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1 year ago

If | 8x -2 | < 4, Which of the following is true of x? Explain as well.

Mathematics

1 answer:

wariber [46]1 year ago

3 0

The true expression of the variable x in the inequality expression given as |8x - 2| < 4 is -0.25 < x < 0.75

<h3>What are inequality expressions?</h3>

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

<h3>How to determine the true expression of the variable x?</h3>

The inequality expression is given as

|8x - 2| < 4

Divide through the above equations by 2

So, we have the following inequality expression

|4x - 1| < 2

Remove the absolute value sign from the inequality expression

So, we have

-2 < 4x - 1 < 2

Add 1 to all sides of the above inequality expression

So, we have

-1 < 4x < 3

Divide through the above inequality expression by 4

So, we have

-0.25 < x < 0.75

Hence, the true expression of the variable x in the inequality expression given as |8x - 2| < 4 is -0.25 < x < 0.75

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A garden table and a bench cost $852 combined. The table is $98 less than the bench. What is the cost of the bench?

Citrus2011 [14]

Answer:

Step-by-step explanation:

b=bench

852=b+(b-98) since the table is less than the bench by 98$

852-b=b-98

950-b=b

950=2b

475=b

3 0

3 years ago

At 11:55 p.m., Thomas ties a weight to the minute hand of a clock. The clockwise torque applied by the

ryzh [129]

Answer:

T(t) = 3sin((t-5)π/30)

Step-by-step explanation:

5 minutes after Thomas ties it on, the torque is zero and increasing. So, the sine function is shifted right 5 minutes. The maximum value is 3, so that is the multiplier of the sine function. The period is 60 minutes, so the coefficient of t is (2π/60) = π/30. The function you want is ...

T(t) = 3sin((t-5)π/30)

7 0

3 years ago

Please help and show working (please)

Alexxandr [17]

In mathematical notation, ∑ means summation. So wherever you see the symbol, you have to sum over all elements in the set. Let's solve the question.

a. ∑m means, to sum all elements in the set m: ∑m = 12 + 15 + 20 + 30 = 77

b. ∑ $f^{2}$ means to sum all elements in the set f as the square of the elements f = $5^{2} + 9^{2} + 10^{2} + 16^{2} = 25 + 81 + 100 + 256 = 462$

c. ∑mf means to sum all elements as the product of the elements of m and f = (12×5) + (15×9) + (20 $(12^{2}(5)) + (15^{2}(9)) + (20^{2}(10)) + (30^{2}(16)) = 21145$ 10) + (30×16) = 875

d. ∑ $m^{2}f$ means to sum all elements as the product of the square of m and f = $((12*12)(5)) + ((15*15)(9)) + ((20*20)(10)) + ((30*30)(16)) = 21145$