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

c. x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

$\frac{little}{big} =\frac{side mn}{side ab}=\frac{side on}{side cb}$ .

$\frac{0.96}{1.2}=\frac{x}{3}$

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

$0.96(3)=1.2(x)\\2.88=1.2x\\\frac{2.88}{1.2}=\frac{1.2x}{1.2} \\2.4=x$

Answer from: Quest

won't that be plagrisim thought?

step-by-step explanation:

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