Answer:
Step-by-step explanation:
<u>Line 1</u>
- -3x + 5y = -4
- 5y = 3x - 4
- y = 3/5x - 4/5
<u>Line 2</u>
- px + 25 y = 4
- 25y = -px + 4
- y = -p/25x + 4/25
<u>The system is inconsistent if slopes are same, so we should have:</u>
- 3/5 = - p/25
- 25*3/5 = -25p/25
- 15 = -p
- p = -15
18 - 2H = 12 - .5H
Combine the variables
18 - 2H + .5H = 12 - .5H + .5H
18 - 1.5H = 12
Combine the whole numbers
18 - 18 - 1.5H = 12 - 18
-1.5H = -6
Divide by -1.5
-1.5H/-1.5 = -6 / -1.5
H = 4
The answer is 4 hours
Answer:
−1.4285714286 you can just put agew if those numbers
Answer:
Here, the given problem,
The total number of hours = ![\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D)
Now, the number of hours to make each invitation card = ![\frac{1}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B12%7D)
Hence, the total number of invitations = ![\text{Total hours}\div \text{Hours needed for an invitation }](https://tex.z-dn.net/?f=%5Ctext%7BTotal%20hours%7D%5Cdiv%20%5Ctext%7BHours%20needed%20for%20an%20invitation%20%7D)
![=\frac{3}{4}\div \frac{1}{12}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3%7D%7B4%7D%5Cdiv%20%5Cfrac%7B1%7D%7B12%7D)
a. Scale the number line from 0 to 1,
In which each unit represents ![\frac{1}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B12%7D)
By the number line,
![\frac{9}{12}\div \frac{1}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B12%7D%5Cdiv%20%5Cfrac%7B1%7D%7B12%7D)
![=9](https://tex.z-dn.net/?f=%3D9)
b. By model,
Take a grid which shows 1 hour and each box of the grid represents 1/12th hour,
By the grid,
![\frac{3}{4}\text{ part of grid}=\frac{9}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%5Ctext%7B%20part%20of%20grid%7D%3D%5Cfrac%7B9%7D%7B12%7D)
![=\frac{3}{4}\div \frac{1}{12}=9](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3%7D%7B4%7D%5Cdiv%20%5Cfrac%7B1%7D%7B12%7D%3D9)
That is, the number of hours to make invitation = 9
c. ![\frac{3}{4}\div \frac{1}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%5Cdiv%20%5Cfrac%7B1%7D%7B12%7D)
![\frac{3}{4}\times 12=3\times 3=9](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%5Ctimes%2012%3D3%5Ctimes%203%3D9)
Answer:
![\text{Area of the figure}=54\text{ unit}^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20the%20figure%7D%3D54%5Ctext%7B%20unit%7D%5E2)
Step-by-step explanation:
Please find the attachment.
Let us divide our given image in several parts and then we will find area of different parts.
First of all let us find the area of our red rectangle with side lengths 6 units and 7 units.
![\text{Area of rectangle}=\text{Length*Width}](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20rectangle%7D%3D%5Ctext%7BLength%2AWidth%7D)
![\text{Area of red rectangle part}=6\text{ units}\times 7\text{ units}](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20red%20rectangle%20part%7D%3D6%5Ctext%7B%20units%7D%5Ctimes%207%5Ctext%7B%20units%7D)
![\text{Area of red rectangle part}=42\text{ units}^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20red%20rectangle%20part%7D%3D42%5Ctext%7B%20units%7D%5E2)
Now let us find area of yellow triangle on the top of red rectangle. We can see that base of triangle is 6 units and height is 1 unit.
![\text{Area of triangle}=\frac{1}{2}\times \text{Base*Height}](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20triangle%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%5Ctext%7BBase%2AHeight%7D)
![\text{Area of triangle}=\frac{1}{2}\times \text{6 units *1 unit}](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20triangle%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%5Ctext%7B6%20units%20%2A1%20unit%7D)
![\text{Area of triangle}=3\text{ unit}^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20triangle%7D%3D3%5Ctext%7B%20unit%7D%5E2)
Let us find the area of green triangle.
![\text{Area of green triangle}=\frac{1}{2}\times \text{3 units *2 units}](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20green%20triangle%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%5Ctext%7B3%20units%20%2A2%20units%7D)
![\text{Area of green triangle}=3\text{ unit}^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20green%20triangle%7D%3D3%5Ctext%7B%20unit%7D%5E2)
Now we will find the area of blue triangle, whose base is 6 units and height is 2 units.
![\text{Area of blue triangle}=\frac{1}{2}\times \text{6 units *2 units}](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20blue%20triangle%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%5Ctext%7B6%20units%20%2A2%20units%7D)
![\text{Area of blue triangle}=6\text{ units}^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20blue%20triangle%7D%3D6%5Ctext%7B%20units%7D%5E2)
Let us add all these areas to find the area of our figure.
![\text{Area of the figure}=42\text{ units}^2+3\text{ unit}^2+3\text{ unit}^2+6\text{ unit}^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20the%20figure%7D%3D42%5Ctext%7B%20units%7D%5E2%2B3%5Ctext%7B%20unit%7D%5E2%2B3%5Ctext%7B%20unit%7D%5E2%2B6%5Ctext%7B%20unit%7D%5E2)
![\text{Area of the figure}=(42+3+3+6)\text{ unit}^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20the%20figure%7D%3D%2842%2B3%2B3%2B6%29%5Ctext%7B%20unit%7D%5E2)
![\text{Area of the figure}=54\text{ unit}^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20the%20figure%7D%3D54%5Ctext%7B%20unit%7D%5E2)
Therefore, area of our given figure is 54 square units.