I.E.D. Warm-up Quiz # 6 Spring 2013

Explanation
The given expression is a combination of like terms. Like terms have the same variables raised to the same powers. In the expression 4y + 7x + 3y - 4x, the terms 4y and 3y are like terms because they both have the variable y raised to the power of 1. Similarly, the terms 7x and -4x are like terms because they both have the variable x raised to the power of 1. By combining the like terms, we get 7y + 3x - 4x, which simplifies to 7y + 3x. Therefore, the correct answer is 3x + 7y.

Explanation
To find the slope of a line passing through two points, we can use the formula (y2 - y1) / (x2 - x1). Plugging in the values from the given points, we get (-7 - (-3)) / (-2 - 8), which simplifies to -4 / -10. This can be further simplified to 2 / 5. Therefore, the slope of the line is 2/5.

Explanation
The sentence states that the opposite of three times a number is more than 75. The word "opposite" indicates that the sign of the inequality should be reversed. Since three times a number is positive, the opposite of it would be negative. Therefore, the correct inequality is -3x > 75.

Explanation
The correct answer is 12, 14, 16. These three consecutive even integers add up to 42. The first even integer is 12, the next even integer is 14, and the third even integer is 16. When we add these three numbers together (12 + 14 + 16), the sum is indeed 42.

Explanation
The area of a triangle is calculated by multiplying the base and the height and then dividing the result by 2. In this case, the base is 2x + 8 and the height is 4. So, multiplying the base and the height gives (2x + 8) * 4 = 8x + 32. Dividing this result by 2 gives the area of the triangle, which is 4x + 16.

Explanation
The value of x in triangle ABC is 30.

Explanation
To convert inches to centimeters, you need to multiply the number of inches by 2.54. In this case, 7 inches multiplied by 2.54 equals 17.78 centimeters, which can be rounded to 17.8 cm. Therefore, the correct answer is 17.8 cm.

Explanation
The most reasonable weight of a car is 4 tons because cars typically weigh several thousand pounds, and a ton is equivalent to 2,000 pounds. Therefore, a car weighing 4 tons would be within a reasonable range for a standard-sized car.

Explanation
The given equation is a quadratic equation in the form of ax^2 + bx + c. To factorize the equation, we need to find two binomials that multiply together to give us the given equation. By using the distributive property, we can expand (2x + 5)(x - 3) to get 2x^2 - 6x + 5x - 15. Simplifying further, we get 2x^2 - x - 15, which matches the given equation. Therefore, (2x + 5)(x - 3) is the correct factorization of the equation.

Explanation
The given equation is -9. To factor this equation, we need to find two numbers that multiply to give -9 and add up to 0. The numbers that satisfy this condition are -3 and 3. Therefore, the correct answer is (x - 3)(x + 3) because when we multiply these factors, we get x^2 - 9, which is equal to -9.

Explanation
The given equation is a quadratic equation in the form of ax^2 + bx + c. To factor the equation, we need to find two binomials that when multiplied together, result in the original equation. In this case, the correct answer is (2x + 5)(x + 3) because when we multiply these two binomials using the distributive property, we get 2x^2 + 6x + 5x + 15, which simplifies to 2x^2 + 11x + 15, matching the original equation.

Explanation
The given equation states that if a certain condition is met, then x equals -10. Without knowing the condition, we can conclude that when this condition is satisfied, the value of x will be -10.