Answer:
21 degrees
Step-by-step explanation:
Triangles have a total angle of 180 degrees.
This makes our equation:
3x+3+4x+135=180
Subtract 135 from both sides and combine like terms
7x + 3 = 45
Subtract 3 from both sides
7x = 42
Divide both sides by 7
x = 6
Plugging the number in:
3x + 3 =
3(6) + 3 =
21
Answer:
Step-by-step explanation:
3 pieces such that each piece is 2 cm longer then the next...
x , x + 2, x + 4
x + x + 2 + x + 4 = 30
3x + 6 = 30
3x = 30 - 6
3x = 24
x = 24/3
x = 8
x + 2 = 8 + 2 = 10
x + 4 = 8 + 4 = 12
check...
8 + 10 + 12 = 30
18 + 12 = 30
30 = 30 (correct)...it checks out
the ribbon lengths are : 8 cm, 10 cm, and 12 cm
It could sometimes be proportional. The reasoning here is that if all the items have different prices it won't be, however if the items you are ordering all have the same price they will be!
Notice that
13 - 9 = 4
17 - 13 = 4
so it's likely that each pair of consecutive terms in the sum differ by 4. This means the last term, 149, is equal to 9 plus some multiple of 4 :
149 = 9 + 4k
140 = 4k
k = 140/4
k = 35
This tells you there are 35 + 1 = 36 terms in the sum (since the first term is 9 plus 0 times 4, and the last term is 9 plus 35 times 4). Among the given options, only the first choice contains the same amount of terms.
Put another way, we have

but if we make the sum start at k = 1, we need to replace every instance of k with k - 1, and accordingly adjust the upper limit in the sum.


Answer: Second option.
Step-by-step explanation:
It is important to remember the Distributive Property in order to solve this exercise.
The Distributive property states that:

In this case you have the following expression provided in the exercise:

Then, in order to write this expression in another way, you can apply the Distributive property. Multiply each number inside the parentheses by "t".
Applying this procedure, you get:

Notice that this expression matches with the one shown in the the second option.