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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Perform the indicated divisions. Express the answer as shown in Example 5 when applicable.(x − 14x2 + 8x3) ÷ (2x − 3)Data from Example 5Perform the divisionBecause there is no x-term in the
Perform the indicated multiplications.(x − 2y − 4)(x − 2y + 4)
Solve the given equations. 4x2(x 2(x-4) 3 = 8
Perform the indicated multiplications.(3y2 + 2)(2y − 9)
Simplify the given algebraic expressions.2[4 − (t2 − 5)]
Perform the indicated divisions. Express the answer as shown in Example 5 when applicable.(2x2 − 5x − 7) ÷ (x + 1)Data from Example 5Perform the divisionBecause there is no x-term in the
Perform the indicated multiplications.(x2 − 1)(2x + 5)
Simplify the given algebraic expressions.−[(A − B) − (B − A)]
Solve the given equations.3 − 6(2 − 3t) = t − 5
Perform the indicated divisions. Express the answer as shown in Example 5 when applicable.(x2 − 3x + 2) ÷ (x − 2)Data from Example 5Perform the divisionBecause there is no x-term in the
Perform the indicated multiplications.(5p − 2q)(p + 8q)
Simplify the given algebraic expressions.−[(4 − 6n) − (n − 3)]
Perform the indicated divisions. Express the answer as shown in Example 5 when applicable.(2x2 + 7x + 3) ÷ (x + 3)Data from Example 5Perform the divisionBecause there is no x-term in the dividend,
Solve the given equations.−4 − 3(1 − 2p) = −7 + 2p
Perform the indicated divisions. Express the answer as shown in Example 5 when applicable.(3t2 − 7t + 4) ÷ (t − 1)Data from Example 5Perform the divisionBecause there is no x-term in the
Perform the indicated multiplications.(2s + 7t)(3s − 5t)
Simplify the given algebraic expressions.−(5t + a2) − 2(3a2 − 2st)
Perform the indicated divisions. Express the answer as shown in Example 5 when applicable.(x2 + 7x − 18) ÷ (x − 2)Data from Example 5Perform the divisionBecause there is no x-term in the
Solve the given equations.1.5x − 0.3(x − 4) = 6
Perform the indicated multiplications.(−3 + 4w2)(3w2 − 1)
Simplify the given algebraic expressions.−7(6 − 3 j) − 2( j + 4)
Perform the indicated divisions. Express the answer as shown in Example 5 when applicable.(x2 + 9x + 20) ÷ (x + 4)Data from Example 5Perform the divisionBecause there is no x-term in the dividend,
Solve the given equations.0.1x − 0.5(x − 2) = 2
Perform the indicated multiplications.(2a − b)(−2b + 3a)
Simplify the given algebraic expressions.3(a − b) − 2(a − 2b)
Solve the given equations.4(7 − F) = −7
Perform the indicated multiplications.(z − 4)(z + 4)
Simplify the given algebraic expressions.3(2r + s) − (−5s − r)
Perform the indicated divisions. 3a(F + T)b² − (F +T) a(F + T)
Solve the given equations.8(y − 5) = −2y
Perform the indicated multiplications.(y + 8)(y − 8)
Simplify the given algebraic expressions.−2(6x − 3y) − (5y − 4x)
Perform the indicated divisions. 6y2n- 4ayn+1 2y"
Solve the given equations.−(x + 2) + 5 = 5x
Perform the indicated multiplications.(4t1 + t2 )(2t1 − 3t2)
Simplify the given algebraic expressions.−(t − 2u) + (3u − t)
Perform the indicated divisions. 2x+2+ 4ax" 2x"
Solve the given equations.−(r − 4) = 6 + 2r
Perform the indicated multiplications.(x + 5)(2x − 1)
Simplify the given algebraic expressions.(4x − y) − (−2x − 4y)
Perform the indicated divisions. -7a²b14ab² - 21a³ 14a²b²
Solve the given equations.3(4 − n) = −n
Perform the indicated multiplications.(a + 7)(a + 1)
Simplify the given algebraic expressions.(a − 3) + (5 − 6a)
Solve the given equations. 2(3q + 4) = 5q
Perform the indicated multiplications.(x − 3)(x + 5)
Solve the given equations. 6 + 4L = 5 − 3L
Perform the indicated divisions. 2π fL - TfR² TfR
Simplify the given algebraic expressions. -2a 2 (b − a) -
Perform the indicated divisions. 4pq³ + 8p²q² 16pq³ 4pq² –
Solve the given equations.3x + 7 = x
Perform the indicated multiplications.xy(tx2)( x + y3)
Perform the indicated divisions. -5a²n - 10an² 5an
Perform the indicated multiplications.−4c2 (−9gc − 2c + g2)
Solve the given equations.5 − 2y = −3
Perform the indicated multiplications.3M(−M − N + 2)
Simplify the given algebraic expressions.5 + (3 − 4n + p)
Perform the indicated divisions. 3rst - 6r²st² 3rs
Solve the given equations. 5D − 2 = 13
Perform the indicated multiplications.a2bc(2ac − 3b2c)
Simplify the given algebraic expressions.2p + (p − 6 − 2p)
Solve the given equations.5t + 9 = −1
Perform the indicated multiplications.5m(m2n + 3mn)
Simplify the given algebraic expressions.−xy2 − 3x2y2 + 2xy2
Solve the given equations.2x = 12
Perform the indicated multiplications.−3b(2b2 − b)
Perform the indicated multiplications.In determining the deflection of a certain steel beam, the expression 27x2 − 24(x − 6)2 − (x − 12)3 is used. Multiply and simplify.
Perform the indicated multiplications.In a particular computer design containing n circuit elements, n2 switches are needed. Find the expression for the number of switches needed for n + 100 circuit
Perform the indicated multiplications.In calculating the temperature variation of an industrial area, the expression (2T3 + 3)(T2 − T − 3) arises. Perform the indicated multiplication.
Perform the indicated multiplications.In using aircraft radar, the expression (2R − X)2 − (R2 + X2) arises. Simplify this expression.
Answer the given questions.Is subtraction associative? That is, in general, does (a − b) − c equal a − (b − c)? Explain.
Perform the indicated multiplications.The weekly revenue R (in dollars) of a flash drive manufacturer is given by R = xp, where x is the number of flash drives sold each week and p is the price (in
Answer the given questions.Is the following simplification correct? Explain. 2x - 3y + 5 - 4x − y + 3 = -2x - 4y + 8 2x - 3y + 5 (4x - y + 3) =
Perform the indicated multiplications.A contractor is designing a rectangular room that will have a pool table. The length of the pool table is twice its width. The contractor wishes to have 5 ft of
Answer the given questions.Is the following simplification correct? Explain. 2a3b4c - (-5a + 3b - 2c) = 2a 3b 4c + 5a 3b - 2c 7a6b6c - -
Solve the given problems.In analyzing a rectangular computer image, the area and width of the image vary with time such that the length is given by the expressionBy performing the indicated division,
Answer the given questions.For any real numbers a and b, is it true that | a − b| = | b − a|? Explain.
Solve the given problems.In analyzing the displacement of a certain valve, the expressionis used. Find the reciprocal of this expression and then perform the indicated division. s²2s2 S4 + 4
Perform the indicated multiplications.A savings account of $1000 that earns r% annual interest, compounded quarterly, has a value of 1000(1 + 0.0025r)2 after 6 months. Perform the indicated
Perform the indicated multiplications.In finding the value of a certain savings account, the expression P(1 + 0.01r)2 is used. Multiply out this expression.
For the following expressions, subtract the third from the sum of the first two: 3a2 + b − c3 , 2c3 − 2b − a2 , 4c3 − 4b + 3.
An athlete who was jogging and wearing a Fitbit found that she burned 250 calories in 20 minutes. At that rate, how long will it take her to burn 400 calories? Assume all numbers are exact.
Perform the indicated multiplications.By multiplication, show that (x + y)(x2 − xy + y2) = x3 + y3.
In order to find the distance x such that the weights are balanced on the lever shown in Fig. 1.16, the equation 210(3x) = 55.3x + 38.5(8.25 − 3x) must be solved. Find x. (3 is exact.) 210
For the expressions 2x2 − y + 2a and 3y − x2 − b find (a) The sum(b) The difference if the second is subtracted from the first.
Solve the given problems.When analyzing the potential energy associated with gravitational forces, the expressionarises. Simplify this expression. GMm[(R+r) (R-r)] 2rR
Solve the given problems.A computer model shows that the temperature change T in a certain freezing unit is found by using the expressionPerform the indicated division. 373 872 +8 T-2
The 2020 Nissan Leaf electric car can travel 226 mi on a fully charged 62-kW · h battery. How much electricity (in kW · h) is required to drive this car on a 350-mi trip? Assume all numbers are
Perform the indicated multiplications.By multiplication, show that (x + y)3 is not equal to x3 + y3.
Each of two suppliers has 2n + 1 bundles of shingles costing $30 each and n − 2 bundles costing $20 each. How much more is the total value of the $30 bundles than the $20 bundles?
Perform the indicated multiplications.Explain how you would perform (x + 3)5. Do not actually do the operations.
A shipment contains x hard drives with 4 terabytes of memory and x + 25 hard drives with 8 terabytes. Express the total number of terabytes of memory in the shipment as a variable expression and
Solve the given problems.In finding the total resistance of the resistors shown in Fig. 1.14, the following expression is used.Simplify this expression. 6R₁ + 6R₂ + R₁ R₂ 6R₁ R₂
In blending two gasolines of different octanes, in order to find the number n of gallons of one octane needed, the equation 0.14n + 0.06(2000 − n) = 0.09(2000) is used. Find n, given that 0.06 and
Simplify the given algebraic expressions. Research on a plastic building material leads toSimplify this expression. [(B + a) + 2(B − a)] - [(B+ a) - (B-a)].
Perform the indicated multiplications.Let x = 3 and y = 4 to show that (a) (x + y)2 ≠ x2 + y2 (b) (x − y)2 ≠ x2 − y2.
One car goes 30 km/h for t − 1 hours, and a second car goes 40 km/h for t + 2 hours. Find the expression for the sum of the distances traveled by the two cars.
Solve the given problems.In the optical theory dealing with lasers, the following expression arises:(μ is the Greek letter mu.) Simplify this expression. 8A5 + 4A?μ?E? - Au4E4 8A4
To find the voltage V in a circuit in a TV remote-control unit, the equation 1.12V − 0.67(10.5 − V) = 0 is used. Find V.
Perform the indicated multiplications.[(x − 2)2 (x + 2)]2

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