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## If x=6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

If x=6 is the only intercept, it means that the quadratic is tangential to the x-axis, or equivalently x=6 is a root with multiplicity 2.
The discriminant is typically zero for multiplicity 2 in a quadratic.
It will be clear looking at the quadratic formula:
if D=b^2-4ac = discriminant of the quadratic, then
x1=(-b+sqrt(D))/2a or x2=(-b-sqrt(D))/2a
if x1=x2 (double root, or multiplicity 2) then clearly D has to be zero.

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## Sam is measuring the velocity of a car at different times. After two hours, the velocity of the car was 50km/h. After six hours, the velocity of the car is 54km/h. Part A: Write an equation in two variables in standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5points) Part B: How can you graph the obtained in Part A for the first seven hours? (5points)

You are given the time and speed so from there you can get the points (2,50) and (6,54) once you got that you can see how the slope is 1 and
b=48
x-y=-48 (standard form)

part B=
1    49
2    50
3    51
4    52
5    53
6    54
7    55

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## The graph represents function 1 and the equation represents function 2: A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function 2 y = 6x + 1 How much more is the rate of change of function 2 than the rate of change of function 1? A. 5 B. 6 C. 7 D. 8

The graph represents function 1 and the equation represents function 2: A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function 2 y = 6x + 1 How much more is the rate of change of function 2 than the rate of change of function 1? A. 5 B. 6 C. 7 D. 8

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## The temperature on a particular day started at -13°F. It rose steadily by 3° each hour. The function y=-13+3xmodels the temperature, ehere x is the number of hpurs and y is the temperature. Graph the equation

The temperature on a particular day started at -13°F. It rose steadily by 3° each hour. The function y=-13+3xmodels the temperature, ehere x is the number of hpurs and y is the temperature. Graph the equation

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## The graph of y = x2 is shown below. If graphed on the same grid, which of the following could be the graph of y = 0.4×2?

1)  The answer is: [B]: r = 5 .
__________________________
Explanation:
__________________________
Given: 7r − 7 = 2r + 18 ; Round your answer to the nearest tenth, if necessary.
____________________________
Since “r” is the only variable given, let us assume we want to solve for “r” (instead of “x”).
___________________________
→ Subtract “2r” from EACH SIDE of the equation; and & add “7” to EACH SIDE of the equation:
_____________
→ 7r − 7 − 2r + 7 = 2r + 18 − 2r + 7 ;  to get: → 5r = 25 ;
_____________
→ Now, divide EACH SIDE of the equation by “5”; to isolate “r” on one side of the equation; and to solve for “r” :
______________
→ 5r / 5 = 25 / 5 → r = 5 → which is: “Answer choice: [B]”.
_________________
Let us check our answer, by plugging in “5” for “r” in the original equation:
_________________
→ 7r − 7 = 2r + 18 ;  →  7(5) − 7 =? 2(5) + 18? ;
______________________
→ 35 − 7 =? 10 + 18 ?;     → 28 =? 28? Yes!
______________________
2) The answer is: [D]: x = 2 .
_____________
Explanation:
_____________
Given: 2x + 12 = 18 − x ; Solve for “x” (round to nearest tenth, if necessary).
_______________
→ Add “x” to EACH SIDE of the equation, & subtract “12” from EACH SIDE of the equation:  → 2x + 12 + x − 12 = 18 − x + x − 12 ;
______________
→ To get: 3x = 6 ;  → Divide EACH SIDE of the equation by “3”;
to isolate “x” on one side of the equation; and to solve for “x”:
_____________
→ 3x / 3 = 6 / 3 ; → x = 2 ; which is: “Answer choice: [D]”.
______________
Let us check our answer, by plugging in “2” for “x” in the original equation:
________________
→ 2x + 12 = 18 − x ; → 2(2) + 12 =? 18 − 2 ?
________________
→ 4 + 12 =? 18 − 2 ? ;   → 16 =? 16?  Yes!
________________________________
3)  The answer is: [A]: x = -3 .
_____________
Explanation:
________________
Given:  8x − 3 = 15x + 18 ; Solve for “x”. Round your answer to the nearest tenth, if necessary.
_________________
→ Subtract “8x” from EACH SIDE of the equation, & add “3” to EACH SIDE of the equation:
_______________
→ 8x − 3 − 8x + 3 = 15x + 18 − 8x + 3 ; to get:
_______________
→ 0 = 7x + 21 ; → Subtract “21” from EACH SIDE of the equation;
_______________
→ 0 − 21 = 7x + 21 − 21 ; to get:
_______________
→  -21 = 7x ; Now divide EACH SIDE of the equation by “7”;
to isolate “x” on one side of the equation; & to solve for “x”:
_______________
→ = -21 / 7 = 7x / 7 ; →  -3 = x ; which is “Answer choice: [A].”
_________________
Let us check our answer, by plugging in “-3” for “x” in the original equation:
________________
→  8x − 3 = 15x + 18 ;  → 8(-3) − 3 =?  15(-3) + 18 ?;
________________________
→ -24 − 3 =?  -45 + 18 ? ;   →  -27 =? -27?  Yes!
___________________________
4)  The answer is: [C]: y = 11 .
_____________
Explanation:
____________
Given: 6y − 6 = 4y + 16 ; Solve for “y”; Round to the nearest tenth, if necessary.
____________
(Note: Since “y” is the only variable given; assume we are to solve for “y” instead of “x”).
____________
→ Subtract “4y” from EACH SIDE of the equation, & add “6” to EACH SIDE of the equation; → 6y − 6 − 4y + 6 = 4y + 16 − 4y + 6 ; to get:
_______________
→ 2y  = 22 ; Now, divide EACH SIDE of the equation by “2”; to isolate “y” one side of the equation; and to solve for “y” ;
_______________
→ 2y / 2 = 22 / 2 ; →  y = 11 → which is “Answer choice: [C]”.
_______________________________
Let us check our answer, by plugging in “11” for “y” in the original equation:
___________________
→  6y − 6 = 4y + 16 ; → 6(11) − 6 =? 4(11) + 16 ?
_______________________
→ 66 − 6  =? 44 + 16 ?  → 60 =? 60 ?  Yes!
__________________
5)  The answer is: [B]: x = -11 .
_____________________
Explanation:
_________________
Given: 3(x − 4) = 5(x + 2) ; Solve for “x”. Round to the nearest tenth, if necessary.
___________
→Note the “distributive property of multiplication”:
_____________
a*(b + c) = ab + ac ;  and: a*(b − c) = ab − ac ;
_______________
→ Let us expand EACH SIDE of our given equation.
____________
3(x − 4) = (3*x)  − (3*4) = 3x − 12;
______________________________
→Now let us expand the “right-hand side” of the given equation:
____________
→  5(x + 2) = (5*x) + (5*2) = 5x + 10 ;
______________
→Now, we can rewrite the original equation:
_______________
→ 3(x − 4) = 5(x + 2) ; by substituting the expanded values for EACH SIDE of the question:   →  3x − 12 = 5x + 10 ;
__________________
→ Subtract “3x” from EACH SIDE of the equation; and add “12” to EACH SIDE of the equation: →  3x − 12 − 3x + 12 = 5x + 10 − 3x + 12 ; to get:
________________
→  0 = 2x + 22;  → Now subtract “22” from EACH SIDE of the equation:
______________
→  0 − 22 = 2x + 22 − 22 ; to get:  →  -22 = 2x ;
__________
→ Divide EACH SIDE of the equation by “2”; to isolate “x” on one side of the equation; & to solve for “x” ;
_____________
→  -22 / 2 = 2x /2 ;  →  -11 = x ; which is “Answer choice: [B]”.
______________
Let us check our answer, by plugging in “-11” for “x” in the original equation:
___________
→ 3(x − 4) = 5(x + 2) ; →  3(-11 − 4) =? 5(-11 + 2) ? ;
_______________________
→3(-15) =? 5(-9) ? ; → -45 =? -45 ?  Yes!
_____________________________________________

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## The following graph shows the demand curve for a group of consumers in the U.S. market (blue line) for Blu-ray players. The market price of a Blu-ray player is shown by the black horizontal line at \$150. Each rectangle you can place on the following graph corresponds to a particular buyer in this market: orange (square symbols) for Antonio, green (triangle symbols) for Caroline, purple (diamond symbols) for Dmitri, tan (dash symbols) for Frances, and blue (circle symbols) for Jake. Use the rectangles to shade the areas representing consumer surplus for each person who is willing and able to purchase a Blu-ray player at a market price of \$150. (Note: If a person will not purchase a Blu-ray player at the market price, indicate this by leaving his or her rectangle in its original position on the palette.

On December 15, 1791, the Bill of Rights (the first ten amendments to the United States Constitution) were ratified by the states.

The Bill of Rights were added to the Constitution to address fears raised by the Anti-Federalists during the ratification of the Constitution that the Constitution did not provide sufficient protection against abuses of power by the federal government.

James Madison, the Father of the Constitution, originally did not think a Bill of Rights was necessary. He thought the Constitution gave no power to the federal government that would allow for a violation of the rights of the people.

Madison later changed his position, persuaded mainly by Thomas Jefferson, and, with the help of others, drafted twenty amendments that were proposed to the first United States Congress in 1789.

Twelve of the proposed amendments were accepted by Congress and were then sent to the states for ratification. Only ten were ratified.

These ten amendments list our basic rights and place limits on the federal government. They include the freedoms of speech and religion, the right to bear arms, the right to be free from unreasonable searches and seizures, and an assurance that the powers not delegated to the federal government in the Constitution are reserved to the states and the people. Many of these provisions were based upon similar protections provided by state constitutions that limited the power of state and local government authorities.

Of the remaining amendments that were not ratified in 1791, one was later adopted in 1992 as the twenty-seventh amendment to the Constitution. That amendment prevents changes in the compensation for senators and representatives until after a subsequent election of representatives. The other proposed amendment has never been adopted.

The Bill of Rights illustrates that our Founders understood that for personal freedoms to be broad, the power of the federal government must be limited.

Our nation, however, has moved away from its founding principles, especially during recent decades. Our ever-growing federal government is intervening into more and more aspects of our lives, especially through bureaucratic regulations, and is reducing our personal freedoms in the process.

Government at all levels is doing more and more things that were once left to private individuals and groups, and the federal government is doing more and more things that were once the province of state and local governments, where greater accountability to the public is often possible.

One need only look at the HHS mandate—forcing employers to violate their religious beliefs, under pain of penalty, by paying for and providing abortion pill insurance coverage—to see the harm caused by an overreaching government.

The preservation of our liberties is a daily battle, something our Founders understood. The process of scaling back the size and role of government and returning limits to it is a long one. But, since the federal government is supposed to be our servant and not our master, no one should doubt the importance of this endeavor.

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## When should a bar graph be used

When should a bar graph be used

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## Greg made pudding every weekend. The more times he made pudding, the more practice he gained. The time he took to make the same amount of pudding every week decreased with practice. The function below shows the number of hours f(x) Greg took to make pudding after he had made it x times: f(x) = 2(0.8)x Which graph best represents the function? graph of function f of x equals 0.8 multiplied by 2 to the power of x graph of function f of x equals 0.8 to the power of x graph of function f of x equals 2 to the power of x function of f of x equal 2 multiplied by 0.8 to the power of x

After Greg makes the pudding 1 time, it takes him  hours to make it.

After Greg makes the pudding 2 times, it takes him  hours to make it

After Greg makes the pudding 2 times, it takes him  hours to make it

so The function is

Answer: f of x equals 2 multiplied by 0.8 to the power of x

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## Look at the graph of this system of equations: y = – x2 + 1 and y = x2. At which approximate points are the two equations equal? A) (-0.7, 0.5) B) (0.5, 0.7) C) (0.7, 0.5) D) (-0.5, 0.7) Note: There can be more than answer. Help me and I will give you brainliest. Thank you. In this picture, there’s the graph.

Y=-x^2+1 and y=x^2

When the two curves intersect their coordinates will be equal, so we can say y=y whenever a solution exists, so:

x^2=-x^2+1  add x^2 to both sides

2x^2=1  divide both sides by 2

x^2=1/2  take the square root of both sides

x=±√(1/2), so there are two solutions, we can use x^2 to find the corresponding y values.

y=x^2, y=1/2 in each instance, so the two point where the curves intersect are:

(-√(1/2), 1/2) and (√(1/2), 1/2)  or if you want approximations….

(-0.7, 0.5) and (0.7, 0.5)

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## Graph the equation to solve the system Here's the picture with the equation and possible answers. Help me please I beg you.

Graph the equation to solve the system Here’s the picture with the equation and possible answers. Help me please I beg you.

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## The graph of y = x 3 is translated so that the point (1, 1) is moved to (1, 4). What is the equation of the new graph?

Step-by-step explanation:

The graph of y = x 3 is translated so that the point (1, 1) is moved to (1, 4).

the point (1, 1) is moved to (1, 4), 1+3=4

So 3 is added with y to get (1,4)

To get the equation of new graph , add 3 with y

To add 3 with y, we put +3 at the end of the given equation

the new equation becomes

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## The graph of f(x) = |x| is reflected across the x-axis and translated to the right 6 units. Which statement about the domain and range of each function is correct? Both the domain and range of the transformed function are the same as those of the parent function. Neither the domain nor the range of the transformed function are the same as those of the parent function. The range but not the domain of the transformed function is the same as that of the parent function. The domain but not the range of the transformed function is the same as that of the parent function.

D. The domain but not the range of the transformed function is the same as that of the parent function.

Step-by-step explanation:

We are given,

The function is reflected across x-axis, which gives .

And then the function is translated to the right by 6 units, which gives .

Thus, the transformed function is

So, from the graph shown below, we get,

Domain of both the functions f(x) and g(x) is set of all real numbers.

Range of f(x) is .

But, Range of g(x) is .

Hence, the correct option is,

D. The domain but not the range of the transformed function is the same as that of the parent function.

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## What is the vertex of the graph of y = −1(x − 2)2 + 3? (3,-2) (-2,3) (3,2) (2,3)

(2,3)

Step-by-step explanation:

An equation of the form

can be expressed in the Vertex Form:

where the vertex is always:

(h, k)

The vertex is the lowest or highest point of the parabola.

When we compare the two functions:

We can see that

a = -1

h = 2

k = 3

So the vertex is:

(h, k) = (2, 3)

I hope this helps!

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## The function h(x) = x2 + 14x + 41 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points) Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points) Part C: Determine the axis of symmetry for h(x). (2 points)

Given the function h(x)=x^2+14x+41, to solve by completing square we procced as follows;
x^2+14x+41=0
x^2+14x=-41
but;
c=(b/2)^2
and b=14
hence;
c=(14/2)^2=49
substituting the value of c in the expression we get:
x^2+14x+49=-41+49
x^2+14x+49=8
(x+7)^2=8
this can be written in vertex form;
h(x)=a(x-h)^2+k
where:
(h,k) is the vertex;
thus
(x+7)^2=8
h(x)=(x+7)^2-8
hence the vertex will be at the point:
(-7,-8)

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## What is the definition of absolute value? a. distance from a certain number on a number line or a coordinate graph c. distance from the origin on a number line or a coordinate graph b. the opposite of a square root of a number d. none of the above

What is the definition of absolute value? a. distance from a certain number on a number line or a coordinate graph c. distance from the origin on a number line or a coordinate graph b. the opposite of a square root of a number d. none of the above

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## What is the definition of absolute value? a. distance from a certain number on a number line or a coordinate graph c. distance from the origin on a number line or a coordinate graph b. the opposite of a square root of a number d. none of the above

What is the definition of absolute value? a. distance from a certain number on a number line or a coordinate graph c. distance from the origin on a number line or a coordinate graph b. the opposite of a square root of a number d. none of the above

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## Timmy writes the equation f(x) = 1/4x – 1. He then doubles both of the terms on the right side to create the equation g(x) = 1/2x – 2. How does the graph of g(x) compare to the graph of f(x)?

Timmy writes the equation f(x) = 1/4x – 1. He then doubles both of the terms on the right side to create the equation g(x) = 1/2x – 2. How does the graph of g(x) compare to the graph of f(x)?

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## Suppose you are testing different soils to determine which grows healthier bean plants. You count and record the number of leaves on each test every three days for six weeks. What type of graph would be best to display your data?

Suppose you are testing different soils to determine which grows healthier bean plants. You count and record the number of leaves on each test every three days for six weeks. What type of graph would be best to display your data?

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## Which of the following statements best describes the graph of x + y = 2? A. It is a line which intersects the x-axis at (2, 2). B. It is a line which intersects the y-axis at (2, 2). C. It is a line joining the points whose x- and y-coordinates add up to 2. D. It is a line joining the points whose x- and y-coordinates add up to 4.

Which of the following statements best describes the graph of x + y = 2? A. It is a line which intersects the x-axis at (2, 2). B. It is a line which intersects the y-axis at (2, 2). C. It is a line joining the points whose x- and y-coordinates add up to 2. D. It is a line joining the points whose x- and y-coordinates add up to 4.

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## Which equation has a graph that is perpendicular to the graph of 4x – 2y = 1?

Which equation has a graph that is perpendicular to the graph of 4x – 2y = 1?

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## Solve the following system by graphing. x – y = 4x + y = 2What is the solution of the system?A. (3, -1)B. (3, 1)C. (-1, 3)You do not have to include the graph, but it would be appreciated.

Solve the following system by graphing. x – y = 4x + y = 2What is the solution of the system?A. (3, -1)B. (3, 1)C. (-1, 3)You do not have to include the graph, but it would be appreciated.

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## The function y = 4x is an exponential growth function. The graph of the function increases as x increases. The variable x is a(n) coefficient term exponent factor

The function y = 4x is an exponential growth function. The graph of the function increases as x increases. The variable x is a(n) coefficient term exponent factor

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## What would 4/5x + 5 < -3 look like in a line graph?

What would 4/5x + 5 < -3 look like in a line graph?

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## Find the distance between point A (5,3) and point B (1,0) on a graph using the Pythagorean theorem

Find the distance between point A (5,3) and point B (1,0) on a graph using the Pythagorean theorem