The question states that after 6 weeks the plant is 54 centimeters tall. Therefore, when w = 6, h(w) = 54. Plug in 6 for w in the answers to see in which answer h(w) equals the target number of 54. In (A) h(w) = 6(6) = 36. Eliminate (A). In (B), h(w) = 9(6) = 54. The correct answer is (B).

Because the operation between the parentheses is addition, the parentheses can be removed, and the resulting expression becomes 12x² + 4x + 5y + 3x² – 2x + 3y. Reorder the terms so that like terms are next to each other: 12x² + 3x² + 4x – 2x + 5y + 3y. Combine like terms to get 15x² + 2x + 8y. The correct answer is (D).

You do not know how the survey is conducted, nor do you know how many veterinarians were surveyed (it may be the case that only 8 were surveyed). Therefore, you cannot infer that the survey accurately measures all veterinarians’ beliefs about Royal Rat Rations. Choice (A) is not supported. First, you do not know what veterinarians believe in general, and second veterinarians may be recommending Royal Rat Rations for a reason other than its nutrition. Choice (B) is similarly not supported. Besides not knowing veterinarians’ beliefs, this choice assumes that no other rat food is acceptable. Choice (C) is not supported because you do not know the sample size of the survey, nor is there any indication that there is only one veterinarian who does not recommend Royal Rat Rations. Choice (D) is the credited response. You know the opinions only of the veterinarians surveyed by Royal Rat Rations.

Use a calculator to translate the fractions into decimals. ​\( \frac{1}{2}t+4=\frac{3}{4}t-5 \)​ becomes 0.5t + 4 = 0.75t – 5. Subtract 0.5t from both sides to get 4 = 0.25t – 5, and then add 5 to both sides. This results in 9 = 0.25t. Use a calculator to divide! t = 36; therefore, the correct answer is (D).

Taking the two  dogs together, Everett has 35 + 55 = 90 pounds of dog. Set up the following proportion to determine the lowest amount of water the dogs need per day: ​\( \frac{8.5ounces}{10lbs}=\frac{x}{90lbs} \)​. Cross-multiply to get 10x = 765, so x = 76.5. Multiply by 7 days to get the weekly amount of water the dogs need: 76.5 × 7 = 535.5 ounces, or approximately 536 ounces. Only (C) includes 536 as the low-end amount. Therefore, the correct answer is (C).