Answer:
a = 4/27 - b/81
Step-by-step explanation:
27a + 1/3 * b = 4
Subtract the term with b from both sides.
27a = 4 - 1/3 *b
Divide both sides by 27.
a = 4/27 - 1/81 * b
a = 4/27 - b/81
Answer: 2 hr.
Explanation: Think back to rate of change. <em>d</em> = <em>rt</em>, <em>r</em> = <em>d/t</em>, <em>t</em> = <em>d/r</em>. In this case, we will be using <em>d</em> = <em>rt</em>. Mph would be <em>r</em>, rate, so you would categorize 15 mph and 8 mph under rate. <em>t</em> should represent the time each cyclist traveled. Tracey's and Emma's distance, <em>d</em>, would be the same as their mph, hence Tracey's being 15<em>t</em> and Emma's would be 8<em>t</em>. When you add Tracey's distance plus Emma's distance, you end up with 46 mi. Now, you need to combine like terms, which should look like 15<em>t</em> + 8<em>t </em> = 46. Add 15 and 8 to get 23, so it should be 23<em>t</em> = 46 now. Then, divide both sides of the equation by 23 and now you should have your answer, <em>t</em> = 2 hr.
Answer: 98.1%
Explanation:
A 10% sale means that the post-sale price of the item is now 90%, or 0.9 of the original cost of the item. We then apply 9% sales tax by multiplying the 0.9 by 109%, or 1.09. 0.9 * 1.09 = .981, so the total cost of the item is 98.1% of the original pre-sale sticker price.
For percentage problems that do not deal with a specific starting number, it is always helpful to plug in 100 for the starting number. Here, we would then have a post-sale price of 90 dollars, and if we calculate the sales tax for the 90-dollar item it would be 90 * 0.09 = $8.10. THis gives us a total cost of 90 + 8.10 = $98.10, or 98.1% of the original 100-dollar price.
Question:
Simplify the following expression:
÷
A.1/12
B. 1/64
C.12
D.64
Answer:
B. 1/64
