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3 years ago

Complete the problems. (From Example 2)

Mathematics

1 answer:

Zarrin [17]3 years ago

7 0

Answer:

Compound interest is $7,037,339.2

Step-by-step explanation:

${ \boxed{ \bf{A=P(1+ \frac{r}{100} ) {}^{n} }}}$

substitute:

${ \sf{ = 50000(1 + \frac{6.4}{100}) {}^{10} }} \\ \\ = { \sf{50000(1.64) {}^{10} }} \\ \\ { = \sf{7037339.2}}$

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Solve the following question

White raven [17]

Answer:

g) $u^{4}\cdot v^{-1}\cdot z^{3}$ , h) $\frac{(x+4)\cdot (x+2)}{3\cdot (x-5)}$

Step-by-step explanation:

We proceed to solve each equation by algebraic means:

g) $\frac{u^{5}\cdot v}{z}\div \frac{u\cdot v^{2}}{z^{4}}$

1) $\frac{u^{5}\cdot v}{z}\div \frac{u\cdot v^{2}}{z^{4}}$ Given

2) $\frac{\frac{u^{5}\cdot v}{z} }{\frac{u\cdot v^{2}}{z^{4}} }$ Definition of division

3) $\frac{u^{5}\cdot v\cdot z^{4}}{u\cdot v^{2}\cdot z}$ $\frac{\frac{a}{b} }{\frac{c}{d} } = \frac{a\cdot d}{b\cdot c}$

4) $\left(\frac{u^{5}}{u} \right)\cdot \left(\frac{v}{v^{2}} \right)\cdot \left(\frac{z^{4}}{z} \right)$ Associative property

5) $u^{4}\cdot v^{-1}\cdot z^{3}$ $\frac{a^{m}}{a^{n}} = a^{m-n}$ /Result

h) $\frac{x^{2}-16}{x^{2}-10\cdot x + 25} \div \frac{3\cdot x - 12}{x^{2}-3\cdot x -10}$

1) $\frac{x^{2}-16}{x^{2}-10\cdot x + 25} \div \frac{3\cdot x - 12}{x^{2}-3\cdot x -10}$ Given

2) $\frac{\frac{x^{2}-16}{x^{2}-10\cdot x+25} }{\frac{3\cdot x - 12}{x^{2}-3\cdot x - 10} }$ Definition of division

3) $\frac{(x^{2}-16)\cdot (x^{2}-3\cdot x -10)}{(x^{2}-10\cdot x + 25)\cdot (3\cdot x - 12)}$ $\frac{\frac{a}{b} }{\frac{c}{d} } = \frac{a\cdot d}{b\cdot c}$

4) $\frac{(x+4)\cdot (x-4)\cdot (x-5)\cdot (x+2)}{3\cdot (x-5)^{2}\cdot (x-4) }$ Factorization/Distributive property

5) $\left(\frac{1}{3} \right)\cdot (x+4)\cdot (x+2)\cdot \left(\frac{x-4}{x-4} \right)\cdot \left[\frac{x-5}{(x-5)^{2}} \right]$ Modulative and commutative properties/Associative property

6) $\frac{(x+4)\cdot (x+2)}{3\cdot (x-5)}$ $\frac{a^{m}}{a^{n}} = a^{m-n}$ / $\frac{a}{b}\times \frac{c}{d} = \frac{a\cdot c}{b\cdot d}$ /Definition of division/Result

3 0

3 years ago

The population of a local species of beetle can be found using an infinite geometric series where a1 = 880 and the common ratio

nasty-shy [4]

Data:

infinite geometric series

A1 = 880

r = 1 / 4

The sum of a geometric series in sigma notation is:

n 1 - r^n
∑ Ai = A ----------- ; where A = A1
i = 1 1-r

When | r | < 1 the infinite sum exists and is equal to:

∞ A
∑ Ai = ---------- ; where A = A1
i = 1 1 - r

So, in this case:

∞ 880
∑ Ai = -------------- = 4 * 880 / 3 = 3520 /3 = 1173 + 1/3
i = 1 1 - (1/4) 

Answer: 1173 and 1/3

6 0

3 years ago

A student has a container with a volume of 1.5 liters. She estimates the volume to be 1.8 liters. By what percent is the student

zalisa [80]

Answer:

20%

Step-by-step explanation:

3 0

3 years ago

Y = 6x + 11 2х - Зу = 7

irakobra [83]

9514 1404 393

Answer:

(x, y) = (-2.5, -4)

Step-by-step explanation:

Since you are given an expression for y, it is convenient to substitute that into the second equation.

2x -3(6x +11) = 7

2x -18x -33 = 7

-16x = 40 . . . . . . add 33

x = -40/16 = -2.5

Using the equation for y, we find ...

y = 6(-2.5) +11 = -15 +11 = -4

The solution is (x, y) = (-2.5, -4).

8 0

3 years ago

Plz help 20 points if you get it right and I will give you brainliest

krek1111 [17]

Answer:

The first one cannot be simplified

reason: usually when simplifying an expression you combine like terms but in the given expression there are no like terms

An example of like terms would be 6a and 9a

Essentially what i am saying is that the variables have to be the same in order for them to be combined

The second one is 36r

This is the answer because they tried to combine like terms that aren't similar

r and f are not the same variable therefore they cannot be combined

Hope this helps :)

5 0

2 years ago

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