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mathematics
basic technical mathematics
Basic Technical Mathematics 12th Edition Allyn J. Washington, Richard Evans - Solutions
Reduce each fraction to simplest form. 3a² - 13a - 10 5 + 4a - a²
Reduce each fraction to simplest form. (x + 5)(x-2)(x + 2)(3x) (2 – x)(5 – x)(3 + x)(2 + x)
Simplify the given expressions.If f(x) = x − 1/x, find f(a + 1).
Perform the indicated operations and express results in simplest form. 4 y 2- 4у 2 y
Simplify the given expressions.If f(x) = 2x − 3, find f[1/f(x)].
Simplify the given expressions.Find A and B if 2x - 9 x²-x-6 A x - 3 + B x + 2
Reduce each fraction to simplest form. x² + y² 2x + 2y
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.A total of 276m3 of water was pumped from a basement for 4 h 50 min. The pumping rate for part of the time was 60.0 m3/h, and was then reduced to 18 m3/h. What volume was
Reduce each fraction to simplest form. (2x - 3)(3x)(x − 7)(3x + 1) (3x + 2)(3-2x)(x - − 3)(7 + x)
Simplify the given expressions.The sum of two numbers a and b is divided by the sum of their reciprocals. Simplify the expression for this quotient.
Simplify the given expressions.Ifshow that X mn m + n and y = mn m - n
Perform the indicated operations and express results in simplest form. 3 10a² 4a3
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.A commuter traveled 36.0 km to work at an average speed of v1 km/h and later returned over the same route at an average speed of 8.00 km/h less. If the total time for the
Perform the indicated operations and express results in simplest form. 6 olx X 7 2x + 3 xy
Reduce each fraction to simplest form. w³8 w2 w² + 2w + 4
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.A jet travels 75% of the way to a destination at a speed of Mach 2 (about 2400 km/h), and then the rest of the way at Mach 1 (about 1200 km/h). What was the jet’s average
Reduce each fraction to simplest form. 2 6x² + 2x 1 + 27x³
Perform the indicated operations and express results in simplest form. T T² + 2 1 27 + T³
Perform the indicated operations. Each expression occurs in the indicated area of application.(transistor theory) 3 4 п зно 4 H П
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.A commuter rapid transit train travels 24 km farther between stops A and B than between stops B and C. If it averages 60 km/h from A to B and 30 km/h between B and C, and an
When adding fractions, explain why it is better to find the lowest common denominator rather than any denominator that is common to the fractions.
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.A jet takes the same time to travel 2580 km with the wind as it does to travel 1800 km against the wind. If its speed relative to the air is 450 km/h, what is the speed of
Perform the indicated operations. Each expression occurs in the indicated area of application.(thermodynamics) 1+ 9 128T 27P 647'3
Reduce each fraction to simplest form. 24 a² 3a³ 4a + 4
After finding the simplest form of each fraction, explain why it cannot be simplified more.a. b. x²(x + 2) x² + 4 zx
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.The current through each of the resistances R1 and R2 in Fig. 6.7 equals the voltage V divided by the resistance. The sum of the currents equals the current i in the rest of
Perform the indicated operations and express results in simplest form. a +1 a a-3 a + 2
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.An engineer travels from Aberdeen, Scotland, to the Montrose oil field in the North Sea on a ship that averages 28 km/h. After spending 6.0 h at the field, the engineer
Perform the indicated operations and express results in simplest form. y y + 2 1 y² + 2y
Perform the indicated operations. Each expression occurs in the indicated area of application.(optics) 2n²-n-4 2n² + 2n - 4 + n-1
Perform the indicated operations. Each expression occurs in the indicated area of application.(magnetic field) b x² + y² 2 2bx² x² + 2x²y² + y4
After finding the simplest form of each fraction, explain why it cannot be simplified more.a.b. 2x + 3 2x + 6
Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits.A fox, pursued by a greyhound, has a start of 60 leaps. He makes 9 leaps while the greyhound makes but 6; but, 3 leaps of the greyhound are equivalent to 7 of the fox. How
Perform the indicated operations and express results in simplest form. 2x x² + 2x - 3 1 6x + 2x²
Evaluate: -1 3 -2 0 2 4-3 5 -4
Make the given changes in the indicated examples of this section and then factor.In Example 2, change −ax2 to +a4x2.Data from Example 2In factoring ax5 − ax2, we first note that each term has a common factor of ax 2. This is factored out to get ax2(x3 − 1). However, the expression is not
Make the given changes in the indicated examples of this section and then factor.In Example 1(a), change the + before the 8 to −.Data from Example 1(a) x³ + 8 = x³ + 2³ 3 3 = (x + 2)[(x)² - 2x + 2²] = (x + 2)(x² - 2x + 4)
Make the given changes in the indicated examples of this section and then factor.In Example 1, change the 3 to 4 and the 2 to 3.Data from Example 1In factoring x2 + 3x + 2, we set it up asThe constant 2 tells us that the product of the required integers is 2. Thus, the only possibilities are 2 and
In Example 2, change the + sign to − and then factor.Data from Example 2Factor: 4ax2 + 2ax.The numerical factor 2 and the literal factors a and x are common to each term. Therefore, the greatest common factor of 4ax2 + 2ax is 2ax. This means that 4ax2 + 2ax = 2ax(2x) + 2ax(1) = 2ax(2x +
In Example 2, set the given expression equal to B and then solve for a.Data from Example 2Factor: 4ax2 + 2ax.The numerical factor 2 and the literal factors a and x are common to each term. Therefore, the greatest common factor of 4ax2 + 2ax is 2ax. This means that 4ax2 + 2ax = 2ax(2x) +
Make the given changes in the indicated examples of this section and then factor.In Example 2(a), change the + before 7x to −.Data from Example 2(a).In order to factor x2 + 7x − 8, we must find two integers whose product is −8 and whose sum is +7. The possible factors of −8 areInspecting
Make the given changes in the indicated examples of this section and then factor.In Example 3, change the + before 11x to −.Data from Example 3To factor 2x2 + 11x + 5, we take the factors of 2 to be +2 and +1 (we use only positive coefficients a and c when the coefficient of x 2 is positive). We
Factor the given expressions completely.x3 + 1
In Example 9(a), change the coefficient of the first term from 20 to 5 and then factor.Data from Example 9(a)In factoring 20x2 − 45, note a common factor of 5 in each term. Therefore, 20x2 − 45 = 5(4x2 − 9). However, the factor 4x2 − 9 itself is the difference of squares. Therefore, 20x2
Factor the given expressions completely.R3 + 27
In Example 10, change both − signs to + and then factor.Data from Example 10Factor: 2x − 2y + ax − ay.We see that there is no common factor to all four terms, but that each of the first two terms contains a factor of 2, and each of the third and fourth terms contains a factor of a. Grouping
Make the given changes in the indicated examples of this section and then factor.In Example 8, change the 8 to 36.Data from Example 8When factoring 2x2 + 6x − 8, first note the common factor of 2. This leads to 2x2 + 6x − 8 = 2(x2 + 3x − 4)Now, notice that x2 + 3x − 4 is also factorable.
Factor the given expressions completely.y3 − 125
Find each product.(x − 7)2
Find the indicated special products directly by inspection.(T + 6)(T − 6)
Factor the given expressions completely.z3 − 8
Find each product.(y + 6)2
Find the indicated special products directly by inspection.(s + 5t)(s − 5t)
Factor the given expressions completely.27 − t3
Find each product.(a + 3b)2
Find the indicated special products directly by inspection.(4x − 5y)(4x + 5y)
Factor the given expressions completely.8r3 − 1
Find each product.(2n + 5m)2
Find the indicated special products directly by inspection.(3v − 7y)(3v + 7y)
Factor the given expressions completely.8a3 − 27b3
Factor the given expressions completely.x2 + 4x + 3
Factor the given expressions completely.7x + 7y
Factor the given expressions completely.64x4 + 125x
Factor the given expressions completely.x2 − 5x − 6
Factor the given expressions completely.3a − 3b
Factor the given expressions completely.4x3 + 32
Factor the given expressions completely.s2 − s − 42
Factor the given expressions completely.5a − 5
Factor the given expressions completely.3y3 − 81
Factor the given expressions completely.a2 + 14a − 32
Factor the given expressions completely.2x2 + 2
Factor the given expressions completely.7n5 − 7n2
Factor the given expressions completely.t2 + 5t − 24
Factor the given expressions completely.r3 − 11r2 + 18r
Factor the given expressions completely.3x2 − 9x
Factor the given expressions completely.64 − 8s9
Factor the given expressions completely.20s + 4s2
Factor the given expressions completely.54x3y − 6x3y4
Factor the given expressions completely.x2 + 8x + 16
Factor the given expressions completely.7b2h − 28b
Factor the given expressions completely.12a3 + 96a3b3
Factor the given expressions completely.D2 + 8D + 16
Factor the given expressions completely.5a2 − 20ax
Factor the given expressions completely.x6y3 + x3y6
Factor the given expressions completely.a2 − 6ab + 9b2
Factor the given expressions completely.72n3 + 24n
Factor the given expressions completely.16r3 − 432
Factor the given expressions completely.b2 − 12bc + 36c2
Factor the given expressions completely.90p3 − 15p2
Factor the given expressions completely.3a6 − 3a2
Factor the given expressions completely. πR3 — ³ πr
Factor the given expressions completely.3x2 − 5x − 2
Factor the given expressions completely.2x + 4y − 8z
Factor the given expressions completely.81y2 − x6
Factor the given expressions completely.6n2 − 39n − 21
Factor the given expressions completely.23a − 46b + 69c
Factor the given expressions completely.12y2 − 32y − 12
Factor the given expressions completely.4pq − 14q2 − 16pq2
Factor the given expressions completely.3ab2 − 6ab + 12ab3
Factor the given expressions completely.0.027x3 + 0.125
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