Answer:
The first term of the sequence is -120.
Step-by-step explanation:
The formula for the "nth" term of a geometric sequence is shown below:
an = a0*r^(n-1)
Where an is the nth term, r is the ratio and n is the position of the term on the sequence. For this problem we want to find what is the initial term, a0, so we will isolate it in the formula as shown below:
a0*r^(n-1) = an
a0 = an/[r^(n-1)]
We then apply the data given to us
a0 = 31.45728/[-0.8^(7-1)]
a0 = 31.45728/[-0.8^6] =31.45728 /-0.262144= -120
The first term of the sequence is -120.
Answer:
Step-by-step explanation:
<u>The two points:</u>
<u>The distance:</u>
-x - y = 8
2x - y = -1
Ok, we are going to solve this in 2 parts. First we have to solve for one of the variables in one of the equation in terms of the other variable. I like to take the easiest equation first and try to avoid fractions, so let's use the first equation and solve for x.
-x - y = 8 add y to each side
-x = 8 + y divide by -1
x = -8 - y
So now we have a value for x in terms of y that we can use to substitute into the other equation. In the other equation we are going to put -8 - y in place of the x.
2x - y = -1
2(-8 - y) - y = -1 multiply the 2 through the parentheses
-16 - 2y - y = -1 combine like terms
-16 - 3y = -1 add 16 to both sides
-3y = 15 divide each side by -3
y = -5
Now we have a value for y. We need to plug it into either of the original equations then solve for x. I usually choose the most simple equation.
-x - y = 8
-x - (-5) = 8 multiply -1 through the parentheses
-x + 5 = 8 subtract 5 from each side
-x = 3 divide each side by -1
x = -3
So our solution set is
(-3, -5)
That is the point on the grid where the 2 equations are equal, so that is the place where they intersect.
The answer is A because the equation is 40/10 which would give you 4 and it asks m/s.
In an equilateral triangle, the measure of each angle is 60 degrees. Then the value of x and y is 17/3 and 65.
<h3>What is the triangle?</h3>
A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In trianlge ΔMNP, PM = 3x - 4, MN = 14, ∠N = 5y - 5.
In an equilateral triangle, all the sides and all the angles are equal.
MN = NP = PM
∠M = ∠N = ∠P
Then we have
PM = MN
3x - 4 = 14
x = 17/3
We know in an equilateral triangle, the measure of each angle is 60 degrees. Then we have
∠N = 60
5y - 5 = 60
5y = 65
y = 13
More about the triangle link is given below.
brainly.com/question/25813512
#SPJ1
=