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3 years ago

What is the solution set of {x | x < -5} ∩ {x | x > 5}?

Mathematics

1 answer:

Pavlova-9 [17]3 years ago

8 0

The first part of the set tells us that x is less than -5.

The second part tells us that x is greater than 5.

The intersection sign in the middle tells us to find "common" item in the first part and second part.

<u><em>Is there any number both greater than 5 and less than -5? No!</em></u>

So our solution doesn't exist and is the empty set.

ANSWER: The empty set

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Nana76 [90]

Look at the picture.

$\csc\theta=\dfrac{1}{\sin\theta}=\dfrac{1}{\frac{y}{r}}=\dfrac{r}{y}$

We have the right triangle x, y and r. From the Pythagorean theorem we have:

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We have the point

$\left(-\dfrac{2}{3};\ \dfrac{\sqrt5}{3}\right)$

Substitute:

$r=\sqrt{\left(-\dfrac{2}{3}\right)^2+\left(\dfrac{\sqrt5}{3}\right)^2}\\\\r=\sqrt{\dfrac{4}{9}+\dfrac{5}{9}}\\\\r=\sqrt{\dfrac{9}{9}}\\\\r=1$

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3 years ago

A DVD was priced at $2.87 last week. This week the same DVD is priced at $10.59. What is the percent increase in price?

solniwko [45]

Answer:

Percentage increase = 269%

Step-by-step explanation:

Price of a DVD last week = $2.87

Price of the same DVD this week = $10.59

Increase in the price of DVD between last week and this week = 10.59 - 2.87

= $7.72

Therefore, percentage increase in the price of DVD = $\frac{\text{Increase in the price}}{\text{Price of DVD last week}}\times 100$

= $\frac{7.72}{2.87}\times 100$

= 268.99

= 269%

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