Find the value of r in (4,,2) so that the slope of the line containing them is -5/3

Answer :  

The value of r in (4,r),(r,2) so that the slope of the line containing them is is 7

Solution:  

Slope of the line which is passes through

→ (1)

From question given that two points are (4, r), (r, 2). Hence we get

By substituting the values in equation (1),

→ (2)

Also given that slope that is m = , so on substituting the value of m in equation (2),

On simplifying,

-5r+20=6-3r

5r-3r=20-6

2r = 14

r  =7

Hence value of r is 7.

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

ok

step-by-step explanation: