He needs to raise it 8 feet but positive not negative this way it will cancel out the -8 and make it 0 (surface level) :D
Let 
be the length of the leg with one tick mark and 
the length of the leg with two tick marks.
In the upper triangle, the law of cosines says
In the lower triangle, it says
Subtract the second equation from the first to eliminate 
:
and are lengths so they must both be positive. 10 is also positive, so in order to preserve the sign on both sides of this equation, we must have
Now we have to be a bit careful. If 
is an acute angle, then as gets larger, the value of 
gets smaller. So if we have two angles 
and 
, with 
, then we would have 
.
This means in our inequality, taking the inverse cosine of both sides would reverse the inequality:
We know that 
is an angle in a triangle, so it must be some positive measure:
So we must have
Hey there!
Let's go through all of our options.
A) It's defintely not curved; it's written in slope intercept form and is indeed a straight line.
B) Yes, the graph is a straight line. Although it's at an angle, it has no curves or flaws, and is completely straight.
C) The graph is not vertical. It has a y intercept and slope and therefore isn't. That's because it has a rate of change, and it crosses the y axis at some point depending on the slope, or rise over run. Vertical lines really don't have that.
D) Yes, the graph is a function. This is because it does not have two x values for one y, and does not fail the straight line test, which states that you can place a straight line anywhere on the graph and it can only go through one point.
E) This is false. If we put in -5 as our input, we add 1 and get -4, which is a negative output. Your output here depends on the input you put in, and the sign usually remains considering it's +1.
F) This graph does not pass through the origin. This is because the origin has a point at 0,0 and since it's x+1, it would be 0,1 instead because your output is adding one to that 0.
Hope this helps!
Answer: 3
(
x
−
8
)
(
x
+
5
)
Step-by-step explanation:
Answer:
x ≥ -3
Step-by-step explanation:
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
-4x - 12 = -4 • (x + 3)
Equation at the end of step 1 :
Step 2 :
2.1 Divide both sides by -4
Remember to flip the inequality sign:
Solve Basic Inequality :
2.2 Subtract 3 from both sides
x ≥ -3
Inequality Plot :
2.3 Inequality plot for
-4.000 X - 12.000 ≥ 0
