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Effectus [21]
3 years ago
8

9e^x-240=6e^x+270 what is the solution

Mathematics
1 answer:
zmey [24]3 years ago
4 0

e^x=170

because you subtract like terms (or add, it depends) then simplify (im bad at explaining)

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Factor completely x^8- 16.
Nataly_w [17]

Answer:

Step-by-step explanation:


So in this example we'll be using the difference of squares which essentially states that: (a-b)(a+b)=a^2-b^2 or another way to think of it would be: a-b=(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b}). So in this example you'll notice both terms are perfect squares. in fact x^n is a perfect square as long as n is even. This is because if it's even it can be split into two groups evenly for example, in this case we have x^8. so the square root is x^4 because you can split this up into (x * x * x * x) * (x * x * x * x) = x^8. Two groups with equal value multiplying to get x^8, that's what the square root is. So using these we can rewrite the equation as:

x^8-16 = (x^4-4)(x^4+4)

Now in this case you'll notice the degree is still even (it's 4) and the 4 is also a perfect square, and it's a difference of squares in one of the factors, so it can further be rewritten:

x^4-4 = (x^2-2)(x^2+2)

So completely factored form is: (x^2-2)(x^2+4)(x^4+4)

I'm assuming that's considered completely factored but you can technically factor it further. While the identity difference of squares technically only applies to difference of squares, it can also be used on the sum of squares, but you need to use imaginary numbers. Because x^2+4 = x^2-(-4). and in this case a=x^2 and b=-4. So rewriting it as the difference of squares becomes: x^4+4 = x^4 - (-4) = (x^2-\sqrt{-4})(x^2+\sqrt{-4}) = (x^2-2i)(x^2+2i) just something that might be useful in some cases.

7 0
2 years ago
Read 2 more answers
Which of the following represents the most accurate estimation of 5+4 5,10,15,20
GalinKa [24]
10 5+4 is 9 so it would be 10
6 0
3 years ago
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There are 30 students in a classroom. The ratio of boys to girls is 2:3.
Arisa [49]
<h3>♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫</h3>

➷ Split 30 into the ratio 2 : 3

12 : 18

12 / 18 + x = 1/5

Cross multiply:

12(5) = 1(18 + x)

60 = 18 + x

Subtract 18 from both sides:

x = 42

42 girls entered the classroom

<h3><u>✽</u></h3>

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

8 0
3 years ago
A chicken can run at a top seed of 9 miles per hour find the top speed of a chicken in miles per minute round to the nearest ten
photoshop1234 [79]
The answer would be o.15 miles per hour.
8 0
3 years ago
Rewrite the equation below so that it does not have fractions.
lidiya [134]

Answer:

\frac{15}{20} x-2=\frac{8}{20}

Step-by-step explanation:

\frac{3}{4} x-2=\frac{2}{5}

3/4 and 2/5 have a common denominator which is twenty so you can rewrite the equation with just knowing that

\frac{3}{4} =\frac{15}{20}

\frac{2}{5} =\frac{8}{20}

\frac{15}{20} x-2=\frac{8}{20}

You can then multiply both sides by twenty to solve this equation.

Hope this helps.

4 0
3 years ago
Read 2 more answers
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