Answer:
D. x ≥ -10
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
Step-by-step explanation:
<u>Step 1: Define</u>
10 - 4x ≤ 50
<u>Step 2: Solve for </u><em><u>x</u></em>
- Subtract 10 on both sides: -4x ≤ 40
- Divide -4 on both sides: x ≥ -10
Here we see that any value <em>x</em> greater than or equal to -10 would be a solution to the inequality.
—The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.
The measure of an inscribed angle is half the measure of the intercepted arc. That is, m∠ABC=12m∠AOC. This leads to the corollary that in a circle any two inscribed angles with the same intercepted arcs are congruent.
So,
Let x represent Joe's weight and y represent Jeff's weight.
"Joe weighs 20 lbs. less than twice Jeff's weight."
x = 2y - 20
"If Jeff would gain 10 lbs., then together they would weigh 250 lbs."
(y + 10) + x = 250
We now have our two open sentences.
x = 2y - 20
(y + 10) + x = 250
Get rid of parentheses.
x = 2y - 20
x + y + 10 = 250
We will use Elimination by Substitution.
2y - 20 + y + 10 = 250
Collect Like Terms.
3y - 10 = 250
Add 10 to both sides.
3y = 260
Divide both sides by 3.

Substitute again.

Multiply.

Subtract.

Check.
"Joe weighs 20 lbs. less than twice Jeff's weight."
Jeff's weight times two is 173 and one-third.
20 lbs. less than that is 153 and one-third lbs. Check.
"If Jeff would gain 10 lbs., then together they would weigh 250 lbs."
86 and two-thirds + 10 = 96 and two-thirds.
96 and two-thirds + 153 and one-third equals 250 lbs. Check.

If you would like to know the factored form of x^6 - 9, you can do this using the following steps:
x^6 - 9 = (x^3 + 3) * (x^3 - 3) = x^3 * x^3 - 3x^3 + 3x^3 - 3 * 3 = x^6 - 9
The correct result would be (x^3 + 3) * (x^3 - 3).