Answer:
Step-by-step explanation:
we have the points
(-3,1) and (0,3)
step 1
Find the slope m of the line
The formula to calculate the slope between two points is equal to
substitute the values
step 2
Find the equation of the line in slope intercept form
we have
----> the y-intercept is the point (0,3)
substitute the values
step 3
Find the equation of the inequality
we know that
The slope is positive
Everything to the left of the line is shaded ( The inequality is of the form y > ax+b or y ≥ ax+b)
Is a dashed line (The inequality is of the form y > ax+ b or y < ax+b)
therefore
The equation of the inequality is of the form y > ax+b
The inequality is
see the attached figure to better understand the problem
We can write the sequence out more fully, as we can see each time it is divided by 6.
60, 60/6, 60/6^2, 60/6^3, and so on.
Therefore we know the sequence can be written as
You can think of this as a graph, i.e. y=60/6^(x-1)
As a result, as x tends to infinity, y tends to 0 (since it effectively becomes 60/infinity). Therefore the sequence
converges toward zero.
Answer:
y=17
Step-by-step explanation:4(y+8)=100
We move all terms to the left:
4(y+8)-(100)=0
We multiply parentheses
4y+32-100=0
We add all the numbers together, and all the variables
4y-68=0
We move all terms containing y to the left, all other terms to the right
4y=68
y=68/4
y=17
You first have to find the slope using the slope formula. That looks like this with our values:
. So the slope is -1/8. Use one of the points to first write the equation in y = mx + b form. We have an x and a y to use from one of the points and we also have the slope we just found. Filling in accordingly to solve for b gives us
and
. Adding 5/8 to both sides and getting a common denominator gives us that
. Writing our slope-intercept form we have
. Standard form for a line is Ax + By = C...no fractions allowed. So let's get rid of that 8 by multiplying each term by 8 to get 8y = -x - 11. Add x to both sides to get it into the correct form: x + 8y = -11
