Mr. Saunier Algebra ii Final Exam
Find a for the given geometric series. Round to the nearest hundredth if necessary. S(n) = 86,895, r = 3.2, n = 4
1,840.68
The Smiths bought an apartment for $75,000. Assuming that the value of the apartment will appreciate at most 4% a year, how much will the apartment be worth in 3 years?
$84,365
Solve for the given inequality √8x-1 +5 ≤ 12
(1/8)≤ x≤ 25/4
Solve for the given equation 1 + √3x+3 = 12
(118/3)
Solve for the given inequality √5x-6 +8 ≤ 6
(6/5)≤x≤2
Express the given logarithm in terms of common logarithms. Then approximate its value to four decimal places. log(3) 6.9
(log6.9)/(log3); 1.7581
Evaluate: log (1/4)2
-(1/2)
Solve: log(4)(2x+1)≤log(4)(x+6)
-(1/2)≤x≤5
Find S(n) for the given arithmetic series. a(1)= 22, d = -7, n = 21
-1008
Write an equation for the nth term of the given geometric sequence. -12, -36, -108, ... a(n)
-12(3)^(n-1)
If y varies directly as x and y = 27 when x = -9, find y when x = 44.
-132
Find S for the given geometric series. Round answers to the nearest hundredth, if necessary. a(1) = -18, a(5) = -180,000, r = 10
-199,998
If y varies inversely as x and y = 114 when x = -13, find y when x = 50. Round your answer to the nearest hundredth, if necessary.
-29.64
Simplify 3√-8a^3b^8
-2ab^2-3√b^2
Simplify the expression: 3x/2x-1 - 5x/2x-1
-2x/2x-1
Find the indicated term of the given geometric sequence. a(1) = -13, r = 5, n = 3
-325
Find the next three terms of the arithmetic sequence. -33, -37, -41, -45, . . .
-49, -53, -57
Find the indicated term of the given arithmetic sequence. a(1) = 85, d = -10, n = 16
-65
Write an equation for the nth term of the given geometric sequence. -7, -21, -63, ... a(n)
-7(3)^n-1
Find the sum of the given arithmetic series. 24 + 17 + 10 + 3 + ... + (-39)
-75
Find S(n) for the given arithmetic series. a(1)= -28, d = -4, n = 14
-756
Find for the following functions. f(x) = 10x^2 - 10x - 6 g(x) = 7x - 6
. 70x^3 - 130x^2 + 18x + 36
Solve the given inequality. If necessary, round to four decimal places. 10^y ≥ 29
. y ≥ 1.4624
Solve: log(6)x ≤ 2
0 ≤ x ≤ 36
Solve the given equation. Round to the nearest ten-thousandth, if necessary. 11 + 5e^(5x) = 18
0.0673
Find a for the given geometric series. Round to the nearest hundredth if necessary. S(n) = 42,170, r = 3.2, n = 12
0.08
Find the domain and range of the function: f(x) = 6√x-10 +16
Domain: {x|x ≥ 10} Range: {f(x)|x ≥ 16}
Identify the domain and range. y = -2log(5)(x-7)+1
Domain:{x|x ≥ 7} Range: All Reals
Identify if the equation if growth or decay, identify the growth/decay factor, and state the domain and range. Y=2(4/3)^(X-3)+10
Growth; Growth factor: (4/3); Domain: All Real Numbers; Range {f(x)|f(x)≤ 10}
Write an equation for the nth term of the given arithmetic sequence. -15, -32, -49, -66, ...
a(n) = -17n+2
Write an equation for the nth term of the given arithmetic sequence. 14, 27, 40, 53, ...
a(n) = 13n + 1
Solve: 6^(x-5) = 216^x+4
x = (-17/2)
Determine the equations of any vertical asymptotes in the graph of the rational function. f(x) = 2/(x^2 -12x+27)
x = 3, x = 9
Where is the asymptote? y = log(3)(x-4)+1
x = 4
f(x) = (3/x-4)+2
x = 4, f(x) = 2
Determine the value of x for any holes in the graph of the rational function. f(x) = (x-9)/(x^2 -11x+18)
x = 9
Solve the given inequality. Round to the nearest ten-thousandth, if necessary. e^(9x) ≤ 20
x ≤ 0.3329
Solve: log(2)x≤log(2)(3x-8)
x ≥ 4
Where is the asymptote? y = 2^(x-3)+5
y = 5
Find the inverse of the given relation. {(1, -10), (4, -4), (3, -5), (16, -6)}
{(-10, 1), (-4, 4), (-5, 3), (-6, 16)}
Which of the points will be on the graph of the following function. log(4)(x+3)
(1,1) (-2,0) (-2.75, -1)
Find the next 3 terms of the arithmetic series: a(1)=5, a(n)=95, S(n)=950
100, 105, 110
Describe the translation of the graph: y = log(2)(x-3)+6
right 3 and up 6
10√32
√22
4√√2410
√7
Find (f + g)(x) for the following functions f(x) = 10x^2+5x+2 g(x) = 2x+5
10x^2+7x+7
Find for the following functions. f(x) = 15x + 16 g(x) = -10x^2 + 8x + 24
10x^2+7x-8
Find (f/g)(x) for the following functions. f(x) = 10x^2-3x-3 g(x) = 12x-5
10x^2-3x-3/12x-5; x/= 5/12
√8x-7 +2=12
107/8
Kronos Industries bought a desktop for $3000. It is expected to depreciate at a rate of 10% per year. What will the value of the desktop be in 4 years? Round to the nearest dollar.
$1968
Eros Industries bought a laser printer for $3400. It is expected to depreciate at a rate of 12% per year. What will the value of the printer be in 3 years? Round to the nearest dollar.
$2317
Solve the given equation. If necessary, round to four decimal places. 13^y = 16
1.081
The Marriott family bought a new apartment three years ago for $65,000. The apartment is now worth $86,515. Assuming a steady rate of growth, what was the yearly rate of appreciation?
10%
28x/16y * 11y^2/56x^3
11y/32x^2
Find the LCM of the set of polynomials. 7a^3c, 2b^4, b^2c^2
14a3b4c2
Simplify (3+√2)(5+√3)
15+3√3+5√2+√6
Simplify the given expression. 19/xy^2 - 7y^2/8x^2
152x-7y^4/8x^2y^2
Use a calculator to approximate the value of 4√(327)^2 to three decimal places.
18.083
Evaluate the expression ln e^19.
19
Solve the given equation. Round to the nearest ten-thousandth, if necessary. 2e^x - 13 = 9
2.3979
Find the indicated term of the given geometric sequence. a(1) = 15, r = 2, n = 5
240
Evaluate log(6)216
3
Simplify the expression: 3x^2-12/3x^2-10x+8 --------/ ------------- 5x + 10 / x^2 - 36
3(x+6)(x-6)/5(3x-4)
Solve the given equation. Check your solution. (1/n+2) + (1/n-2) = (3/n^2-4)
3/2
Find the indicated term of the given arithmetic sequence. a(14) for 390, 386, 382, ...
338
Find S for the given geometric series. Round answers to the nearest hundredth, if necessary. a(1) = 0.22, a(5) = 285.12, r = 6
342.1
Simplify: 4√81a^32b^20
3a^8b^5
Evaluate: log(3)81
4
Find the sum of the given arithmetic series. 20 + 40 + 60 + 80 + ... + 400
4,200
Find the next three terms in the geometric sequence. 3, 6, 12, 24, ...
48, 96, 192
Simplify (4√6)/(4√2)
4√3
Simplify √384+√54-√96
7√5
Find the next three terms in the geometric sequence. 128, 64, 32, 16, ...
8, 4, 2
Simplify 5√2/5
5√(1250)/5
√192+√245-√27+√80
5√3+11√5
Simplify √72x^5y^12
6x^2y^6√2x
Simplify (√11/6-√5)
6√11-√55/31
Solve the given equation. If necessary, round to four decimal places. log(2) 2 + log(2) a = log(2) 17
8.5
5/4x^2-36 + 4/2x+6
8x-19/(2x+6(x-6))
Write the given radical using rational exponents. 11√9x5y10
9^(1/11)x^(5/11)y^(10/11)
Determine whether each pair of functions are inverse functions. 1) f(x) = 6x - 4, g(x) = (x + 4) 2) f(x) = 2x + 2, g(x) = 2x - 2
Only 1 is an inverse function.
Identify the asymptote: y = 3log(2)(x-6)+5
X=6
Find [g of h](x) and [h of g](x) g(x) = 2x h(x) = -7x3 + 5x2 - 4x + 1
[g of h] = -14x^3 + 10x^2 - 8x + 2 [h of g] = -56x^3 + 20x^2 - 8x + 1
Is the following sequence Arithmetic, Geometric, or Neither? 1, -2, -5, -8, ...
arithmetic
Simplify each expression. (b^-3/4)^(-7/8)
b^(21/32)
Simplify each expression. b^(4/5)/b^1/8
b^(27/40)
Find the inverse of the given function. f(x) = 3x - 7
f-1(x) = (x+7/3)
Is the following sequence Arithmetic, Geometric, or Neither? 12, 36, 108, 324, ...
geometric
Rewrite as a logarithmic form. 5^4 = 625
log(5)625 = 4
Is the following sequence Arithmetic, Geometric, or Neither? 6, 9, 14, 21, ...
neither