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lapo4ka [179]
3 years ago
12

Evaluate.

Mathematics
1 answer:
const2013 [10]3 years ago
6 0

9514 1404 393

Answer:

  -1/6

Step-by-step explanation:

A suitable calculator can evaluate this for you and show you the result as a fraction.

You start with the multiplication in the inner-most set of brackets. Here, those brackets are the absolute value function.

  -2(-1/3) = +2/3

Then the sum in those brackets:

  -5/6 +2/3 = -5/6 +4/6 = -1/6

The absolute value changes the sign of this back to positive, so the value in square brackets is ...

  3 -(1/6) = 18/6 -1/6 = 17/6

Finally, this value is divided by -17, so you have ...

  \dfrac{17}{6}\div(-17)=\dfrac{17}{6}\cdot\dfrac{-1}{17}=-\dfrac{17\cdot1}{17\cdot6}=\boxed{-\dfrac{1}{6}}

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Anyone know what 5x-4=36 is? I’m looking to solve the (x).
k0ka [10]

Answer:

x=8

Step-by-step explanation:

add 4 to both sides

divide 40 by 5

then you are left with x=8

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3 years ago
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Please help? What is the tangent ratio of angle B?
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Answer:

Step-by-step explanation:

The tangent equation = side opposite angle / side beside angle

which in this case is tan\alpha =AC/ BC

which is the third choice

Hope that helps!

5 0
3 years ago
Evelyn drinks 8 glasses of water,which is 56 glasses of water a week.How many glasses of water does she drink in a year?(1 year
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Evelyn drinks 2,912 glasses of water a year.
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3 years ago
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A worker was paid a salary of $10,500 in 1985. Each year, a salary increase of 6% of the previous year's salary was awarded. How
Mazyrski [523]
Note that 6% converted to a decimal number is 6/100=0.06. Also note that 6% of a certain quantity x is 0.06x.

Here is how much the worker earned each year:


In the year 1985 the worker earned <span>$10,500. 

</span>In the year 1986 the worker earned $10,500 + 0.06($10,500). Factorizing $10,500, we can write this sum as:

                                            $10,500(1+0.06).



In the year 1987 the worker earned

$10,500(1+0.06) + 0.06[$10,500(1+0.06)].

Now we can factorize $10,500(1+0.06) and write the earnings as:

$10,500(1+0.06) [1+0.06]=$10,500(1.06)^2.


Similarly we can check that in the year 1987 the worker earned $10,500(1.06)^3, which makes the pattern clear. 


We can count that from the year 1985 to 1987 we had 2+1 salaries, so from 1985 to 2010 there are 2010-1985+1=26 salaries. This means that the total paid salaries are:

10,500+10,500(1.06)^1+10,500(1.06)^2+10,500(1.06)^3...10,500(1.06)^{26}.

Factorizing, we have

=10,500[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]=10,500\cdot[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]

We recognize the sum as the geometric sum with first term 1 and common ratio 1.06, applying the formula

\sum_{i=1}^{n} a_i= a(\frac{1-r^n}{1-r}) (where a is the first term and r is the common ratio) we have:

\sum_{i=1}^{26} a_i= 1(\frac{1-(1.06)^{26}}{1-1.06})= \frac{1-4.55}{-0.06}= 59.17.



Finally, multiplying 10,500 by 59.17 we have 621.285 ($).


The answer we found is very close to D. The difference can be explained by the accuracy of the values used in calculation, most important, in calculating (1.06)^{26}.


Answer: D



4 0
3 years ago
29. Which of the following expressions will result in a real answer after being simplified? Select all that apply.
nexus9112 [7]

Answer: A, B, C, and E

Step-by-step explanation:

If both sides are real numbers, then the product will be a real number.

If in at least one of the sides we have a complex number, then the product will be real if:

The other number is zero.

The other number is the conjugate of the first.

This is when:

Suppose we have a number:

z = a + b*i

The conjugate will be:

w = a - b*i

And the product between them is:

(a + b*i)*(a - b*i) = a^2 + a*b*i - a*b*i + b^2 = a^2 + b^2

Then the options that will have a real answer are:

A. (4+5i)(4-5i) = 4^2 + 5^2 = 16 + 25 = 41

B. (4 + 91)*(41 - 9) = 3040

C. (3 + 2*i)*(3 -2*i) = 3^2 + 2^2 = 9 + 4 = 13

E. (312 + 7i)*(312 - 7i) = 312^2 + 7^2 = 97,393

5 0
3 years ago
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