TEAS Test Math Questions - Nurselytic

Correct Answer: C

Rationale:
To solve for x, add 5 to both sides of the equation: 3x - 5 + 5 = 16 + 5, which simplifies to 3x = 21. Next, divide both sides by 3: x = 21 · 3 = 7.
Therefore, the correct answer is x = 7, making option A the correct choice. Option C, '8,' is incorrect as it is not the solution obtained from the correct calculations. Options B and D, '5' and '9,' are also incorrect and not the solution to the given equation.

Correct Answer: B

Rationale: From Equation 1: 2x + y = 0. Solve for y: y = -2x. Substitute y = -2x into Equation 2: x - 2(-2x) = 8. Simplify to x + 4x = 8, then 5x = 8, and x = 8 · 5 = 1.6. Substitute x = 1.6 back into y = -2x to find y = -3.2.
Therefore, one solution is (1.6, -3.2).
To find the second solution, use -1.6 for x to get (-1.6, 3.2). Thus, the correct answer is B, representing the solutions (1.8, -3.6) and (-1.8, 3.6).

Choices A, C, and D contain incorrect values that do not match the solutions derived from solving the system of equations.

Correct Answer: D

Rationale:
To find the fourth vertex of a parallelogram, we can use the properties of a parallelogram. Opposite sides of a parallelogram are parallel and equal in length.
Therefore, we can determine the fourth vertex by extending the line formed by the first two points. If we extend the line from (1, 2) to (3, 4), we find that it has a slope of 1. This means that extending the line from (3, 4) by the same slope will give us the fourth vertex. By adding 2 units to both x and y coordinates of (5, 6), we get (7, 8) as the coordinates of the fourth vertex.
Therefore, the correct answer is (7, 8).

Choices A, B, and C are incorrect as they do not satisfy the properties of a parallelogram and the given coordinate points.

Correct Answer: C

Rationale:
To create a 5:1 solution in 2.5 liters, 0.5 liters are needed for HCl, which translates to 5 grams. The correct answer is 5 grams, as this amount corresponds to the 5:1 ratio specified in the solution.

Choices A, B, and D are incorrect because they do not align with the 5:1 ratio and the volume of the solution.

Correct Answer: A

Rationale:
To multiply fractions, multiply the numerators together and the denominators together. For (3/5) * (5/8), you get (3*5) / (5*8) = 15 / 40, which simplifies to 3/8.
Therefore, the correct answer is A.
Choice B (3/5) is incorrect as it is one of the original fractions being multiplied.
Choice C (15/40) is the result of the multiplication but not simplified to its lowest terms.
Choice D (3/30) is incorrect as the numerator is not the result of multiplying 3 and 5 together.