Question

Can someone help with these 8 problems and show your work please.

Answer 1

Part 1) option a.
`y=(x+1)^(2)`

Part 2) option c.
`y(x)=10x+1`

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

Part 4) option b.
`y=2x+4`

Part 5) option b.
`m=-2`

Part 6) option c.
`y=4x+14`

Part 7) option c.
`y=4x+5`

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

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

`y=(x+1)^(2)`

For x=1, y=4

`4=(1+1)^(2)`

`4=4` ----> is true

For x=2, y=9

`9=(2+1)^(2)`

`9=9` ----> is true

For x=3, y=16

`16=(3+1)^(2)`

`16=16` ----> is true

therefore

The function pass through the three points

case b) we have

`y=(x+3)^(2)`

For x=1, y=4

`4=(1+3)^(2)`

`4=16` ----> is not true

therefore

The function not pass through the three points

case c) we have

`y=7x-5`

For x=1, y=4

`4=7(1)-5`

`4=2` ----> 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

`y(x)=10x+1`

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
`y=2x+4`

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

`m=(y2-y1)/(x2-x1)`

we have

`A(3,5)\ B(2,7)`

substitute the values

`m=(7-5)/(2-3)`

`m=-2`

Part 6) we know that

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

`y-y1=m(x-x1)`

we have

`m=4`

`point(-3,2)`

substitute the values

`y-2=4(x+3)`

Convert to slope intercept form

`y=4x+12+2`

`y=4x+14`

Part 7) we know that

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

The equation of the given line is
`y=4x-2`

so

The slope of the given line is
`m=4`

therefore

The line
`y=4x+5` is parallel to the given line

Because the slope is equal to
`m=4`

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