (-1 -2) and (0, 2)
[tex]\mathrm{The \ slope \ of \ the \ graph \ of \ f(x)} =\dfrac{-2 - 2}{-1 - 0} = 4[/tex]
The equation of f(x) is; y - (-2) = 4·(x - (-1)), which gives;
y = 4·x + 4 - 2 = 4·x + 2
The y-intercept = 2
The slopes of the graphs of f(x) and g(x) are equal, therefore, f(x) ║ g(x)
The difference or the transformation that takes the y-intercept of f(x) to the
y-intercept of g(x) is; k = y-intercept(g(x)) - y-intercept(f(x)) = -3 - 2 = -5
Therefore, k = -5
Which gives;
g(x) = f(x) - 5
The value of k that transforms f into g is; k = -5
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Related Questions
A surveyor observes that point A is located on level ground 25 feet from a flag pole. The base of the flagpole represents point B. Approximate the height of the flagpole to the nearest tenth of a foot when the angle between the ground and the top of the flagpole is:______.(a) 30° (b) 38° (c) 45°
Answers
Answer:
Step-by-step explanation:
The set up will give a right angled triangle
Given
Distance of point A from the flagpole = 25feet
If angle of elevation is 30°
Required
Height of flagpole (opposite)
Using TOA
tan theta = opp/adj
tan30° = opp/25
opp = 25tan30°
opp = 14.4feet
Hence the height of flagpole when the angle of elevation is 30° is 14.4feet
If angle of elevation is 38°
Required
Height of flagpole (opposite)
Using TOA
tan theta = opp/adj
tan38° = opp/25
opp = 25tan38°
opp = 19.53feet
Hence the height of flagpole when the angle of elevation is 38° is 19.5feet
If angle of elevation is 45°
Required
Height of flagpole (opposite)
Using TOA
tan theta = opp/adj
tan45° = opp/25
opp = 25tan45°
opp = 25feet
Hence the height of flagpole when the angle of elevation is 45° is 25feet
John is eating out with friends, and it is his turn to pay gratuity. The bill for the food is $48.53. If he plans to tip 20%, what should the tip be?
Answers
Answer:
$9.76
Step-by-step explanation:
20% is 1/5 of the bill. The answer is 48.53 +( 48.53*1/5) which is 9.76 so the $9.76
Plz mark brainliest if correct!
Hope this helps
Answer:
Step-by-step explanation: well you can just plug it into a calculator.
the answer is 9.706 or 9.7 if you simplify it and if you are rounding to the nearest tenth then its 10.
hope this helps!
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided
Harry rides his bike 25 miles Karen rides her bike 25 miles Who rides farther?
Answers
So no one rides farther .
The steps i took was compare and contrast both of their miles and they were the same amount
you wrote ehte question wrong
The LMC of 6 and 7 is
Answers
Answer:
6, 12, 18, 24, 30, 36. 42, 46, 52, 58, 64,
7, 14, 21, 29, 36
Your answer is 36.
Step-by-step explanation:
LCM means the multiple which the two numbers share with the least value. So, I just found the multiples of each number until I found the one which was common. If you would like me to explain this in more depth, tell me! I'd be glad to help.
HELP ME SOLVE THis Plz Solve last one plz
Answers
Answer:
the last one is 128.9
How do you do this question?
Answers
Answer:
S(50) = 0
Step-by-step explanation:
The initial condition is S(0) = 0, so start at the origin. The slope there is approximately 1. So as t increases by a small amount, S increases by the same amount. Continuing this logic, we end up tracing the vector field until we get to t=50, where S is approximately 0.
Each little tickmark is a slope value telling you which direction to go. If you place yourself at the origin (0,0) then the tick mark here tells us to go roughly in the northeast direction. As you step forward to the northeast just a tiny bit, the slope value changes to aim more toward the east (rather than north). For more information, check out Euler's method. Specifically it's Euler's method dealing with slope fields.
The diagram below shows what could be each step of this process. Each red dot is a stepping stone, so to speak, going from (0,0) to (50,0). This is an approximation. Without the actual function F(t, S), it's hard to say where exactly S(50) is located. But S(50) = 0 is a fairly good guess I think. MathPhys has a great diagram showing what could be the solution for S(t) given the initial condition S(0) = 0. Note how they drew a curve through all of the red points I've marked.
A savings bond currently made Jamar $2,112.64 worth of interest in 7 years. If the investment gained 5.5% annual simple interest each year, approximately how much was the bond originally bought for?
Answers
Answer:
$5487.38
Step-by-step explanation:
Given that:
Interest currently made = $2112.64
Time = 7 years
Rate of interest = 5.5% annual
To find:
The price for which the bond was originally bought ?
Solution:
We need to find nothing but the principal amount.
First of all, let us have a look at the formula for Simple Interest.
[tex]Simple\ Interest = \dfrac{PRT}{100}[/tex]
Where [tex]P[/tex] is the principal amount
[tex]R[/tex] is the Rate of Interest
[tex]T[/tex] is the time for which the investment is made
Let us put the given values in the formula:
[tex]2112.64 = \dfrac{P\times 5.5\times 7}{100}\\\Rightarrow P =\dfrac{2112.64\times 100}{5.5\times 7}\\\Rightarrow P =\dfrac{211264}{38.5} \\\Rightarrow \bold{P =\$5487.38}[/tex]
Does the ratio 15/12 and 5/4 form a proportion?
Answers
Answer:
yes
Step-by-step explanation:
5 times 3 is 15 and 12 and 15 and 12 divided by 3 you will get 5/4
Expression A: 3(x + 2) Expression B: 3x + 6....... Which statement does not show that these expressions are equivalent? O A. Substituting any value of x makes the expressions equivalent B. The expressions name the same number regardless of the value of x. O C. Both expressions involve addition. O D. 3(x+2) can be rewritten as 3x + 6 using the distributive property. SUBMIT E PREVIOUS
Answers
Answer:
D. 3(x+2) can be rewritten as 3x + 6 using the distributive property
Step-by-step explanation:
Given
[tex]3(x + 2) = 3x + 6[/tex]
Required
Explain
From the list of given options, option D answers the question.
This is because, the expression above involves distributive property and only option D correctly states that.
A distributive property is:
[tex]a*(b + c) = a*b + a * c[/tex]
In this case:
[tex]a = 3[/tex] [tex]b = x[/tex] and [tex]c = 2[/tex]
So:
[tex]a*(b + c) = a*b + a * c[/tex]
Substitute values for a, b and c
[tex]3*(x + 2) = 3 * x + 3 * 2[/tex]
[tex]3(x + 2) = 3x + 6[/tex]
Answer:
C. Both expressions involve addition.
Step-by-step explanation:
I tried it, and it was correct
PLEASE HELP IT IS 3:30 AM
FIND THE EQUATION OF THE LINE
USE EXACT NUMBERS
y= ( )x + ( )
Answers
Answer:
The answer is y = -1/3x + 5 !
Step-by-step explanation:
If you observe the line, the y-intercept is 5, from the point in the graph (0,5). From that point, we can see that the rise over run is -1/3. Thus, y = -1/3x + 5.
In solving the problem 7(2x - 4) + 7 = 0 what order are the steps?
A. Distributive property, inverse, simplify
B. Inverse, combine like terms, inverse
C. Distributive property, combine like terms, inverse, inverse, simplify
D. Combine like terms, inverse, distributive property, simplify
Answers
whats the answer to this MARKING BRAINLIEST
Answers
Answer:
400 square feet
Step-by-step explanation:
20 x 20 = 400
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Answer:
400 square feet
Step-by-step explanation:
Area = length x width
A = lw
A = 20 x 20
20 x 20 = 400
Area = 400 ft^2
The weight, in pounds, of a newborn baby tt months after birth can be modeled by W.W. The table below has select values showing the linear relationship between tt and W.W. Determine the weight of the baby at birth.
Answers
Answer:
12 pounds
Step-by-step explanation:
Please give me thanks
When you give me thanks
Have a good day :)
The weight of the baby at birth is 8 pounds.
Given,
The weight, in pounds, of a newborn baby tt months after birth, can be modeled by W.
The table below has select values showing the linear relationship between
t and W.
We need to determine the weight of the baby at birth.
The table is given as:
t w1 10
4.5 17
9 26
How do we read the tables given?The table has two columns and it always has a relationship between them depending on the question.
Example:
Miles. Hours
2. 3
6. 9
8. 12
Here we see that every 1-5 hours there's a mile increase.
We have,
W = weight of the baby
t = number of months.
From the table:
The baby weight-
At 1 month = 10
At 4.5 months = 17
At 9 months = 26
We see that,
In,
(4.5 - 1) = 3.5 months there is an increase of (17 - 10) = 7 pounds.
So we can write it as:
3.5 months = 7 pounds
1 month = 7/3.5
1 month = 70/35 = 10/5 = 2 pounds
This means in after every month there is an increase of 2 pounds.
We have,
1In the first month, the weight of the baby is 10 pounds.
And every month there is an increase of 2 pounds.
So,
The weight of the baby at birth is:
= 10 - 2
= 8 pounds
Thus the weight of the baby at birth is 8 pounds.
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Johnny took a test. All the questions have equal value. He answered 38 of the questions correctly. This was 95% of the questions. How many questions were on the test?
Answers
Answer:
40 questions
Step-by-step explanation:
38=.95x where x is the total tests
38/.95 = x
40 = x
Write the following as a base-10 numeral in standard form.
4 x 105 + 2 x 102 + 7 =
Answers
9514 1404 393
Answer:
400207
Step-by-step explanation:
Any calculator can form this sum for you. It is ...
4×10^5 +2×10^2 +7
= 400,000 +200 +7
= 400207
A car dealership sold 84 cars in April. The dealership wants to increase the number of cars sold by 25% in May. How many cars will the dealership need to sell to reach their goal?
Answers
Answer:
The car dealer must sell 105 cars in May to reach his goal.
Step-by-step explanation:
Given that the car dealer sold 84 cars in April, and wants to increase his May sales by 25%, to determine the number of cars he must sell to reach his goal it is necessary to perform the following calculation:
84 + (84 x 0.25) = X
84 + 21 = X
105 = X
Therefore, the car dealer must sell 105 cars in May to reach his goal.
4 1/3 divided by 4/7
Answers
Answer:
The answer is 91/12 in exact form or 7 7/12 in mixed number form.
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Select " Yes" or " No" to indicate whether the ordered pair is on the graph of the function f(x)= -9^x+1. ( Make sure you look at the picture. Need help Asap Please
Answers
Answer:
yes
no
no
Step-by-step explanation:
An orange punch is 45% juice and a mango punch is 20% juice. By combining the two, a company is making 500 L of a fruit punch that is 40% juice. How many liters of orange punch are needed for the company’s concoction? Make sure to include units. PLEASE FAST. AND SHOW WORK
Answers
Answer:
400 liters of orange punch and 100 liters of mango punch are required to create a mixture with 40% juice.
Step-by-step explanation:
Given that the orange punch has 45% juice and the mango punch has 20% juice, if you want to create a mixture of 500 liters of fruit punch that has 40% juice, to determine the percentage of punch of each fruit to be used, the following calculation must be performed:
45 x 1 + 20 x 0 = 45
45 x 0.9 + 20 x 0.1 = 42.5
45 x 0.8 + 20 x 0.2 = 40
Therefore, it takes 80% orange punch and 20% mango punch to create a mixture with 40% juice. Thus, since 500 x 0.8 equals 400, 400 liters of orange punch and 100 liters of mango punch are required to create a mixture with 40% juice.
Can anyone pls help? Will give brainliest if you're correct.
Answers
Answer:
2 ninths, or 2/9
Step-by-step explanation:
Multiply -2/3 by -1/3 to get the answer
Answer: f=2/9
you have to multiply 2/-3 and -3/2f
Trust me it will work
what is the value of tan(arrcos( -[tex]\sqrt{2}[/tex] /2)?
Answers
Answer:
tan(arrcos( -√2 /2)) = -1
(result in radians)
Step-by-step explanation:
please answer i need help
Answers
Answer:
first answer is 9.84
Step-by-step explanation:
9.84 is the square root of 97, rounded to the nearest hundredth.
the legs measure 9 x 9 and 4 x 4 = 81 and 16.
81 + 16 = 97, so your answer is the square root of 27, which rounded to the nearest hundredth, equals 9.84. Rounding towards the nearest whole, 10 would be your best bet.
hope this helps!!
In a-d, choose whether the fraction and percent are equivalent.
50/33 and 117% yes or no (HURRY UP)
Answers
Answer: no
Step-by-step explanation:
117% equals 1.17 and 50/33 equals 1.51 repeating so they aren’t equal.
-2(y-1)=9 what is the answer
Answers
-2(y-1) = 9
Use distributive property:
-2y + 2 = 9
Subtract 2 from both sides
-2y = 7
Divide both sides by-2:
Y = -7/2
Factor the algebraic
12a+20=
Answers
Answer:
4(3a+5)
Step-by-step explanation:
When you factor an algebraic expression, you divide the initial expression by a common factor to produce your answer.
have a gr8 day (:
Explanation: Factor 4 out of 12a +20.
PLEASE HELP ME ASAP
Which graph best represents the solution set of y > 3x - 4
Answers
Answer:
Step-by-step explanation:
THE MIDDLE ONE
Please need help thank
Answers
Answer:
10
Step-by-step explanation:
Answer:
I think it’s 10:)
Step-by-step explanation:
A market trader bought 100 loaves at 84p each
Answers
Answer:
8400p.
Step-by-step explanation:
I'm assuming you're asking about the total price of the loaves here. Please specify your question further next time.
(84*100)p
= 8400p
Hope that helped!
12. F(x) = 4x squared
Answers
Answer:
y-intercept: [tex]y=0[/tex]
axis of symmetry: [tex]x=0[/tex]
vertex: [tex](0,0)[/tex]
Step-by-step explanation:
To find the y-intercept, set x = 0 and solve for y.
I am assuming f(x) = y
[tex]y=4x^2[/tex]
[tex]y=4(0)^2[/tex]
[tex]y=0[/tex]
The y-intercept of the equation is y = 0.
Now, for the axis of symmetry, you need the equation [tex]x=\frac{-b}{2a}[/tex]
In an equation.. [tex]y=ax^2+bx+c[/tex]
In this case, there is only an a, so plug in the values into the equation.
[tex]x=\frac{0}{2(4)}[/tex]
[tex]x=0[/tex]
The axis of symmetry is x = 0.
To find the vertex, change the format of the equation from standard form to vertex form.
Vertex form: [tex]y=a(x-h)^2+k[/tex]
The vertex is [tex](h,k)[/tex]
[tex]y=4x^2 = 4(x+0)^2+0[/tex]
[tex](h,k)=(0,0)[/tex]
The vertex in this case is (0,0).
Graphing makes things a lot easier. If you can graph it, all you have to do is look at the graph and the answers are all there!
Hope this helped you!
If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.3 minutes and a standard deviation of 1 minute, find the point in the distribution in which greater than 75.8% of the college students in trying to find a parking spot in the library parking lot.
A. 2.6 minutes
B.2.8 minutes
C.3.2 minutes
D.4.2 minutes
Answers
Answer:
i believe its c
Step-by-step explanation: