3.
| x | y |
| -6 | 12 |
| -5 | 14 |
| -4 | 16 |
| -3 | 18 |
| -2 | 20 |
a. equation: ____________
b. how much will y be if the x values continue to 2? ____________
4.
| x | y |
| -14 | 3 |
| -12 | 6 |
| -10 | 9 |
| -8 | 12 |
| -6 | 15 |
a. equation: ____________
b. how much will y be if the x value continues to -4? ____________
5.
| hours | cost |
| 5 | 20 |
| 5.5 | 30 |
| 6 | 40 |
| 6.5 | 50 |
a. equation: ____________
b. how much will the cost be at 9.5 hours? ____________
6.
| hours | cost |
| 5 | 25 |
| 5.5 | 30 |
| 6 | 35 |
| 6.5 | 40 |
a. equation: ____________
b. how much will the cost be at 7.5 hours? ____________
7. consider the function represented by this table of values.
| x | y |
| -6 | -33 |
| -5 | -27 |
| -4 | -21 |
| -3 | -15 |
| -2 | -9 |
which function could have produced the values in the table?
a ( y = x - 39 )
b ( y = 6x + 3 )
c ( y = 6x - 96 )
d ( y = -6x + 3 )
8. round your answer to the nearest hundredth.
cone diagram with slant height 2 ft, height 10 ft? wait, no, the diagram has a cone, with a radius (maybe) labeled z ft, height 10 ft. enter the volume of the cone.
9.
a swimming pool has 35 gallons of water in it. water was added to the pool at a rate of 3 gallons per second.
which equation models the relationship between t, the number of gallons of water, and w, the number of seconds water is being added to the pool?
a ( t = 35w + 3 )
b ( t = w + 38 )
c ( t = 38w )
d ( t = 3w + 35 )
10. a swimming pool containing 600 gallons of water is emptied at a constant rate of 500 gallons every 1 hour.
enter an equation in the form ( y = mx + b ) that represents the amount of water y, in gallons, remaining in the pool after x hours.

Question

Accepted Answer

### Problem 3
#### Part A: Find the Equation
# Explanation:
## Step 1: Calculate the slope (m)
We use two points, say $(-6, 12)$ and $(-5, 14)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
$m=\frac{14 - 12}{-5 - (-6)}=\frac{2}{1} = 2$
## Step 2: Use point - slope form $y - y_1=m(x - x_1)$
Using the point $(-6,12)$ and $m = 2$:
$y-12=2(x + 6)$
$y-12=2x+12$
$y = 2x+24$
#### Part B: Find y when x = 2
# Explanation:
## Step 1: Substitute x = 2 into the equation $y = 2x+24$
$y=2\times2 + 24$
## Step 2: Calculate the value of y
$y = 4+24=28$
# Answer (Part A): $y = 2x + 24$
# Answer (Part B): 28

### Problem 4
#### Part A: Find the Equation
# Explanation:
## Step 1: Calculate the slope (m)
Using points $(-14,3)$ and $(-12,6)$. $m=\frac{6 - 3}{-12-(-14)}=\frac{3}{2}=1.5$
## Step 2: Use point - slope form $y - y_1=m(x - x_1)$
Using the point $(-14,3)$ and $m = 1.5$:
$y - 3=1.5(x + 14)$
$y-3 = 1.5x+21$
$y=1.5x + 24$
#### Part B: Find y when x=-4
# Explanation:
## Step 1: Substitute x=-4 into the equation $y = 1.5x+24$
$y=1.5\times(-4)+24$
## Step 2: Calculate the value of y
$y=-6 + 24=18$
# Answer (Part A): $y = 1.5x+24$ (or $y=\frac{3}{2}x + 24$)
# Answer (Part B): 18

### Problem 5
#### Part A: Find the Equation
# Explanation:
## Step 1: Calculate the slope (m)
Using points $(5,20)$ and $(5.5,30)$. $m=\frac{30 - 20}{5.5 - 5}=\frac{10}{0.5}=20$
## Step 2: Use point - slope form $y - y_1=m(x - x_1)$
Using the point $(5,20)$ and $m = 20$:
$y - 20=20(x - 5)$
$y-20=20x-100$
$y=20x - 80$
#### Part B: Find cost when hours = 9.5
# Explanation:
## Step 1: Substitute x = 9.5 into the equation $y = 20x-80$
$y=20\times9.5-80$
## Step 2: Calculate the value of y
$y = 190-80=110$
# Answer (Part A): $y = 20x - 80$
# Answer (Part B): 110

### Problem 6
#### Part A: Find the Equation
# Explanation:
## Step 1: Calculate the slope (m)
Using points $(5,25)$ and $(5.5,30)$. $m=\frac{30 - 25}{5.5 - 5}=\frac{5}{0.5}=10$
## Step 2: Use point - slope form $y - y_1=m(x - x_1)$
Using the point $(5,25)$ and $m = 10$:
$y - 25=10(x - 5)$
$y-25=10x-50$
$y=10x - 25$
#### Part B: Find cost when hours = 7.5
# Explanation:
## Step 1: Substitute x = 7.5 into the equation $y = 10x-25$
$y=10\times7.5-25$
## Step 2: Calculate the value of y
$y = 75-25=50$
# Answer (Part A): $y = 10x - 25$
# Answer (Part B): 50

### Problem 7
# Explanation:
We can test each function with the given x - values.
- For option A: $y=x - 39$. When $x=-6$, $y=-6-39=-45
eq - 33$. So A is wrong.
- For option B: $y = 6x+3$. When $x=-6$, $y=6\times(-6)+3=-36 + 3=-33$. When $x=-5$, $y=6\times(-5)+3=-30 + 3=-27$. When $x=-4$, $y=6\times(-4)+3=-24 + 3=-21$. When $x=-3$, $y=6\times(-3)+3=-18 + 3=-15$. When $x=-2$, $y=6\times(-2)+3=-12 + 3=-9$. All values match.
- For option C: $y=6x - 96$. When $x=-6$, $y=6\times(-6)-96=-36-96=-132
eq - 33$. So C is wrong.
- For option D: $y=-6x + 3$. When $x=-6$, $y=-6\times(-6)+3=36 + 3=39
eq - 33$. So D is wrong.
# Answer: B. $y = 6x+3$

### Problem 9
# Explanation:
The initial amount of water is 35 gallons. Water is added at a rate of 3 gallons per second. So the total amount of water $t$ (in gallons) after $W$ seconds is the initial amount plus the amount added. The amount added is $3\times W$ gallons. So $t=3W + 35$.
- Option A: $t = 35W+3$ is wrong as the rate is 3 gallons per second, not 35.
- Option B: $t=W + 38$ is wrong as it does not represent the correct relationship.
- Option C: $t = 38W$ is wrong as there is an initial amount of 35 gallons.
- Option D: $t=3W + 35$ is correct.
# Answer: D. $t = 3W+35$

### Problem 10
# Explanation:
The general form of a linear equation is $y=mx + b$, where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value). The initial amount of water $b = 600$ gallons. The pool is emptied at a rate of 500 gallons per hour, so the rate of change $m=-500$ (negative because the amount of water is decreasing). So the equation is $y=-500x + 600$.
# Answer: $y=-500x + 600$

### Problem 8 (Volume of Cone)
Assuming the radius $r = z$ and height $h = 10$ (from the diagram, but since $z$ is not given, if we assume $z$ is the radius, the volume of a cone is $V=\frac{1}{3}\pi r^{2}h$. But since the value of $z$ is not provided in the question, we can't calculate the numerical value. However, if we assume $z$ is given (for example, if there was a typo and $z$ is a number), the formula is $V=\frac{1}{3}\pi r^{2}h$. If we assume $r = z$ and $h = 10$, $V=\frac{1}{3}\pi z^{2}\times10=\frac{10}{3}\pi z^{2}$. But as the value of $z$ is not given in the problem as presented, we can't compute the final numerical answer. If we assume $z$ is a known value (e.g., if $z = 6$ (a common radius), then $V=\frac{1}{3}\pi\times6^{2}\times10=\frac{1}{3}\pi\times36\times10 = 120\pi\approx376.99$). But since $z$ is not given, we can only provide the formula.
# Answer: The formula for the volume of the cone is $V=\frac{1}{3}\pi r^{2}h$ (where $r$ is the radius and $h = 10$ is the height). If $r = z$, then $V=\frac{10}{3}\pi z^{2}$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 3

Part A: Find the Equation

Step 1: Calculate the slope (m)

Step 2: Use point - slope form \(y - y_1=m(x - x_1)\)

Part B: Find y when x = 2

Step 1: Substitute x = 2 into the equation \(y = 2x+24\)

Step 2: Calculate the value of y

Step 1: Calculate the slope (m)

Step 2: Use point - slope form \(y - y_1=m(x - x_1)\)

Part B: Find y when x=-4

Answer: