semester review part 1
1) list three other names for x. list three other names for y
(some text is unclear here)
2) what is the equation of the line ( x - 7y = 14 ) in slope - intercept form?
3) which of the following numbers is not a solution to the inequality ( -7leq4n + 1lt5 )?
a) -2 b) -1 c) 0 d) 1
(there is some red - inked work here)
4) the perimeter of the triangle below is 53 feet. find the value of x.
(the triangle has sides ( 4x ), ( 4(2x - 1) ), ( 3(3x - 2) ))
5) 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) )
6) write the equation of the line that passes through the points ( (-8,-4) ) and ( (4,-7) ).
7) use the following non - standard operation ( aotimes b = 5a^{4}+4b ) to evaluate ( -3otimes1 ).

Question

semester review part 1
1) list three other names for x. list three other names for y
(some text is unclear here)
2) what is the equation of the line ( x - 7y = 14 ) in slope - intercept form?
3) which of the following numbers is not a solution to the inequality ( -7leq4n + 1lt5 )?
a) -2  b) -1  c) 0  d) 1
(there is some red - inked work here)
4) the perimeter of the triangle below is 53 feet. find the value of x.
(the triangle has sides ( 4x ), ( 4(2x - 1) ), ( 3(3x - 2) ))
5) 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) )
6) write the equation of the line that passes through the points ( (-8,-4) ) and ( (4,-7) ).
7) use the following non - standard operation ( aotimes b = 5a^{4}+4b ) to evaluate ( -3otimes1 ).

Accepted Answer

### Question 2:
# Explanation:
## 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 $y=\frac{1}{7}x-2$.

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

### Question 3:
# Explanation:
## Step1: Solve the inequality $-7\leq4n + 1\lt5$
First, solve the left - hand side of the compound inequality $-7\leq4n + 1$. Subtract 1 from both sides: $-7-1\leq4n$, so $-8\leq4n$. Divide both sides by 4: $-2\leq n$.

Then, solve the right - hand side $4n + 1\lt5$. Subtract 1 from both sides: $4n\lt5 - 1=4$. Divide both sides by 4: $n\lt1$.

The solution to the compound inequality is $-2\leq n\lt1$.

## Step2: Check each option
- Option A: $n=-2$. Since $-2$ is equal to the lower bound of the solution set $-2\leq n\lt1$, $-2$ 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 solution set is $n\lt1$, so $1$ is not a solution.

# Answer: D) 1

### Question 4:
# Explanation:
## Step1: Recall the formula for the perimeter of a triangle
The perimeter $P$ of a triangle is the sum of the lengths of its three sides. Given the sides $4x$, $4(2x - 1)$ and $3(3x - 2)$ and $P = 53$ feet. So we can write the equation: $4x+4(2x - 1)+3(3x - 2)=53$.

## Step2: Expand the expressions
Expand $4(2x - 1)=8x-4$ and $3(3x - 2)=9x - 6$. The equation becomes $4x + 8x-4+9x - 6=53$.

## Step3: Combine like terms
Combine the $x$ terms: $4x+8x + 9x=21x$. Combine the constant terms: $-4-6=-10$. So the equation is $21x-10 = 53$.

## Step4: Solve for $x$
Add 10 to both sides: $21x=53 + 10=63$. Divide both sides by 21: $x = 3$.

# Answer: $x = 3$

### Question 5:
# Explanation:
## Step1: Recall the definition of a function
A function is a relation where each input (x - value) has exactly one output (y - value). So we need to check which ordered pair $(x,y)$ does not repeat an $x$ - value that is already in the set $\{(-7,17),(-2,7),(5,-7)\}$.

## Step2: Check each option
- Option A: The ordered pair is $(5,-12)$. The $x$ - value is $5$, which is already in the pair $(5,-7)$ in the relation. So this would not be a function.
- Option B: The ordered pair is $(-7,15)$. The $x$ - value is $-7$, which is already in the pair $(-7,17)$ in the relation. So this would not be a function.
- Option C: The ordered pair is $(0,3)$. The $x$ - value is $0$, which is not in the set of $x$ - values $\{-7,-2,5\}$ of the given relation. So this can be a part of the function.
- Option D: The ordered pair is $(-2,16)$. The $x$ - value is $-2$, which is already in the pair $(-2,7)$ in the relation. So this would not be a function.

# Answer: C) $(0,3)$

### Question 6:
# Explanation:
## Step1: Find the slope $m$
The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. For the points $(-8,-4)$ and $(4,-7)$, $x_1=-8,y_1 = - 4,x_2 = 4,y_2=-7$. So $m=\frac{-7-(-4)}{4-(-8)}=\frac{-7 + 4}{4 + 8}=\frac{-3}{12}=-\frac{1}{4}$.

## Step2: Use point - slope form
The point - slope form of a line is $y - y_1=m(x - x_1)$. Let's use the point $(-8,-4)$. So $y-(-4)=-\frac{1}{4}(x - (-8))$, which simplifies to $y + 4=-\frac{1}{4}(x + 8)$.

## Step3: Convert to slope - intercept form
Expand the right - hand side: $y+4=-\frac{1}{4}x-2$. Subtract 4 from both sides: $y=-\frac{1}{4}x-2 - 4$, so $y=-\frac{1}{4}x-6$. We can also verify with the other point. If $x = 4$, $y=-\frac{1}{4}(4)-6=-1 - 6=-7$, which matches the $y$ - value of the point $(4,-7)$.

# Answer: $y=-\frac{1}{4}x - 6$

### Question 7:
# Explanation:
## Step1: Use the non - standard operation
Given $a\otimes b = 5a^{4}+4b$. We need to evaluate $-3\otimes1$, so $a=-3$ and $b = 1$.

## Step2: Substitute the values
First, calculate $a^{4}$ when $a=-3$. $(-3)^{4}=(-3)\times(-3)\times(-3)\times(-3)=81$. Then $5a^{4}=5\times81 = 405$. And $4b=4\times1 = 4$.

## Step3: Find the result
Add the two results: $5a^{4}+4b=405 + 4=409$.

# Answer: 409

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QUESTION IMAGE

Question

Explanation:

Question 2:

Step1: Recall slope - intercept form

Step2: Isolate the \(y\) term

Step3: Solve for \(y\)

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

Step2: Check each option

Step1: Recall the formula for the perimeter of a triangle

Step2: Expand the expressions

Step3: Combine like terms

Step4: Solve for \(x\)

Answer:

Question 3: