NJGPA PRACTICE (Non Calculator Section)

• -4, 2, 6.

• -8, 0, 8.

• -2, 4, 48.

• -6, 0, 6.

Answer explanation

To find the zeros of f(x) = (x^2 + 2x - 8)(x - 6), set each factor to zero. The first factor gives x^2 + 2x - 8 = 0, which factors to (x - 2)(x + 4) = 0, yielding x = -4 and x = 2. The second factor gives x = 6. Thus, the zeros are -4, 2, and 6.

What is the x- and y- intercept of the line 6x + 4y = 48? Sketch the graph of the function.

• x-intercept is 6; y-intercept is 4

• x-intercept is 4; y-intercept is 6

• x-intercept is 8; y-intercept is 12

• x-intercept is 12; y-intercept is 8

Answer explanation

To find the x-intercept, set y=0: 6x=48, x=8. For the y-intercept, set x=0: 4y=48, y=12. Thus, the x-intercept is 8 and the y-intercept is 12, confirming the correct choice.

If rx - st = r, which expression represents x?

Answer explanation

To isolate x, start with rx - st = r. Rearranging gives rx = r + st. Dividing both sides by r yields x = (r + st)/r, which matches the correct choice: \(\frac{r + st}{r}\).

• h = 3VB

Answer explanation

To express h in terms of B and V, start with the volume formula V = (1/3)Bh. Rearranging gives h = 3V/B. Thus, the correct answer is h = \frac{3V}{B}.

• f(n) = -n(12n + 11) + 15

• f(n) = (-4n + 3)(3n + 5)

• f(n) = -(4n + 3)(3n + 5)

• f(n) = (4n + 3)(-3n + 5)

Answer explanation

The correct factorization is f(n) = (-4n + 3)(3n + 5). This reveals the zeros by setting each factor to zero: -4n + 3 = 0 and 3n + 5 = 0, leading to the solutions n = 3/4 and n = -5/3.

Answer explanation

To simplify (3x^5 + 8x^3) - (7x^2 - 6x^3), distribute the negative sign: 3x^5 + 8x^3 - 7x^2 + 6x^3. Combine like terms: 3x^5 + (8x^3 + 6x^3) - 7x^2 = 3x^5 + 14x^3 - 7x^2. Thus, the correct answer is 3x^5 + 14x^3 - 7x^2.

Answer explanation

Since triangles GHJ and PQR are similar, the ratio of the lengths of the sides corresponding to angle H and angle P can be used to find \tan H. Given the sides, \tan H = \frac{8}{15}, which is the correct choice.

Answer explanation

To simplify (2x^2 - 3x + 4) - (x^2 + 5x - 6), distribute the negative sign: 2x^2 - 3x + 4 - x^2 - 5x + 6. Combine like terms: (2x^2 - x^2) + (-3x - 5x) + (4 + 6) = x^2 - 8x + 10. Thus, the correct answer is x^2 - 8x + 10.

• x = 14

• x = -14

• x = -4

• x = 4

Answer explanation

To solve for x, subtract 2x from both sides: 3x - 2x + 5 = 9. This simplifies to x + 5 = 9. Next, subtract 5 from both sides: x = 4. Thus, the correct answer is x = 4.

Answer explanation

To simplify (5y^3 - 2y^2) + (3y^2 - 4y^3), combine like terms: (5y^3 - 4y^3) + (-2y^2 + 3y^2) = y^3 + y^2. Thus, the correct answer is y^3 + y^2.