Mathematics, 26.03.2020 20:34 amorenextdoor

Find the solution set to each inequality. Express the solution in set notation.
6+2 < 5−4
a/5 +8 ≤ 13
−3 −7 > −27
8(−6) > 4(−4)

Answers: 2

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Answers

Answer from: dajahp

First, solve each inequality. I'll solve the first one first.

≥

−

≥

Therefore, x could be any number less than or equal to 6. In interval notation, this looks like:

(

−

∞

]

The parenthesis means that the lower end is not a solution, but every number above it is. (In this case, the lower end is infinity, so a parenthesis must be used, since infinity is not a real number and so it cannot be a solution.) The bracket means that the upper end is a solution. In this case, it indicates that not only could

be any number less than 6, but it could also be 6.

Let's try the second example:

−

Therefore, x could be any number greater than 6, but x couldn't be 6, since that would make the two sides of the inequality equal. In interval notation, this looks like:

(

∞

)

The parentheses mean that neither end of this range is included in the solution set. In this case, it indicates that neither 6 nor infinity are solutions, but every number in between 6 and infinity is a solution (that is, every real number greater than 6 is a solution).

Now, the problem used the word "OR", meaning that either of these equations could be true. That means that either

is on the interval

(

−

∞

]

or the interval

(

∞

)

. In other words,

is either less than or equal to 6, or it is greater than 6. When you combine these two statements, it becomes clear that

could be any real number, since no matter what number

is, it will fall in one of these intervals. The interval "all real numbers" is written like this:

(

−

∞

)

Final Answer

Answer from: Quest

fghrtyhrtsyut jyt u6su

step-by-step explanation:

Answer from: Quest

answer: the answer is (b) amie should have multiplied

$54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

$v_s=\pi r^2h=\pi r^3,$

and the volume of the cylinder will be

$v_c=\dfrac{4}{3}\pi r^3=54~\textup{m}^3.$

therefore, we have

$v_c=\dfrac{4}{3}v_s=\dfrac{4}{3}\times 54=72~\textup{m}^3.$

thus, ammie should have multiplied the volume of the sphere $54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

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Find the solution set to each inequality. Express the solution in set notation.
6+2 < 5−4

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