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2 years ago

What is 7n + 3 = 3n + 27

Mathematics

1 answer:

icang [17]2 years ago

4 0

7n + 3 = 3n + 27

7n -3n =27-3
4n =24
n= 6.

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Two times x is 8 more than y. The sum of x and two times y is 14. Write two equations and graph to find the value of y.

Sauron [17]

Option B: $y=4$ is the value of y

Explanation:

It is given that "Two times x is 8 more than y". Writing it as expression, we have,

$2x=8+y$

It is also given that "The sum of x and two times y is 14". Writing it as expression, we have,

$x+2y=14$

To find the value of y, let us solve the two equations using substitution method.

From the equation $2x=8+y$ , let us find the value of x.

$x=\frac{8+y}{2}$

$x=\frac{8}{2} +\frac{y}{2}$

$x=4+\frac{y}{2}$

Now, substituting $x=4+\frac{y}{2}$ in the equation $x+2y=14$ , we get,

$4+\frac{y}{2}+2y=14$

$4+\frac{5y}{2} =14$

$\frac{5 y}{2}=10$

$5y=20$

$y=4$

Thus, the value of y is $y=4$

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3 years ago

What is the equation of the line perpendicular to 3x+y=6 that passes through the point (0,8)

Alekssandra [29.7K]

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$3x + y = 6$

$y = - 3x + 6$

The coefficient of x is the slope of the line , So the slope of the above equation is -3 .

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Remember from now on ,

Product of multiplying the slopes of two lines which are perpendicular to each other , is -1 .

Thus ;

$( - 3) \times (m) = - 1$

m is the slope of the line which we want.

$- 3m = - 1$

Negatives simplifies

$3m = 1$

Divide sides by 3

$\frac{3m}{3} = \frac{1}{3} \\$

$m = \frac{1}{3} \\$

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We have following equation to find the point-slope form of the linear functions :

$y - y(0) = m(x - x(0))$

x(0) and y(0) are the coordinates of the point which the line passed through.

$y - 8 = \frac{1}{3} (x - 0) \\$

$y - 8 = \frac{1}{3} x \\$

Add sides 8

$y = \frac{1}{3} x + 8 \\$

Done....

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3 years ago

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