Show Work Question Help Decide whether or not the ordered pair is a solution to

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Show Work Question Help Decide whether or not the ordered pair is a solution to the equation 4x 2y 24; (4,4) Show your work in the pop-up show work window using a step-by-step process. If the show work window does not automatically pop up, click on the show work button. After you complete your work in the show work window, click on Yes below to verify that you have shown your work and go on to the next question. O Yes O No Show Work | Question Help Find an equation of the line having the specified slope and containing the indicated point. Write your answer in slope-intercept form. m 6,(2, 3) Show your work in the pop-up show work window using a step-by-step process. If the show work window does not automatically pop up, click on the show work button. After you complete your work in the show work window, click on Yes below to verify that you have shown your work and go on to the next question. O Yes No Show Work | Question Find the x-intercept and y-intercept for the equation. Show your work in the pop-up show work window using a step-by-step process. If the show work window does not automatically pop up, click on the show work button. After you complete your work in the show work window, click on Yes below to verify that you have shown your work and go on to the next question. O Yes O No

Explanation / Answer

1) Given equation is 4x + 2y = 24

i.e., 4x +2y -24 = 0...........(i)

given ordered pair is (4,4).

Now, replacing (x,y) by the point (4,4) in the expression 4x + 2y -24, we get,

4.(4) + 2.(4) - 24 =16 + 8 -24 = 24 -24 = 0

Therefore, the ordered pair (4,4) is a solution to the equation 4x + 2y = 24.

2) Let the equation of the line be y = mx + c ...........(i)

given slope of the line is 6.

Then the equation of the line becomes, y = 6x + c ............(ii)

Also given that the line passes through the point (2,3).

Therefore, 3 = 6.(2) + c

i.e., c = 3 - 12

i.e., c = -9

Hence, the equation of the line is, y = 6x -9.

3) Given equation is, x - 3y = -9 ..............(i)

Dividing both sides of (i) by -9 we get,

[x / (-9)] + [(-3y) / (-9)] = 1

i.e., [x / (-9)] + [y / 3] = 1

Therefore, the x-intercept for the equation is (-9,0) and the y-intercept for the equation is (0,3).

4) Let, the length of the base of the given triangle be x cm.

Here given, one side of the triangle is twice the length of the base and the other side is 4 cm longer than the base.

Then, the lengths of two other sides are 2x cm and (x + 4) cm respectively.

Now, the perimeter of the triangle is = [x + 2x + (x + 4)] cm

= 4x + 4 cm

By the given conditions, 4x + 4 > 36

i.e., 4x + 4 - 4 > 36 - 4

i.e., 4x > 32

i.e., (4x / 4) > (32 / 4)

i.e., x > 8

Hence, the length of the base must be greater than 8 cm.

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