a) The solution to the transformation of the function is h ( x ) = 4x - 5
b) The reflection of function g ( x ) over y axis is f ( x ) = -x³ + x² + 3x - 1
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the function be represented as g ( x )
Now , the value of g ( x ) = 4x - 3
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
On transformation of the function by a vertical shift of 2 units , we get
h ( x ) = g ( x ) - 2
Substituting the values in the equation , we get
h ( x ) = 4x - 3 - 2
h ( x ) = 4x - 5
So , the transformed function is h ( x ) = 4x - 5
b)
On reflecting the function g ( x ) over y axis , f ( x ) = g ( -x )
Substituting the value of x as -x in the function , we get
g ( -x ) = ( -x )³ + ( -x )² - 3 ( -x ) - 1
So , f ( x ) = -x³ + x² + 3x - 1
Hence , the transformed function is h ( x ) = 4x - 5
To learn more about transformation of function click :
https://brainly.com/question/26896273
#SPJ2
Which expression is equivalent to
(5^-2)(5^-1)
-1/125
-1/5
1/125
1/5
Answer:
1/5
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
(Blank) Divided by 4 = 8 Remainder 3
Mrs. Washington is scooping 4 1/2 cups of peanuts with a scoop that holds 1/3 cup. How many scoops wil she fill
Answer:
12.5
Step-by-step explanation:
3 scoops = 1 cup
6 scoops = 2 cups
9 scoops = 3 cups
12 scoops = 4 cups
In two or more complete sentences explain how to balance the chemical equation and classify its reaction type. ___NaI + ___Pb(SO4)2 ⟶ ___PbI4 + ___Na2SO4
Answer:
4112
Step-by-step explanation:
Answer:
By applying law of conservation of mass.
Explanation:
Every balanced chemical equation follows law of conservation of mass.
This law states that mass can neither be created nor can be destroyed but it can only be transformed from one form to another form.
This law also states that the total number of individual atoms on the reactant side must be equal to the total number of individual atoms on the product side.
For the given reaction, the balanced chemical equation follows:
4Na1+Pb(SO4)__Pb14+2Na2SO4
On reactant side:
Number of sodium atoms = 4
Number of iodine atoms = 4
Number of lead atoms = 1
Number of sulfur atoms = 2
Number of oxygen atoms = 8
On product side:
Number of sodium atoms = 4
Number of iodine atoms = 4
Number of lead atoms = 1
Number of sulfur atoms = 2
Number of oxygen atoms = 8
Hence, the balanced chemical equation is written above.
Step-by-step explanation:
barb exercises for 22 hours each week. how many hours does she exercise in 14 weeks. use the array drawn on the grid go help multiply
Answer:
308 hours
Step-by-step explanation:
22 x 13
for his phone service, Jonh pays a monthly fee of $30, and he pays and additional $0.05 per minute of use. the least he has been charged in a month is $99.45
what are the possible number of minutes he has used his phone in a month?
use m for the numbers of minutes, and solve your inequality for m.
Answer:
m= 1395
Step-by-step explanation:
99.45 -30=
69.45
69.45 divided by 0.05
what is the equation for 15% of 24
Answer:
5 / 5 = 100% Nov 18 11:54 UTC (GMT)
15 / 24 = 62.5% Nov 18 11:54 UTC (GMT)
255 / 280 = 91.071428571429% Nov 18 11:54 UTC (GMT)
0.067 = 6.7% Nov 18 11:54 UTC (GMT)
51 / 50 = 102% Nov 18 11:54 UTC (GMT)
Answer:
24 times .15
Step-by-step explanation:
15% is equal to .15, and in this case, if you are trying to find the answer, it is 3.6
Suppose Karen $1000 that she invests in an account that pays 3% interest compounded annually. How much money does Karen have at the end of 3 years?Solve for the interest
Please I need Help I beg Please Help Meeeeeeeeeeeee
help plzzzzzz!!! The ratio of green marbles to total marbles in a bag is 2:9. The ratio of red marbles to total marbles in the same bag is 1:3. Which of the following statements is true?
There are more red marbles in the bag.
There are more green marbles in the bag.
There is the same number of red and green marbles in the bag.
Answer:
There are more red marbles in the bag
Step-by-step explanation:
2/9 = .2222 green
1/3 = .33333 red
Can somebody help me on this
Y=2/3x+5
Y=x+3
How do I solve for x I’m confused with the fraction part ?
Answer:
(6,9)
Step-by-step explanation:
Y=2/3x+5
Y=x+3
2/4x + 5 = x + 3
Solve the equation
x=6
Substitute the value of x
y=6+3
Solve the equation again.
Now we know y=9
(x,y) = (6,9)
Check the solution
9=2/3 x 6 + 5
9=6+3
Simplify
A spring balance measures?
Answer:
A spring balance measures the weight of an object by opposing the force of gravity acting with the force of an extended spring.
mrk brainliest?
i need help with this ^
Rectangle ABCD is dilated with center at (0, 0) and scale factor 2. Select the three statements that are true about the dilation.
Answer:
Options (3), (4) and (6)
Step-by-step explanation:
Coordinates of the vertices of the given rectangle are,
A(1, 5), B(3, 2), C(-3, -2) and D(-5, 1)
When rectangle ABCD is dilated by a scale factor of 2 about the origin,
Rule to be followed for the dilation,
(x, y) → (2x, 2y)
Therefore, image of the rectangle ABCD will be,
A(1, 5) → A'(2, 10)
B(3, 2) → B'(6, 4)
C(-3, -2) → C'(-6, -4)
D(-5, 1) → D'(-10, 2)
- Hence point B' is located at (6, 4).
- Rectangle ABCD and A'B'C'D' are similar as all the angles of image will be same as the pre-image after rigid transformation (dilation).
- Let the equation of the line B'C' is,
y = mx + b
Slope (m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{4-2}{6-3}[/tex]
= [tex]\frac{2}{3}[/tex]
Since B'C' will pass through origin, y-intercept will be zero.
Therefore, equation of B'C' will be,
y = [tex]\frac{2}{3}x[/tex]
Options (3), (4) and (6) are the correct options.
Answer:
well im confused but dont you have to find the prime too
Step-by-step explanation:
Which statement is the lie?
Part A: Prompt: \large 4n-3
A. Three less than four times a number
B. Four times a number less than 3
C. Four times a number decreased by 3
Answer:
C. Four times a number decreased by 3
I ordered 8 pizzas for my son’s birthday party. Each pizza had 8 slices. If my son and his friends ate 47 slices of pizza at the party, how many slices will I have leftover?
Answer:
17
Step-by-step explanation:
8*8 = 64
64 - 47 = 17
-(-3 / -2)= ???? I need help pleasee
Answer: -(-3 / -2)= ?
Step-by-step explanation:
Answer:
1.5
Step-by-step explanation:
- - = +
so 3 ÷ 2 is 1.5
hope it helps!
A customer requires a car service for 80 miles,
How much money will the customer save by taking Sal's Car Rides instead of Ray's Limo? Enter the answer in the box.
Answer:
$25
Step-by-step explanation:
Derive an equation to represent the cost of using each ride.
Sal's Car Rides:
Using 2 pairs of values from the table, (0, 40) and (20, 80), find the slope, m (fee per mile).
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{80 - 40}{20 - 0} = \frac{40}{20} = 2 [/tex]
The y-intercept, b, is the one-time fee for fuel. This is the value of the cost ($) when number of miles traveled is 0.
Thus, b = 40.
Substitute m = 2, and b = 40 into [tex] y = mx + b [/tex].
Equation for the total cost for Sal's Car Rides would be:
[tex] y = 2x + 40 [/tex].
Find the total cost to be charged if a customer requires the a car service for 80 miles if he chooses Sal's Car Rides.
Simply substitute x = 80 in [tex] y = 2x + 40 [/tex].
[tex] y = 2(80) + 40 = 200 [/tex]
The customer would pay $200.
Ray's Limo:
The equation that represents the total cost (y) to be charged for number of miles (x), given that $2.50 is charged per mile plus a one-time fee of $25 for fuel, would be:
[tex] y = 2.5x + 25 [/tex].
If a customer uses Ray's Limo services for 80 miles, the cost charged would be:
Substitute x = 80 in [tex] y = 2.5x + 25 [/tex].
Thus:
[tex] y = 2.5(80) + 25 = 225 [/tex].
The fee the customer would pay = $225 for using Ray's Limo services.
Therefore, if the customer takes Sal's Car Rides instead of Ray's Limo, he would save, $225 - $200 = $25.
The customer would save $25.
What is 24 + x = 29?
Answer:
The answer is x=5
Step-by-step explanation:
hope this helps
Given:24 + x = 29
Solutions: To find the x subtract both side by 24.
24-24 + x = 29-24
x=5
Answer:
x=5
Step-by-step explanation:
24+x=29 - subtract 24 from both sides to isolate variable
x=5
Identify a and b for the hyperbola with equation. (y^2/b^2)-(x^2/a^2)=1
The value of (a) and (b) for the hyperbola are [tex]\sqrt 3[/tex] and 2
The equation of the hyperbola is given as:
[tex]\frac{y^2}{b^2} - \frac{x^2}{a^2} = 1[/tex]
The curve of the graph passes through points (0,2) and (-4,3).
So, we have:
[tex]\frac{2^2}{b^2} - \frac{0^2}{a^2} = 1[/tex] and [tex]\frac{(-4)^2}{b^2} - \frac{3^2}{a^2} = 1[/tex]
[tex]\frac{2^2}{b^2} - \frac{0^2}{a^2} = 1[/tex] becomes
[tex]\frac{4}{b^2} = 1[/tex]
Cross multiply
[tex]b^2 = 4[/tex]
Take positive square root of both sides
[tex]b = 2[/tex]
[tex]\frac{(-4)^2}{b^2} - \frac{3^2}{a^2} = 1[/tex] becomes
[tex]\frac{(-4)^2}{2^2} - \frac{3^2}{a^2} = 1[/tex]
[tex]\frac{(-4)^2}{4} - \frac{9}{a^2} = 1[/tex]
[tex]4 - \frac{9}{a^2} = 1[/tex]
Collect like terms
[tex]- \frac{9}{a^2} = -3[/tex]
Cross multiply
[tex]-3a^2 = -9[/tex]
Divide both sides by -3
[tex]a^2 = 3[/tex]
Take square roots of both sides
[tex]a = \sqrt 3[/tex]
Hence, the value of (a) and (b) for the hyperbola are [tex]\sqrt 3[/tex] and 2
Read more about hyperbolas at:
https://brainly.com/question/14503968
What is the domain and range of each relation
Answer:
1 ans
domain=(-2,0,2,4)
range=(-3,-1,0)
2 ans
domain=(-3,-1,0,3)
range=(-1,0,1,2,3)
Step-by-step explanation:
Morgan is 5 feet tall. There are 2 .54 centimeter in 1 inch. What is Morgan’s height in centimeters?
Answer:
152.4cm
Step-by-step explanation:
12 Inches per foot.
5 x 12
60
1 inch in cm is 2.54
60 x 2.54
152.4cm
Hope this helped!
16/17 rounded to the nearest hundredth
Answer:
0.941
Step-by-step explanation:
Which equation is parallel to
y =2/3x – 6 and passes through (9, -3)?
Answer:
y=2/3x -3
Step-by-step explanation:
y=mx+c
If the gradient(m) is the same then it's parallel.
The line passes through -3 so the y intercept(c) is -3
Answer:
Y=2/3x-9
Step-by-step explanation:
Y=mx+c
y=2/3x+c
Then substitute the coordinates
y=-3
x=9
-3=2/3*(9)+c
-3=6+c
Make c the subject by subtracting 6 from both sides.
-9=c
so the answer is
Y=2/3x-9
Write a linear function f with f(0) = 7 and f(3) = 1.
f(x) = 0
Here is a system of linear equations:
equation 1: 2x + 7y = 8
equation 2: 2x + y=14
Solve this system with either the substitution method
OR the elimination method. Type your answer as an
ordered pair, then explain how you found the solution to
the system.
Answer:
X=7.5 y=-1
Step-by-step explanation:
[tex]2x + 7y = 8 \\ 2x + y = 14[/tex]
I multiplied the equation with - 1 to than I sum it with the second one to get rid of x
[tex] - 6y = 6 \\ y = - 1[/tex]
Now you put Y in on of the equation and you get x.
[tex]2x - 1 = 14 \\ 2x = 15 \\ x = 7.5[/tex]
n − 2/3 = 25 3/4 help now
Answer:
26 5/12
Step-by-step explanation:
n − 2/3 = 25 3/4 Add 2/3 to both sides
n - 2/3 + 2/3 = 25 3/4 + 2/3 Combine
n = 25 3/4 + 2/3
Work with the fractions
3/4 + 2/3 The lowest common denominator is 12
(3*3)/(3*4) = 9 / 12
(2*4)/(3*4) = 8/ 12
9/12 + 8/12 = 17/12 = 1 5/12
Now you need to add 1 to 25
1 + 25 = 26
And add the fraction 5/12
The answer is 26 5/12
There are two dimes and a nickel in your pocket. You randomly pick a coin from your pocket and place it on the counter. Then you pick a second coin from your pocket.
Answer:
each coin has a 1/3% chance of being picked
Step-by-step explanation:
Which of the following is true about a linear function? (4 points)
A. It may curve in some parts and be horizontal in others.
B. It must cross the origin.
C. It has a constant rate of change.
D. It must contain only positive values.
Answer:
The answer is c
Step-by-step explanation:
Answer:
the answer is C. It has a constant rate of change.
Step-by-step explanation:
Triangle PQR is similar to triangle VWX. What is the length of PR?
Answer:10.5
Step-by-step explanation:I’m smart
Answer: 10 i promise u it is.
Step-by-step explanation:
