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torisob [31]
3 years ago
5

Find the value of x in the solution to the system of equations shown.

Mathematics
1 answer:
I am Lyosha [343]3 years ago
8 0

To solve this system of equations, the easiest method to use is substitution. Both of our equations are already in terms of y (set equal to y), so we can substitute in the equivalent x values to create an equation with only one variable.


y = 14x - 6

y = -4x + 48


-4x + 48 = 14x - 6


To simplify, we are going to add 4x and add 6 to both sides of the equation to get all of the constant terms on one side of the equation and all of the variable terms on the other. We are also going to simplify by combining like terms.


-4x + 4x + 48 + 6 = 14x + 4x - 6 + 6

48 + 6 = 14x + 4x

54 = 18x


Finally, we must divide both sides of the equation by 18 because division is the inverse operation of multiplication, which allows us to cancel out the coefficient of 18.


54/18 = 18x/18

3 = x


Therefore, your answer is B. x = 3.


Hope this helps!

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Alexandra [31]

Answer:

a. ∆ABC ~ ∆A'B'C'

b. Enlargement

c. Scale factor = 4

Step-by-step explanation:

a. <A corresponds to <A'

<B corresponds to <B'

<C corresponds to <C',

Therefore, the similarity statement would be: ∆ABC ~ ∆A'B'C'

b. The image of the dilation is an enlargement of the original figure because the side lengths of ∆A'B'C are larger than the corresponding side lengths of ∆ABC.

c. Scale factor = the ratio of the corresponding sides

Thus:

Scale factor = A'B'/AB = B'C'/BC = A'C'/AC

Scale factor = 24/6 = 48/12 = 60/15 = 4

Scale factor = 4

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3 years ago
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VMariaS [17]
1/7 cups per serving

6 0
2 years ago
In Covina, California, the population is 47,000. The population increases 18% every year. Determine how long it will take to rea
Alexxandr [17]

Answer: 8.5 years

Step-by-step explanation:

Hi, to answer this question we have to apply an exponential growth function:

A = P (1 + r) t  

Where:

p = original population

r = growing rate (decimal form)  =18/100 = 0.18

t= years

A = population after t years

Replacing with the values given:

192,000 = 47,000 (1+ 0.18)^t

Solving for t:

192,000/47,000 = 1.18^t

4.08 =1.18^t

ln 4.08 = ln 1.18^t

ln 4.08 =t (ln 1.18)

ln 4.08 / ln 1.18  =t

8.5 years = t

Feel free to ask for more if needed or if you did not understand something.

8 0
3 years ago
You have a bag of marbles. 4 are blue, 3 are red, 2 are green, 2 are yellow are 4 are purple. What is the probability that you p
valkas [14]

Answer:

2/35

Step-by-step explanation:

There are 15 marbles in total.

\frac{4\\}{15} ×\frac{3}{14}

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2 years ago
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Answer:

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Step-by-step explanation:

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