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3 years ago

.46 repeating as a fraction in simplest form

Mathematics

1 answer:

My name is Ann [436]3 years ago

4 0

Answer:

7/15

Step-by-step explanation:

0.4 6 = 0 . 6 - 0.2

0.46 = 6/9 ⋅ 0.9 - 0.2

0.46 = 6/9 - 1/5

0.46 = 2/3 - 1/5

0.46 = 10/15 - 3/15

0.46 = 7/15

Note that 7 and 15 have no common factors larger than 1 , so this is in simplest terms.

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16. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.

il63 [147K]

Answer:

Given equation are:

$y = -\frac{1}{4}x+8$ ......[1]

$-2x+8y = 4$ .....[2]

The two lines are parallel lines then their slopes will be equal.

When two lines are perpendicular then, the slope of lines are the negative reciprocals of each other.

Now, Equation of a line is in the form of y =mx+b where m is the slope of the line.

Slope $(m_1)$ of equation of line in [1] is;

$y = -\frac{1}{4}x+8$

then;

$m_1= -\frac{1}{4}$

Slope $(m_2)$ of equation of line in [2];

$-2x+8y = 4$

Add both sides 2x we get;

-2x + 8y + 2x = 2x + 4

Simplify:

8y = 2x +4

Divide both sides by 8 we get;

$y = \frac{1}{4} x + \frac{1}{2}$

then;

$m_2 = \frac{1}{4}$

Therefore, the given two lines are neither parallel nor perpendicular.

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3 years ago

Tim must read 2 books from a list of 7 recommended books for his summer reading program. In how many different ways can Tim choo

Marianna [84]

There are 21 ways Tim choose 2 books from the 7 recommended book

Solution:

Given that Tim must read 2 books from a list of 7 recommended books for his summer reading program

To find: different ways can Tim choose 2 books from the 7 recommended books

This is a combination problem

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected

The formula for combinations is:

$n C_{r}=\frac{n !}{r !(n-r) !}$

where n represents the number of items, and r represents the number of items being chosen at a time

Here we have to choose 2 books from 7 books

Therefore, n = 7 and r = 2

Substituting values in above formula, we get

$\begin{aligned}&7 C_{2}=\frac{7 !}{2 !(7-2) !}\\\\&7 C_{2}=\frac{7 !}{2 ! \times 5 !}\end{aligned}$

For a number n, the factorial of n can be written as,

$n !=n \times(n-1) \times(n-2) \dots \dots \times 2 \times 1$

Therefore, we get

$7 C_{2}=\frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 5 \times 4 \times 3 \times 2 \times 1}\\\\7C_2 = 7 \times 3 = 21$

Thus there are 21 ways Tim choose 2 books from the 7 recommended book

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Paula has two fish tanks that are leaking. The first fish tank hold 50 gallons of water and is leaking at a rate of 5 gallons pe

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Answer:what is the question

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Answer:

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3 years ago

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Answer:

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Step-by-step explanation:

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