Make a proportion
x = the amount of miles walked in 137.5 min
25 137.5
--- = --------
2 x
cross multiply
25x = 275
divide both sides by 25
x = 11
paul walked 11 miles in 137.5 minutes
Equation format for a slope, m and a point (x1, y1)
y - y1 = m(x - x1) (Try and memorize this formula)
8) for (3,-4), m = 6. x1 = 3, y1 = -4, Substituting
y - y1 = m(x - x1)
y - (-4) = 6(x - 3)
y + 4 = 6x - 18
y = 6x - 18 - 4
y = 6x - 22
10) for (-2,-7), m = 4/5. x1 = -2, y1 = -7, Substituting
y - y1 = m(x - x1)
y - (-7) = (4/5)*(x - (-2))
y + 7 = (4/5) *(x +2) 4/5 = 0.8
y + 7 = 0.8x + 1.6
y = 0.8x + 1.6-7
y = 0.8x - 6.4
y = (4/5)x - (64/10)
y = (4/5)x - (32/5)
So same approach to solve others. Cheers.
____________________________________________________
Answer:
x = 4
____________________________________________________
Explanation:
We're solving the equation: -8=-(x+4)
Solve:
-8=-(x+4)
Distribute the negative to the variables in the parenthesis.
-8 = -x - 4
Add 4 to both sides
-4 = -x
Divide by -1
4 = x (same as x = 4)
____________________________________________________
Answer: It's more likely it's a Tuesday
========================================================
Explanation:
The odds of it being a Tuesday is 1/7 since there's 1 day of the week that's Tuesday out of 7 total.
The odds of it being January is 1/12 because we have 1 month we want out of 12 total.
Now the question is: which fraction is larger?
For now, assume they are equal. We'll cross multiply like so
1/7 = 1/12
1*12 = 7*1
12 = 7
We get a false statement at the end, but we can fix things by replacing the equal sign with a greater than sign to get this new set of steps
1/7 > 1/12
1*12 > 7*1
12 > 7
which leads us to a true statement. Therefore, 1/7 is the larger fraction and the more likely event.
-----------------
Alternatively, you can use your calculator to find that:
- 1/7 = 0.143 approximately
- 1/12 = 0.083 approximately
Then for each decimal, move the decimal point 3 spots to the right. The values 0.143 and 0.083 become 143 and 83 respectively. We can see that 143 is larger, which means 0.143 is larger, and lastly 1/7 is larger. Think of it like a chain.
