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Black_prince [1.1K]
3 years ago
10

Two cars traveling toward each are 200 miles apart. Car A is traveling 20 miles per hour faster than car B. The cars pass after

2 hours. How fast is each car traveling?
Mathematics
1 answer:
AleksAgata [21]3 years ago
7 0

Answer:

Step-by-step explanation:

d = 200 miles

B rate = x

A Rate = x + 20

Each has traveled two hours

The total distance each travels after two hours is 200 miles (they pass each other).

d = r * t

2*x + 2*(x + 20) = 200      Remove the brackets

2x + 2x + 40 = 200           Combine like terms

4x + 40 = 200                   Subtract 40 from each side

4x = 200 - 40                  

4x = 160                           Divide by 4

x = 160/4

x = 40

There B's rate is 40 miles / hour

A's rate is 40 + 20 = 60 miles / hour

     

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The chemistry class was making 300 gallons of 30% isopropyl alcohol. They mixed 12% with 42%. How much of each did they use?
alexgriva [62]

Answer:

<u>The chemistry class mixed 120 gallons of 12% isopropyl alcohol and 180 gallons of 42% isopropyl alcohol.</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Amount of isopropyl alcohol made by the chemistry class = 300 of 30%

Amount of 12% isopropyl alcohol mixed by the chemistry class = x

Amount of 42% isopropyl alcohol mixed by the chemistry class = 300 - x

2. How much of each did they use?

Let's write our equation to solve for x, this way:

30% = 0.3, 12% = 0.12, 42% = 0.42

0.12x + 0.42 (300 - x) = 0.3 * 300

0.12x + 126 - 0.42x = 90

-0.3x = 90 - 126

-0.3x = -36

x = -36/-0.3

<u>x = 120 ⇒ 300 - x = 180</u>

<u>Let's prove x = 120 is correct</u>

0.12x + 0.42 (300 - x) = 0.3 * 300

0.12 * 120 + 0.42 (300 - 120) = 0.3 * 300

14.4 + 75.6 = 90

90 = 90

<u>We proved x = 120 is correct</u>

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33) Given the graphs of f(x) = x - 1 and g(x) = -x - 7, what is the solution to the equation f(x) = g(x)?
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Answer:

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Step-by-step explanation:

The solution is the point of intersection of the 2 lines

The lines intersect at (- 3, - 4 ), then

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Answer:

Step-by-step explanation:

for the first one it's (x + 5) x (x - 7)

second one it's  (x + 5) x (x + 7)

third one is (x - 5) x ( x + 7)

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What equation can be used?
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Answer:

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Step-by-step explanation:

$1800 is spent on a washing machine. This number never changes, so we just need to add that to our annual total

$89 is spent every year. This means that this number needs to be with our variable, x, as it is dependent on the number of years that occur. When we put these two things together, we get the following equation:

f(x)=89x+1800

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