Me solve the system of equations. y=x+6 y=x^2 + 8x +16 enter your answers in the boxes as ordered pairs.

It should be -2,4 or -5,1.

since both answers = y then you put them equal to each other and then solved for x.

x+6=x^2 +8x +16
0=x^2 +7x +10
0=(x+2)(x+5)

x=-2 or -5

and for y I input the two separately into one of the equations

y= (-2)+6

y=4

y=(-5)+6

y=1

and then I double checked by imputing my y's and x's  into the remaining equation.

(4)=(-2)^2 +8(-2)+16
4=4-16+16
4=4

(1)=(-5)^2 +8(-5)+16
1=25-40+16
1=1

I hope your tests go well with the help of this knowledge.

Here BD & AB represent the string.

Now in triangle DBC, CD is opposite to 25° and BD = 50 is the hypotenuse.

The trigonometry ratio associating opposite and hypotenuse is sin.

So we have

Multiplying by 50 on both sides

CD = 50 × sin 25°

CD = 21.13 feet

Now in triangle ABC, BC = opposite and AB =50 is hypotenuse with respect to 45°.

So we have

Multiplying by 50 on both sides

AC = 50 × sin45°

AC = 35.36 feet

Hence the kite moves up by = 35.36-21.13 = 14.23 feet.

The approximate difference in the height of the kite is 14.2 feet

Option a) is the right answer.