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3 years ago

The price of a pair of shoes plus 5% sales tax

Mathematics

2 answers:

Sergeeva-Olga [200]3 years ago

6 0

100%+ 5%= 105%= 1.05

S= shoes

The expression is 1.05s.

Hope this helps!

sesenic [268]3 years ago

6 0

Multiply the price of the shoes times .5 and then add that number to the original price.

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Simplify 81p6q2÷3p2q5 HELPPP

goldfiish [28.3K]

Answer:

$\displaystyle \frac{81\, p^{6}\, q^{2}}{3\, p^{2} \, q^{5}} = \frac{27\, p^{4}}{q^{3}}$ .

Step-by-step explanation:

Make use of the fact that for any $x \ne 0$ and integer $n$ :

$\displaystyle \frac{1}{x^{n}} = x^{-n}$ .

For example, in this question:

$\displaystyle \frac{1}{p^{2}} = p^{-2}$ .

$\displaystyle \frac{1}{q^{5}} = q^{-5}$ .

Thus, the original expression would be equivalent to:

$\begin{aligned}& \frac{81\, p^{6}\, q^{2}}{3\, p^{2} \, q^{5}} \\ =\; & \frac{81}{3}\, (p^{6}\, p^{-2})\, (q^{2}\, q^{-5}) \\ =\; & 27\, (p^{6}\, p^{-2})\, (q^{2}\, q^{-5})\end{aligned}$ .

Also make use of the fact that for any $x \ne 0$ , integer $m$ , and integer $n$ :

$x^{m}\, x^{n} = x^{m + n}$ .

Thus:

$\begin{aligned}& 27\, (p^{6}\, p^{-2})\, (q^{2}\, q^{-5}) \\=\; & 27\, p^{6 + (-2)}\, q^{2 + (-5)} \\ =\; & 27\, p^{4}\, q^{-3} \\ =\; & \frac{27\, p^{4}}{q^{3}}\end{aligned}$ .

3 0

2 years ago

An equilateral triangle with a side length of 6mm and a height of 5.2mm is divided vertically into halves. Find the area of one

Viefleur [7K]

There are two ways you could go about solving this.

You could divide the length of the base (6mm) by 2 and use that to find the area or you could find the area of the whole triangle using 6mm and divide that by 2.

I will use the first method I described:

base = 6/2

base = 3 mm

height = 5.2 mm

area = bh/2

area = (3 * 5.2)/2

area = 7.8 square mm

(don't forget your units)

Using the other method would look like this:

area = bh/2

b = 6

h = 5.2

area = (6 * 5.2)/2

area = 15.6 square mm

area/2 = 7.8 square mm

As you can see either method yields the same result.

Hope this helped.

Cheers and good luck,

Brian

8 0

3 years ago