Question

semester review part i

1. list three other names for x list three other names for y

1. what is the equation of the line x - 7y = 14 in slope - intercept form?

1. which of the following numbers is not a solution to the inequality -7 ≤ 4n + 1 < 5?

a) -2 b) -1 c) 0 d) 1

1. the perimeter of the triangle below is 53 feet. find the value of x.

(there is a triangle with sides 4x, 4(2x - 1), 3(3x - 2))

1. if the following relation is a function, which ordered pair could be the missing point?

{(-7, 17), (-2, 7), (5, -7), (x, y)}
a) (5, -12) b) (-7, 15) c) (0, 3) d) (-2, 16)

1. write the equation of the line that passes through the points (-8, -4) and...

Explanation:

Question 2:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We need to solve the equation $x-7y = 14$ for $y$.

Step2: Isolate the $y$ term

Subtract $x$ from both sides of the equation: $-7y=-x + 14$.

Step3: Solve for $y$

Divide each term in the equation $-7y=-x + 14$ by $-7$. So $y=\frac{-x}{-7}+\frac{14}{-7}$, which simplifies to $y=\frac{1}{7}x-2$.

Step1: Solve the inequality $-7\leq4n + 1\lt5$

First, subtract 1 from all parts of the compound inequality: $-7-1\leq4n+1 - 1\lt5 - 1$, which gives $-8\leq4n\lt4$.

Step2: Divide by 4

Divide each part of the inequality $-8\leq4n\lt4$ by 4. We get $\frac{-8}{4}\leq\frac{4n}{4}\lt\frac{4}{4}$, so $-2\leq n\lt1$.

Step3: Check the options

• Option A: $n = - 2$, since $-2\leq - 2\lt1$, $-2$ is a solution.
• Option B: $n=-1$, since $-2\leq - 1\lt1$, $-1$ is a solution.
• Option C: $n = 0$, since $-2\leq0\lt1$, $0$ is a solution.
• Option D: $n = 1$, but our inequality is $n\lt1$, so $1$ is not a solution.

Step1: Recall the perimeter of a triangle

The perimeter of a triangle is the sum of the lengths of its three sides. The sides are $4x$, $4(2x - 1)$ and $3(3x - 2)$, and the perimeter is 53 feet. So we set up the equation: $4x+4(2x - 1)+3(3x - 2)=53$.

Step2: Expand the terms

Expand $4(2x - 1)$ to get $8x-4$ and $3(3x - 2)$ to get $9x - 6$. The equation becomes $4x+8x-4 + 9x-6=53$.

Step3: Combine like terms

Combine the $x$ terms: $4x+8x + 9x=21x$, and the constant terms: $-4-6=-10$. So the equation is $21x-10 = 53$.

Step4: Solve for $x$

Add 10 to both sides: $21x=53 + 10=63$. Then divide both sides by 21: $x=\frac{63}{21}=3$.

Answer:

$y=\frac{1}{7}x - 2$

Question 3: