The linear inequality of the graph is: -x + 2y + 1 > 0
<h3>How to determine the
linear inequality?</h3>
First, we calculate the slope of the dashed line using:
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
Two points on the graph are:
(1, 0) and (3, 1)
The slope (m) is:
![m = \frac{1 - 0}{3 - 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B1%20-%200%7D%7B3%20-%201%7D)
This gives
m = 0.5
The equation of the line is calculated as:
![y = m(x -x_1) + y_1](https://tex.z-dn.net/?f=y%20%3D%20m%28x%20-x_1%29%20%2B%20y_1)
So, we have;
![y = 0.5(x -1) + 0](https://tex.z-dn.net/?f=y%20%3D%200.5%28x%20-1%29%20%2B%200)
This gives
![y = 0.5x -0.5](https://tex.z-dn.net/?f=y%20%3D%200.5x%20-0.5)
Multiply through by 2
![2y = x - 1](https://tex.z-dn.net/?f=2y%20%3D%20x%20-%201)
Now, we convert the equation to an inequality.
The line on the graph is a dashed line. This means that the inequality is either > or <.
Also, the upper region of the graph that is shaded means that the inequality is >.
So, the equation becomes
2y > x - 1
Rewrite as:
-x + 2y + 1 > 0
So, the linear inequality is: -x + 2y + 1 > 0
Learn more about linear inequality at:
brainly.com/question/19491153
#SPJ1
<u>Complete question</u>
Find a linear inequality with the following solution set. Each grid line represents one unit. (Give your answer in the form ax+by+c>0 or ax+by+c
0 where a, b, and c are integers with no common factor greater than 1.)
Hi there!
We know that the formula for the area of a rectangle is height * width. Thus, we can multiply these two expressions together:
![2x^4\cdot (x^2+8x+15)\\](https://tex.z-dn.net/?f=2x%5E4%5Ccdot%20%28x%5E2%2B8x%2B15%29%5C%5C)
Now, we know through the distributive property that we can distribute the
to everything in the parenthesis. Once this is done, we get:
![2x^4 \cdot x^2+2x^4\cdot8x+2x^4\cdot15](https://tex.z-dn.net/?f=2x%5E4%20%5Ccdot%20x%5E2%2B2x%5E4%5Ccdot8x%2B2x%5E4%5Ccdot15)
Now, we know through the power rule that when two exponents are multiplied together with the same base, the exponent can be added together
. This then would make our equation:
![2x^{4+2}+16x^{4+1}+30x^4\\](https://tex.z-dn.net/?f=2x%5E%7B4%2B2%7D%2B16x%5E%7B4%2B1%7D%2B30x%5E4%5C%5C)
Giving us for our final answer:
![2x^{6}+16x^{5}+30x^4\\](https://tex.z-dn.net/?f=2x%5E%7B6%7D%2B16x%5E%7B5%7D%2B30x%5E4%5C%5C)
Hope this helps!
Answer:
19
Step-by-step explanation:
i took the quiz
Answer:
1428 in³
Step-by-step explanation:
To find the volume of this figure, we will need to use two formulas. The volume of a Rectangular Prism (
) and volume of a triangular prism. ![A = \frac{1}{2}(b*h)](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28b%2Ah%29)
If we look at the Rectangular Prism, we can find that l = 17, w = 8, and h = 5. Multiply these to find the volume:
17 × 8 × 5 = 680 in³.
Solving for the triangular prism gives us:
A = 1/2 (11 × 8 × 17)
A = 748.
Add these two volumes to find the volume of the composite figure:
748 + 680 = 1428 in³