(a) One unique triangle. This is an equilateral triangle since all sides are the same length. Through the SSS property, we can prove that only one triangle is possible here.
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(b) Cannot make a triangle. The triangle inequality theorem says that adding any two sides of a triangle must result in a value larger than the third side. Add up the first two sides (1 and 2) to get 1+2 = 3, which is not larger than the third side (3 units long). I recommend cutting out strips of paper that are 1 inch, 2 inches and 3 inches long, and trying to form a triangle. You'll find that a triangle is not possible. The 1 inch and 2 inch strips will line up to form a straight line that is 3 inches long, and basically you have a flat line (or a triangle with area 0)
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(c) More than one triangle. The angles add up to 180 since 35+60+85, so we can form a triangle. It turns out we can form infinitely many of them. The AA (angle angle) similarity theorem allows us to scale any triangle to make it larger or smaller compared to the original.
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(d) Cannot make a triangle. I'm assuming the 509 should actually be 50°. If so, then a triangle is not possible because the three angles (50, 50, 50) do not add to 180. We have instead 50+50+50 = 150. For any triangle, the three angles must always add to 180 degrees.
<h3>
Answer: </h3><h3>Fred has <u>20 students</u> and Lee has <u>22 students</u></h3>
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Work Shown:
L = number of students in Lee's class
F = number of students in Fred's class
Lee has 1.1 times as many students compared to Fred
This means we have this equation
L = 1.1F
Whatever the value of F is, we multiply that by 1.1 to get the value of L
The two amounts L and F add to 42 total students
L+F = 42
1.1F + F = 42 .... replace L with 1.1F
2.1F = 42
F = 42/(2.1)
F = 20 .... Fred has 20 students
L = 1.1*F
L = 1.1*20
L = 22 .... Lee has 22 students
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Check:
L+F = 22+20 = 42
this confirms the answer
4t+(-7t) is the same as you saying 4t-7t, so 4t-7t= -3t. 9=-3t, divide each side by -3 and t is equal to -3
Answer:
Each minute Seung fills one less bag than Razi.
Step-by-step explanation:
Find the rate of change.
<u>Razi's rate of change:</u>
<u>Seung's rate of change:</u>
This means Razi packs 4 bags per minute, Seung packs 3 bags per minute.
<u>Difference</u> = 4 - 3 = 1 bag
Each minute Seung fills one less bag than Razi.
Step-by-step explanation:
= 10x - 5 + 3x - 2
= (10 + 3)x + (-5 - 2)
= 13x - 7
