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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

For numbers a and b, determine which of the following expressions equals the given expression.(a) a + b (b) a − b (c) b − a (d) −a − b−a − (−b)
For numbers a and b, determine which of the following expressions equals the given expression.(a) a + b (b) a − b (c) b − a (d) −a − b−b − (−a)
For numbers a and b, determine which of the following expressions equals the given expression.(a) a + b (b) a − b (c) b − a (d) −a − bb − (−a)
For numbers a and b, determine which of the following expressions equals the given expression.(a) a + b (b) a − b (c) b − a (d) −a − b−a + (−b)
After 5s, the pressure on a valve is less than 60lb/in.2 (pounds per square inch). Using t to represent time and p to represent pressure, this statement can be written “for t > 5 s, p <
Determine which of the fundamental laws of algebra is demonstrated.(3 × 6) × 7 = 7 × (3 × 6)
In a laboratory report, a student wrote “−20°C > −30°C.” Is this statement correct? Explain.
The computer design of the base of a truss is x ft long. Later it is redesigned and shortened by y in. Give an equation for the length L, in inches, of the base in the second design.
In an electric circuit, the reciprocal of the total capacitance of two capacitors in series is the sum of the reciprocals of the capacitancesFind the total capacitance of two capacitances of 0.0040F
A sensitive gauge measures the total weight w of a container and the water that forms in it as vapor condenses. It is found that where c is the weight of the container and t is the time of
Determine which of the fundamental laws of algebra is demonstrated.8(3 − 2) = 8(3) − 8(2)
The memory of a certain computer has a bits in each byte. Express the number N of bits in n kilobytes in an equation.
Determine which of the fundamental laws of algebra is demonstrated.3 + (5 + 9) = (3 + 5) + 9
Alternating-current (ac) voltages change rapidly between positive and negative values. If a voltage of 100 V changes to −200V, which is greater in absolute value?
Determine which of the fundamental laws of algebra is demonstrated.4(5 × π) = (4 × 5)(π)
Evaluate each of the given expressions by performing the indicated operations. 31-9-2(-3)| 1 + (-10)
Determine which of the fundamental laws of algebra is demonstrated.6(3 + 1) = 6(3) + 6(1)
Evaluate each of the given expressions by performing the indicated operations. 20(-12) 40(-15) 98-1-981
Determine which of the fundamental laws of algebra is demonstrated.6 + 8 = 8 + 6
Evaluate each of the given expressions by performing the indicated operations. .-7- 1-141 2(2-3) 316-81
A complex number is defined as a + bj, where a and b are real numbers and j = √−1. For what values of a and b is the complex number a + bj a real number?
Evaluate each of the given expressions by performing the indicated operations. -6 −7(−3) + = − 1 -3 -1-91
Determine which of the fundamental laws of algebra is demonstrated.6(7) = 7(6)
For a number x < 0, describe the location on the number line of the number with a value of |x| .
Evaluate each of the given expressions by performing the indicated operations. 24 3+ (-5) - 4(-9) ÷ (-3)
For a number x > 1, describe the location on the number line of the reciprocal of x.
Evaluate each of the given expressions by performing the indicated operations. - 18 3 4-1-61 - 1 -4-1
Describe the location of a number x on the number line when(a) |x| < 1 (b) |x| > 2.
Describe the location of a number x on the number line when(a) x > 0 (b) x < −4.
Evaluate each of the given expressions by performing the indicated operations. 7-1-51 -1(-2)
For any positive or negative rational number: (a) Is its absolute value always a rational number? (b) Is its reciprocal always a rational number?
For any positive or negative integer: (a) Is its absolute value always an integer? (b) Is its reciprocal always a rational number?
Evaluate each of the given expressions by performing the indicated operations. 1-21 (-2)(-5) -2
If a and b represent positive integers, what kind of number is represented by (a) a + b, (b) a / b (c) a × b
If a and b are positive integers and b > a, what type of number is represented by the following?(a) b − a (b) a − b(c) b − a/b + a
Find the absolute value of each real number.3, −3, π/4 , √−1
Evaluate each of the given expressions by performing the indicated operations. 8 -20-00+11
List the following numbers in numerical order, starting with the smallest: 1/5 , −√10, |−6|, −4, 0.25,|−π|.
Evaluate each of the given expressions by performing the indicated operations. (7-7)(2) (7-7)(-1)
List the following numbers in numerical order, starting with the smallest: −1, 9, π, √5, |−8| , −|−3|, −3.1.
Evaluate each of the given expressions by performing the indicated operations.−20 + 8 ÷ 4
Evaluate each of the given expressions by performing the indicated operations. 17 - 7 7-7
If b > a and a > 0, is |b − a| < |b| − |a|?
Evaluate each of the given expressions by performing the indicated operations.8 − 3(−4)
True or False: A nonterminating, nonrepeating decimal is an irrational number.
Is the repeating decimal 2.7̅2 rational or irrational?
Locate (approximately) each number on a number line as in Fig. 1.2.Data from Fig 1.2 2.5, 12 5 v3. 3 4
What is the reciprocal of the reciprocal of any positive or negative number?
Evaluate each of the given expressions by performing the indicated operations. - 64 -214-81
Locate (approximately) each number on a number line as in Fig. 1.2.Data from Fig 1.2 2 2. 123 19 7 3
Evaluate each of the given expressions by performing the indicated operations.(7 − 7) ÷ (5 − 7)
Locate (approximately) each number on a number line as in Fig. 1.2.Data from Fig 1.2 2 2. 123 19 7 3
Is −2.17 rational? Explain.
Evaluate each of the given expressions by performing the indicated operations.−9 − |2 − 10|
Is an absolute value always positive? Explain
Evaluate each of the given expressions by performing the indicated operations.−20 ÷ 5(−4)
Find the reciprocal of each number. 3,- 4 20
Evaluate each of the given expressions by performing the indicated operations.16 ÷ 2(−4)
Find the reciprocal of each number.−1/3, 0.25, 2x
Evaluate each of the given expressions by performing the indicated operations.2(2 − 7) ÷ 10
Evaluate each of the given expressions by performing the indicated operations.−3(−4)(−6)
Insert the correct sign of inequality (> or <) between the given numbers.−0.6 0.2
Insert the correct sign of inequality (> or <) between the given numbers. انیا | نا
Evaluate each of the given expressions by performing the indicated operations. -28 -7(5-6)
Evaluate each of the given expressions by performing the indicated operations. -6(20 - 10) -3
Evaluate each of the given expressions by performing the indicated operations.−2(4)(−5)
Insert the correct sign of inequality (> or <) between the given numbers.−√2 −1.42
Insert the correct sign of inequality (> or <) between the given numbers.−4 −|−3|
Evaluate each of the given expressions by performing the indicated operations.−9/3
Insert the correct sign of inequality (> or <) between the given numbers.−4 0
Find the absolute value of each real number. -0.857, √2, 19 4 √-5 -2
Evaluate each of the given expressions by performing the indicated operations.−7(−5)
Insert the correct sign of inequality (> or <) between the given numbers.π 3.1416
Evaluate each of the given expressions by performing the indicated operations.−9(3)
Insert the correct sign of inequality (> or <) between the given numbers.7 5
Evaluate each of the given expressions by performing the indicated operations.7(−4)
Evaluate each of the given expressions by performing the indicated operations.−8 − (−10)
Evaluate each of the given expressions by performing the indicated operations.−19 − (−16)
Evaluate each of the given expressions by performing the indicated operations.18 − 21
Designate each of the given numbers as being an integer, rational, irrational, real, or imaginary.−√−6, −2.33
Designate each of the given numbers as being an integer, rational, irrational, real, or imaginary.√7/3 , −6
Designate each of the given numbers as being an integer, rational, irrational, real, or imaginary. π 9 |∞0
Evaluate each of the given expressions by performing the indicated operations.−4 + (−7)
Evaluate each of the given expressions by performing the indicated operations.−3 + 9
Evaluate each of the given expressions by performing the indicated operations.5 + (−8)
Designate each of the given numbers as being an integer, rational, irrational, real, or imaginary.3√−4
In Example 6(b), change 18 to −18 and then evaluate.Data from Example 6(b)18/-6 + 5 -(-2)(3) = −3 + 5 -(-6) = 2 + 6 = 8
In the rightmost illustration in Example 9, interchange the 6 and the 0 above the 6. Is any other change needed?Data from Example 9 2|5 0 is undefined is undefined 7x0 0x6 is indeterminate
In Example 6, change the 2/3 to 3/2 What other changes must then be made?Data from Example 6.The reciprocal of 7 is 1/7. The reciprocal of 2/3 isThe reciprocal of 0.5 is 1/0.5 = 2 The reciprocal of
In the left figure of Example 5, change the 2 to −6. What other changes must then be made?Data from Example 5 -4 2>-4 2 is to the right of -4 -2 0 3-7 Pointed toward smaller number -1
In Example 6(d), interchange the 2 and 8 in the first denominator and then evaluate.Data from Example 6(d) -12 2 8 + 5-1 2(-1) = -12 4 + -6 -2 = 2 + (-2) 2 - 2 = 0 =
In Example 4, change the 6 to −6. What other changes must then be made in the first paragraph?Data from Example 4The absolute value of 6 is 6, and the absolute value of −7 is 7. We write these as
In Example 5(c), change 3 to −( 2) and then evaluate.Data from Example 5(C)[16 − 2 × 3 is evaluated by first multiplying 2 by 3 and then subtracting. We do not first subtract 2 from 16.]

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