The function f(x) = x2 – 4x + 4 is shifted 3 units to the right to create g(x).
A. g(x) = (x – 3)2 – 4(x – 3) + 4
B. g(x) = (x2 – 4x + 4) – 3
C. g(x) = (x2 – 4x + 4) + 3
D. g(x) = (x + 3)2 – 4(x + 3) + 4
Answer:
answer is A for APEX..
Step-by-step explanation:
The function f(x) = [tex]x^{2} -4x+4[/tex] is shifted 3 units to the right to create
g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex] .
What is shifting of a function?A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.
Given
f(x) = [tex]x^{2} -4x+4[/tex]
The function f(x) = x2 – 4x + 4 is shifted 3 units to the right to create g(x).
If the function is shifted to the left it is going to plus(+).
If the function is shifted to the right it is going to minus(-).
So, x = x - 3
g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex]
The function f(x) = [tex]x^{2} -4x+4[/tex] is shifted 3 units to the right to create
g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex] .
Option A is correct.
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Rational Exponent
Explain why the square root of a number is defined to be equal to that number to the 1/2 power.
Answer:
Sample Response:
Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.
Step-by-step explanation:
Suppose that 4 fair dice are rolled.let m be the minimum of 4 numbers rolled.what are the possible values of m
Solve the below system of equations using the best method. Please describe the method used [substitution, graphing, elimination, etc], and give your answer in the form (x,y).
y = 2x + 3
y = -x - 5
If you shift the linear parent function, f(x) = x, down 6 units, what is the equation of the new function?
A. g(x) = x + 6
B. g(x) = x
C. g(x) = 6x
D. g(x) = x – 6
Answer:
Option D is correct
[tex]g(x) = x-6[/tex]
Step-by-step explanation:
Vertically down :
If y =f(x) is a parent function, then the new function g(x) b units vertically down is, g(x) = f(x) -b.
As per the statement:
Given the parent function:
[tex]f(x) = x[/tex]
To shift linear parent function vertically down 6 units.
By definition we have;
g(x) = f(x) -6
⇒[tex]g(x) = x-6[/tex]
Therefore, the equation of new function g(x) is, [tex]g(x) = x-6[/tex]
The expression below represents the number of bacteria in a petri dish after t hours.
Interpret the meaning of the expression.
A. The initial number of bacteria is 57, and the growth rate is 3.1% per hour.
B. The initial number of bacteria is 57, and the growth rate is 31% per hour.
C. The initial number of bacteria is 131, and the growth rate is 5.7% per hour.
D. The initial number of bacteria is 131, and the growth rate is 57% per hour.
Solving this problem requires the supplement of the actual expression. However I believe you forgot to include it with the question.
However I believe that the expression is in the form of:
y = A e^(-k t)
where,
y is the number of bacteria after time t
A is a constant and represents the initial number of bacteria
k is the growth rate in decimal form
t is time
So whatever is located in A is the initial number of bacteria, while k times 100% is the growth rate.
Answer:
A
Step-by-step explanation:
a ride at an amusement park rises 8 feet every horizontal change of 2 feet. how could you determine the slope of the ride?
I only just started learning Algebra, and my teacher just threw all these worksheets at us without explaining much. Can someone please explain the concept of Algebra? Staring with this question, please:
Answer:
x = -8
Step-by-step explanation:
Hello!
Algebra is based on the concept of unknown values called variables, the value of each variable must remain the same in each problem.
Here are steps to solve your problem!
1. Pull out like terms:
-x - 8 = -1 • (x + 8)
2. Solve -x-8 = 0
Add 8 to both sides of the equation:
-x = 8
Multiply both sides of the equation by (-1)
x = -8
Therefore, x = -8
Hope this Helps!
Graph the relation shown in the table. Is the relation a function? Why or why not?
{(–3, –2), (–1, 0), (1, 0), (5, –2)}
No; the relation passes the vertical-line test.
Yes; only one range value exists for each domain value.
Yes; two domain values exist for range value –2.
No; two domain values exist for range value –2.
Jenna saved $100. She wants to buy 6 games that cost $20 each. Dose Jenna have enough money? Explain.
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The total amount Jenna have is only $100.
But the cost of 6 games is $120.
No, Jenna doesn't have enough money to buy 6 games.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Amount saved = $100
Cost of each game = $20
The cost of 6 games that cost $20:
= 20 x 6
= $120
The total amount Jenna have is only $100.
But the cost of 6 games is $120.
This means,
Jenna doesn't have enough money to buy 6 games.
Thus,
The total amount Jenna have is only $100.
But the cost of 6 games is $120.
No, Jenna doesn't have enough money to buy 6 games.
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Translate this equation into a real life situation. 4m = -8
One die is rolled 3 times, what is the chance of getting all 4's?
The chances of getting 4 when a die is rolled three times will be 216.
What is the combination?A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Given that a die is rolled 3 times. The chances of getting 4's will be calculated as:-
In a die, there are 6 numbers from 1 to 6. At one time only one number will come. the combination will be
Combination = 6 x 6 x 6
Combination = 216
Therefore, the chances of getting 4 when a die is rolled three times will be 216.
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|3x-2|+2y if x=-4,y=7,and z=-9
Karl runs a car wash. On the Monday, he recorded a loss of $80 and recorded it as -$80. On Tuesday he earned a profit of $120. What is Karl's balance at the end of Tuesday?
Karl's balance at the end of Tuesday is a net profit of $40, after combining his loss of $80 from Monday with his profit of $120 from Tuesday.
To find Karl's balance at the end of Tuesday, we need to combine his loss from Monday with his profit from Tuesday. Karl recorded a loss of -$80 on Monday. On Tuesday, he made a profit of $120. Add the two amounts together to find Karl's total balance after these two days.
Monday: -$80
Tuesday: +$120
Combining them, -$80 (loss) + $120 (profit) equals to a net profit of $40.
Therefore, Karl's balance at the end of Tuesday is $40.
50 POINTS! + BRAINLIEST! PLEASE HELP
slope = rise over run = y/x
A (-1,3) slope = 3/-1 = -3
B (1,2) slope = 2/1 = 2
C (-3,-1) slope = -1/-3 = 1/3
2 lines need to be negative reciprocals in order to be a right triangle
negative reciprocal of -3 is 1/3
so this is a right triangle
Answer: yes it is
Step-by-step explanation: put into a graph and it will become clear
For the following geometric sequence, find the recursive formula.
{-80, 20, -5, ...}
Answer:
[tex]a_n =-\frac{1}{4} \cdot a_{n-1}[/tex]
Step-by-step explanation:
{-80, 20, -5, ...}
General recusive formula for geometric sequence is
[tex]a_n = r \cdot a_{n-1}[/tex]
Where 'r' is the common ratio
To find common ratio 'r' we divide second term by first term
[tex]r=\frac{20}{-80} =-\frac{1}{4}[/tex]
Replace 'r' with -1/4
First term is -80
Recursive formula becomes
[tex]a_n =-\frac{1}{4} \cdot a_{n-1}[/tex]
Solve the following system of equations.
x − 2y = 5
−3x + 2y = 7
A. x = 3, y = −1
B. x = 11, y = 11/2
C. x = 3, y = 1
D. x = −6, y = -11/2
Jordan makes 100 3-point shots per basketball practice. She makes 44 of these shots. What decimal represents the number of the shots she made?
What is 9,333,625 rounded to the nearest hundred thousand?
8. Evaluate the following expression for the given value.
-3x^2-4x+4 for x=-2
A) 0
B) 4
C) 12
D) 20
based off of the graph which of the following statements are true. select all that apply
The correct options are A, D, and G.
Correct statements about the graph are:
A. It has a minimum.
D. Vertex at (-1, -9).
G. Y-intercept at (0, -8).
To determine the truth of the statements given about the graph, we will analyze the graph step by step:
1. **Identify the Vertex**: The vertex of a parabola is the highest or lowest point of the graph, depending on whether it opens upwards or downwards. This graph opens upwards, so the vertex will be the minimum point.
2. **Find the Vertex**: We need to locate the vertex on the graph by looking for the point where the graph changes direction.
3. **Check for Maximum or Minimum**: Since this parabola opens upwards, it will have a minimum point but not a maximum.
4. **Determine the Zeros**: Zeros are the points where the graph crosses the x-axis. These are also known as the roots or solutions of the quadratic function when set to zero.
5. **Locate the Y-Intercept**: The y-intercept is the point where the graph crosses the y-axis.
6. **Examine the Solutions**: The solutions of the quadratic function are the x-coordinates of the zeros of the function.
7. **Assess the Y-Intercept**: We will find the y-coordinate of the point where the graph intersects the y-axis.
Now, let's examine the graph based on these steps:
A. **The graph has a minimum** - True. The parabola opens upwards, which means it has a minimum point where the vertex is located.
B. **The graph has a maximum** - False. Since the graph opens upwards, it does not have a maximum point; the vertex represents a minimum.
C. **The graph has zeros of -4 and 2** - False. The zeros of the graph (where it crosses the x-axis) appear to be different from -4 and 2, as the graph does not touch the x-axis at these points.
D. **The vertex is located at (-1,-9)** - True. By looking at the graph, it appears that the vertex, which is the minimum point, is indeed at the point (-1,-9).
E. **The graph has y-intercepts at (-4,0) and (2,0)** - False. A graph can only have one y-intercept, which is where it crosses the y-axis. The points given are actually x-intercepts or zeros of the function.
F. **The solution of the quadratic function represented by the graph is (-1,-9)** - False. The solution to a quadratic function is typically the x-values where the function crosses the x-axis (the zeros). The vertex is not the solution to the function; it is simply the minimum or maximum point.
G. **The y-intercept of the graph is (0,-8)** - True. The y-intercept is where the graph crosses the y-axis, which appears to be at (0,-8) according to the graph.
Hence, the correct statements are A, D, and G. The graph has a minimum at the vertex (-1, -9) and a y-intercept at (0, -8). It does not have a maximum, and the zeros are not at -4 and 2 as stated in option C. The solutions to the quadratic function would be the x-values of the zeros, not the vertex coordinates.
The complete question is here:
Which of the following statements are true about the graph? Check all that apply.
(GRAPH IS GIVEN BELOW)
A. The graph has a minimum.
B. The graph has a maximum.
C. The graph has zeros of -4 and 2 .
D. The vertex is located at (-1,-9).
E. The graph has y-intercepts at (-4,0) and (2,0).
F. The solution of the quadratic function represented by the graph is (-1,-9).
G. They-intercept of the graph is (0,-8).
The statements that are true from the graph are:
A. The graph has a minimum. D. The vertex is located at (-1,-9). G. The y-intercept of the graph is (0,-8).Why are the statements true ?
There is a vertex on the graph, which implies that there is either a minimum or maximum point. In this case, since the vertex is shown, it indicates a minimum point on the graph.
The vertex of a quadratic function in the form y = ax ² + bx + c is given by the coordinates (-b / 2a, f(-b/2a)), where a, b, and c are coefficients of the quadratic equation.
The y-intercept is the point where the graph crosses the y-axis, and it occurs when x = 0. This is shown to be the point ( 0, - 8 ).
The full question is:
Based off of the graph which of the following statements are true. select all that apply
A. The graph has a minimum.
B. The graph has a maximum.
C. The graph has zeros of -4 and 2 .
D. The vertex is located at (-1,-9).
E. The graph has y-intercepts at (-4,0) and (2,0).
F. The solution of the quadratic function represented by the graph is (-1,-9).
G. They-intercept of the graph is (0,-8).
What is the slope is the x the top ordered pairs or the bottom !??? HELLPPP
Randy is twice as old as his sister jane. together the sum of their ages is 15. how old is randy?
Final answer:
Randy is 10 years old.
Explanation:
The question is about solving a simple algebraic equation involving ages.
We are told Randy is twice as old as his sister Jane, and the sum of their ages is 15 years.
If we let Jane's age be represented by 'j', then Randy's age would be '2j' as he is twice as old as Jane.
The equation to represent the sum of their ages is:
j + 2j = 15
To find Jane's age, we combine the like terms:
3j = 15
Now, we divide both sides of the equation by 3 to isolate 'j':
j = 15 / 3
j = 5
Therefore, Jane is 5 years old. To find Randy's age, we multiply Jane's age by 2:
Randy's age = 2 * Jane's age
Randy's age = 2 * 5
Randy's age = 10
So, Randy is 10 years old.
Please help!!!
System of Equations Applications
Bill and Cody are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and packages of double chocolate chip cookie dough. Bill sold 9 packages of white chocolate chip cookie dough and 2 packages of double chocolate cookie dough for a total of $200. Cody sold 2 packages of white chocolate chip cookie dough and 13 packages of double chocolate chip cookie dough for a total of $283. find the cost each of one package of white chocolate chip cookie dough and one package of double chocolate chip cookie dough.
Find the y-intercept of the line whose equation is 2x - 3y = -6.
to find y intercept, make x = 0 then solve equation:
2x-3y=-6
2(0) - 3y=-6
-3y =-6
y = -6 / -3
y=2
so y intercept is (0,2)
Amy has 1/2 hour to do 5 chores. She plans to spend the same fraction of an hour on each chore. She wants to use the number line to help her determine what fraction of an hour she can spend on each chore.
during the 2009-2010 basketball season, the number of points scored in each game by the boston celtics was approximately normally distributed with a mean of 99.2 points and a standard deviation of 10.5 pthe mean number of points scored by los angeles lakers was 101.7. in what proportion of their games did the celtics score more than the lakers' mean score?
To solve this problem, we use the z statistic. The z formula is:
z = (x – u) / s
where x is lakers score = 101.7, u is Celtics score = 99.2, s is standard dev = 10.5
z = (101.7 – 99.2) / 10.5 = 0.24
using the normal distribution table at z = 0.24, the P value is:
P (z = 0.24) = 0.5984 = 59.84%
Suppose you have a $8-off coupon at a fabric store. You buy fabric that costs $7.50 per yard. Write an equation that models the total amount of money y you pay if you buy x yards of fabric. What is the graph of the equation?
The sides of a triangle are in the ratio 5:12:13. Describe the length of the shortest side is the perimeter is not more than 120 inches
The Great Foods Warehouse contains 9435 pounds of watermelons. There are 6555.569 pounds of watermelons in the Tasty Food Warehouse. How many more pounds does the Tasty Food Warehouse need to have the same amount of watermelons as the Great Food Warehouse?
Answer: 2879.431 pounds
Step-by-step explanation:
Given : The Great Foods Warehouse contains 9435 pounds of watermelons.
There are 6555.569 pounds of watermelons in the Tasty Food Warehouse.
Clearly , 9435 > 6555.569.
By using Subtraction operation, The amount of watermelon needed by Tasty Food Warehouse to have to get the same amount of watermelons as the Great Food Warehouse will be :-
9435-6555.569=2879.431 pounds
Hence, the Tasty Food Warehouse needs to have 2879.431 pounds to gwt the same amount of watermelons as the Great Food Warehouse.