Distributive property is used when you have a number outside a set of numbers in parenthesis.
Using the distributive property, you multiply the number outside the parenthesis by each number inside the parenthesis.
The first answer is correct because they are multiplying 9 by 20 and adding it to 9 multiplied by 6.
13. The words are telling you
.. HT +TS = HM +MS +2
.. (2x +1) +(x) = (x +1) +(x +2) +2
.. 3x +1 = 2x +5 . . . . . . . . . . . . . . collect terms
.. x = 4 . . . . . . . . . . . . . . . . . . . . . add -2x-1
HT +TS = 3x +1 = 3*4 +1 = 13 miles
The route via the theater is 13 miles.
Via the mall, the route is 11 miles.
14. Solve this the way you would any 2-step linear equation. Subtract terms that don't have h, and divide by the coefficient of h.
S = 2πr^2 +2πrh
S -2πr^2 = 2πrh
(S -2πr^2)/(2πr) = h
If you like, you can rearrange this to
.. h = (S/(2πr)) -r
The speed of a boat in still water (b) is 50km/h. It takes the same time (t) for the boat to travel 10km (x) upstream as it does to travel 20km (y) downstream. Find the speed of the current.
upstream speed (u) = speed in still water (b) - stream speed (s) = b-s = 50-s
downstream speed (d) = speed in still water (b) + stream speed (s) = 50+s
time (t) = x/u = y/d
10/(50-s) = 20/(50+s)
10(50+s) = 20(50-s)
500 + 10s = 1000 - 20s
30s = 500
stream speed (s) = 500/30 = 16.6 km/h
I don't know how your teacher chooses to solve this problem (or your text) but I do it this way.
Divide 81 by 3. You get 27.
Use 27 as your middle integer and go one odd integer up and down for the other 2.
25, 27, 29
the largest would be 29.
This works because 3 of the middle number equals 81, so the middle number plus a number 2 greater and a number 2 less would still be the same as adding 3 of the same number.
Check by adding the 3 numbers.
25 + 27 + 29 = 81
Answer:
x=10
Step-by-step explanation:
Since the two given expressions are alternate interior angles ( as a result of the parallel line, which are indicated by the arrows on the two lines going through the middle line, the transversal) you can set them equal to each other.
5x-10 = 3x+10
add 10 on both sides
5x = 3x + 20
subtract 3x on both sides
2x=20
divide by 2 on both sides
x=10
