Answer: a) base = 1 ft b) height = 4 ft
<u>Step-by-step explanation:</u>
Set this up as a right triangle where base = x, height = 2x + 2, and hypotenuse (length of the ladder) = 13
Use Pythagorean Theorem to create a quadratic equation, factor, then apply the Zero Product Property to solve for x.
(x)² + (2x + 2)² = 13²
x² + 4x² + 8x + 4 = 169
5x² + 8x - 165 = 0
(5x + 13) (x - 1) = 0
x = -13/5 x = 1
We know that distance cannot be negative so disregard x = -13/5.
The only valid answer is x = 1
base = x --> x = 1
height = 2x + 2 --> 2(1) + 2 = 4
Answer:
Room and board
30%
Step-by-step explanation:
If you look at the numbers in the table, you can easily see Room and board is the largest expense, with $127.50, three times more than the second place.
Now, to find the percent of that expense vs her income we just have to divide this big expense ($127.50) by the total income she has ($425).
% = $127.50 / $425 = 30%
So, that expense is 30% of her income, that's a big chunk, but it's normal for lodging expenses.
You must find the factors of each number...
9 = 1, 3, 3, 9
6 = 1, 2, 3, 6
Next, determine the common multiple...
9 = 1, 3, 3, 9
6 = 1, 2, 3, 6
Therefore, the most groups Lavinia can make without any glasses or mugs left to spare is 3.