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Questions and Answers of College Algebra

Write each rational expression in lowest terms. x + 2y x² - 4y²
Writein lowest terms. 6x² 13x 13x - 5 9x³ - x
Give the domain of each rational function using (a) Set-builder notation (b) Interval notation. f(x) || 5x+17 x² - 7x + 10
Solve each equation for the specified variable. P = kR + R - u for R
Perform the indicated operations. 2 1 3 4
Solve each equation for the specified variable.2k + ar = r - 3y for r
Each exercise presents a familiar formula. Give the letter of the choice that is an equivalent form of the formula. V = LWH (geometry) LW V A. H = B. L = V WH C. L = WH V D. W = H VL
The binomial x6 - y6 may be considered as either a difference of squares or a difference of cubes. Factor x6 - y6 by first factoring as a difference of squares. Then factor further by considering one
Multiply or divide as indicated. (x + 3)² 4 6 2x + 6
Write each rational expression in lowest terms. x² + 2x - 15 x²-x-6
Give the domain of each rational function using (a) Set-builder notation (b) Interval notation. f(x) = 9 x² 18x + 81
Perform the indicated operations. 3 4 6
Perform the indicated operations. 2 5 + sla m 3m²
Perform the indicated operations. 3 5 -4- ÷ 1 2
Each exercise presents a familiar formula. Give the letter of the choice that is an equivalent form of the formula. m= (physics) F a A. a = mF B. F = m a C. F = m D. F = ma
Perform the indicated operations. 9 2 3-x x - 3
Multiply or divide as indicated. y² 16 y²-25 y² + 2y - 15 y² 7y + 12
Write each rational expression in lowest terms. 12x² + 6x 24x+12
Multiply or divide as indicated. 3-t t-3 5 10
Each exercise presents a familiar formula. Give the letter of the choice that is an equivalent form of the formula. R A. R = (electricity) I E B. R = IE C. E || I R D. E = RI
Write each rational expression in lowest terms. 25m² -n² 25m² - 10mn + n²
Perform the indicated operations. -3 X 1 + 2 x + 1 X
Use personal experience or intuition to determine whether the situation suggests direct or inverse variation.The number of movie tickets purchased and the total price for the tickets
In work with electric circuits, the formulaoccurs. Find b if a = 8 and c = 12. 1 a || 1 b + 1 C
Perform the indicated operations. 3. X +9 5 1 X
Multiply or divide as indicated. x²-9 x² + x - 12 ÷ x³ + 3x²x³ + 9x² + 20x
Perform the indicated operations.-8.75 + 3.08
Write each rational expression in lowest terms. r-2 4 - 1²
Use personal experience or intuition to determine whether the situation suggests direct or inverse variation.The rate and the distance traveled by a pickup truck in 3 hr
Multiply or divide as indicated. (2y + 3)² бу 15y3 4y²9
A gas law in chemistry says thatSuppose that T = 300, t = 350, V = 9, P = 50, and v = 8. Find p. PV T pv t
Perform the indicated operations. 4y + 16 30 2y + 8 5
Perform the indicated operations.5.25 ÷ 100
Evaluate. (a) 5² (b) -5² (c) (-5)² (d) V25 (e) - V25 (f) V-25
Use personal experience or intuition to determine whether the situation suggests direct or inverse variation.The amount of pressure put on the accelerator of a car and the speed of the car
The following exercises are based on the “Bait Box Puzzle,” featured in an “Ask Marilyn” column in Parade Magazine.Write an equation that describes the situation depicted in FIGURE B. Use the
A formula from anthropology says thatFind L if c = 80 and b = 5. C = 100b L
Complete each factoring. y² + 11y + 18 = (y + 2)(_
Perform the indicated operations.43.6 × 100
Use personal experience or intuition to determine whether the situation suggests direct or inverse variation.The percentage off an item that is on sale and the price of the item
Find the least common denominator for the group of denominators.t2 + t - 6, t2 + 3t, t2
Solve each equation. (x + 7) (x + 3) = 0
Solve. 3.x - 1 5 + x+ 2 2 3 10
Solve each equation. (3k + 8) (2k-5) = 0
Complete each factoring. m² - 10m + 21 (m - 3)(
Factor completely.9x2 + 13xy - 3y2
Factor.x2 + 2x + 1 - 4z2
Solve each equation. 32(x + 3) < 4x
Complete each factoring. n² 14n+ 48 =(n-6)(_)
Factor each polynomial. k2 - 9
The following exercises are of mixed variety. Factor each polynomial.18m3n + 3m2n2 - 6mn3
Solve. 2x + 4 5
Factor by grouping.x2 + 5y + 5x + xy
Factor completely.15y3 + 20y2
Factor.a3 + 2a2 - ab2 - 2b2
Factor each polynomial.25x2 - 4
Solve each equation. (3q4) (2q + 5) = 0
Complete each factoring. 12u²+ 10uv + 2v² = 2(3u + v) (___
A game board has the shape of a rectangle. The longer sides are each 2 in. longer than the distance between them. The area of the board is 288 in.2. Find the length of the longer sides and the
The following exercises are of mixed variety. Factor each polynomial.6b2 - 17b - 3
Factor by grouping.2m + 6 - am - 3a
Solve each equation. 2(x - 1)²-7(x - 1) - 150
Factor completely.25z2 - 30zm + 9m2
Factor.9k2 - 121j2
A rectangular parking lot has a length 20 ft more than its width. Its area is 2400 ft2. What are the dimensions of the lot? W W + 20 088 The area is 2400 ft².
Factor.-x2 + x + 30
Factor completely.9x2 + 4xy - 2y2
Solve each equation. 4(2x + 3)² (2x + 3)-3=0 -
Factor.125 - 216y6
Graph 4x + 2y = -8.
Factor. 100x4 - 81
Factor. 8p3 + 27
Solve each equation.8x2 + 14x + 3 = 0
Factor each trinomial. 2x3y3 - 48x2y4 + 288xy5
The following exercises are of mixed variety. Factor each polynomial.2x2 - 2x - 40
Factor each polynomial. 27a3 - 8b3
Factor each trinomial.6m3n2 - 60m2n3 + 150mn4
The following exercises are of mixed variety. Factor each polynomial.27x3 - 3y3
A rock is projected directly upward from ground level. After t seconds, its height (if air resistance is neglected) is modeled by the functionAfter how many seconds will the rock return to the
Factor each trinomial. - z (q + p) ₂99 z(9 + v)qp - z(q + v) ₂p
Use the the method of factoring by grouping to factor each polynomial.64m2 - 512m3 - 81n2 + 729n3
Factor each polynomial.343p3 + 125q3
The following exercises are of mixed variety. Factor each polynomial.16x3 + 32x2 - 9x - 18
The following exercises are of mixed variety. Factor each polynomial.x2 + 4 + x2y + 4y
Solve each equation for the specified variable. A = P + Prt for P
Factor each trinomial. m²(m − p)² – mp(m − p)² - 12p²(m − p)² - -
Factor out the greatest common factor. (x + 3) (4x 1) - (x+3)(3x + 2) -
The following exercises are of mixed variety. Factor each polynomial.3a2pq + 3abpq - 90b2pq
When asked to factor x2y2 - 6x2 + 5y2 - 30, a student gave the following incorrect answer.What is the correct answer? (9 - ) + (9 - )
Factor completely.8 - a3
A student solved the following formula incorrectly for L as shown. S = 2HW + 2LW + 2LH = 2LH S2LW-2HW S2LW-2HW 2H = L
Evaluate for p = -4, q = -2, and r = 5. Vr -p+2q
Factor out the greatest common factor. (z + 1) (z − 4) + (z + 1)(2z + 3) -
A student incorrectly factoredExplain this error. x³ + 8 as (x+2) ³.
Factor.4p2 + 3pq - q2
Complete each factoring. x² + 8x + 15 = = (x+5)(_____)
The following exercises are of mixed variety. Factor each polynomial.49z2 - 16
Factor completely.81k2 - 16
Factor.16a2 + 40ab + 25b2
A student incorrectly factoredExplain this error. x² +4 as (x + 2)².

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