Answer:
(a) b = (4/7)c
(b) Bill: 40 shingles/hour; Chip: 70 shingles/hour
Step-by-step explanation:
Let b and c represent Bill's and Chip's rates in shingles per hour, respectively. Then we have ...
7b = 4c
c - b = 30 . . . . shingles per hour difference in rates
(a) Bill's rate in terms of Chip's rate can be found by dividing the first equation by 7
b = (4/7)c . . . . . Bill's rate is 4/7 of Chip's rate
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(b) To find the rates, we can multiply the second equation by 7 and substitute using the first equation:
7c -7b = 210
7c -4c = 210
c = 210/3 = 70
b = (4/7)(70) = 40
Bill's rate is 40 shingles per hour; Chip's rate is 70 shingles per hour.
Answer:
The method would use to prove that the two Δs ≅ is AAS ⇒ D
Step-by-step explanation:
Let us revise the cases of congruence:
- SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ
- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ
- AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ
- HL ⇒ hypotenuse and leg of the 1st right Δ ≅ hypotenuse and leg of the 2nd right Δ
In the given figure
∵ The two triangles have an angle of measure 30°
∵ The two triangles have an angle of measure 70°
∵ The two triangles have a side of length 10
∴ The two triangles have two equal angles and one equal side
→ By using rule 4 above
∴ The two triangles are congruent by the AAS rule
∴ The method would use to prove that the two Δs ≅ is AAS
Answer:
x>-4
Step-by-step explanation:
flip sign when dealing with negative
