the Answer C: 4
Step-by-step explanation:
Answer:
y = -1/4x - 2.25
Step-by-step explanation:
If you do this algebraically then use formula:
M= (y2 - y1) / (x2 - x1)
In other words, M= (-3 - (-1)) / (3 - (-5))
M= (-2) / (8)
M= -1/4 <-- This is your slope
To find y-intercept:
Substitute M in the slope-intercept equation (y=mx+b) with -1/4, y=-1/4x+b
Next, Substitute y and x with either point (-5, -1) or (3,-3)
-1 = -1/4(-5) + b <-- Solve for B
-1.25 -1 = 1.25 + b -1.25
-2.25 = b
Now just substitute b and m, and there's your answer:
y = -1/4x - 2.25
Hope this helps!
Answer:
Step-by-step explanation:
<u>Rational Inequality</u>
We are given the solution of rational inequality:
(-2,-1) U (1,∞)
The first set suggests a limited zone than can be obtained by a quadratic equation of the form:
Where a and b are the roots of the equation, which coincide with the endpoints of the interval. Thus, to get the interval, we can use:
Operating:
The second set is an open infinite interval, that can be modeled as a third binomial that changes signs in x=1 and is in the denominator, so x=1 is not included.
Thus, one possible inequality is:
Answer:
a) -8/9
b) The series is a convergent series
c) 1/17
Step-by-step explanation:
The series a+ar+ar²+ar³⋯ =∑ar^(n−1) is called a geometric series, and r is called the common ratio.
If −1<r<1, the geometric series is convergent and its sum is expressed as ∑ar^(n−1) = a/1-r
a is the first tern of the series.
a) Rewriting the series ∑(-8)^(n−1)/9^n given in the form ∑ar^(n−1) we have;
∑(-8)^(n−1)/9^n
= ∑(-8)^(n−1)/9•(9)^n-1
= ∑1/9 • (-8/9)^(n−1)
From the series gotten, it can be seen in comparison that a = 1/9 and r = -8/9
The common ratio r = -8/9
b) Remember that for the series to be convergent, -1<r<1 i.e r must be less than 1 and since our common ratio which is -8/9 is less than 1, this implies that the series is convergent.
c) Since the sun of the series tends to infinity, we will use the formula for finding the sum to infinity of a geometric series.
S∞ = a/1-r
Given a = 1/9 and r = -8/9
S∞ = (1/9)/1-(-8/9)
S∞ = (1/9)/1+8/9
S∞ = (1/9)/17/9
S∞ = 1/9×9/17
S∞ = 1/17
The sum of the geometric series is 1/17
The numerical value of 70,000 is in standard form.
