I need help on this step to step problem please..

A) Rachel runs faster. Her rate is 14 feet per seconds.

B) y = 14x is the function which represents Rachel's speed

C) See the attached figure.

D) Rachel will catch up to Aleyna at 10 seconds, after running 140 feet.

Step-by-step explanation:

The equation which represents Aleyna speed. ⇒ y = 6x + 80

And the given table represents Rachel speed

The general form of the line ⇒ y = mx + c

Where m is the slope or rate of change and c is y intercept.

A) Rate of Aleyna runs is the slope of the equations = 6 ft/sec.

Rate of Rachel runs = (y₂-y₁)/(x₂-x₁) = (56-28)/(4-2) = 28/2 = 14  ft/sec.

So, Rachel runs faster. Her rate is 14 feet per seconds.

B) The linear function which represents Rachel's speed

The general form of the line ⇒ y = mx + c

c = y-intercept = 0

m = slope =  (y₂-y₁)/(x₂-x₁) = (56-28)/(4-2) = 28/2 = 14

y = 14x is the function which represents Rachel's speed

C) See the attached figure.

The solid blue line represents Aleyna's speed and the dot red line represents Rachel's speed.

D) By finding the intersection between Aleyna's speed and Rachel's speed, we will find the point at which Rachel will catch up to Aleyna.

Aleyna speed. ⇒ y = 6x + 80 (1)

Rachel's speed. ⇒ y = 14x      (2)

Substitution from (2) at (1) and solve for x

14x = 6x + 80

8x = 80

x = 80/8 = 10

y = 14x = 140

Which is agree with the result on the graph.

So, Rachel will catch up to Aleyna at 10 seconds, after running 140 feet.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1