ACT Math Practice

The square root of 63 is 7.937. Both 6 and 7 are less than that, therefore 8 is the smallest integer greater than 7.937.

If the motorcycle is losing 5 ounces every minute, it is losing 300 ounces per hour since there are 60 minutes in an hour. (5 × 60 = 300). Since the motorcycle can hold 600 fluid ounces total it will take 2 hours for the motorcycle to run out of oil (600 ÷ 300 = 2). If the motorcycle is traveling at 45 mph, in two hours it will have traveled 90 miles total. (45 𝑚𝑖𝑙𝑒𝑠 × 2 ℎ𝑜𝑢𝑟𝑠 = 90 𝑚𝑖𝑙𝑒𝑠 𝑡𝑜𝑡𝑎𝑙)

Since Josie started with 65 wreaths, and had 57 left after day one, she sold 8 wreaths on day one (65 − 57 = 8). After day two, she sold 8 wreaths on day two (57 − 49 = 8). Since Josie had 41 wreaths left after day three, she sold 8 wreaths on day three (49 − 41 = 8). Continuing this pattern, of selling 8 wreaths per day, at the end of day four Josie would have 41-8= 33 wreaths. After day five, 33-8= 25 wreaths. Finally, at the end of day six, Josie would have 25-8= 17 wreaths. Thus, Josie would have 17 wreaths left after day six.

To solve for 𝑥 we need to distribute to eliminate parentheses. After distributing, we have 3𝑥 − 24 + 𝑥 = 24. Next, we can combine the like terms on the left side of the equation. The 3𝑥 and 𝑥 can be combined to have 4𝑥 − 24 = 24. We use inverse operations to eliminate the − 24, so we add 24 to both sides which gives us 4𝑥 = 48. We use inverse operations again and divide both sides by 4 to get x by itself. This gives us 𝑥 = 12.

Using the properties of parallelograms, we know that ∠𝐹 is equal to ∠𝐷, so ∠𝐷 = 50°. We must then know that the sum of the angles of a triangle always equals 180°. This means ∠𝐶 + ∠𝐷 + ∠𝐸 = 180°. We will then substitute the measure of our angles into this equation to get 54° + 50° + ∠𝐸 = 180°. At this point, we will solve our equation to find ∠𝐸 = 76°.