When counting any sequence, it helps to have a simpler sequence to compare it to. The simplest one that I can think of is
because you instantly can tell the number of terms in the sequence by looking at the last number. We can see from the graph that the first few terms of the sequence a are 1, -3, -7, and we're told that its last term is -83. Our goal then is to turn this sequence:
into this one:
The first thing which stands out in this sequence is the number of negative terms, so let's fix that by multiplying every term by -1:
Now, the main property of any arithmetic sequence is that they <em>increase or decrease by some constant amount</em>. Here, that number is 4, since -3 = 1 - 4 and -7 = -3 - 4. Knowing the importance of 4 in this sequence, our next step might be to turn every term into a multiple of 4 by adding 1:
and since we're dealing with multiples of 4, a natural next step might be to divide every term by 4:
And lastly, we can add 1 to every term to get our sequence into easily-countable form:
So, the sequence a has 22 terms.
Answer:
d. -7/25
Step-by-step explanation:
π<θ<3π/2 in third quadrant
tanθ = 4/3
sinθ = - 4/5
cosθ = - 3/5
cos 2θ = cos²θ - sin²θ = (- 3/5)² - (- 4/5)² = 9/25 - 16/25 = - 7/25
Answer:
angle 1= 76 degrees
angle 2= 61 degrees
Step-by-step explanation:
if you draw a line down the middle of the trapezoid and think of the two halves as parallel lines cut by a transversal, your angle are alternate interior, which makes them equal to each other or congruent. another way to find the measure is by finding the supplement to your angle that are already labeled.
just subtract 76 and 119 from 180 to find the supplements, which are 104 and 61, respectively. now that you have two angles labeled inside the trapezoid, you can use your quadrilateral rules to find the other ones. the rule in this case is "consecutive angles equal 180." so, the angle right below to angle R (119 degrees) is angle 2. using subtraction rule, 180-119= 61.
repeat for angle Q to find the measure of angle 1, 180-104= 76.
Answer:
5m^5-m^3-3
Step-by-step explanation:
What you do is you have to distribute the negative sign into the equation.
-m^5-2m^3+4m-6. Next, you will either add or subtract from the other equation.
6m^5-m^5=5m^5.
m^3-2m^3=-m^3.
-4m+4m=0m or you don't put anything.
3-6=-3. Then you put it all together to get.
5m^5-m^3-3 as your answer.
