11. graph ( y = \frac{2}{3}x )
12. winston won 3 races in 4 weeks. at that rate, how long will it take him to win 10 races?
13. solve: ( \frac{7}{a} = \frac{12}{5} )
14. complete the table of equivalent ratios.
solids | 16 | 24 | |
gases | 2 | | 5 | 12
15. add: ( \frac{4}{5} + \frac{5}{6} )
16. convert 1.02 to a simplified mixed number and a percentage.
17. evaluate: ( (-5)(+6) - (-4)(+3) - (-2) )
18. evaluate: ( 2^4 + 2^3 - 2^2 + 2^1 - 2^0 )
19. find the perimeter and area of this parallelogram. dimensions are in yards.
(parallelogram with base 26, side 8, height 7)
20. find the perimeter and area of this triangle. dimensions are in yards.
(triangle with sides 17, 15, base 8)

Question

11. graph ( y = \frac{2}{3}x )
12. winston won 3 races in 4 weeks. at that rate, how long will it take him to win 10 races?
13. solve: ( \frac{7}{a} = \frac{12}{5} )
14. complete the table of equivalent ratios.
solids | 16 | 24 |  |
gases | 2 |  | 5 | 12
15. add: ( \frac{4}{5} + \frac{5}{6} )
16. convert 1.02 to a simplified mixed number and a percentage.
17. evaluate: ( (-5)(+6) - (-4)(+3) - (-2) )
18. evaluate: ( 2^4 + 2^3 - 2^2 + 2^1 - 2^0 )
19. find the perimeter and area of this parallelogram. dimensions are in yards.
(parallelogram with base 26, side 8, height 7)
20. find the perimeter and area of this triangle. dimensions are in yards.
(triangle with sides 17, 15, base 8)

Accepted Answer

### Question 11: Graph $ y = \frac{2}{3}x $
# Explanation:
## Step 1: Identify the slope and y-intercept
The equation is in slope-intercept form $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept. Here, $ m = \frac{2}{3} $ and $ b = 0 $, so the line passes through the origin $(0,0)$.
## Step 2: Find another point using the slope
The slope $ \frac{2}{3} $ means for every 3 units we move to the right (increase in $ x $ by 3), we move up 2 units (increase in $ y $ by 2). From $(0,0)$, moving 3 units right and 2 units up gives the point $(3, 2)$.
## Step 3: Plot the points and draw the line
Plot the points $(0,0)$ and $(3, 2)$ on the coordinate plane and draw a straight line through them.
# Answer:
The graph is a straight line passing through $(0,0)$ and $(3, 2)$ (and other points following the slope $ \frac{2}{3} $).

### Question 12: Winston won 3 races in 4 weeks. At that rate, how long will it take him to win 10 races?
# Explanation:
## Step 1: Set up a proportion
Let $ t $ be the time (in weeks) to win 10 races. The rate is constant, so $ \frac{3 \text{ races}}{4 \text{ weeks}} = \frac{10 \text{ races}}{t \text{ weeks}} $.
## Step 2: Cross-multiply to solve for $ t $
$ 3t = 4 \times 10 $
$ 3t = 40 $
$ t = \frac{40}{3} \approx 13.33 $
# Answer:
It will take him $ \frac{40}{3} $ weeks (or approximately 13.33 weeks).

### Question 13: Solve $ \frac{7}{a} = \frac{12}{5} $
# Explanation:
## Step 1: Cross-multiply
$ 12a = 7 \times 5 $
## Step 2: Solve for $ a $
$ 12a = 35 $
$ a = \frac{35}{12} $
# Answer:
$ a = \frac{35}{12} $

### Question 14: Complete the table of equivalent ratios.
| Solids | 16 | 24 |? |? |
|--------|----|----|----|----|
| Gases  | 2  |?  | 5  | 12 |

# Explanation:
## Step 1: Find the ratio of Solids to Gases
From the first pair, $ \frac{16}{2} = 8 $, so the ratio of Solids to Gases is 8:1.
## Step 2: Find the missing values
- For Solids = 24, Gases = $ \frac{24}{8} = 3 $
- For Gases = 5, Solids = $ 5 \times 8 = 40 $
- For Gases = 12, Solids = $ 12 \times 8 = 96 $
# Answer:
| Solids | 16 | 24 | 40 | 96 |
|--------|----|----|----|----|
| Gases  | 2  | 3  | 5  | 12 |

### Question 15: Add $ \frac{4}{5} + \frac{5}{6} $
# Explanation:
## Step 1: Find a common denominator
The least common denominator of 5 and 6 is 30.
## Step 2: Convert the fractions
$ \frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30} $
$ \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} $
## Step 3: Add the fractions
$ \frac{24}{30} + \frac{25}{30} = \frac{49}{30} = 1\frac{19}{30} $
# Answer:
$ \frac{49}{30} $ (or $ 1\frac{19}{30} $)

### Question 16: Convert 1.02 to a simplified mixed number and a percentage.
# Explanation:
## Step 1: Convert to a mixed number
$ 1.02 = 1 + 0.02 = 1 + \frac{2}{100} = 1 + \frac{1}{50} = 1\frac{1}{50} $
## Step 2: Convert to a percentage
Multiply by 100: $ 1.02 \times 100 = 102\% $
# Answer:
Mixed number: $ 1\frac{1}{50} $; Percentage: $ 102\% $

### Question 17: Evaluate $ (-5)(+6) - (-4)(+3) - (-2) $
# Explanation:
## Step 1: Multiply the terms
$ (-5)(+6) = -30 $
$ (-4)(+3) = -12 $, so $ -(-4)(+3) = -(-12) = 12 $
$ -(-2) = 2 $
## Step 2: Combine the results
$ -30 + 12 + 2 = -16 $
# Answer:
$ -16 $

### Question 18: Evaluate $ 2^4 + 2^3 - 2^2 + 2^1 - 2^0 $
# Explanation:
## Step 1: Calculate each power
$ 2^4 = 16 $
$ 2^3 = 8 $
$ 2^2 = 4 $
$ 2^1 = 2 $
$ 2^0 = 1 $
## Step 2: Combine the terms
$ 16 + 8 - 4 + 2 - 1 = 21 $
# Answer:
$ 21 $

### Question 19: Find the perimeter and area of this parallelogram. Dimensions are in yards.
(Diagram: base = 26, side = 8, height = 7)
# Explanation:
## Step 1: Calculate the perimeter
Perimeter of a parallelogram: $ 2 \times (base + side) $
$ 2 \times (26 + 8) = 2 \times 34 = 68 $ yards
## Step 2: Calculate the area
Area of a parallelogram: $ base \times height $
$ 26 \times 7 = 182 $ square yards
# Answer:
Perimeter: 68 yards; Area: 182 square yards

### Question 20: Find the perimeter and area of this triangle. Dimensions are in yards. (Sides: 17, 15, 8)
# Explanation:
## Step 1: Calculate the perimeter
Perimeter of a triangle: sum of all sides
$ 17 + 15 + 8 = 40 $ yards
## Step 2: Calculate the area (it's a right triangle, legs 8 and 15)
Area of a right triangle: $ \frac{1}{2} \times leg_1 \times leg_2 $
$ \frac{1}{2} \times 8 \times 15 = 60 $ square yards
# Answer:
Perimeter: 40 yards; Area: 60 square yards

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 11: Graph \( y = \frac{2}{3}x \)

Step 1: Identify the slope and y-intercept

Step 2: Find another point using the slope

Step 3: Plot the points and draw the line

Step 1: Set up a proportion

Step 2: Cross-multiply to solve for \( t \)

Step 1: Cross-multiply

Step 2: Solve for \( a \)

Answer:

Question 12: Winston won 3 races in 4 weeks. At that rate, how long will it take him to win 10 races?