19) 48 alligators; 7/8 of the alligators were asleep. How many were not asleep?
8/8 - 7/8 = 1/8
48 * 1/8 = 48/8 = 6 alligators were not asleep.
20) 2/3 of the student population participated. 1,500 is the student population of the school. HOw many attended the bike rally?
1500 * 2/3 = 1500*2 / 3= 3000 / 3 = 1000 students attended.
21) 18 times at bat:
Kayla 5/6 of the time = 18 * 5/6 = 18*5 / 6 = 90/6 = 15 hits
Tia 8/9 of the time = 18 * 8/9 = 18*8 / 9 = 144/9 = 16 hits
Tia got more hits.
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Answer:
1
Step-by-step explanation:
You can't construct more than 1 triangle. If either of the angles shift, the triangle won't close. And a equilateral triangle must close to be considered, well, a triangle.
The answer is 10 2/3, 5
Proof:
Solve the following system:
{x/2 + y/3 = 7 | (equation 1)
{x/4 + (2 y)/3 = 6 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{x/2 + y/3 = 7 | (equation 1)
{0 x+y/2 = 5/2 | (equation 2)
Multiply equation 1 by 6:
{3 x + 2 y = 42 | (equation 1)
{0 x+y/2 = 5/2 | (equation 2)
Multiply equation 2 by 2:
{3 x + 2 y = 42 | (equation 1)
{0 x+y = 5 | (equation 2)
Subtract 2 × (equation 2) from equation 1:
{3 x+0 y = 32 | (equation 1)
{0 x+y = 5 | (equation 2)
Divide equation 1 by 3:
{x+0 y = 32/3 | (equation 1)
{0 x+y = 5 | (equation 2)
Collect results:
Answer: {x = 10 2/3, y = 5
