Advanced Algebra 1 Review Quiz

1.

4k + 39 = 7k + 6 Solve for k

Explanation
The given equation is a linear equation in terms of k. To solve for k, we need to isolate it on one side of the equation. By subtracting 4k from both sides, we get 39 = 3k + 6. Then, by subtracting 6 from both sides, we get 33 = 3k. Finally, by dividing both sides by 3, we find that k = 11. Therefore, the answer is k = 11, and it is also correct to say that 11 = k.

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2.

53.84 - 0.32s = 48.17 - 0.18s

Explanation
The given equation states that when subtracting 0.32s from 53.84, it is equal to subtracting 0.18s from 48.17. To find the value of s, we can solve for it by isolating the variable. By subtracting 48.17 from both sides of the equation and combining like terms, we get -0.32s + 0.18s = 53.84 - 48.17. Simplifying further, we have -0.14s = 5.67. To solve for s, we divide both sides of the equation by -0.14, resulting in s = 5.67 / -0.14 = 40.5. Therefore, the correct answer is s = 40.5, and we can also express it as 40.5 = s.

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3.

K/4 - k/6 = 0.5Solve for k

Explanation
The equation k/4 - k/6 = 0.5 can be solved by finding a common denominator for the fractions. The common denominator is 12. Multiplying both sides of the equation by 12, we get 3k - 2k = 6. Simplifying, we have k = 6. Therefore, the answer is k = 6, which is equivalent to 6 = k.

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4.

Which of the following is the opposite of 2/9?

A.

-2/-9
B.

-2/9
C.

9/2
D.

-9/2

Correct Answer
B. -2/9

Explanation
The opposite of a fraction is obtained by changing the sign of the numerator or the denominator, or both. In this case, the given fraction is 2/9. To find its opposite, we change the sign of either the numerator or the denominator, or both. Changing the sign of the numerator gives -2/9, which is the opposite of 2/9.

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5.

8x - (3x - 7)Simplify

Correct Answer
5x + 7

Explanation
To simplify the expression 8x - (3x - 7), we need to distribute the negative sign to both terms inside the parentheses. This gives us 8x - 3x + 7. Combining like terms, we get 5x + 7. Therefore, the simplified expression is 5x + 7.

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6.

-2( 7h - 1) + hSimplify

Correct Answer
-13h + 2

Explanation
To simplify the given expression, we can start by distributing the -2 to both terms inside the parentheses. This gives us -2 * 7h and -2 * -1, which simplifies to -14h and +2, respectively. Then, we can combine like terms by adding the -14h and +2. This gives us the final simplified expression of -14h + 2. Therefore, the correct answer is -14h + 2.

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7.

-7x greater than or equal to 126Solve

Correct Answer
x is less than or equal to -18
-18 is greater than or equal to x

Explanation
The given answer states that x is less than or equal to -18 and -18 is greater than or equal to x. This means that x can take any value that is less than or equal to -18, and -18 can take any value that is greater than or equal to x. Therefore, the answer is correct as it satisfies the original inequality -7x ≥ 126.

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8.

0.3n + 7 + -7 greater than or equal to 70 + -7

Correct Answer
n is greater than or equal to 210

Explanation
The given equation states that 0.3n + 7 + -7 is greater than or equal to 70 + -7. By simplifying the equation, we can cancel out the +7 and -7 terms on both sides. This leaves us with 0.3n is greater than or equal to 70. By dividing both sides of the equation by 0.3, we find that n is greater than or equal to 210.

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9.

(1/12) T + (1/15) T = 129

Correct Answer
T = 860

Explanation
The equation given is a simple linear equation with one variable, T. By combining the fractions and multiplying both sides of the equation by the least common denominator, we can simplify the equation to 27T/180 = 129. By cross-multiplying and solving for T, we get T = 860.

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10.

X/6 + 17/36 - x/4 = -7

Correct Answer
x = 269/3
x = (approx.) 89.67

Explanation
The equation x/6 + 17/36 - x/4 = -7 can be solved by finding a common denominator for the fractions and combining like terms. After simplifying the equation, we can solve for x by isolating it on one side. The solutions are x = 269/3 and x ≈ 89.67.

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11.

Use to answer 11-13A TV that normally sells for $400 is on sale for $340. The tax on the reduced price is $23.80, so the total cost with tax is $363.80 What is the Discount rate?

Correct Answer
Discount rate = .15
or 15%

Explanation
The discount rate can be calculated by finding the difference between the original price and the sale price, which in this case is $400 - $340 = $60. The tax on the reduced price is $23.80, so the total cost with tax is $363.80. To find the discount rate, we divide the discount amount ($60) by the total cost with tax ($363.80) and multiply by 100 to get a percentage. Therefore, the discount rate is ($60 / $363.80) * 100 = 16.47%, which can be approximated to 15%.

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12.

What is the tax rate?

Correct Answer
Tax rate = .07
or 7%

Explanation
The tax rate is given as .07 or 7%. This means that for every dollar of taxable income, 7 cents or 7% will be paid as tax.

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13.

Including tax, how much would a customer save by buying the the TV on sale?

Correct Answer
$64.20

Explanation
A customer would save $64.20 by buying the TV on sale. This means that the sale price of the TV is $64.20 less than the original price, including tax. Therefore, if the customer purchases the TV on sale, they would pay $64.20 less than they would if they bought it at the original price.

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14.

Determine the probability of selecting each of the following cards...A. the ace of spadesB. a 5C. a 5 or a 9

Correct Answer
A. 1/52 B. 1/13 C. 2/13

Explanation
The probability of selecting the ace of spades is 1 out of 52 because there is only one ace of spades in a standard deck of 52 cards. The probability of selecting a 5 is 1 out of 13 because there are four 5s in a deck of 52 cards. The probability of selecting a 5 or a 9 is 2 out of 13 because there are four 5s and four 9s in a deck of 52 cards.

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15.

A dishwasher normally costs $320, but it's on sale for 15% off. What was the sale price?

Correct Answer
$272

Explanation
The sale price of the dishwasher can be found by subtracting the discount from the original price. In this case, the discount is 15% of $320, which is $48. Subtracting $48 from $320 gives us a sale price of $272.

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16.

7% of what number is 91?

Correct Answer
1300

Explanation
To find 7% of a number, we can multiply the number by 0.07. In this case, if we multiply 1300 by 0.07, we get 91. Therefore, 7% of 1300 is indeed 91.

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17.

If the temperature is -12, by how much will it need to increase to reach 14?

Correct Answer
26
26 degrees
twenty-six
twenty-six degrees

Explanation
The question asks for the amount by which the temperature needs to increase to reach 14. The given answer options all indicate an increase of 26 degrees, which is the correct answer.

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