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3 years ago

What is the first step when adding 1.45 x 108 and 3.9 x 107?

Mathematics

1 answer:

garik1379 [7]3 years ago

8 0

We need to add 1.45 x 10^8 and 3.9 x 10^7.

Please see..

We have given numbers in scientific form.

<em>We can't add the decimal numbers in front, because those numbers are being multiplied with 10 exponents and the exponents of 10's are not same.</em>

<em>So, we always convert the exponents of 10 as same.</em>

<em>1.45 x 10^8 could be converted to 14.5 x 10^7 to get exponent of 10 as 7 as other number 3.9 x 10^7 also has exponent of 10 as 7.</em>

<em>After this step we can just add the 14.5 and 3.9 and put × 10^7 with it.</em>

So, first correct step is:

<h3> 2. Convert 1.45 x 108 to 14.5 x 107.</h3>

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A. $x = \frac{9}{4}$

B. $x = 1$

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1. Rewrite the same expression, but multiplied and divided by the same number that has the squared variable.

$4(\frac{4x^2-13x+9}{4})$

2. Take this expression to the expression $x^{2} +bx+c$ , you can do this by grouping. (4)( $4x^{2}$ ) can be grouped as $(4x)^2$ ; since what we want is to keep the (4x) in parenthesis, we don't multiply by 13. leaving it like 13(4x). Finally, we multiply 4 * 9 = 36. The denominator remains. Leaving the expression like:

$\frac{(4x)^2-13(4x)+36}{4}$

So you see, we now have the expression $x^2+bx+c$

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$c = 36$

3. Solve the expression by making 2 parenthesis, extracting (4x) and putting it into both of them like so.

(4x) (4x)

The sign in the first parenthesis is going to be the same as the second number; in this case, negative.

(4x -) (4x)

The sign in the second parenthesis is going to be the multiplication of the second and third signs in front of the numbers. In this case (-) (+) = -

(4x -) (4x -)

Next, we have to find a number that multiplied by another number be equal to ''c'' and added up or substracted (depending on the signs) be equal to ''b''. In this case, since we have the same signs in both parenthesis, we must only find a number which multiplied by another number be equal to 36 and substracted by that number be equal to 13. These two numbers are: 9 and 4 because 9 * 4 = 36 and - 9 + (-4) = -13

Remember that everything is being divided by 4 in this problem.

$\frac{(4x-9)(4x-4)}{4}$

4. Factor. If you have done everything correctly, the factor number will be the same as the one in the denominator. In this case, it's 4.

$(4x-4)$ is factorable. Their common factor number is 4. If you do not remember how to factor, it's basically dividing by a common number or variable.