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3 years ago

Solve the system using substitution. 2x = 5y + 14 x = 5y

Mathematics

1 answer:

andrew-mc [135]3 years ago

7 0

Answer:

Step-by-step explanation:

To solve an equation, we can only have one variable. In this case, we are given the system 2x = 5y + 14. However, we are given the value of x in terms of y. We can substitute 10y in for 2x and solve.

10y = 5y + 14

First, we need to get all the variables on one side of the equation, so we subtract 5y.

5y = 14

Divide by 5

y = 14/5 or 2 4/5 or 2.8

Now for the x part.

2x = x + 14

Subtract 1x

x = 14

Now we check our answer.

2(14) = 5(2.8) + 14

28 = 14 + 14

28 = 28

Because 28 equals 28, our solutions are correct.

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3 years ago

The first term of an arithmetic sequence is 9 and the common difference is –2. What is the seventh term? A. 0 B. –3 C. –1 D. –5

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Answer:

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Step-by-step explanation:

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Is the value of the fraction 7−2y/6 greater than the value of the fraction 3y−7/12 ?

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Complete Question:

Is the value of the fraction 7−2y/6 greater than the value of the fraction 3y−7/12 ? For what values?(Make sure to use an inequality)

Answer:

y < 3

Step-by-step explanation:

The given two fractions are:

$\frac{7-2y}{6}$ and $\frac{3y-7}{12}$

We have to tell for which range of values is the value of first fraction larger than the second fraction. This can be done by setting up an inequality as shown:

$\frac{7-2y}{6} >\frac{3y-7}{12}$

The range of y which will satisfy this inequality will result in first fraction of larger value as compared to the second fraction.

Multiplying both sides of inequality by 12, we get:

$12 \times \frac{7-2y}{6} > 12 \times \frac{3y-7}{12} \\\\ 2(7-2y)>3y-7\\\\ 14-4y>3y-7\\\\ 14+7>3y+4y\\\\ 21>7y\\\\ 3>y\\\\ y$

This means, for y lesser than 3, the value of first fraction is larger than the second one.

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Answer:

A <u>bi-conditional statement</u> represents the idea of "if and only if." Its symbol is a $\leftrightarrow$ .

Step-by-step explanation:

We have been given an incomplete sentence. We are supposed to fill in the given blank.

A _______ represents the idea of "if and only if." Its symbol is a $\leftrightarrow$ .

We know that "if and only if" stands for bi-conditional statement, which represents either both statements are true or both are false.

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Therefore, our complete statement would be: A <u>bi-conditional statement</u> represents the idea of "if and only if." Its symbol is a $\leftrightarrow$ .

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