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3 years ago

2/5 (x-4) =2x. Solve for x

1 answer:

7 0

$\dfrac{2}{5}(x-4)=2x\ \ \ \ |multiply\ both\ sides\ by\ 5\\\\2(x-4)=10x\ \ \ \ |use\ distributive\ property:a(b-c)=ab-ac\\\\2x-8=10x\ \ \ |add\ 8\ to\ both\ sides\\\\2x=10x+8\ \ \ \ |subtract\ 10x\ from\ both\ sides\\\\-8x=8\ \ \ \ |divide\ both\ sides\ by\ (-8)\\\\\boxed{x=-1}$

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Rationalize the denominator of sqrt -49 over (7 - 2i) - (4 + 9i)

zubka84 [21]

$\sqrt{ \frac{-49}{(7-2i)-(4+9i) } } 
$

This one is quite the deal, but we can begin by distributing the negative on the denominator and getting rid of the parenthesis:

$\frac{ \sqrt{-49}}{7-2i-4-9i}$

See how the denominator now is more a simplification of like terms, with this I mean that you operate the numbers with an "i" together and the ones that do not have an "i" together as well. Namely, the 7 and the -4, the -2i with the -9i.
Therefore having the result:

$\frac{ \sqrt{-49} }{3-11i}$

Now, the $\sqrt{-49}$ must be respresented as an imaginary number, and using the multiplication of radicals, we can simplify it to $\sqrt{49} \sqrt{-1}$
This means that we get the result 7i for the numerator.

$\frac{7i}{3-11i}$

In order to rationalize this fraction even further, we have to remember an identity from the previous algebra classes, namely: $x^2 - y^2 =(x+y)(x-y)$
The difference of squares allows us to remove the imaginary part of this fraction, leaving us with a real number, hopefully, on the denominator.

$\frac{7i (3+11i)}{(3-11i)(3+11i)}$

See, all I did there was multiply both numerator and denominator with (3+11i) so I could complete the difference of squares.
See how $(3-11i)(3+11i)= 3^2 -(11i)^2$ therefore, we can finally write:

$\frac{7i(3+11i)}{3^2 - (11i)^2 }$

I'll let you take it from here, all you have to do is simplify it further.
The simplification is quite straightforward, the numerator distributed the 7i. Namely the product $7i(3+11i) = 21i+77i^2$ .
You should know from your classes that i^2 = -1, thefore the numerator simplifies to $-77+21i$
You can do it as a curious thing, but simplifying yields the result:
$\frac{-77+21i}{130}$

7 0

3 years ago

What is the probability of tossing one coin for two 'tails' in a row?

Tasya [4]

Assuming the coin is fair, probability of getting one tail is 50%, probability of getting two tails in a row is 50%*50% = 25% or 1/4

4 0

2 years ago

Read 2 more answers

In what time will 64000 amount to 68921 at a rate of 5 % per annum comp half yearly

andre [41]

Answer:

Time = T half–years , Rate = 5 % per half year

4 0

3 years ago

Read 2 more answers

A class voted for either rollerblading, swimming, or biking as their favorite summer activity. If rollerblading got 27% percent

emmasim [6.3K]

Answer:

All you have to do is find the rest of the percentage. Percentage adds up to 100%. So you will have to add the two percentages they gave you. 27+33=60%. Now you have to take away 60 from 100. 100-60=40%.

40%- That's the answer.

Hope this helps.

4 0

2 years ago

F (n)=3+4 (n-1). find f(5) and f(6)

Rasek [7]

3+16=19,

3+20=23

So the correct answer would be 19 and 23

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2 years ago