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3 years ago

Please help me simplify the expression and please show work!!! <3

Mathematics

1 answer:

gizmo_the_mogwai [7]3 years ago

8 0

Step-by-step explanation:

$\frac{x + 4}{3 {x}^{2} - 12x - 96} = \frac{x + 4}{3( {x}^{2} - 4x - 32) } = \frac{x + 4}{3(x - 8)(x + 4)}$

$= \frac{1}{3(x - 8)} = \frac{1}{3x - 24}$

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Driving to your friend's house, you travel at an average rate of 35 miles per hour. On your way home, you travel at an average r

kenny6666 [7]

Answer:

14 miles

Explanation:

The relation that will be used to solve this problem is:

$Distance = Velocity*Time$

which can be rewritten as:

$Time = \frac{Distance}{Velocity}$

Assume that:

Distance from your house to your friend's house is d

Time taken from your house to your friend's house is t₁

Time taken from your friends house to your house is t₂

1- From your house to your friend's house:

Average rate = 35 miles/hour

Therefore:

$t_{1} = \frac{d}{35}$

2- From your friend's house to your house:

Average rate = 40 miles per hour

Therefore:

$t_{2} = \frac{d}{40}$

3- Round trip:

We know that the round trip took 45 minutes which is equivalent to 0.75 hours

This means that:

t₁ + t₂ = 0.75 hours

$\frac{d}{35}+\frac{d}{40}=0.75\\ \\\frac{40d + 35d}{1400}=0.75\\ \\\frac{75d}{1400}=0.75\\ \\ 1050 = 75d\\ d=14 miles$

Hope this helps :)

3 0

4 years ago

PLEASE HELP 15 POINTS...PLEASE HELP

sasho [114]

Answer:

-4

Step-by-step explanation: it is intercepting the -4 so i think -4 is the right answer

8 0

3 years ago

Read 2 more answers

Playland park charges 7 dollars admission plus 75 crnts per ride. Funland park charges 12.50$ admission plus 50 cents per ride.

WINSTONCH [101]

Answer:

22 rides

Step-by-step explanation:

Both the parks has a fixed cost (admission fee) and a variable cost (per ride cost). We can model 2 equations in "x" [let x be number of rides], equate them and find "x".

Playland Park:

Fixed Cost = 7

Variable Cost = 0.75x (in dollars)

Equation = 7 + 0.75x

Funland Park:

Fixed Cost = 12.50

Variable Cost = 0.50x (in dollars)

Equation = 12.50 + 0.50x

Now we equate and solve for x:

$7+0.75x=12.50 + 0.50x\\0.75x-0.50x=12.50-7\\0.25x=5.50\\x=\frac{5.50}{0.25}\\x=22$

Hence,

the cost would be same for both parks for 22 rides

8 0

3 years ago

Write an equation of the line passing through point P(0,-1) that is parallel to the line y=-2x+3

irinina [24]

The answer to this question is:

y = -2x - 1

8 0

4 years ago

Jack stands 9 feet from the primate

liq [111]

Answer:

16.2 ft

Step-by-step explanation:

3 0

3 years ago