Question

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

Answer 1

Answer:

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

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

$y=(x+1)^{2}$

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

$m=\frac{y2-y1}{x2-x1}$

we have

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

substitute the values

$m=\frac{7-5}{2-3}$

$m=-2$

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