SOLUTION: i have selected 10 problems i am having trouble with if anyone could PLEASE help i would be so grateful. thank you so much :) Two terms of an arithmetic sequence are a9 = 85

Question 388654: i have selected 10 problems i am having trouble with if anyone could PLEASE help i would be so grateful. thank you so much :)

Two terms of an arithmetic sequence are a9 = 85 and a30 = 295. Find a rule for the nth term.
−5 + 12n
−5 + 10n
5 + 10n
5 + 12n

Q2) What is the measure of the angle θ in the triangle shown?
θ 31.07
θ 58.93
θ 62.70
θ 27.30

Q3) Solve 3 tan x −√3 = 0.
x = π/6 + nπ
x = π/6 or x = 7π/6
x = π/6 + 2nπ
x = √2 or x = √3

Q4) Two terms of an arithmetic sequence are a8 = 76 and a28 = 296. Find a rule for the nth term.
−12 + 11n
12 + 13n
12 + 11n
−12 + 13n

Q5) MONSTER TRUCKS A monster truck drives off a ramp in order to jump onto a row of cars. The ramp has a height of 8 feet and a horizontal length of 28 feet. What is the angle θ of the ramp? Round your answer to the nearest integer, if necessary.
θ 16
θ 14
θ 12
θ 10

Q6) Solve cos x − 1 = 0 on the interval 0 ≤x ≤ π/2.
x = π/3
x =0
x = π/6
x = π/4

Q7) Describe the pattern, write the next term, and write a rule for the nth term of the sequence 5, 5.3, 5.6, 5.9. . . What is the next term in the pattern? The next term in the pattern is
5.9
6.5
6.9
6.2

Q8) What is the measure of the angle θ in the triangle shown?
θ 63.43
θ 30.00
θ 60.00
θ 26.57

Q9) Graph f(x) = sin (x − 2π) − 1. Vertical shift =?
Vertical shift = -2
Vertical shift = -1
Vertical shift = -3
Vertical shift = 0

Q10) Two terms of an arithmetic sequence are a7 = 33 and a22 = 138. Find a rule for the nth term.
16 + 10n
16 + 7n
−16 + 10n
−16 + 7n

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two terms of an arithmetic sequence are
a(9) = 85 and a(30) = 295.
Find a rule for the nth term.
a(30) = a+29d = 295
a(9) = a+8d = 85
---------------------
Subtract and solve for "d":
21d = 210
d = 10
---
Solve for "a":
a+8*d = 85
a = 5
----
Therefore: a(n) = 5+(n-1)10 = 5+10n-10 = -5+10n

−5 + 12n
−5 + 10n
5 + 10n
5 + 12n
===============================================================
Q2) What is the measure of the angle θ in the triangle shown?
θ 31.07
θ 58.93
θ 62.70
θ 27.30
----
Triangle not shown.
===============================================================
Q3) Solve 3 tan x −√3 = 0.
tan(x) = sqrt(3)/3
x = invtan(sqrt(3)/3) = pi/6 or (7/6)pi
------------------------------------------
x = π/6 + nπ
x = π/6 or x = 7π/6
x = π/6 + 2nπ
x = √2 or x = √3
===========================
Q4) Two terms of an arithmetic sequence are a8 = 76 and a28 = 296. Find a rule for the nth term.
−12 + 11n
12 + 13n
12 + 11n
−12 + 13n
---
Follow the pattern above to get the answer.
========================================================================
Q5) MONSTER TRUCKS A monster truck drives off a ramp in order to jump onto a row of cars. The ramp has a height of 8 feet and a horizontal length of 28 feet. What is the angle θ of the ramp? Round your answer to the nearest integer, if necessary.
---
invtan(8/28) = 15.95 degrees
θ 16
θ 14
θ 12
θ 10
===========================================================
Q6) Solve cos x − 1 = 0 on the interval 0 ≤x ≤ π/2.
x = π/3
x =0
x = π/6
x = π/4
-------------------
Done elsewhere
==========================
Q7) Describe the pattern, write the next term, and write a rule for the nth term of the sequence 5, 5.3, 5.6, 5.9. . . What is the next term in the pattern? The next term in the pattern is
5.9
6.5
6.9
6.2
---
Done elsewhere
============================
Q8) What is the measure of the angle θ in the triangle shown?
θ 63.43
θ 30.00
θ 60.00
θ 26.57
---
Triangle not shown
==============================
Q9) Graph f(x) = sin (x − 2π) − 1. Vertical shift = -1
Vertical shift = -2
Vertical shift = -1
Vertical shift = -3
Vertical shift = 0
================================
Q10) Two terms of an arithmetic sequence are a7 = 33 and a22 = 138. Find a rule for the nth term.
16 + 10n
16 + 7n
−16 + 10n
−16 + 7n
---
Follow the pattern above to get the answer.
=================================================
Cheers,
Stan H.

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