Mathematics, 05.07.2019 06:00 zubeenakhtar1386

Which statements are true check all that apply

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Answer from: bellabarfield4286

The true statements are:

Statement 1: The equation |-x -4| = 8 will have two solutions

Statement 5: The equation | 0.5x - 0.75 | + 4.6 = 0.25 will have no solutions.

Explanation:

These are six completely different and independent statements. Every one has one equation that needs to be solved.

Which statements are true?

A. Statement 1: The equation |-x -4| = 8 will have two solutions

true

Justification:

1. First step is to remove the bars of the absolute value function:

| - x - 4 | = 8

⇒ - x - 4 = 8 or - x - 4 = - 8

2. Solve first equation: - x - 4 = 8

addition property of equality (add 4): - x = 8 + 4combine like terms: - x = 12multiplication property of equality (multiply by -1): x = - 12

3. Solve second equation: - x - 4 = - 8

addition property of equality (add 4): - x = -8 + 4combine like terms: - x = - 4multiplication propery (multiplicate by -1): x = 4

Hence, the equation has two solutions x = - 12 and x = 4

B. Statement 2: The equation 3.4|0.5x - 42.1| = - 20.6 will have one solution.

false.

Justification:

The left hand side cannot be negative, because the absolute value is always positive, and the right hand side is negative, hence, the equality is false.

C. Statement 3: The equation | (1/2)x - 3/4 | = 0 has no solutions

false

Justification:

Since 0 is not either positive or negative the only solution of that equation is (1/2x) - 3/4 = 0By the addition property: (1/2)x = 3/4By the multiplication property: x = 2(3)/4 = 3/2

Therefore, the equation has one solution.

D. Statement 4: |2x - 10 | = - 20 will have two solutions

false

Justification:

The left hand side is cannot be negative, and the right hand side is negative, hence the equality can never be true.

E. Statement 5: The equation | 0.5x - 0.75 | + 4.6 = 0.25 will have no solutions.

true.

Justification:

Since the absolute value cannot be negative, when you add it to 4.6, you will obtain a number greater than or equal to 4.6, hence the left hand side will never be equal to the right hand side (0.25), making the statement false.

F. Statement 6: the equation | (1/8)x - 1 | = 5 will have infinetely many solutions.

false:

Justification:

1. Remove the bars:

| (1/8)x - 1 | = 5 ⇒ (1/8)x - 1 = 5 or (1/8)x - 1 = - 5

2. You do not need to solve the equations to see that you will obtain only two solutions. Hence, the statement is false.

Answer from: Quest

Agreed i also had the same answer

Answer from: Quest

$30.32

step-by-step explanation:

65.00*.12=2.80

65.00-2.80=57.20

57.20*1.06=60.632

60.632/2=30.316

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