science math skills
solve for x: solve for x:
1. ( x + 7 = 19 )
2. ( 5x = 45 )
3. ( x - 12 = -4 )
4. ( x div 6 = 8 )
5. ( 3x + = 26 ) (note: there may be a typo here)
6. ( 2x - 9 = 15 )
7. ( 4x + 6 = 2x + 18 )
8. ( \frac{x}{4} + 7 = 13 )

use the formula: slope = rise/run
9. a line passes through the points ( (2,4) ) and ( (6,12) )
a. calculate the slope

10. a graph shows that when time increases from 2 minutes to 6 minutes, oxygen concentration increases from 10 mg/l to 18 mg/l.
a. what is the slope?
b. what does this slope represent biologically?

use the given formulas. solve for the unknown variable.
density formula: ( d = \frac{m}{v} )
11. a substance has a mass of 60 g and a volume of 15 ml.
a. what is its density?

12. a liquid has a density of 2 g/ml and a mass of 50 g.
a. what is the volume?

Question

science math skills
solve for x: solve for x:
1. ( x + 7 = 19 )
2. ( 5x = 45 )
3. ( x - 12 = -4 )
4. ( x div 6 = 8 )
5. ( 3x + = 26 ) (note: there may be a typo here)
6. ( 2x - 9 = 15 )
7. ( 4x + 6 = 2x + 18 )
8. ( \frac{x}{4} + 7 = 13 )

use the formula: slope = rise/run
9. a line passes through the points ( (2,4) ) and ( (6,12) )
   a. calculate the slope

10. a graph shows that when time increases from 2 minutes to 6 minutes, oxygen concentration increases from 10 mg/l to 18 mg/l.
    a. what is the slope?
    b. what does this slope represent biologically?

use the given formulas. solve for the unknown variable.
density formula: ( d = \frac{m}{v} )
11. a substance has a mass of 60 g and a volume of 15 ml.
    a. what is its density?

12. a liquid has a density of 2 g/ml and a mass of 50 g.
    a. what is the volume?

Accepted Answer

### Problem 1: $ x + 7 = 19 $
# Explanation:
## Step 1: Subtract 7 from both sides
To isolate $ x $, we subtract 7 from both sides of the equation.
$ x + 7 - 7 = 19 - 7 $
## Step 2: Simplify both sides
Simplifying the left side gives $ x $, and simplifying the right side gives $ 12 $.
$ x = 12 $
# Answer: $ x = 12 $

### Problem 2: $ 5x = 45 $
# Explanation:
## Step 1: Divide both sides by 5
To solve for $ x $, we divide both sides of the equation by 5.
$ \frac{5x}{5} = \frac{45}{5} $
## Step 2: Simplify both sides
Simplifying the left side gives $ x $, and simplifying the right side gives $ 9 $.
$ x = 9 $
# Answer: $ x = 9 $

### Problem 3: $ x - 12 = -4 $
# Explanation:
## Step 1: Add 12 to both sides
To isolate $ x $, we add 12 to both sides of the equation.
$ x - 12 + 12 = -4 + 12 $
## Step 2: Simplify both sides
Simplifying the left side gives $ x $, and simplifying the right side gives $ 8 $.
$ x = 8 $
# Answer: $ x = 8 $

### Problem 4: $ x \div 6 = 8 $ (or $ \frac{x}{6} = 8 $)
# Explanation:
## Step 1: Multiply both sides by 6
To solve for $ x $, we multiply both sides of the equation by 6.
$ \frac{x}{6} \times 6 = 8 \times 6 $
## Step 2: Simplify both sides
Simplifying the left side gives $ x $, and simplifying the right side gives $ 48 $.
$ x = 48 $
# Answer: $ x = 48 $

### Problem 5: (Assuming the equation is $ 3x + 0 = 26 $ or there was a typo, let's assume $ 3x = 26 $ for now, but if it's $ 3x + c = 26 $ with a missing constant, we'll correct. Wait, maybe it's $ 3x + 1 = 26 $? Wait, the original problem has a typo. Let's assume it's $ 3x = 26 $ (or maybe $ 3x + 1 = 26 $, but since it's unclear, maybe the intended equation is $ 3x = 26 $ or $ 3x + \text{something} = 26 $. Wait, maybe it's a typo and the equation is $ 3x + 1 = 26 $, but let's check. Alternatively, maybe $ 3x = 26 $. Wait, let's proceed with $ 3x = 26 $ (if the missing term is 0).
# Explanation:
## Step 1: Divide both sides by 3
To solve for $ x $, we divide both sides by 3.
$ \frac{3x}{3} = \frac{26}{3} $
## Step 2: Simplify
$ x = \frac{26}{3} \approx 8.67 $
But if the equation was $ 3x + 1 = 26 $, then:
## Step 1: Subtract 1 from both sides
$ 3x + 1 - 1 = 26 - 1 $
$ 3x = 25 $
## Step 2: Divide by 3
$ x = \frac{25}{3} \approx 8.33 $
Since the original problem has a typo, we'll assume the intended equation is $ 3x = 26 $ (or correct the typo). Alternatively, maybe it's $ 3x + 0 = 26 $, so $ x = \frac{26}{3} $.
# Answer: $ x = \frac{26}{3} $ (or $ \approx 8.67 $) (depending on the corrected equation)

### Problem 6: $ 2x - 9 = 15 $
# Explanation:
## Step 1: Add 9 to both sides
To isolate the term with $ x $, we add 9 to both sides.
$ 2x - 9 + 9 = 15 + 9 $
## Step 2: Simplify
$ 2x = 24 $
## Step 3: Divide both sides by 2
$ \frac{2x}{2} = \frac{24}{2} $
## Step 4: Simplify
$ x = 12 $
# Answer: $ x = 12 $

### Problem 7: $ 4x + 6 = 2x + 18 $
# Explanation:
## Step 1: Subtract $ 2x $ from both sides
To get the $ x $ terms on one side, we subtract $ 2x $ from both sides.
$ 4x - 2x + 6 = 2x - 2x + 18 $
## Step 2: Simplify
$ 2x + 6 = 18 $
## Step 3: Subtract 6 from both sides
$ 2x + 6 - 6 = 18 - 6 $
## Step 4: Simplify
$ 2x = 12 $
## Step 5: Divide both sides by 2
$ \frac{2x}{2} = \frac{12}{2} $
## Step 6: Simplify
$ x = 6 $
# Answer: $ x = 6 $

### Problem 8: $ \frac{x}{4} + 7 = 13 $
# Explanation:
## Step 1: Subtract 7 from both sides
To isolate the term with $ x $, we subtract 7 from both sides.
$ \frac{x}{4} + 7 - 7 = 13 - 7 $
## Step 2: Simplify
$ \frac{x}{4} = 6 $
## Step 3: Multiply both sides by 4
$ \frac{x}{4} \times 4 = 6 \times 4 $
## Step 4: Simplify
$ x = 24 $
# Answer: $ x = 24 $

### Problem 9a: Slope between (2,4) and (6,12)
# Explanation:
## Step 1: Recall the slope formula
The slope $ m $ between two points $ (x_1, y_1) $ and $ (x_2, y_2) $ is $ m = \frac{y_2 - y_1}{x_2 - x_1} $
## Step 2: Identify the points
Here, $ x_1 = 2 $, $ y_1 = 4 $, $ x_2 = 6 $, $ y_2 = 12 $
## Step 3: Substitute into the formula
$ m = \frac{12 - 4}{6 - 2} $
## Step 4: Simplify
$ m = \frac{8}{4} = 2 $
# Answer: The slope is $ 2 $

### Problem 10a: Slope for time (2 to 6 minutes) and oxygen (10 to 18 mg/L)
# Explanation:
## Step 1: Recall the slope formula (rise over run)
Slope $ m = \frac{\text{change in } y}{\text{change in } x} $
Here, $ x $ is time (minutes) and $ y $ is oxygen concentration (mg/L)
## Step 2: Calculate change in $ y $ and change in $ x $
Change in $ y = 18 - 10 = 8 $ mg/L
Change in $ x = 6 - 2 = 4 $ minutes
## Step 3: Substitute into the formula
$ m = \frac{8}{4} = 2 $
# Answer: The slope is $ 2 $ mg/L per minute

### Problem 10b: Biological meaning of the slope
# Brief Explanations:
The slope represents the rate of change of oxygen concentration with respect to time. In this case, it means that for each additional minute, the oxygen concentration increases by 2 mg/L. This could represent the rate of oxygen production (e.g., in photosynthesis) or consumption (e.g., in respiration), depending on the context. If it's an increase, it might be the rate at which oxygen is being added to the system (e.g., in a pond with aquatic plants producing oxygen).
# Answer: The slope represents the rate of increase of oxygen concentration, meaning the oxygen concentration increases by 2 mg/L per minute.

### Problem 11a: Density of a substance with mass 60 g and volume 15 mL
# Explanation:
## Step 1: Recall the density formula
Density $ d = \frac{m}{v} $, where $ m $ is mass and $ v $ is volume.
## Step 2: Substitute the values
$ m = 60 $ g, $ v = 15 $ mL
$ d = \frac{60}{15} $
## Step 3: Simplify
$ d = 4 $ g/mL
# Answer: The density is $ 4 $ g/mL

### Problem 12a: Volume of a liquid with density 2 g/mL and mass 50 g
# Explanation:
## Step 1: Recall the density formula $ d = \frac{m}{v} $ and solve for $ v $
Rearranging the formula: $ v = \frac{m}{d} $
## Step 2: Substitute the values
$ m = 50 $ g, $ d = 2 $ g/mL
$ v = \frac{50}{2} $
## Step 3: Simplify
$ v = 25 $ mL
# Answer: The volume is $ 25 $ mL

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: \( x + 7 = 19 \)

Step 1: Subtract 7 from both sides

Step 2: Simplify both sides

Step 1: Divide both sides by 5

Step 2: Simplify both sides

Step 1: Add 12 to both sides

Step 2: Simplify both sides

Answer:

Problem 2: \( 5x = 45 \)