Mathematics, 16.07.2020 18:01 GhostElite6383

which inequality best represents the statement. reduced movie price tickets are available for the following ages (a): children 13 or under and adults 65 years or older

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Answer from: Jsquad8879

13 $\geq$ a $\geq$ 65

Step-by-step explanation:

Let's first look at the beginning of the statement: Reduced movie tickets are available for the following ages (a): children 13 or under. In other words, we know that if you are 13, you can purchase reduced tickets, and if you are ANY age YOUNGER than (or below) 13, you are part of the age range. This tells us that a means your age is equal to 13, or it is less than 13. Because of this conclusion we have come to, we can see that we must use the less than or equal to sign, like this: a $\leq$ 13.

Now, for the second part of the statement that communicates that those 65 and older have this ability as well! In other words, if your age is equal to 65 or it is greater than 65, you are part of the age group that qualifies for the reduced tickets. This means we can use the greater than or equal to sign: a $\geq$ 65.

Just a little bit of work left to go, you're almost done!

Finally, we must figure out how to combine these to come to the correct answer. We have: a $\leq$ 13 and a $\geq$ 65. If we get a in the middle, we will be able to merge these two inequalities! It would make the most sense to keep 13 on the left side, numerically speaking, so we need to mirror everything in that inequality. this gives us: 13 $\geq$ a, which means the EXACT same thing!!! Now, we just add the other inequality to the end of the first to get our final answer of 13 $\geq$ a $\geq$ 65.

If this helped you, I encourage you to leave a "thanks" in order to let others know that this is a valid answer! Thank you for your time!

Answer from: Quest

Dis a correct answer

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

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which inequality best represents the statement. reduced movie price tickets are available for the fo...