For what values of x is the following statement true?
log42x2 = 1 – log422x – 1
- -2, 4
- 2, -4
- -1, -3
- 1, 3
- 1,-3
Set 15
Batting Average Improvement
Mike enters the Vermilion game with a batting average of .274. After going 3-for-4 in the game, his average has gone up to .289. How many hits did he have for the season before the game started?
Three Equations, Three Unknowns
| nx | + | y | = | 1 | ||
| ny | + | z | = | 1 | ||
| x | + | nz | = | 1 |
If n is a real number, then the simultaneous system to the right has no solution if and only if n is equal to:
- -1
- 0
- 1
- 0 or 1
- ½
Miller, Pounds and Kilos
A Dutch miller keeps 1/10 of the grain he grinds as his fee. How many pounds of grain must Henk de Bruyn take to the miller so that he will come home with exactly 100 kilos of ground grain?
Difference of Squares
Show that x4 – 1 is divisible by 16 whenever x is an odd integer.
Factoring by Grouping
Factor completely: ac + a + bc – bd – ad + b.
Factoring Backwards (a – b)2
Find the value of this expression without using a calculator and without doing a lot of work. (Use your algebra eyes to see what’s going on.)
(1379)2 – (2) · (1379) · (379) + (379)2
Visible Cubes in Big Cube
Suppose n3 little cubes have been assembled into one large cube. Find a formula for the maximum number of little cubes that can be seen from a single location.
Maximum Product, Use All Digits
Using each of the 10 digits once, find two 5-digit numbers with the largest possible product.
Three Integers, Product is Prime
Find three integers in arithmetic progression whose product is prime.