Final Exam Study Guide

The given question asks for the expression "45/7" to be written as an improper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. In this case, the numerator is 45, which is greater than the denominator of 7. Therefore, the correct answer is "45/7".

To find 20% of a number, you multiply the number by 0.2. In this case, multiplying 180 by 0.2 gives us 36. Therefore, 36 is 20% of 180.

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To find the number of on-demand movies Joseph watched, we need to subtract the cost of the basic cable package from his total bill. His bill was $39.70 and the basic cable package cost $24.95, so the remaining amount ($39.70 - $24.95 = $14.75) must be the cost of the on-demand movies. Since each on-demand movie costs $2.95, we can divide the remaining amount by the cost per movie to find the number of movies watched ($14.75 / $2.95 = 5). Therefore, Joseph watched 5 on-demand movies.

The given expression is 4x^3/y. To simplify this expression, we can divide both the numerator and denominator by 4, giving us x^3/y. Therefore, the correct answer is x^3/y.

The given expression can be simplified as follows: 1 - 1 + 5/3 - 1/4. The first two terms cancel each other out (1 - 1 = 0). Then, we can find a common denominator for the remaining terms, which is 12. So, the expression becomes (20/12 - 3/12) = 17/12. Simplifying further, we get 1 and 5/12. However, the given answer is -1, which does not match the calculated value. Therefore, the given answer is incorrect.

The given set of inequalities states that x is greater than -12 and x is also less than -12. However, this is not possible as a number cannot be simultaneously greater than and less than -12. Therefore, the correct answer is x

The expression "Triple a quantity increased by ten" means that we need to multiply a quantity by 3 and then add 10 to it. The expression that represents this is 3(x + 10), where x is the quantity. This expression simplifies to 3x + 30, which means that the quantity is tripled and then 10 is added to it. Therefore, the correct answer is 3x + 30.

The given trinomial can be factored as (y + 5)(y - 7) by using the FOIL method. The First terms are y multiplied by y, which gives y^2. The Outer terms are y multiplied by -7, which gives -7y. The Inner terms are -5 multiplied by y, which gives -5y. And the Last terms are -5 multiplied by -7, which gives +35. Combining like terms, we get y^2 - 7y - 5y + 35, which simplifies to y^2 - 12y + 35. Therefore, the correct answer is (y + 5)(y - 7).

The given system of equations can be solved using the addition method. By multiplying the first equation by 3 and the second equation by 2, we can eliminate the y variable when we add the two equations together. This results in the equation 12x + 6y = 30. When we subtract this equation from the original second equation, 2x + 3y = 7, we get -10x = -23. Solving for x, we find that x = 2. Substituting this value back into the first equation, we can solve for y and find that y = 1. Therefore, the solution to the system of equations is x = 2 and y = 1.

The given expression is 8x - y + 13xy + 9. To combine like terms, we add or subtract the coefficients of the same variables. In this expression, the like terms are 8x and -13xy, as they both have the variable x. The coefficient of x in 8x is 8, and in -13xy it is -13. Therefore, when we combine these like terms, we get 8x - 13xy. The remaining terms -y and 9 do not have any like terms to combine with. Hence, the final expression after combining like terms is 8x - y - 13xy + 9.

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The given expression can be factored using the difference of two squares formula, which states that for any two terms a and b, (a^2 - b^2) can be factored as (a + b)(a - b). In this case, the terms are 2x and 3y, so the expression (2x + 3y)(2x - 3y) is the correct factorization.

Robyn exchanged $500 U.S. dollars when she arrived in New Zealand. The exchange rate was 1.4 New Zealand dollars per every 1 U.S. dollar. To find out how much she received in New Zealand dollars, we can multiply the amount she exchanged ($500) by the exchange rate (1.4). This gives us $700, which is the amount she received in New Zealand dollars.

To find the value of y that completes the ordered pair (1, ?) as a solution to the equation 2x + 5y = 12, we substitute x=1 into the equation. Plugging in x=1, we get 2(1) + 5y = 12. Simplifying this equation gives us 2 + 5y = 12. By subtracting 2 from both sides, we obtain 5y = 10. Dividing both sides by 5, we find that y = 2. Therefore, the correct answer is 2.

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The given expression can be factored by finding the greatest common factor (GCF) of all the terms. The GCF of 5x^2 and 5x^2 (2x - 7y) is 5x^2. Therefore, factoring out the GCF from the expression gives 5x^2 (2x - 7y).

To find g(3), we substitute the value of x as 3 in the given expression. Since the answer is -5, it means that g(3) is equal to -5.

To solve for x and y using substitution, we first solve the first equation for x in terms of y: x = 18 - 3y. Then, we substitute this expression for x into the second equation: 2(18 - 3y) + y = 11. Simplifying this equation, we get 36 - 6y + y = 11. Combining like terms, we have -5y = -25. Dividing both sides by -5, we find that y = 5. Substituting this value back into the first equation, we can solve for x: x = 18 - 3(5) = 18 - 15 = 3. Therefore, the solution is x = 3, y = 5.

The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (2, -3) and (-1, 4). Plugging these values into the formula, we get (-3 - 4) / (2 - (-1)) = -7 / 3. Therefore, the slope of the line passing through these points is -7/3.

The given expression is a fraction with two polynomials in the numerator and denominator. To simplify this expression, we need to factor both the numerator and denominator. After factoring, we can cancel out any common factors between the numerator and denominator. However, in this case, none of the answer choices match the simplified form of the expression. Therefore, the given correct answer is incorrect or incomplete.

The given expression can be factored using the slide and divide method. By multiplying the first terms of both binomials (2x and x), we get 2x^2. By multiplying the outer terms (-1 and x), we get -x. By multiplying the inner terms (2x and 7), we get 14x. Finally, by multiplying the last terms (-1 and 7), we get -7. Combining these terms, we get 2x^2 - x + 14x - 7, which simplifies to 2x^2 + 13x - 7. Therefore, the correct answer is (2x - 1)(x + 7).

The equation for the line in the given graph is y = 1/4x - 2. This can be determined by observing that the line has a positive slope (1/4) and intersects the y-axis at -2.