Step-by-step explanation:
The Triangle Sum Theorem states that the interior angles of a triangle add up to 180 degrees. A square for an angle symbolizes that the angle is 90 °, as is the case with angle ∠ACB.
Therefore, as ∠CAB = 2x and ∠ABC = 3x, and angles ∠ACB, ∠CAB, and ∠ABC make up the interior angles of the triangle, we can say that ∠ACB + ∠CAB + ∠ABC = 180, so 90 + 2x + 3x = 180
90 + 2x + 3x = 180
90 + 5x = 180
subtract 90 from both sides to separate the x and its coefficient
5x = 90
divide both sides by 5 to separate the x
x = 18
(a) ∠CAB = 2x = 18(2) = 36
(b) ∠ABC = 3x = 18(3) = 54
(c) Any triangle with a 90° angle is called a right triangle. This has a 90° triangle, and is therefore a right triangle. Similarly, a 90° angle in a triangle is called a right angle.
Answer:
at least three are dimes
so we have 20 coins with a total of 3.50
if the rest are all quarters then there would be 4*3+2=14 but we need 20
so we are 6 short
we must have dimes in multiples of 5
12 q + 5 d=3.50 but only 17 coins
10q +10 dimes=3.50 with 20 coins
10 q +13 dimes total
algebraic solution
d+q=23
25q+10d=380
d=23-q
Consider the attached tree.
You start from the root, and with each level you create a sub-branch for each of the choices you have.
So, the root has two children, white and multigrain bread.
Each of those children has three children, because you have three meat choices
Each of those children has two children, because you have two cheese choices.
Then, you identify all the sandwiches by choosing a leaf, and read the label that lead you there.
For example, leaf number 4 represents a sandwich with white bread, turkey and provolone.
Yes, because 11 2/3 is rounded to 12. and 2 5/6 is rounded to 3. 12 divided by 3 is 4. 4 2/17 is rounded to 4. 4 =4
Chance of a 2: 1/10. Chance of a 3: 1/10. These are disjoint events (they can’t happen at the same time) but we need the probability that either can happen. So 1/10+1/10=2/10=1/5.
This intuitively makes sense since there are 2 numbers out 10
