Can someone with these 8 problems and show your work .

Part 1) option a.

Part 2) option c.

Part 3) option a. Yes , d=-2

Part 4) option b.  

Part 5) option b.

Part 6) option c.

Part 7) option c.

Part 8) option a. y=2x-1 and y=x+1

Step-by-step explanation:

Part 1)

we know that

If a ordered pair satisfy a function, then the function pass through the ordered pair

Verify each function with the points (1,4), (2,9) and (3,16)

case a) we have

For x=1, y=4

----> is true

For x=2, y=9

----> is true

For x=3, y=16

----> is true

therefore

The function pass through the three points

case b) we have

For x=1, y=4

----> is not true

therefore

The function not pass through the three points

case c) we have

For x=1, y=4

----> is not true

therefore

The function not pass through the three points

Part 2)

Let

y------> the number of laps

x-----> the number of hours

we know that

The linear equation that represent this situation is

Part 3) we have

{4,2,0,-2,-4,-6,...}

Let

a1=-4

a2=2

a3=0

a4=-2

a5=-4

a6=-6

we know that

a2-a1=2-4=-2 -----> a2=a1-2

a3-a2=0-2=-2 ----> a3=a2-2

a4-a3=-2-0=-2 -----> a4=a3-2

a5-a4=-4-(-2)=-2----> a5=a4-2

a6-a5=-6-(-4)=-2----> a6=a5-2

therefore

Is an arithmetic sequence, the common difference is -2

Part 4) we know that

The y-intercept of the graph is (0,4)

The x-intercept of the graph is (-2,0)

therefore

the function is

because

For x=0 -----> y=2(0)+4 -----> y=4

For y=0 ----> 0=2x+4 --------> x=-2

Part 5) we know that

The formula to calculate the slope between two points is equal to

we have

substitute the values

Part 6) we know that

The equation of the line into slope point form is equal to

we have

substitute the values

Convert to slope intercept form

Part 7) we know that

If two lines are parallel, then their slopes are the same

The equation of the given line is

so

The slope of the given line is

therefore

The line is parallel to the given line

Because the slope is equal to

Part 8) we know that

If a ordered pair is a solution of a system of equations, then the ordered pair must satisfy both equations of the system

Verify each case for (2,3)

case a)

y=2x-1 -----> equation 1

y=x+1 -----> equation 2

Substitute the value of x and the value of y in each equation and then compare the results

Verify equation 1

3=2(2)-1

3=3 -----> is true

Verify equation 2

3=2+1

3=3 -----> is true

therefore

The point (2,3) is a solution of the system of equations case a

case b)

y=2x+1 -----> equation 1

y=x-1 -----> equation 2

Substitute the value of x and the value of y in each equation and then compare the results

Verify equation 1

3=2(2)+1

3=5 -----> is not true

therefore

The point (2,3) is not a solution of the system of equations case b

case c)

y=4x-5 -----> equation 1

y=2x -----> equation 2

Substitute the value of x and the value of y in each equation and then compare the results

Verify equation 1

3=4(2)-5

3=3 -----> is true

Verify equation 2

3=2(2)

3=4 -----> is not true

therefore

The point (2,3) is not a solution of the system of equations case c

good luck!

cutie~