Question

short answer

1. solve $20 = 14 - 2x$
2. solve $45q - 29 = 52q - 99$
3. calista raised $345 for her softball teams fundraiser. she wants to raise at least $515. write and solve an inequality to determine how much more money calista must raise to reach her goal. let $d$ represent the amount of money in dollars calista must raise to reach her goal.
4. solve the inequality $-8(z - 9) < -8z + 2$
5. solve the inequality. $|x - 18| + 5 > 2$
6. give the domain and range of the relation.

$x$	$y$
8	17
0	0
-3	-5

1. find the $x$- and $y$-intercepts of $2x - y = -10$
2. use intercepts to graph the line described by the equation $-x + 2y = 6$
3. find the slope of the line that contains $(-5, -8)$ and $(-10, 5)$
4. the water level of a river is 34 feet and it is receding at a rate of 0.5 foot per day. write an equation that represents the water level, $w$, after $d$ days. identify the slope and $y$-intercept and describe their meanings. how many days will the water level be 26 feet?
5. a toy rocket is launched from a platform 50 feet above the ground at a speed of 91 feet per second. the height of the rocket in feet is given by the polynomial $-16t^2 + 91t + 50$, where $t$ is the time in seconds. how high will the rocket be after 3 seconds?
6. multiply. $ab(5a^4b^3 - 3ab)$
7. multiply. $(5x - 3)(x^3 - 5x + 2)$

Explanation:

To solve these problems, we'll address each one step by step. Let's start with problem 2: Solve \( 45q - 29 = 52q - 99 \).

Step 1: Subtract \( 45q \) from both sides

To get all the \( q \)-terms on one side, we subtract \( 45q \) from both sides:

$$ 45q - 29 - 45q = 52q - 99 - 45q $$

Simplifying both sides:

$$ -29 = 7q - 99 $$

Step 2: Add 99 to both sides

To isolate the term with \( q \), we add 99 to both sides:

$$ -29 + 99 = 7q - 99 + 99 $$

Simplifying both sides:

$$ 70 = 7q $$

Step 3: Divide both sides by 7

To solve for \( q \), we divide both sides by 7:

$$ \frac{70}{7} = \frac{7q}{7} $$

Simplifying both sides:

$$ 10 = q $$

So the solution to \( 45q - 29 = 52q - 99 \) is \( q = 10 \).

Answer:

To solve these problems, we'll address each one step by step. Let's start with problem 2: Solve \( 45q - 29 = 52q - 99 \).

Step 1: Subtract \( 45q \) from both sides

To get all the \( q \)-terms on one side, we subtract \( 45q \) from both sides:

$$ 45q - 29 - 45q = 52q - 99 - 45q $$

Simplifying both sides:

$$ -29 = 7q - 99 $$

Step 2: Add 99 to both sides

To isolate the term with \( q \), we add 99 to both sides:

$$ -29 + 99 = 7q - 99 + 99 $$

Simplifying both sides:

$$ 70 = 7q $$

Step 3: Divide both sides by 7

To solve for \( q \), we divide both sides by 7:

$$ \frac{70}{7} = \frac{7q}{7} $$

Simplifying both sides:

$$ 10 = q $$

So the solution to \( 45q - 29 = 52q - 99 \) is \( q = 10 \).