Remark
You could convert base two to base 10 and then convert base 10 to base 8. That's the long way. The procedure below is the short way.
Step One
Write the base 2 number in groups of 3 starting from the right and going left
11 100 111
Step Two
Convert the base 2 numbers in groups of 3 to base 8. The largest result will be a 7
11 = 2*1 + 1 = 2 + 1 = 3
100 = 1*2^2 = 4
111 = 1*2^2 + 1*2 + 1 = 7
Step Three
Read the answer going down.
347 is the answer
Answer
347(8) = C
Every "normal" hour worked by Julio is paid
dollars. He works 29 "normal" hours per week.
Every extra hour worked by Julio is paid
dollars.
If he worked 34 hours last week, he worked the usual 29 hours, plus 5 extra hours. This means that he earned
dollars.
We know that this equals 479.55, so we have
![34.5r = 479.55 \iff r = \dfrac{479.55}{34.5} = 13.9](https://tex.z-dn.net/?f=%2034.5r%20%3D%20479.55%20%5Ciff%20r%20%3D%20%5Cdfrac%7B479.55%7D%7B34.5%7D%20%3D%2013.9%20)
Answer:
see explanation
Step-by-step explanation:
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
Express in standard form, that is 6x² - 7x - 3
product = 6 × - 3 = - 18, sum = - 7
The factors are - 9 and + 2
Use these factors to split the middle term
6x² - 9x + 2x - 3 ( factor the first/second and third/fourth terms )
= 3x(2x - 3) + 1(2x - 3) ← factor out (2x - 3)
= (2x - 3)(3x + 1)
To obtain zeros equate to zero
(2x - 3)(3x + 1) = 0
Equate each factor to zero and solve for x
2x - 3 = 0 ⇒ x = ![\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D)
3x + 1 = 0 ⇒ x = - ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
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The relationship between the zeros and the coefficients is
sum of zeros = -
and
product of zeros = ![\frac{c}{a}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7Ba%7D)
-
= -
and
-
= ![\frac{7}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B6%7D)
× -
= -
and
=
= - ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
Verifying both relationships