Answers
Answer:
f(x) ⇒ Graph C
g(x) ⇒ Graph D
h(x) ⇒ Graph A
j(x) ⇒ Graph E
Step-by-step explanation:
* Lets revise the quadratic function and its inverse
- The quadratic function if f(x) = x², its vertex is the origin
- To find its inverse, switch x and y and solve for y
∵ y = x² ⇒ switch x and y
∴ x = y² ⇒ solve for y
∴ y = ± √x
- If y = √x , then the graph is up the x-axis
- If y = -√x , the graph is down the x-axis
∴ The inverse function is y = √x
* Now lets solve the problem
- All the figure are the inverses of the quadratic function y = x²
∵ f(x) = √(x - 1)
# x - 1 means the graph move to the right 1 unit
∴ Its vertex is (1 , 0)
* The graph of f(x) = √(x - 1) is graph C
∵ g(x) = -√x
# The sign (-) means the graph reflected about the x-axis
∴ Its vertex is (0 , 0) but the graph under the x-axis
* The graph of g(x) = -√x is graph D
∵ h(x) = √x
∴ Its vertex is (0 , 0)
- It is the inverse of y = x² , the graph up to the x-axis
* The graph of h(x) = √x is graph A
∵ j(x) = -√(x - 1)
# x - 1 means the graph move to the right 1 unit
# The sign (-) means the graph reflected about the x-axis
∴ Its vertex is (1 , 0) , the graph down the x-axis
* The graph of j(x) = -√(x - 1) is graph E
Related Questions
find the greatest common factor of the following monomials: u3v6 u6v2
Answers
Answer:
1 2 3 1
Step-by-step explanation:
To find the greatest common factor (GCF) between monomials, take each monomial and write it's prime factorization. Then, identify the factors common to each monomial and multiply those common factors together. Bam!
Answer:
The GCF is [tex]u^3v^2[/tex]
Step-by-step explanation:
The given monomials are:
[tex]u^3v^6[/tex]
and
[tex]u^6v^2[/tex]
The greatest common factor is the product of the least powers of the common factors.
The least of the powers of the common factors are:
[tex]u^3[/tex] and [tex]v^2[/tex].
Their product is [tex]u^3v^2[/tex]
Therefore the Greatest Common Factors is [tex]u^3v^2[/tex]
The scale of a model car is 1 : 100. The length of the model car is 1.6m. Find, in centimetres, the width of the model car.
Answers
Answer:
1600
Step-by-step explanation:
first, 1.6 m is 160 cm.
160 cm is 1 in 1:100
converting the proportion into a fract., it is 1/100.
160=1/100x
1600=x
To find the width of the model car in centimeters, we need to follow a different approach, because the information given doesn't include the width of the actual car or the ratio of length to width. Since only the scale of the model and the length of the model car are given, without additional information about the actual car or its dimensions, we cannot directly calculate the width of the model car.
However, I can explain the general process of how to calculate the width of the model car if the necessary information was provided:
1. **Find the width of the actual car**: If the width of the actual car (in meters or any other units) is given, we could proceed to the next step. Without this information, we cannot continue, so let's assume hypothetically that this information is available.
2. **Convert the width of the actual car to centimeters**: Since the dimensions of the model car are sought in centimeters, we need to convert the actual car's width from meters to centimeters by the following conversion:
\[ \text{width in centimeters} = \text{width in meters} \times 100 \].
3. **Apply the scale ratio**: After converting the actual car's width to centimeters, we need to apply the scale ratio to calculate the width of the model car. The scale is 1:100, which means that one unit of measurement on the model represents 100 of the same units on the actual car.
4. **Calculate the width of the model car**: Divide the width of the actual car in centimeters by the scale ratio (which is 100 in this case) to calculate the width of the model car in centimeters:
\[ \text{width of model car in centimeters} = \frac{\text{width of actual car in centimeters}}{100} \].
If we suppose that the actual car is twice as long as it is wide, and we have the model's length (1.6 m), we could assume that the actual car's length is 160 m (since 1.6 m times the scale factor of 100). With an assumption of the actual car being twice as long as wide, we can deduce that the actual car's width would be 80 m (160 m divided by 2). Converting that to centimeters would be 8000 cm (since 80 m times 100 cm/m). Dividing that by 100 (scale factor) would yield a result of 80 cm for the width of the model car.
However, please note, without the essential information about the actual car's width or its length-to-width ratio, this is just a hypothetical scenario. To proceed with a real calculation, you would need to clarify the actual width of the car or provide the proportional dimensions.
3√16-5=
please help asap
Answers
Answer:
[tex]\large\boxed{3\sqrt{16}-5=7}[/tex]
Step-by-step explanation:
[tex]3\sqrt{16}-5=3(4)-5=12-5=7\\\\\sqrt{16}=4\ \text{because}\ 4^2=16[/tex]
Help please this is due I will give brainliest
Answers
Hope this helps :)
Answer:
A = 340,000 square feet
B = 467,500 square feet
C = 361,250 square feet
D = 180,625 square feet
What is the median ??
Answers
Answer:
9
Step-by-step explanation:
The median is the middle entry of the data set in ascending order. If there is no exact middle then it is the average of the values either side of the middle.
Arrange the data in ascending order
4, 8, 8, 9, 11, 13, 17
↑
The median = 9
Answer:
9
Step-by-step explanation:
Order the numbers from least to greatest, then find the number that is in the middle. If there are two numbers that are in the middle then add the two numbers together and then divide by 2.
Drag the correct steps into order to evaluate 16+j⋅4 for j=8
Answers
To evaluate 16+j⋅4 for j=8, substitute j with 8, multiply the result by 4, and add it to 16 to get the final result of 48.
Explanation:To evaluate 16+j⋅4 for j=8, follow these steps:
Substitute the given value of j into the expression. So, replace j with 8 in the expression 16+j⋅4.Perform the multiplication. Multiply 8 by 4 to get 32.Add the result to 16. Add 32 to 16 to obtain the final result.16 + j * 4 = 16 + 8 * 4 = 16 + 32 = 48
After performing these steps, we find that the expression 16+j⋅4 for j=8 is equal to 16+32, which is 48.
Can somebody help me pls
Answers
Which outcomes are in a or b is answer B
find the trinomial below 4x^2 + 12x + 9
Answers
Answer:
4x² + 12x + 18
Step-by-step explanation:
This would be the trinomial.
Answer:
if you mean to factor it, it would be, (2x + 3)(2x + 3) but if you do mean the trinomial, that is already the answer.
Step-by-step explanation:
4x^2 + 12x + 9
you can split 12x into 6x + 6x so now it's
4x^2 + 6x + 6x + 9
then simplify it into:
2(2x + 3) + 3(2x + 3)
then into:
(2x + 3)(2x + 3)
Find the percent increase from $3.50 to $12.00. Round to the nearest percent.
Answers
Answer:
15.00 once you add percent
Answer:
The increase from $3.50 to $8.50 was 243%.
Step-by-step explanation:
The increase from $3.50 to $12.00 was $8.50.
We need to compare this to the original $3.50 by writing the following ratio, evaluating it and converting the result to a percentage:
$8.50
--------- = 2.43
$3.50
Multiply this result by 100%: (100%)(2.43) = 243%
The increase from $3.50 to $8.50 was 243%.
What is the scale factor ? And given that QY’ = 4.125 what is QY?
Answers
Answer:
Step-by-step explanation:
1.5
Gabby received change worth $2.10. She received 3 more dimes than nickels and 4 less quarters than nickels. How many of each kind of coins did she receive?
Answers
Answer:
Gabby received
7 nickels
10 dimes
3 quarters
Step-by-step explanation:
Let
x----> the number of dimes
y----> the number of nickels
z---> the number of quarters
Remember that
1 dime=$0.10
1 nickel=$0.05
1 quarter=$0.25
we know that
0.10x+0.05y+0.25z=2.10 ------> equation A
x=y+3-----> equation B
z=y-4 -----> equation C
substitute equation B and equation C in equation A and solve for y
0.10(y+3)+0.05y+0.25(y-4)=2.10
0.10y+0.30+0.05y+0.25y-1=2.10
0.40y=2.10-0.30+1
0.40y=2.80
y=7 nickels
Find the value of x
x=y+3 -----> x=7+3=10 dimes
Find the value of z
z=y-4 -----> z=7-4=3 quarters
therefore
Gabby received
7 nickels
10 dimes
3 quarters
P(x|y)
What is this formula?
Answers
Answer:
If x and y are independent events;
[tex]P(x/y)=\frac{P(xny)}{P(y)}=\frac{P(x)*P(y)}{P(y)}=P(x)[/tex]
If x and y are dependent events then;
[tex]P(x/y)=\frac{P(xny)}{P(y)}[/tex]
Step-by-step explanation:
The expression;
P(x|y) in probability represents the conditional probability of an event x occurring given that an event y has already occurred. An example of such would be; the probability that a student passes the examination given that he attempted all the assignments.
If x and y are independent events, that is the occurrence of y does not in any way influence the occurrence of x, then;
[tex]P(x/y)=\frac{P(xny)}{P(y)}=\frac{P(x)*P(y)}{P(y)}=P(x)[/tex]
If x and y are dependent events then;
[tex]P(x/y)=\frac{P(xny)}{P(y)}[/tex]
[tex]P(xny)[/tex] represents the probability of both x and y occurring together;
n denotes intersection
The function g(x) = 2^x. The function f(x) = 2^x + k and k < 0. Which of the following statements is true?
Answers
The graph of f(x) is shifted k units above the graph of g(x). Therefore, the option C is the correct answer.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions are g(x) = 2ˣ and f(x) = 2ˣ+k
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Parent Function: g(x)=2x
Horizontal Shift: None
Vertical Shift: None
Reflection about the x-axis: None
Vertical Compression or Stretch: None
So, from graph of g(x) to the graph of f(x), it shifted k units up.
Therefore, the option C is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
The function g(x) = 2ˣ. The f(x) = 2ˣ+k and k < 0. Which of the following statements is true?
A) The graph of f(x) is shifted k units to the left of the graph of g(x).
B) The graph of f(x) is shifted k units to the right of the graph of g(x).
C) The graph of f(x) is shifted k units above the graph of g(x).
D) The graph of f(x) is shifted k units below the graph of g(x).
The automatic car wash at a service station can wash 96 cars over a 4-hour period. What is the average number of cars that can be washed in 30 minutes?
A. 4
B. 12
C. 25
D.48
Answers
Answer:
Divide 96/4 to get how many cars can be washed within a single hour. Cut that in half to get 12.
Step-by-step explanation:
96÷4=24 cars/hr
24÷2=12 Cars for every 30 minutes.
The diagram is not drawn to scale
Find the value of x.
Answers
Therefore we can use midpoint theorem to say that x = 60 ( the line joining the midpoints of two lines is parallel and half of the third line in a triangle)
The value of x is 60.
How to find the value of x?The Midpoint theorem states that :
The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side
By Midpoint theorem
DE = 30
AC = x
DE = [tex]\frac{1}{2}[/tex] AC
30 = [tex]\frac{x}{2}[/tex]
x = 60
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Rewrite 4n^2+2n as a factorial.
Answers
Answer:
4n²+2n as a factorial is given as:
[tex]= (2n+1)!/(2n-1)![/tex]
Step-by-step explanation:
We are given an expression which has to be converted into factorial form.
The expression is as follows:
[tex]4n^{2} + 2n\\ = 2n(2n+1)\\ = (2n+1)2n\\[/tex]
Now we know that 2n+1 and 2n differs by '1' and the next smaller term is '2n-1'.
Hence, multiplying and dividing by '(2n-1)!'; we get:
[tex]= ((2n+1)(2n)(2n-1)!)/(2n-1)![/tex]
we know that x(x-1)(x-2)! = x!, so:
[tex]= (2n+1)!/(2n-1)![/tex]
In the diagram NM bisects ENL find ML
A. 2
B. 3
C. 6
D. 12
Answers
Answer:
Option C. 6
Step-by-step explanation:
we know that
If NM bisects the angle ENL
then
∠MNL=∠MNE
In the right triangle MLN
sin(∠MNL)=ML/MN -----> equation A
In the right triangle MEN
sin(∠MNE)=6/MN -----> equation B
equate equation A and equation B
ML/MN=6/MN
Simplify
ML=6
what is the answer to x (x+8)=9
Answers
Answer:
x=1 or x=−9
Step-by-step explanation:
Let's solve your equation step-by-step.
x(x+8)=9
Step 1: Simplify both sides of the equation.
x2+8x=9
Step 2: Subtract 9 from both sides.
x2+8x−9=9−9
x2+8x−9=0
Step 3: Factor left side of equation.
(x−1)(x+9)=0
Step 4: Set factors equal to 0.
x−1=0 or x+9=0
x=1 or x=−9
Hey there!
(x + 8) = 9
➡️ x + 8 = 9
SUBTRACT 8 to BOTH SIDES
x + 8 - 8 = 9 - 8
CANCEL out: 8 - 8 because that gives you 0
KEEP: 9 - 8 because it helps solve for the x-value
x = 9 - 8
9 - 8 = x
9 - 8 = 1
Therefore your answer is: x = 1
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
What is the domain of the function graphed below?
Answers
Answer:
Domain is (0,∞)
Step-by-step explanation:
We need to find the domain of the function graphed
Domain are the values of x for which the function is defined.
For domain, we look at the x values of the graph.
We have graph for x values greater than 0. the graph goes close to y axis but does not cross y axis.
For x values greater than 0 there is a value for y.
There is no graph for negative value of x
So , domain is set of all x values greater than 0
Domain is (0,∞)
I really need help with this
Answers
Answer:
Josh won the race 5 seconds ahead of Rafael
Step-by-step explanation:
The winner of the race is the individual who completes the race in the shortest time. From the graph, Josh reaches the finish line at the 15 seconds mark while Rafael finishes at the 20 seconds mark.
The difference in the time is thus;
20 - 15 = 5 seconds.
Therefore, Josh won the race 5 seconds ahead of Rafael
A shoe box measures 15 in. by 7 in. by 4 in.What is the surface area of the box?
Answers
Answer:
A=2(wl+hl+hw)
2·(4·7+15·7+15·4)
386
Step-by-step explanation:
What is the value of a?
A)25
B)20
C)10
D)15
Answers
Answer:
B) 20
Step-by-step explanation:
Subtract 10 from both sides of the equation.
6 a = 130 - 10
Subtract 10 from 130 .
6a=120
Divide each term by 6 and simplify.
6 a/ 6 = 120 /6
Reduce the expression by cancelling the common factors.
a=120/6
Divide 120 by 6 .
a = 20
Hope this helps.
The value of a is 20.
What are the properties of a parallelogram?Parallelogram's characteristics
The opposing sides are congruent and parallel.The opposing angles are congruent.The following angles complement one another.All of the angles will be at right angles if any one of them is a right angle.The two diagonals cut across one another.Given
6a + 10 = 130 [The opposing angles congruent.]
6a = 120
a = 20
Therefore, The value of a is 20.
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Need Help Please!!!!!!!!!!
Answers
You add each number by 6n - fourth choice. I am not sure if this is the right answer.
ANSWER
6n
EXPLANATION
The given sequence is
6,12,18,24,...
We can rewrite the terms of the sequence to observe some pattern.
The first term is 6(1)=6
The second term is 6(2)=12
The third term is 6(3)=18
The fourth term is 6(4)=24
Based on this pattern we can generalize that, the nth term of the sequence is 6(n).
Therefore the rule of the sequence is 6n
A coordinate plane graph is shown. A line passes through the y-axis at 3 and through the point 2 comma 4. Which equation best represents the line?
Answers
Answer:
A coordinate plane graph is shown. A line passes through the y-axis at 3 and through the point 2 comma 4. Which equation best represents the line?
y=6x+3
Step-by-step explanation:
Y intercept and x intercept definitions
Answers
Answer:
"The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis."
Step-by-step explanation:
:)
Final answer:
The y-intercept is the point where a graph crosses the y-axis, while the x-intercept is the point where a graph crosses the x-axis.
Explanation:
The y-intercept is the point where a graph crosses the y-axis. It is represented by the coordinate (0, b), where b is the y-coordinate of the intercept. The y-intercept can be found by analyzing the equation of the line y = mx + b, where b is the y-intercept.
The x-intercept, on the other hand, is the point where a graph crosses the x-axis. It is represented by the coordinate (a, 0), where a is the x-coordinate of the intercept. To find the x-intercept, set y equal to 0 in the equation y = mx + b and solve for x.
What is the rate of change in y per unit change in x for the function 30x+5y=15
Answers
Step-by-step explanation:
To find the answer you have to put it into y=mx+b format.
This means that it will be 5y=-30x+15
So it will simplify to y=-6x+3
This means that:
If y=2
You substitute then…
2=-6x+3
So x would equal 1/6.
The rate of change in y per unit change in x for the function 30x+5y=15 is 1/6.
What is the rate of change of a linear equation?Suppose that the considered linear equation is of the form y=mx+c
Then, when we change x by 1 unit, then:
[tex]y + \delta y = m(x + 1) + c\\mx + c + \delta y = mx + c + m\\\delta y = m[/tex]
where[tex]\delta[/tex] y shows the change in y as x changes by 1 unit. We found that this change is the value of 'm'. It is called slope of the line this equation represents (each linear equation represents a line).
To find the answer we have to put it into y=mx+b format.
Given the function 30x+5y=15
This means that it will be;
5y = -30x+15
So it will simplify and gives;
y=-6x+3
If y=2
substitute then;
2=-6x+3
x =1/6
Thus x would equal 1/6.
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What is the degree of vertex B and G?
Answers
Answer:
degree of vertex B = 2
degree of vertex g = 4
Step-by-step explanation:
Using given picture we need to find about what is the degree of vertex B and G.
In graph theory, we know that the degree (or valency) of a vertex of a graph is the number of edges incident to the vertex.
So we just need to count how many edges are incindent on vertex B and G.
From picture we see that number of edges incident on vertex B = 2
Hence degree of vertex B = 2
From picture we see that number of edges incident on vertex G = 4
Hence degree of vertex g = 4
Write the equation of G(x)
Answers
Answer:
[tex]G(x)=\frac{1}{2}(x-3)^3+2[/tex]
Step-by-step explanation:
The given function is
[tex]F(x)=x^{3}[/tex]
The transformations to this graph are in the form;
[tex]G(x)=a(x-b)^3+c[/tex]
where [tex]a=\frac{1}{2}[/tex] is the vertical compression by a factor of [tex]\frac{1}{2}[/tex]
b=3 is a shift to the right by 3 units.
c=2 is an upward shift by 2 units.
Therefore [tex]G(x)=\frac{1}{2}(x-3)^3+2[/tex]
Answer:
The equation is
[tex]G(x)=-\frac{1}{2}(x-3)^3 +2[/tex]
Step-by-step explanation:
If the graph of the function [tex]G(x)=cf(x+h) +b[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]0 <|c| <1[/tex] then the graph is compressed vertically by a factor c.
If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c
If [tex]c <0[/tex] then the graph is reflected on the x axis.
If [tex]b> 0[/tex] the graph moves vertically upwards.
If [tex]b <0[/tex] the graph moves vertically down
If [tex]h <0[/tex] the graph moves horizontally h units to the right
If [tex]h >0[/tex] the graph moves horizontally h units to the left
In this problem we have the function [tex]G(x)[/tex] and our parent function is [tex]f(x) = x^3[/tex]
We know that G(x) is equal to f(x) but reflected on the x-axis ([tex]c <0[/tex]), compressed vertically by a multiple of 1/2 ([tex]0 <|c| <1[/tex] and [tex]c = -\frac{1}{2}[/tex]), displaced 2 units upwards ([tex]b = 2>0[/tex]) and moved to the right 3 units ([tex]h = -3<0[/tex])
Then:
[tex]G(x)=-\frac{1}{2}f(x-3) +2[/tex]
[tex]G(x)=-\frac{1}{2}(x-3)^3 +2[/tex]
Geometry Question, will give Brainliest, Image attached
Answers
Answer:
5 sin 38 should be the length.
I’m pretty sure it’s the last answer. 5 sin 38
There are 399 items advertised in a catalog. If the catalog is 75 pages long, what is the average number of items per page?
Answers
Answer:
Step-by-step explanation:
Well, we can divide 399 and 75 so it would be 5.32. Round that and it would be about 5 items per page
The required average number of items per page is 5.32.
What is the unit rate?A rate with a second term of one is referred to as a unit rate. To put it another way, a unit rate compares two quantities, with the second number being expressed as 1. Unit rates, such as price per item, speed per hour, or cost per pound, are frequently used to describe a rate per unit of measurement.
Here,
To find the average number of items per page, we need to divide the total number of items by the number of pages:
The average number of items per page = Total number of items / Number of pages
Substitute the given values, and we get:
The average number of items per page = 399 / 75
Simplifying the expression, we get:
The average number of items per page = 5.32 (rounded to two decimal places)
Therefore, the average number of items per page is 5.32.
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