06.02.2023

Which of the following is the graph of y = |x - 3|

. 4

Faq

Mathematics
Step-by-step answer
P Answered by PhD
#1) A
#2) B
#3) C
#5) A
#7) D
#10) D
#11) D
#14) A
#15) D
#16) A
#19) D

Explanation
#1)  If the data set is linear, the slope will be constant throughout the entire data set.  For data set A, the slope between the first two points is:
m = (y₂-y₁)/(x₂-x₁) = (1--2)/(3-1) = 3/2
Between the second two points,
m=(4-1)/(5-3) = 3/2
Between the third pairs of points,
m=(7-4)/(7-5) = 3/2

The slope is constant throughout the entire set.  The set is also increasing; as x increases, y increases as well.

#2)  Substituting 4 for y and 1 for x, 
y = (x+1)²
4 = (1+1)² = 2²
9 = (1+2)² = 3²
16 = (1+3)² = 4²
This works for each point, so this is the solution.

#3) Since he runs 10 laps per hour t, this is 10t.  Adding the first lap to this, we get y=10t+1.

#5) If a sequence is arithmetic, each term is found by adding a constant (called the common difference) to the previous term.  If the common difference is 2, this means that 2 was added each time.  This only works for choice A.

#7) For x to vary directly as y, this means that y/x = k; in other words, the quotient of y and x is constant for every point.

#10) The formula for slope is:
m=(y₂-y₁)/(x₂-x₁)

Using the information we're given, we have
3=(d-5)/(4-2)
3=(d-5)/2

Multiply both sides by 2:
3*2 = ((d-5)/2)*2
6 = d-5

Add 5 to both sides:
6+5 = d-5+5
11 = d

#11) Using point slope form,
y-y₁ = m(x-x₁)
y-1 = 3(x--2)
y-1 = 3(x+2)

Using the distributive property,
y-1 = 3*x + 3*2
y-1 = 3x + 6

Add 1 to both sides:
y-1+1 = 3x+6+1
y=3x+7

#14) If two lines are parallel, they have the same slope.  The slope of the given equation is 4; the only one with a slope of 4 is A.

#15) If two lines are perpendicular, they have slopes that are negative reciprocals (opposite signs and flipped).  The slope of the given equation is 2; this means the slope of the perpendicular line would be -1/2.  The only one with this slope is D.

#16)  The two equations are not the same, so there are not infinitely many solutions.  The variables do not both cancel, so there is at least one solution.  This only leaves one solution as the answer.

#19)  Using 1 for 7 and 4 for x, we check each equation.  The only one that comes out correct is D.
Mathematics
Step-by-step answer
P Answered by PhD
#1) A
#2) B
#3) C
#5) A
#7) D
#10) D
#11) D
#14) A
#15) D
#16) A
#19) D

Explanation
#1)  If the data set is linear, the slope will be constant throughout the entire data set.  For data set A, the slope between the first two points is:
m = (y₂-y₁)/(x₂-x₁) = (1--2)/(3-1) = 3/2
Between the second two points,
m=(4-1)/(5-3) = 3/2
Between the third pairs of points,
m=(7-4)/(7-5) = 3/2

The slope is constant throughout the entire set.  The set is also increasing; as x increases, y increases as well.

#2)  Substituting 4 for y and 1 for x, 
y = (x+1)²
4 = (1+1)² = 2²
9 = (1+2)² = 3²
16 = (1+3)² = 4²
This works for each point, so this is the solution.

#3) Since he runs 10 laps per hour t, this is 10t.  Adding the first lap to this, we get y=10t+1.

#5) If a sequence is arithmetic, each term is found by adding a constant (called the common difference) to the previous term.  If the common difference is 2, this means that 2 was added each time.  This only works for choice A.

#7) For x to vary directly as y, this means that y/x = k; in other words, the quotient of y and x is constant for every point.

#10) The formula for slope is:
m=(y₂-y₁)/(x₂-x₁)

Using the information we're given, we have
3=(d-5)/(4-2)
3=(d-5)/2

Multiply both sides by 2:
3*2 = ((d-5)/2)*2
6 = d-5

Add 5 to both sides:
6+5 = d-5+5
11 = d

#11) Using point slope form,
y-y₁ = m(x-x₁)
y-1 = 3(x--2)
y-1 = 3(x+2)

Using the distributive property,
y-1 = 3*x + 3*2
y-1 = 3x + 6

Add 1 to both sides:
y-1+1 = 3x+6+1
y=3x+7

#14) If two lines are parallel, they have the same slope.  The slope of the given equation is 4; the only one with a slope of 4 is A.

#15) If two lines are perpendicular, they have slopes that are negative reciprocals (opposite signs and flipped).  The slope of the given equation is 2; this means the slope of the perpendicular line would be -1/2.  The only one with this slope is D.

#16)  The two equations are not the same, so there are not infinitely many solutions.  The variables do not both cancel, so there is at least one solution.  This only leaves one solution as the answer.

#19)  Using 1 for 7 and 4 for x, we check each equation.  The only one that comes out correct is D.
Mathematics
Step-by-step answer
P Answered by Master

1.) Let's find out the slope. Checking the Graph, locating two coordinate points. Looking at the graph picking (-4,0) and (0,1)

Inserting those points into that slope formula:

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{1-0}{0-(-4)} \\ m=\frac{1}{4}

2) According to the second picture. Let's pick two other points. (1,0) and (1,1)

Inserting those points into the formula:

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{1-0}{1-1)} \\ m=\frac{1}{0}

a)0. False.

Thus it can't be 0, since it's not a constant function, and its line it's not parallel to axis x.

b) 1. False 1≠ 1/0

c) True. This quotient is not defined for the set of Real Numbers.

d) False.

3) In a perpendicular line its slope is given by -\frac{-1}{m} of another line.

In addition to this we need to know the line general equation

(y-y_{0})=m(x-x_{0}) .

From this equation y - 2 = 7/3(x + 5) let's get the slope of our perpendicular line: m= -3/7x

The point (-4, 9) will supply the other two points, let's insert them all

y -9=-3/7(x+4)

C)

4)

a) True.  Easily checked by looking at the graph interception.

b) False.

c) False

d) False

5)

B) True. Since the y- intercept of y=|x| is 3.


Will get  1. find the slope of the line:  a.) -4 b.) -1/4 c.) 1/4 d.) 4 2. what is the slope of the
Mathematics
Step-by-step answer
P Answered by Specialist

1.) Let's find out the slope. Checking the Graph, locating two coordinate points. Looking at the graph picking (-4,0) and (0,1)

Inserting those points into that slope formula:

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{1-0}{0-(-4)} \\ m=\frac{1}{4}

2) According to the second picture. Let's pick two other points. (1,0) and (1,1)

Inserting those points into the formula:

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{1-0}{1-1)} \\ m=\frac{1}{0}

a)0. False.

Thus it can't be 0, since it's not a constant function, and its line it's not parallel to axis x.

b) 1. False 1≠ 1/0

c) True. This quotient is not defined for the set of Real Numbers.

d) False.

3) In a perpendicular line its slope is given by -\frac{-1}{m} of another line.

In addition to this we need to know the line general equation

(y-y_{0})=m(x-x_{0}) .

From this equation y - 2 = 7/3(x + 5) let's get the slope of our perpendicular line: m= -3/7x

The point (-4, 9) will supply the other two points, let's insert them all

y -9=-3/7(x+4)

C)

4)

a) True.  Easily checked by looking at the graph interception.

b) False.

c) False

d) False

5)

B) True. Since the y- intercept of y=|x| is 3.


Will get  1. find the slope of the line:  a.) -4 b.) -1/4 c.) 1/4 d.) 4 2. what is the slope of the
Mathematics
Step-by-step answer
P Answered by PhD
These are four questions and four answers:

Question 1. Eliminate the parameter. x = 5t, y = t + 8
 
option B: y = (x / 5) + 8 ↔ x divided by 5 + 8

Explanation:

1) From x = 5t => t = x / 5

2) Substitute t in y = t + 8 => y = (x / 5) + 8

Which is the option B) y = the division of x by 5, added to 8.

Question 2. Eliminate the parameter.

There is an error in the question, because it says x = √x

If the righ question is x = √t , y = 3t + 7 , then the answer is the option A) y = 3x^2 + 7

Explanation:

1) Given: x = √t , y = 3t + 7

2) from x = √t => t = x^2

3) Substitute t = x^2 in y = 3t + 7

=> y = 3 x^2 + 7 ↔ option A) y = x^2 + 7

Question 3. Eliminate the parameter.

x = t^2 + 2, y = t^2 - 4

option A) y = x - 6

Explanation:

1) From x = t^2 + 2 => t^2 = x - 2

2) Substitute t^2 in y = t^2 - 4

=> y = x - 2 - 4

=> y = x - 6, since t^2  is ≥ 0, then x ≥ 0

=> option A) y = x - 6, x ≥ 1

Question 4. Eliminate the parameter.
x = 4 cos t, y = 4 sin t

x^2 + y^2 = 16

Explanation:

1) Square both sides of x = 4 cost

=> x^2 = (4 cos t)^2

x^2 = 16 (cos t)^2

2) Square both sides of y = 4 sin t

y^2 = 16 (sin t)^2

3) Add x^2 and  y^2

x^2 + y^2 = 16(cos t)^2 + 16 (sin t)^2

=> x^2 + y^2 = 16 [ (cos t)^2 + (sin t)^2 ]

4) since (cos t)^2 + (sin t)^2 = 1

x^2 + y^2 = 16
Mathematics
Step-by-step answer
P Answered by PhD
These are four questions and four answers:

Question 1. Eliminate the parameter. x = 5t, y = t + 8
 
option B: y = (x / 5) + 8 ↔ x divided by 5 + 8

Explanation:

1) From x = 5t => t = x / 5

2) Substitute t in y = t + 8 => y = (x / 5) + 8

Which is the option B) y = the division of x by 5, added to 8.

Question 2. Eliminate the parameter.

There is an error in the question, because it says x = √x

If the righ question is x = √t , y = 3t + 7 , then the answer is the option A) y = 3x^2 + 7

Explanation:

1) Given: x = √t , y = 3t + 7

2) from x = √t => t = x^2

3) Substitute t = x^2 in y = 3t + 7

=> y = 3 x^2 + 7 ↔ option A) y = x^2 + 7

Question 3. Eliminate the parameter.

x = t^2 + 2, y = t^2 - 4

option A) y = x - 6

Explanation:

1) From x = t^2 + 2 => t^2 = x - 2

2) Substitute t^2 in y = t^2 - 4

=> y = x - 2 - 4

=> y = x - 6, since t^2  is ≥ 0, then x ≥ 0

=> option A) y = x - 6, x ≥ 1

Question 4. Eliminate the parameter.
x = 4 cos t, y = 4 sin t

x^2 + y^2 = 16

Explanation:

1) Square both sides of x = 4 cost

=> x^2 = (4 cos t)^2

x^2 = 16 (cos t)^2

2) Square both sides of y = 4 sin t

y^2 = 16 (sin t)^2

3) Add x^2 and  y^2

x^2 + y^2 = 16(cos t)^2 + 16 (sin t)^2

=> x^2 + y^2 = 16 [ (cos t)^2 + (sin t)^2 ]

4) since (cos t)^2 + (sin t)^2 = 1

x^2 + y^2 = 16
Mathematics
Step-by-step answer
P Answered by Specialist
1. The answer would be (D). This is because you will plug is the (x) of the ordered pair into the equation(y=-2x), so first off would be (y=-2(-2)). since your multiplying a negative time a negative, you will get your (y) which is 4. Now you do this with the rest. -2(1)=-2 and -2(3)=-6.
2. This would be (A). This answer is simple. First you will take one of the equations (y=-x-1) and plug x into it's place so, y=-3-1, getting your answer(y) as being -4. Now you do the same with the other pair. y=-5-1, getting -6, showing (A) as your answer.
3.The answer will be (A)y is 2 times x. this is because you wou would make out the equation from the answer (y=2x). Now knowing your equation, all thats left is plugging in your (x) factors. so y=2(1), getting your (y) value of 2 and you would do this with the rest of your x factors. 
4. y=5+x
    y=5+(2)= 7
    y=5+(3)= 8
    y=5+(4)= 9
5. (B)y is 3 times x
    y=3(x)
    y=3(3)=9
    y=3(4)=12
    y=3(5)=15
6. (C)y is 6 less than x
    y=6-(x)
    y=6-(8)=2
    y=6-(9)=3
    y=6-(10)=4
Mathematics
Step-by-step answer
P Answered by PhD

Each output for y = x - 3 is 3 less than the corresponding output for y = x

The graph of y = x - 3 is the graph of y = x translated down 3 units ⇒ 3rd

answer

Step-by-step explanation:

- If the function f(x) translated vertically down  by k units, then the image

  of the function is g(x) = f(x) – k

- Remember: x is the input and y is the output of the function

∵ y = x

∵ y = x - 3

- That means the output of the first function (y) is subtracted by 3

∴ y = x is the parent function of y = x - 3

∴  y = x - 3 is the image of the function y = x by translation

   3 units down

* Each value of y in the function y = x - 3 is 3 less than

  the value of corresponding y in the function y = x

∵ The graph of the function y = x passing through the origin point (0 , 0)

- When we subtract from the y-coordinate of the origin 3 the new point

  will be (0 , -3)

∴ The graph of the function y = x -3 intersect the y-axis at point (0 , -3)

* The graph of y = x - 3 is the graph of y = x translated 3 units down

The answer is:

Each output for y = x - 3 is 3 less than the corresponding output for

y = x

The graph of y = x - 3 is the graph of y = x translated down 3 units.

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