Answer:
y = 3.8 - 0.2x.
Step-by-step explanation:
y = k - 0.2x where k is the thickness of the ice before the melting starts and x = the number of weeks.
When x = 7, y = 2.4 therefore:
2.4 = k - 0.2*7
k = 2.4 + 1.4 = 3.8.
So our equation is y = 3.8 - 0.2x.
84 + x + 59 x + 51 =180
2x + 194 = 180
2x + 194 - 194 = 180 - 194 (subtract both sides by 194)
2x = -14
2x/2 = -14/2 (divide both sides by 2)
x = -7
In general to be able to add or subtract fractions you need to have the same denominator so that you can add the numerators.
The easiest way to find the same denominator is to identify the lowest common denominator (LCD).
You can find the LCD by finding the prime factors of the denominators in question and multiplying them all together. If the denominators share a prime factor, only multiply it once.
Sometimes you can just eyeball the numbers to find the LCD, which might be faster.
For #W we need to find the LCD of 10 and 6, so prime factorize:
10 = 2 x 5
6 = 2 x 3
LCD = 2 x 5 x 3 = 30
The LCD is 30, so we need to change the fraction to reflect that. Remember, what you do to the denominator you need to do to the numerator as well. So:
-9/10 becomes -27/30 (both multiplied by 3)
-1/6 becomes -5/30 (both multiples by 5)
Now you can easily add:
-27/30 + (-5/30) = -32/30
In summary:
Step #1: find LCD (prime factor or eyeball)
Step #2: multiply the numerator of each fraction by the factor needed to obtain the LCD in that denominator
Step #3: add the fractions now that they have the LCD
Here’s the solution to #G:
-¾ + (-7/12)
Step #1:
4 = 2 x 2
12 = 2 x 2 x 3
LCD = 2 x 2 x 3 (count each unique prime factor once)
Step #2:
-¾ becomes -9/12 (both multiplied by 3)
-7/12 stays the same (it already has the LCD)
Step #3:
-9/12 + (-7/12) = -16/12
Let me know if you have any questions. Try to work though the others!
I'm assuming you want help with numbers 7 and 8 because multiplication should be easy
so
7. rico average=15.5mph or 15.5/h
in 2.5 hours how far travel
15.5 in 1 hour
in 2 hours he will travel 2 times 15.5 miles
so in 2.5 hours he will travel 15.5 times 2.5 miles or 38.75
8. use estimation to show reasonable
15.5 can be rounded to 16
16 times 2 is 32
16 times 3 is 48
0.5 is half of 1 so the average is about the answer
(32+48)/2=80/2=40
he will travel about 40 miles (less since you rounded 15.5 up to 16)
so it is reasonable