Answer:
$20.
Step-by-step explanation:
Given:
In the clip from the Simpsons, Ralph charges Bart twice the fair from Tucson to Flagstaff, minus 2/3 the fair from Albuquerque to El Paso.
It costs $40 to travel from Tucson to Flagstaff,
And $90 to travel from Albuquerque to El Paso.
Question asked:
How much does Bart need to pay ?
Solution:
Fair to travel from Tucson to Flagstaff = $40
Fair to travel from Albuquerque to El Paso = $90
<u>As Ralph charges Bart twice the fair from Tucson to Flagstaff, minus 2/3 the fair from Albuquerque to El Paso. </u>
Thus, Bart need to pay $20.
Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify!
You need to know three exponent rules to simplify these expressions:
1)
The
negative exponent rule says that when a
base has a negative exponent, flip the base onto the other side of the
fraction to make it into a positive exponent. For example,
.
2)
Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example,
.
3) The
zero exponent rule<span> says that any number
raised to zero is 1. For example,
.
</span>
Back to the Problem:
Problem 1
The x-values are in the left column. The title of the right column tells you that the function is
. The x-values are:
<span>
1) x = 0</span>Plug this into
to find letter a:
<span>
2) x = 2</span>Plug this into
to find letter b:
<span>
3) x = 4</span>Plug this into
to find letter c:
<span>
Problem 2
</span>The x-values are in the left column. The title of the right column tells you that the function is
. The x-values are:
<span>
1) x = 0</span>Plug this into
to find letter d:
<span>
2) x = 2
</span>Plug this into
to find letter e:
<span>
3) x = 4
</span>Plug this into
to find letter f:
<span>
-------
Answers: a = 1b = </span>
<span>
c = </span>
d = 1e = 
f = 
Answer:
12
Step-by-step explanation:
The least common multiple of {6,8,12} is 24. This can be intuitively figured by noting that any multiple of 12 is a multiple of 6 and that 12 is 1.5x larger than 8. That means we only have so multiple 12 by 2 and 8 by 3 for them to be equal. The GCF of {20,42,72} is 2 as the prime factorization of 20 is 2x2x5 and 42 is 2x3x7. That means even without having to check 72 (which is clearly even so 2 is a factor), we know that 2 is the greatest common factor that they could share. So X/Y = 24/2 = 12
