9th Grade Math Quiz

Substitute x with -3 in the equation. Calculate the result following the order of operations (PEMDAS). 2(-3)² + 5(-3) - 1 = 18 - 15 - 1 = -16.

The slope formula is (y2 - y1) / (x2 - x1). Substitute the given points into the formula: (9 - 5) / (4 - 2) = 4 / 2 = 2.

Find the largest perfect square that divides 72, which is 36. Rewrite 72 as 36 * 2. The square root of 36 is 6, so the simplified expression is 6√2.

Subtract 3x from both sides: -7 = 2x + 11. Subtract 11 from both sides: -18 = 2x. Divide both sides by 2: x = -9.

The formula for the area of a circle is A = πr². Substitute the given area into the formula: 36π = πr². Divide both sides by π: 36 = r². Take the square root of both sides: r = 6.

This is a difference of squares. The formula for factoring a difference of squares is a² - b² = (a + b)(a - b). In this case, a = x and b = 3.

You can solve this system using substitution or elimination. One way is to add the two equations together to eliminate y: 3x = 6. Divide both sides by 3: x = 2. Substitute x = 2 into one of the original equations to find y: 2(2) + y = 5, so y = 1.

Rewrite 16 as a power of 2: 2^(x+1) = 2^4. Since the bases are the same, the exponents must be equal: x + 1 = 4. Subtract 1 from both sides: x = 3.

The midpoint formula is ((x1 + x2)/2, (y1 + y2)/2). Substitute the given points into the formula: ((-4 + 6)/2, (2 + 8)/2) = (1, 5).

Use the Pythagorean theorem: a² + b² = c², where a and b are the legs and c is the hypotenuse. Substitute the given values: 6² + b² = 10². Simplify: 36 + b² = 100. Subtract 36 from both sides: b² = 64. Take the square root of both sides: b = 8.