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2 years ago

9

Write a equivalent fraction 2/8

2 answers:

Charra [1.4K]2 years ago

7 0

Multiply or divide any number of the same number that will go into the numerator and denominator and it will always be an equivalent fraction

2/8 = 1/4

2/2 = 1
8/2 = 4

o-na [289]2 years ago

6 0

1/4 is equivalent to 2/8

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Find the 10th partial sum of the arithmetic sequence defined by

Evgesh-ka [11]

Answer:

22.5

Step-by-step explanation:

If you expand the series, you can see the first few terms of the series:

Putting 1 in $n$ , $\frac{1}{2}(1)-\frac{1}{2}=0$
Putting 2 in $n$ , $\frac{1}{2}(2)-\frac{1}{2}=0.5$
Putting 3 in $n$ , $\frac{1}{2}(3)-\frac{1}{2}=1$
Putting 4 in $n$ , $\frac{1}{2}(4)-\frac{1}{2}=1.5$

We can see the series is 0, 0.5, 1, 1.5, ....

This is an arithmetic series with common difference (the difference in 2 terms) 0.5 and first term 0.

We know formula for sum of arithmetic series:

$s_{n}=\frac{n}{2}(2a+(n-1)d)$

Where,

$S_{n}$ denotes the nth partial sum
$a$ is the first term (in our case it is 0)
$n$ is the term (in our case it is 10 since we want to find 10th partial sum -- sum until first 10 terms)
$d$ is the common difference (difference in term and the previous term) (in our case it is 0.5)

Substituting these into the formula, we get the 10th partial sum to be:

$s_{10}=\frac{10}{2}(2(0)+(10-1)(0.5))\\s_{10}=5(0+(9)(0.5))\\s_{10}=5(0+4.5)\\s_{10}=5(4.5)\\s_{10}=22.5$

So the sum of the first 10 terms is 22.5. Third answer choice is right.

8 0

2 years ago

Read 2 more answers

PLEASE HELP FAST simplify: sqrt 8 + 2 sqrt 15

Ket [755]

Answer:

2 $\sqrt{2}$ + 2 $\sqrt{15}$

Step-by-step explanation:

$\sqrt{8}$ = $\sqrt{4}$ $\sqrt{2}$ = 2 $\sqrt{2}$

7 0

2 years ago

Express 0.0057 in scientific notation

andrew-mc [135]

Answer:

$5.7 \times {10}^{ - 3}$

Step-by-step explanation:

0.0057

first number

5

then the rest

7

equal

5.7

There's <u>three</u> zeros <u>behind</u> the number 5 which mean it will be -3

$\times {10}^{ - 3}$

final answer

$5.7 \times {10}^{ - 3}$

another example and it will be clear

0.0000403

first number

4

then the rest

03

equal

4.03

There's <u>five</u> zeros <u>behind</u> the number 4 which mean it will be -5

$\times {10}^{ - 5}$

final answer

$4.03 \times {10}^{ - 5}$

3 0

2 years ago

How to solve this system of equal: x+y+z=1;x^2+y^2+z^2=1

swat32

There are infinitely many solutions.

Algebraically, we can eliminate $z$ and try to solve for $x,y$ :

$x+y+z=1\implies z=1-x-y$

Then

$x^2+y^2+(1-x-y)^2=1$

$\implies x^2+y^2+1-2x+x^2-2y+y^2+2xy=1$

$\implies x^2-x+y^2-y+xy=0$

which is the equation of an ellipse.

5 0

3 years ago

keiko, chang, and scott sent a total of 130 text messages over their cell phones during the weekend. Scott sent 10 fewer message

Olenka [21]

Keiko sent 30 text messages Scott sent 20 text messages chang sent 80

8 0

2 years ago