Alg Equivalency Test

Answer explanation

To simplify the expression, distribute: 1.5(4j-10k) = 6j - 15k and -2.5(8j+6k) = -20j - 15k. Combine like terms: (6j - 20j) + (-15k - 15k) = -14j - 30k. Thus, the correct answer is -14j - 30k.

Answer explanation

To simplify \( \sqrt{50} \), we can factor it as \( \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2} \). Thus, the equivalent expression is \( 5\sqrt{2} \).

Answer explanation

To factor the expression 5x^2 - 30x - 80, we can use the factorization method. The correct factor is x - 8, as substituting x = 8 makes the expression equal to zero, confirming it is a root.

Answer explanation

To find the equivalent expression, apply the distributive property: (2k^2)(3k) + (2k^2)(-4) + (-3m)(3k) + (-3m)(-4). This simplifies to 6k^3 - 8k^2 - 9km + 12m, matching the correct choice.

Answer explanation

To simplify the expression, we recognize that multiplying by a positive real number and adjusting exponents leads us to the equivalent form. The correct choice is \(\tfrac{1}{3}x^{15}\), which matches the required transformation.

Answer explanation

The inequality y > 5x - 3 indicates that we are looking for all points above the line y = 5x - 3. Since the inequality is strict (greater than), the line itself is not included, hence it is represented as a dashed line.

Answer explanation

To solve (2x+1)^2=25, take the square root: 2x+1=5 or 2x+1=-5. Solving these gives x=2 and x=-3. Thus, the correct answers are x=-3 and x=2.

Which graph best represents the solution set for the system of inequalities?

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Answer explanation

Graph A correctly represents the solution set for the system of inequalities, as it accurately shows the regions defined by the inequalities, including the correct boundaries and shading.

Answer explanation

The expression 6x^2 + 3x - 9 can be factored as 3(2x^2 + x - 3) and 3(2x + 3)(x - 1). The other options do not simplify to the original expression.

Answer explanation

To simplify \( \frac{(6y^3)^{-2}}{y} \), first rewrite \( (6y^3)^{-2} \) as \( \frac{1}{(6y^3)^2} = \frac{1}{36y^6} \). Then, divide by \( y \): \( \frac{1}{36y^6} \div y = \frac{1}{36y^7} \). Thus, the correct answer is \( \frac{1}{36y^7} \).