For the line segment whose endpoints are r(1, 2) and s(6, 7), find the y value for the point located 3 over 4 the distance from r to s. (6 points)

The y value for the point located 3 over 4 the distance from R to S is 23/4=5.75

Step-by-step explanation:

Initial point: R=(1,2)=(xr,yr)→xr=1, yr=2

Final point: S=(6,7)=(xs,ys)→xs=6. ys=7

Point: P=(x,y), y=?

RP=(3/4)RS

Then PS=(1/4)RS

And the ratio:

r=RP/PS

r=(3/4)RS / [(1/4)RS]

r=(3/4) / (1/4)

r=(3/4)*(4/1)

r=(3*4)/(4*1)

r=12/4

r=3

Then:

y=(yr+r ys)/(1+r)

y=[2+3(7)](1+3)

y=(2+21)/4

y=23/4

y=5.75

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15