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:
33
Step-by-step explanation:
You can do this by repeated addition:
11 + 11 + 11
If you add these up, you get the final answer:
11 + 11 + 11 = 33
Steps:
1. calculate the values of y at x=0,1,2. using y=5-x^2
2. calculate the areas of trapezoids (Bottom+Top)/2*height
3. add the areas.
1.
x=0, y=5-0^2=5
x=1, y=5-1^2=4
x=2, y=5-2^2=1
2.
Area of trapezoid 1 = (5+4)/2*1=4.5
Area of trapezoid 2 = (4+1)/2*1=2.5
Total area of both trapezoids = (4.5+2.5) = 7
Exact area by integration:
integral of (5-x^2)dx from 0 to 2
=[5x-x^3/3] from 0 to 2
=[5(2-0)-(2^3-0^3)/3]
=10-8/3
=22/3
=7 1/3, slight greater than the estimation by trapezoids.
Answer:
Step-by-step explanation:
When taking a square root and making it a radical, we need to list out it's factors and find which one we can take the square root of.
The factors of 40 are:
1, 2, 4, 5, 8, 10, 20, 40.
Out of these, we need to look for one that we can find the square root of.
We know that the square root of 4 is 2.
Therefore, we can make 
into 
.
The square root of 4 is 2. Therefore, we can put that outside the radical.
.
Hope this helped!
Step-by-step explanation:
<em>In the second column, we can see that every value of n is being added by 6. </em>
- Thus, the expression is n + 6.
<em>Now, let's substitute the value of n in each column to verify each column. Then, using the expression, let's find the value of n + 6 where n = 28.</em>
<u>When n is 12:</u>
- n + 6 = 18
- 12 + 6 = 18
- 18 = 18
<u>When n is 15:</u>
- n + 6 = 21
- 15 + 6 = 21
- 21 = 21
<u>When n is 21:</u>
- n + 6 = 27
- 21 + 6 = 27
- 27 = 27
<em>Thus, the expression is proven correct. Now, let's find n + 6 when n is 28.</em>
<u>Finding n + 6 when n is 28:</u>
- n + 6 = x
- 28 + 6 = x
- 34 = x
Thus, the missing value in the table is 34.
