Plzz help 22 points, 11 if brainliest

What are the characteristics of a good definition?

Gnom [1K]

Answer: excellent geometry definition will classify, quantify, and not have a counterexample once parallel lines are defined, they can be used in the definition of a parallelogram.

5 0

2 years ago

What is the following sum?<br>(please show how you worked it out)

AleksAgata [21]

Answer:

$4\sqrt[3]{2}x(\sqrt[3]{y}+3xy\sqrt[3]{y} )$

Step-by-step explanation:

Let's start by breaking down each of the radicals:

$\sqrt[3]{16x^3y}$

Since we're dealing with a cube root, we'd like to pull as many perfect cubes out of the terms inside the radical as we can. We already have one obvious cube in the form of $x^3$ , and we can break 16 into the product 8 · 2. Since 8 is a cube root -- 2³, to be specific, we can reduce it down as we simplify the expression. Here our our steps then:

$\sqrt[3]{16x^3y}\\=\sqrt[3]{2\cdot8\cdot x^3\cdot y}\\=\sqrt[3]{2} \sqrt[3]{8} \sqrt[3]{x^3} \sqrt[3]{y} \\=\sqrt[3]{2} \cdot2x\cdot \sqrt[3]{y} \\=2x\sqrt[3]{2}\sqrt[3]{y}$

We can apply this same technique of "extracting cubes" to the second term:

$\sqrt[3]{54x^6y^5} \\=\sqrt[3]{2\cdot27\cdot (x^2)^3\cdot y^3\cdot y^2} \\=\sqrt[3]{2}\sqrt[3]{27} \sqrt[3]{(x^2)^3} \sqrt[3]{y^3} \sqrt[3]{y^2}\\=\sqrt[3]{2}\cdot 3\cdot x^2\cdot y \cdot \sqrt[3]{y^2} \\=3x^2y\sqrt[3]{2} \sqrt[3]{y}$

Replacing those two expressions in the parentheses leaves us with this monster:

$2(2x\sqrt[3]{2}\sqrt[3]{y})+4(3x^2y\sqrt[3]{2} \sqrt[3]{y})$

What can we do with this? It seems the only sensible thing is to look for terms to factor out, so let's do that. Both terms have the following factors in common:

$4, \sqrt[3]{2} , x$

We can factor those out to give us a final, simplified expression:

$4\sqrt[3]{2}x(\sqrt[3]{y}+3xy\sqrt[3]{y} )$

Not that this is the same sum as we had at the beginning; we've just extracted all of the cube roots that we could in order to rewrite it in a slightly cleaner form.

6 0

3 years ago

3x - y = 8 <br>how do I solve this linear equation?

Effectus [21]

1. Add y to each side
That will get you 3x=8+y
2. Subtract 8 on each side
That will get you y=3x-8

8 0

4 years ago

Six girls share 5 pints of milk equally what fraction of a pint of milk does each girl get?

konstantin123 [22]

To answer this we need to divide 5 by 6.

First we need to convert the numbers to fractions (since we need a fraction for an answer).

$\frac{5}{1} \frac{6}{1}$

When dividing fraction, multiply the first fraction by the reciprocal of the second fraction. (A reciprocal is an upside down fraction)

$\frac{5}{1} * \frac{1}{6} = \frac{5}{6}$

The answer is $\frac{5}{6}$

Hopefully this helps! If you have any more questions or don't understand, feel free to DM me, and I'll get back to you ASAP! :)

8 0

3 years ago

Tiana was designing a fish tank that could hold 5,364 ml of water. She's already filled the tank a quarter of the way. How many

gavmur [86]

Answer: 4.023 litres

Step-by-step explanation:

Find out what a quarter of the capacity of the tank is first:

= 5,364 * 1/4

= 1,341 ml

The number of ml left to fill up the tank is:

= 5,364 - 1,341

= 4,023 ml

1 litre = 1,000 ml

4,023 ml in litres = 4,023 / 1,000

= 4.023 litres

7 0

3 years ago