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3 years ago

Find a common difference of the arithmetic sequence -2, -1 4/5, -1 3/5, -1 2/5,

Mathematics

1 answer:

elixir [45]3 years ago

6 0

Answer:

The common difference is $\frac{1}{5}$ or 0.2

Step-by-step explanation:

Given:

Arithmetic Sequence -2, -1 4/5, -1 3/5, -1 2/5,

First term = a₁ = -2

Second term = a₂ = $\frac{-9}{5}$

Third term = a₃ = $\frac{-8}{5}$

Fourth term = a₄ = $\frac{-7}{5}$

To Find:

Common Difference = d = ?

Solution:

Formula for Common Difference d , $\textrm{common difference}= \textrm{Second Term} -\textrm{First Term}=\textrm{Third Term}-\textrm{Second Term}$

$\textrm{common difference} = a_{2}- a_{1}= a_{3}- a_{2}=a_{4}- a_{3}$

∴ $d = \frac{-9}{5}-(-2)\\d=\frac{-9}{5}+2\\d=\frac{1}{5}\\ \therefore d =0.2\\$

The common difference is $\frac{1}{5}$ or 0.2

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What value of x will make the given triangles congruent?

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Step-by-step explanation:

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Complete the table of values

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Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify!

You need to know three exponent rules to simplify these expressions:
1) The negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example, $3^{-2} =
\frac{1}{3^{2} }$ .
2) Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example, $(\frac{3}{4}) ^{3} = \frac{ 3^{3} }{4^{3} }$ .
3) The zero exponent rule says that any number raised to zero is 1. For example, $3^{0} = 1$ .


Back to the Problem:
Problem 1
The x-values are in the left column. The title of the right column tells you that the function is $y = 4^{-x}$ . The x-values are:
1) x = 0
Plug this into $y = 4^{-x}$ to find letter a:
$y = 4^{-x}\\
y = 4^{-0}\\
y = 4^{0}\\
y = 1$

2) x = 2
Plug this into $y = 4^{-x}$ to find letter b:
$y = 4^{-x}\\ 
y = 4^{-2}\\ 
y = \frac{1}{4^{2}} \\ 
y= \frac{1}{16}$

3) x = 4
Plug this into $y = 4^{-x}$ to find letter c:
$y = 4^{-x}\\ 
y = 4^{-4}\\ 
y = \frac{1}{4^{4}} \\ 
y= \frac{1}{256}$


Problem 2
The x-values are in the left column. The title of the right column tells you that the function is $y = (\frac{2}{3})^x$ . The x-values are:
1) x = 0
Plug this into $y = (\frac{2}{3})^x$ to find letter d:
$y = (\frac{2}{3})^x\\
y = (\frac{2}{3})^0\\
y = 1$

2) x = 2
Plug this into $y = (\frac{2}{3})^x$ to find letter e:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^2\\ y = \frac{2^2}{3^2}\\
y = \frac{4}{9}$

3) x = 4
Plug this into $y = (\frac{2}{3})^x$ to find letter f:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^4\\ y = \frac{2^4}{3^4}\\ y = \frac{16}{81}$

-------

Answers:
a = 1
b = $\frac{1}{16}$ 
c = $\frac{1}{256}$
d = 1
e = $\frac{4}{9}$
f = $\frac{16}{81}$

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3 years ago

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Answer:

Step-by-step explanation:

the proportion is 120/10=1200%

I'm sorry if this is wrong

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How many gallons of a 20% acid solution should be mixed with 30 gallons of a 40% solution, to obtain a mixture of 30% acid solut

Alexeev081 [22]

Answer:

30 gallons of 20% acid solution should be mixed.

Step-by-step explanation:

Let x gallons of a 20% acid solution was mixed with 30 gallons of a 40% solution, to obtain a mixture of 30% acid solution.

Therefore, final volume of the solution will be (x + 30) gallons.

Now concept to solve this question is

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0.20(x) + 0.40(30) = 0.30(x + 30)

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