1.
Correct Answer
A. [ 4, -1]
[-12 4]
Explanation
The given answer is a 2x2 matrix that represents a transformation of a 2D vector. The first column of the matrix corresponds to the transformation of the x-coordinate of the vector, and the second column corresponds to the transformation of the y-coordinate. In this case, the matrix represents a transformation that scales the x-coordinate by a factor of 4 and the y-coordinate by a factor of -1. Therefore, the correct answer is [ 4, -1] [-12 4].
2.
Question No Image
Correct Answer
C. [-6 -9]
[2 3]
Explanation
The answer is [-6 -9] because it is the only option that matches the pattern of the given matrices. The first row of the answer matrix is obtained by subtracting the corresponding elements in the first row of the given matrices. The second row of the answer matrix is obtained by subtracting the corresponding elements in the second row of the given matrices. This pattern is consistent with the given matrices, making [-6 -9] the correct answer.
3.
Question No Image
Correct Answer
B. [-5 -2 -4]
[-13 -12 8]
Explanation
The given answer is the third row of the matrix. In the matrix, each row represents a set of coordinates in 3D space. The answer represents the coordinates (-5, -2, -4).
4.
Question No Image
Correct Answer
B. [8 -8]
[12 -3]
[-16 23]
5.
Question No Image
Correct Answer
B. [4 11]
[12 3]
Explanation
The answer [4 11] [12 3] is the correct answer because it is the only pair of numbers that is not in the original matrix. The original matrix contains the pairs [5 -4], [0 6], [12 3], and [6 0]. Therefore, the pair [4 11] [12 3] is the only option that is not already included in the matrix.
6.
Factor the trinomial
Correct Answer
C. (x + 1)(x + 4)
Explanation
The given trinomial can be factored as (x + 1)(x + 4). This can be determined by using the FOIL method, which states that when multiplying two binomials, the product is equal to the sum of the products of the First terms, Outer terms, Inner terms, and Last terms. In this case, the First terms are x and x, the Outer terms are x and 4, the Inner terms are 1 and x, and the Last terms are 1 and 4. When simplified, the sum of these products is x^2 + 5x + 4, which matches the original trinomial. Therefore, (x + 1)(x + 4) is the correct answer.
7.
Factor the trinomial
Correct Answer
A. (x - 3)(x - 1)
Explanation
The given trinomial can be factored as (x - 3)(x - 1). This can be determined by using the FOIL method, which stands for First, Outer, Inner, Last. When we multiply the first terms of each binomial (x and x), we get x^2. When we multiply the outer terms (-3 and x), we get -3x. When we multiply the inner terms (x and -1), we get -x. And when we multiply the last terms (-3 and -1), we get 3. Combining these terms, we get x^2 - 3x - x + 3, which simplifies to x^2 - 4x + 3. Therefore, the correct answer is (x - 3)(x - 1).
8.
Factor the trinomial
Correct Answer
D. (x - 2)(x - 6)
Explanation
The trinomial can be factored as (x - 2)(x - 6). This is the correct answer because it is the only option that results in a trinomial when multiplied out. The other options either do not result in a trinomial or do not match the given trinomial.
9.
Factor the trinomial
Correct Answer
A. Cannot be factored
Explanation
The given trinomial cannot be factored because it does not have any common factors or any factors that can be multiplied to give the trinomial.
10.
Factor the trinomial
Correct Answer
C. (p - 2)(p - 3)
Explanation
The given trinomial can be factored as (p - 2)(p - 3) because it has two terms with a common factor of (p - 2) and (p - 3).
11.
Solve the equation.
Correct Answer
C. {4, -2}
Explanation
The answer {4, -2} is the solution to the equation. By substituting the values of x and y from the answer into the equation, we can verify that it satisfies the equation.
12.
Solve the equation.
Correct Answer
A. {7, 7}
Explanation
The equation is asking for the solution to the equation, but it is not clear what the equation is. Therefore, it is not possible to provide an explanation for the given answer.
13.
Solve the equation.
Correct Answer
C. {-3, 1}
Explanation
The given equation is solved by finding the set of values that satisfy it. By plugging in the values from each set, it can be observed that only the set {-3, 1} satisfies the equation. Therefore, the answer is {-3, 1}.
14.
Solve the equation.
(a + 1) (a + 2) = 0
Correct Answer
B. {-1, -2}
Explanation
The equation (a + 1) (a + 2) = 0 can be solved by setting each factor equal to zero. Therefore, a + 1 = 0 or a + 2 = 0. Solving these equations, we find that a = -1 or a = -2. Thus, the answer is {-1, -2}.
15.
Solve the equation.
y = x^2 + 6x + 8
Correct Answer
D. {-4, -2}
Explanation
The answer {-4, -2} is the solution to the equation y = x^2 + 6x + 8. To find the solution, we can substitute the values of x from the answer choices into the equation and check if they satisfy the equation. By substituting -4 and -2 into the equation, we get y = (-4)^2 + 6(-4) + 8 = 16 - 24 + 8 = 0, and y = (-2)^2 + 6(-2) + 8 = 4 - 12 + 8 = 0. Therefore, {-4, -2} is the correct answer.