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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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 =
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
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.
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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