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Questions and Answers of College Algebra

In Problems 15–42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, write, “Not applicable”. 2x + 4y = 16 (3x-5y=-9
In Problems 9–26, use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, write “not defined”. 03
In Problems 17–50, find the partial fraction decomposition of each rational expression. x² (x - 1)²(x + 1)
In Problems 15–42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, write, “Not applicable”. 3x-2y = 4 6x - 4y = 0
Write the fourth term of the expansion of (3a + 2b)19.
Use the binomial theorem to expand each binomial. (3t³ - s²)4
Evaluate the sum of the terms of each geometric sequence. In Exercises give answers to the nearest thousandth. 4 4 3' 9' 27 این 4 81 4 243 4 729
Use the binomial theorem to expand each binomial. (x² + 3y)4
Graph. y = log1/3 x
Write the first four terms of each binomial expansion. (m + 3n) 20
Write each series as a sum of terms and then find the sum. 6 Σ (i + 9) 1=!
Evaluate the sum of the terms of each geometric sequence. In Exercises give answers to the nearest thousandth. 1 1 1 1 1 4' 16' 64' 256' 1024
Find the number of terms in each arithmetic sequence. 3 2, 2 1, 1 2 -5
Find the number of terms in each arithmetic sequence. 3 21 3, 4 4 …., 12
Graph. g(x) 3 X
Evaluate the sum of the terms of each geometric sequence. In Exercises give answers to the nearest thousandth. 1 1 1 1 1 3'9'27' 81' 243
Write each series as a sum of terms and then find the sum. 5 Σ (i + 3) i=1
Write the first four terms of each binomial expansion. 12 (r + 2s) ¹2
Use the binomial theorem to expand each binomial. (2p - q)5
Perform the indicated operations. (4p + 2) (5p - 3)
Graph. f(x) = 2(x - 2)²3
Determine an expression for the general term of each arithmetic sequence. Then find a25. 3, 15 9 21 4'2' 4
Find the indicated term for each geometric sequence. a₁ = 2, r = 5; 910
A certain car loses 1/2 of its value each year. If this car cost $40,000 new, what is its value at the end of 6 yr?
During the summer months, the population of a certain insect colony triples each week. If there are 20 insects in the colony at the end of the first week in July, how many are present by the end of
Christian bought a new bicycle for $300. He agreed to pay $20 per month for 15 months, plus interest of 1% each month, on the unpaid balance. Find the total cost of the bicycle.
Determine an expression for the general term of each arithmetic sequence.a1 = -4, d = -5
Evaluate the sum of the terms of each geometric sequence. In Exercises give answers to the nearest thousandth. 5 16' 5 5 32'64' 5 5 128' 256
Evaluate the sum of the terms of each geometric sequence. In Exercises give answers to the nearest thousandth. 小 25
Graph. x² + 9 25 II. 1
Write each series as a sum of terms and then find the sum. 4 i=1 (i³ + 3)
Write the first four terms of each binomial expansion. (2p - 3g) 11
Graph. f(x) 1 x - 3
Write each series as a sum of terms and then find the sum. 3 Σ (i2 + 2) =1
Write the first four terms of each binomial expansion. (3x - y) ¹4 14
A student incorrectly claimed that the common difference for the arithmetic sequence is -5. Find the correct common difference. -15, -10, -5, 0, 5, ...
A student incorrectly claimed that there are 100 terms in the arithmetic sequenceHow many terms are there? 2, 4, 6, 8, ..., 100.
Write the fifth term of the expansion of 2x alm 12
Find the indicated term for each sequence. an 5n - 9 3n + 8' a16
Determine an expression for the general term of each geometric sequence. 1 8, -2, 77... 2
Find the indicated term for each arithmetic sequence.a6 = 12, a8 = 18; a25
Determine an expression for the general term of each arithmetic sequence. Then find a25.a1 = 5, d = 3
Evaluate each expression.13C2
Simplify. Assume that all variables represent nonzero real numbers. alm 3 -2
Nuts worth $3 per lb are to be mixed with 8 lb of nuts worth $4.25 per lb to obtain a mixture that will be sold for $4 per lb. How many pounds of the $3 nuts should be used?
Find the indicated term for each sequence. an || 3n + 7 2n - 5' a14
Expand (3k - 5)4.
Evaluate each expression.13C11
Determine an expression for the general term of each geometric sequence. 23.... 10, -2,
Solve each system of equations. x + 2y + z = 8 2xy + 3z = 15 -x + 3y 3z = -11 -
Solve each system of equations. xy = -5 2x + y = 3
Determine an expression for the general term of each arithmetic sequence. Then find a25.a1 = 2, d = 5
Find the indicated term for each arithmetic sequence.a1 = -2, d = 5; a16
Find the indicated term for each sequence. an -3n+7; 912
Evaluate each expression.12C10
Determine an expression for the general term of each geometric sequence. -3, လယ 3
Evaluate each expression.7C4
Write the first five terms of each arithmetic sequence.a1 = 0.25, d = 0.55
The Fibonacci sequence begins 1, 1, 2, 3, 5, 8, . . . . What is the eleventh term of this sequence?
Determine whether each sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference d. If it is geometric, find the common ratio r. 64, 32, 8, . . . 2²
Write the first five terms of each sequence. U I U= u="p
Evaluate each expression.6! · 7
Write the first five terms of each arithmetic sequence.a1 = -3, d = -5
Evaluate each sum if it exists. 00 i=1 19
If the given sequence is geometric, find the common ratio r. If the sequence is not geometric, say so. 2 3' ان 2 2 15' 75' 2 375
Determine an expression for the general term of each geometric sequence.-2, -6, -18, . . .
Find the standard form of the equation of the line passing through (-2, 10) and parallel to the line with equation 3x + y = 7.
Evaluate each expression. 5! 5!0!
Evaluate each expression.4! · 5
Determine whether each sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference d. If it is geometric, find the common ratio r. 1 1 3' 3'6' 2/3 1 12'
Write the first five terms of each arithmetic sequence.a1 = -2, d = -4
If the given sequence is geometric, find the common ratio r. If the sequence is not geometric, say so. 1, 1 1 2'4' 1 8
Determine whether each sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference d. If it is geometric, find the common ratio r.-1, 1, -1, 1, -1, . . .
Determine an expression for the general term of each geometric sequence.-5, -10, -20, . . .
Find the slope of the line passing through (4, -5) and (-12, -17).
Write the first five terms of each arithmetic sequence.a1 = 6, d = 7
Write the first five terms of each sequence. an = 6(-1)n+1
Solve each equation or inequality. logg x + logg (x + 2) = 1
Evaluate each sum if it exists. 00 i=1 4
Write the first five terms of each sequence. an = 5(-1) ¹-1
Evaluate each expression. 4! 0!4!
Solve each equation or inequality. 32x-1 = 81
Write the first five terms of each arithmetic sequence.a1 = 5, d = 4
Evaluate each sum if it exists. 3 Σ i=1 (4²) 2
Determine whether each sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference d. If it is geometric, find the common ratio r.-6, -2, 2, 6, 10, . . .
If the given sequence is geometric, find the common ratio r. If the sequence is not geometric, say so.2, -8, 32, -128, . . .
Write the first five terms of each sequence. An 2 n²
Evaluate each expression. 7! 3!4!
Can the sum of the terms of the infinite geometric sequence defined by an = 5(2)n be found? Explain.
Solve each equation or inequality. 4 6 x 3 x + 3 24 x²-9
If the given sequence is arithmetic, find the common difference d. If the sequence is not arithmetic, say so.-6, -10, -14, -18,. . .
Evaluate each sum if it exists. 500 i=1
Determine whether each sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference d. If it is geometric, find the common ratio r.2, 5, 8, 11, . . .
If the given sequence is geometric, find the common ratio r. If the sequence is not geometric, say so.1, -3, 9, -27, 81, . . .
Write the first five terms of each sequence. An 1 n²
Consider the repeating decimal number 0.55555 . . . .(a) Write it as the sum of the terms of an infinite geometric sequence.(b) What is r for this sequence?(c) Find this infinite sum if it exists,
Evaluate each expression. 6! 4!2!
Find the indicated term for each sequence. an (5n 2) (3n+1); a10 = -
Evaluate each expression.10C3
Determine an expression for the general term of each arithmetic sequence. Then find a25. 57 1, 3, 7, 3, .. 3

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