Which linear inequality is represented by the graph?
1 answer:
Answer:
y ≥ x - 1
Step-by-step explanation:
First, determine the slope of the line. We can see that the slope is , because the slope has less than 1 y interval per every x interval. This means that the line is less steep. There are only 2 slope choices,
, -
, and 3. We can tell that the slope is positive, but it must be
because it is clearly less steep than a 3 slope line.
Now, look at the portion that is shaded. It is above the line, and this means that y is greater than the equation given. We can tell it is greater than or equal to, because the line that represents the equation is shaded as well. If it was only greater than and not equal to, the line would not be shaded.
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y = - x - 1
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange - 7x + 5y = 12 into this form
add 7x to both sides
5y = 7x + 12 ( divide all terms by 5 )
y = x +
← in slope- intercept form
with slope m =
given a line with slope m then the slope of a line perpendicular to it is
perpendicular slope = - = -
The partial equation of the perpendicular line is
y = - x + c
to find c substitute (- 7, 4 ) into the partial equation
4 = 5 + c ⇒ c = 4 - 5 = - 1
y = - x - 1 ← in slope- intercept form
the first term is 2 and the 20th term is 1048576 .
<u>Step-by-step explanation:</u>
Here we have , If the sum of the first 12 terms of a geometric series is 8190 and the common ratio is 2. We need to Find the first term and the 20th term. Let's find out:
We know that Sum of a GP is :
⇒
So ,Sum of first 12 terms is :
⇒
⇒
⇒
⇒
Now , nth term of a GP is
⇒
So , 20th term is :
⇒
⇒
⇒
Therefore , the first term is 2 and the 20th term is 1048576 .