To solve this equation, we need to isolate the variable y.
Start by subtracting 3x from both sides of the equation:
-7y = -3x + 4
Next, divide both sides of the equation by -7 to solve for y:
y = (-3x + 4) / -7
Therefore, the answer is y = (-3x + 4) / -7.
So, the correct option is:
C) y = (-3x + 4) / -7, or y = -3x/7 + 4/7.
3x - 7y = 4
Question 2 options:
A) y = , or y =
B) y = , or y =
C) y = , or y =
D) y = , or y =
23 answers
Perform the indicated operation. Write the answer without exponents.
(7 × 10-2) × (2 × 105) × (2 × 103)
Question 6 options:
A)
28,000,000
B)
28 × 10^6
C)
2,800,000
D)
28 × 10^-30
(7 × 10-2) × (2 × 105) × (2 × 103)
Question 6 options:
A)
28,000,000
B)
28 × 10^6
C)
2,800,000
D)
28 × 10^-30
To perform the indicated operation, we can multiply the numbers together and add the exponents of 10.
(7 × 10^(-2)) × (2 × 10^(5)) × (2 × 10^(3))
First, multiply the numbers together:
(7 × 2 × 2) × (10^(-2) × 10^(5) × 10^(3))
= 28 × (10^(-2+5+3))
= 28 × 10^(6)
Therefore, the answer is:
B) 28 × 10^6
(7 × 10^(-2)) × (2 × 10^(5)) × (2 × 10^(3))
First, multiply the numbers together:
(7 × 2 × 2) × (10^(-2) × 10^(5) × 10^(3))
= 28 × (10^(-2+5+3))
= 28 × 10^(6)
Therefore, the answer is:
B) 28 × 10^6
But it wants the answer without exponents
I apologize for the confusion. To write the answer without exponents, we can convert it to a decimal form.
Recall that 10^6 means moving the decimal point 6 places to the right. Therefore, we can rewrite the answer as:
B) 28,000,000
Recall that 10^6 means moving the decimal point 6 places to the right. Therefore, we can rewrite the answer as:
B) 28,000,000
Convert as indicated.
4.9 ft to centimeters
4.9 ft to centimeters
To convert from feet to centimeters, we need to use the conversion factor 1 ft = 30.48 cm.
So, to convert 4.9 ft to centimeters, we can multiply 4.9 by the conversion factor:
4.9 ft * 30.48 cm/1 ft = 149.352 cm
Therefore, 4.9 ft is equal to 149.352 cm.
So, to convert 4.9 ft to centimeters, we can multiply 4.9 by the conversion factor:
4.9 ft * 30.48 cm/1 ft = 149.352 cm
Therefore, 4.9 ft is equal to 149.352 cm.
Answers:
A)
12.4 cm
B)
147 cm
C)
124.5 cm
D)
192.9 cm
A)
12.4 cm
B)
147 cm
C)
124.5 cm
D)
192.9 cm
The correct answer is:
C) 124.5 cm
C) 124.5 cm
Use a proportion to solve the problem.
The ratio of the distances a 7-iron and a 5-iron will drive a golf ball is 5 to 6. If a golfer averages 177 yards with a 7-iron, how far should he average with a 5-iron?
Question 9 options:
A)
166 yards
B)
212.4 yards
C)
148 yards
D)
188 yards
The ratio of the distances a 7-iron and a 5-iron will drive a golf ball is 5 to 6. If a golfer averages 177 yards with a 7-iron, how far should he average with a 5-iron?
Question 9 options:
A)
166 yards
B)
212.4 yards
C)
148 yards
D)
188 yards
To solve this problem using a proportion, we can set up the following ratio:
7-iron distance / 5-iron distance = 5/6
Let's denote the unknown 5-iron distance as x. We are given that the 7-iron distance is 177 yards.
So, we can set up the proportion:
177 / x = 5 / 6
To solve for x, we can cross-multiply:
6 * 177 = 5 * x
1062 = 5x
Next, divide both sides by 5:
x = 1062 / 5
x = 212.4 yards
Therefore, the golfer should average 212.4 yards with a 5-iron.
So, the correct option is:
B) 212.4 yards
7-iron distance / 5-iron distance = 5/6
Let's denote the unknown 5-iron distance as x. We are given that the 7-iron distance is 177 yards.
So, we can set up the proportion:
177 / x = 5 / 6
To solve for x, we can cross-multiply:
6 * 177 = 5 * x
1062 = 5x
Next, divide both sides by 5:
x = 1062 / 5
x = 212.4 yards
Therefore, the golfer should average 212.4 yards with a 5-iron.
So, the correct option is:
B) 212.4 yards
Solve the problem.
Andrea's sleeping bag is designed for camping in temperatures of -3°C or warmer. For what Fahrenheit temperatures is her sleeping bag designed? Round to the nearest tenth of a degree.
Question 10 options:
A) 26.6° F or warmer
B) 52.2° F or warmer
C) -19.4° F or warmer
D) -33.7° F or warmer
Andrea's sleeping bag is designed for camping in temperatures of -3°C or warmer. For what Fahrenheit temperatures is her sleeping bag designed? Round to the nearest tenth of a degree.
Question 10 options:
A) 26.6° F or warmer
B) 52.2° F or warmer
C) -19.4° F or warmer
D) -33.7° F or warmer
To convert from Celsius to Fahrenheit, we can use the formula:
°F = (°C * 9/5) + 32
We are given that Andrea's sleeping bag is designed for temperatures of -3°C or warmer. Plugging -3°C into the formula, we get:
°F = (-3 * 9/5) + 32
°F = (-27/5) + 32
°F = -5.4 + 32
°F = 26.6
Therefore, Andrea's sleeping bag is designed for temperatures of 26.6°F or warmer.
So, the correct option is:
A) 26.6°F or warmer
°F = (°C * 9/5) + 32
We are given that Andrea's sleeping bag is designed for temperatures of -3°C or warmer. Plugging -3°C into the formula, we get:
°F = (-3 * 9/5) + 32
°F = (-27/5) + 32
°F = -5.4 + 32
°F = 26.6
Therefore, Andrea's sleeping bag is designed for temperatures of 26.6°F or warmer.
So, the correct option is:
A) 26.6°F or warmer
Solve the problem.
Matthew has $5500 invested in the stock market. This amounts to 10% of his total savings. How much has Matthew saved?
Question 11 options:
A) $55,010
B) $550,000
C) $55,000
D) $55,100
Matthew has $5500 invested in the stock market. This amounts to 10% of his total savings. How much has Matthew saved?
Question 11 options:
A) $55,010
B) $550,000
C) $55,000
D) $55,100
Let's denote the total savings of Matthew as x. We are given that $5500 represents 10% of his total savings, so we can set up the equation:
10% of x = $5500
To solve for x, we can start by converting 10% to a decimal by dividing by 100:
0.10 * x = $5500
Next, we can solve for x by dividing both sides of the equation by 0.10:
x = $5500 / 0.10
x = $55,000
Therefore, Matthew has saved $55,000.
So, the correct option is:
C) $55,000
10% of x = $5500
To solve for x, we can start by converting 10% to a decimal by dividing by 100:
0.10 * x = $5500
Next, we can solve for x by dividing both sides of the equation by 0.10:
x = $5500 / 0.10
x = $55,000
Therefore, Matthew has saved $55,000.
So, the correct option is:
C) $55,000
Find the circumference and area of a circle having the given diameter or radius. Use 3.14 for π. Round your results to the nearest tenth.
d = 33 yd
Question 12 options:
A) 51.8 yd; 3419.5 yd2
B) 103.6 yd; 854.9 yd2
C) 103.6 yd; 103.6 yd2
D) 51.8 yd; 207.2 yd2
d = 33 yd
Question 12 options:
A) 51.8 yd; 3419.5 yd2
B) 103.6 yd; 854.9 yd2
C) 103.6 yd; 103.6 yd2
D) 51.8 yd; 207.2 yd2
The formula for the circumference of a circle is C = π * d, where d is the diameter. To find the area of a circle, we use the formula A = π * r^2, where r is the radius (which is half the diameter).
Given that the diameter is 33 yd, we can calculate:
Circumference = π * d = 3.14 * 33 = 103.62 yd (rounded to the nearest tenth)
Radius = d / 2 = 33 / 2 = 16.5 yd
Area = π * r^2 = 3.14 * (16.5^2) = 854.91 yd^2 (rounded to the nearest tenth)
Therefore, the correct option is:
B) 103.6 yd; 854.9 yd^2
Given that the diameter is 33 yd, we can calculate:
Circumference = π * d = 3.14 * 33 = 103.62 yd (rounded to the nearest tenth)
Radius = d / 2 = 33 / 2 = 16.5 yd
Area = π * r^2 = 3.14 * (16.5^2) = 854.91 yd^2 (rounded to the nearest tenth)
Therefore, the correct option is:
B) 103.6 yd; 854.9 yd^2
Solve the problem. Round to the nearest tenth if necessary.
Last year, Maria earned $343 per week. This year, her salary increased to $379 per week. What is the percent of increase?
Question 13 options:
A)
89.5%
B)
10.5%
C)
9.5%
D)
90.5%
Last year, Maria earned $343 per week. This year, her salary increased to $379 per week. What is the percent of increase?
Question 13 options:
A)
89.5%
B)
10.5%
C)
9.5%
D)
90.5%
To find the percent increase, we can use the formula:
Percent Increase = (New Value - Old Value) / Old Value * 100
Given that Maria's old salary was $343 per week and her new salary is $379 per week, we can calculate the percent increase:
Percent Increase = (379 - 343) / 343 * 100
Percent Increase = 36 / 343 * 100
Percent Increase ≈ 10.5%
Therefore, the correct option is:
B) 10.5%
Percent Increase = (New Value - Old Value) / Old Value * 100
Given that Maria's old salary was $343 per week and her new salary is $379 per week, we can calculate the percent increase:
Percent Increase = (379 - 343) / 343 * 100
Percent Increase = 36 / 343 * 100
Percent Increase ≈ 10.5%
Therefore, the correct option is:
B) 10.5%
Evaluate the arithmetic expression by performing the operations in the appropriate order.
24 ÷ 4 ∙ (12 - 6)
Question 15 options:
A)
66
B)
36
C)
108
D)
78
24 ÷ 4 ∙ (12 - 6)
Question 15 options:
A)
66
B)
36
C)
108
D)
78
To evaluate the arithmetic expression by performing the operations in the appropriate order, we need to use the order of operations (also known as PEMDAS).
First, we need to evaluate the parentheses:
12 - 6 = 6
Next, we need to perform the division:
24 ÷ 4 = 6
Finally, we need to perform the multiplication:
6 ∙ 6 = 36
Therefore, the answer is:
B) 36
First, we need to evaluate the parentheses:
12 - 6 = 6
Next, we need to perform the division:
24 ÷ 4 = 6
Finally, we need to perform the multiplication:
6 ∙ 6 = 36
Therefore, the answer is:
B) 36
Find the volume of the specified solid. Use 3.14 as the approximate value of π, and round your answer to the nearest whole number.
A cone with height 9 cm and diameter 4 cm
Question 18 options:
A)
38 cm^3
B)
151 cm^3
C)
75 cm^3
D)
226 cm^3
A cone with height 9 cm and diameter 4 cm
Question 18 options:
A)
38 cm^3
B)
151 cm^3
C)
75 cm^3
D)
226 cm^3
The volume of a cone can be calculated using the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height.
Given that the diameter is 4 cm, we can find the radius by dividing the diameter by 2:
r = 4 cm / 2 = 2 cm
Next, we can substitute the values into the formula:
V = (1/3) * 3.14 * (2 cm)^2 * 9 cm
V ≈ (1/3) * 3.14 * 4 cm^2 * 9 cm
V ≈ 12.56 cm^2 * 9 cm
V ≈ 113.04 cm^3
Rounding to the nearest whole number, we have:
V ≈ 113 cm^3
Therefore, the correct option is:
None of the given options are correct.
Given that the diameter is 4 cm, we can find the radius by dividing the diameter by 2:
r = 4 cm / 2 = 2 cm
Next, we can substitute the values into the formula:
V = (1/3) * 3.14 * (2 cm)^2 * 9 cm
V ≈ (1/3) * 3.14 * 4 cm^2 * 9 cm
V ≈ 12.56 cm^2 * 9 cm
V ≈ 113.04 cm^3
Rounding to the nearest whole number, we have:
V ≈ 113 cm^3
Therefore, the correct option is:
None of the given options are correct.