Answer:
Step-by-step explanation:
Question 1: Assumption: This is a 30-60-90 triangle.
Remember that the sides of a 30-60-90 triangle are in the ratio 1:√3:2
The side opposite the 90° angle is 16, so the side opposite the 30° angle is 16/2 = 8
x = 8 units.
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Question 2: Assumption: This is an isosceles triangle.
Draw the altitude to the vertex angle and you get a 30-60-90 triangle.
The side opposite the 90° angle has length 22, so the side opposite the 30° angle has length 11.
x/2 = 11
x = 22 units
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Question 3: Assumption: This is a 45-45-90 triangle.
The sides of a 45-45-90 triangle are in the ratio 1:1:√2
The sides opposite the 45° angles are 19 and x.
x = 19
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Question 4: Assumption: This is an isosceles triangle.
x = 13 units
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Question 5: Assumption: This is a right triangle.
sin(54°) = x/45
x = 45sin(54°) ≅ 36.4 units
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Question 6: Assumption: This is a right triangle.
sin(35°) = z/23
z = 23sin(35°) ≅ 13.2 units
Let s = #small notebooks
Let L = #large notebooks
We Can set up two equations from the info given.
s + L = 6 bought 6 notebooks total
8s + 10L = 56 spent $56
Solve equation 1 for one variable.
L = 6-s
Plug 6-s in equation 2 in place of L
and solve for s
8s + 10(6-s) = 56
8s + 60 - 10s = 56
-2s + 60 = 56
-2s = -4
s = (-4)/(-2)
s = 2
We know s+L = 6 and s=2
2+L = 6
L = 4
4 large notebooks and 2 small notebooks
were purchased
Step-by-step explanation:
y=kx
say that y is the original prince and x is the sale price
15=k(10)
15/10=k
3/2=k
you can check with the next problem to check if it is the same
25=k(20)
25/20=k
5/4=k
so you take 5/4-3/2=-1/4 so the constant is -1/4
Hope that helps :)
Answer:
x = 10
z = 116°
Step-by-step explanation:
By the definition of supplementary angles, we have:
Step 1: Find <em>x</em>
7x + 46 + 5x + 14 = 180
12x + 60 = 180
12x = 120
x = 10
Step 2: Find the supplementary angle to <em>z</em>
5(10) + 14
50 + 14
64
Step 3: Find <em>z</em>
180 - 64 = 116
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Answer:
Step-by-step explanation:
Let q represent the number of quarters. Then the number of nickels is 68-q, and the number of cents in the jar is ...
25q +5(68 -q) = 800
20q +340 = 800 . . . . simplify
20q = 460 . . . . . . . . subtract 340
q = 23 . . . . . . . . . . . divide by 20; this is the number of quarters
68-q = 45 . . . . . . . find the number of nickels
The jar contains 23 quarters and 45 nickels.
