Answer:
Step-by-step explanation:
The formula for this is
∠G = 1/2(arcEH - arcHF)
We have angle G (5x - 10) and we have arcEH (195) so we have to solve for x to find the measure of arcEHF so we can add arcEH + arcHF = arcEHF
Filling in the formula with what we have:
which simplifies down a bit to
which simplifies down a bit more to
Multiply both sides by 2 to get rid of the fraction and get:
2(5x - 10) = 178 - 8x which of course simplifies to
10x - 20 = 178 - 8x. Now add 8x to both sides and at the same time add 20 to both sides to get:
18x = 198 so
x = 11. Now we can find the measure of arcHF:
arcHF is 8x + 17, so arcHF is 8(11) + 17 which is 105°.
arcEH + arcHF = arcEHF so
195 + 105 = arcEHF so
arcEHF = 300°
The answer is 0 unless I did the math wrong
If so someone correct me. Other than that, hope this helped!
Complete Question
Let P (n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. The parts of this exercise outline a strong induction proof that P (n) is true for n ≥ 18.
Show statements P (18), P (19), P (20), and P (21) are true, completing the basis step of the proof.
Answer:
P(18) is true
P(19) is true
P(20) is true
P(21) is true
Step-by-step explanation:
a. When n = 18
18 cents can be formed using two 7cents and one 4cents
i.e. 2 * 7 + 4 = 18
So, P(18) is true
b. When n = 19
19 cents can be formed using one 7cents and three 4cents
i.e. 1 * 7 + 3 * 4 = 19
So, P(19) is true
c. When n = 20
18 cents can be formed using five 4cents
i.e. 5 * 4 = 20
So, P(20) is true
d. When n = 21
18 cents can be formed using three 7cents
i.e. 3 * 7 = 21
So, P(21) is true
