Some members of the track team are practicing running along a marathon course. Their position along the course is given by the variable d, in miles. The variable t represents the amount of time after 9:00 a. m., in hours. Some runners started running before 9:00 a. m. The position of runner Cheng is given by d=8(t+0.5). The position of runner Antonelli is given by d=4+8t. Which is true?

Runner Antonelli will catch and pass runner Cheng.

Runner Cheng is running at a fixed distance behind runner Antonelli.

Runner Cheng and runner Antonelli are at the same point along the course.

The runners started together, but now runner Antonelli is ahead.
(gives 15 points)

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

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b

3

step-by-step explanation: