Answer: 36 square units
Step-by-step explanation:
Divide the figure into 2 shapes: a rectangle and a triangle. Count the squares to find the dimensions of each figure. The rectangle has a width of 4 units and a length of 6 units. The triangle has a base of 6 units and a height of 4 units.
The formula for the area of a rectangle is length * width. The area of the rectangle is 4*6 = 24 square units.
The formula for the area of a triangle is (base * height)/2. The area of the triangle is (4*6)/2 = 24/2 = 12 square units.
Add the areas of both the rectangle and triangle. 24+12 = 36 square units.
Using proportions, it is found that the best estimate for the raccoon population is of 930.
<h3>Proportions:</h3>
- This question is solved by <em>proportions</em>, using a rule of three.
- Out of 620 raccoons, 38 had tags. How many raccoons are there if the scientist tagged 57?
The <em>rule of three is:</em>
620 raccoons - 38 tagged
x raccoons - 57 tagged
Applying cross multiplication:
![38x = 620(57)](https://tex.z-dn.net/?f=38x%20%3D%20620%2857%29)
![x = \frac{620(57)}{38}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B620%2857%29%7D%7B38%7D)
![x = 930](https://tex.z-dn.net/?f=x%20%3D%20930)
The best estimate for the raccoon population is of 930.
You can learn more about proportions at brainly.com/question/24372153
Answer:
no of movies (m), by Tim = 13
Step-by-step explanation:
Julie payment = constant 70 + 4.25 per additional movie = 70 + 4.25 m
Tim payment = constant 49.5 + 5.5 per additional movie = 49.5 + 5.5 m
Julie order = 12 movies. So, final payment = 70 + 4.25 (12) = 70 + 51 = 121
Equalising Tim's equation, for finding Tim's movies for same final amount , 121 = 49.5 + 5.5 m → 5.5m = 121 - 49.5 = 71.5 → m = 71.5 / 5.5 = 13
Answer:
![(\frac{1}{2},-4 )](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%2C-4%20%29)
Step-by-step explanation:
the system of equations is:
![-6x+9y=-39\\8x+y=0](https://tex.z-dn.net/?f=-6x%2B9y%3D-39%5C%5C8x%2By%3D0)
First, we multiply the second equation by -9:
![-9(8x+9y=0)\\-72x-9y=0](https://tex.z-dn.net/?f=-9%288x%2B9y%3D0%29%5C%5C-72x-9y%3D0)
and now we add this to the first original equation:
![-6x+9y=-39\\-72x-9y=0\\-------\\-78x+0y=-39](https://tex.z-dn.net/?f=-6x%2B9y%3D-39%5C%5C-72x-9y%3D0%5C%5C-------%5C%5C-78x%2B0y%3D-39)
we have eliminated the y variable, so we can solve for x:
![-78x=-39\\x=-39/(-78)\\x=0.5=\frac{1}{2}](https://tex.z-dn.net/?f=-78x%3D-39%5C%5Cx%3D-39%2F%28-78%29%5C%5Cx%3D0.5%3D%5Cfrac%7B1%7D%7B2%7D)
with this value of x, we substitute it on the second of the original set of equations to find the value of y:
![8x+y=0\\8(0.5)+y=0\\4+y=0\\y=-4](https://tex.z-dn.net/?f=8x%2By%3D0%5C%5C8%280.5%29%2By%3D0%5C%5C4%2By%3D0%5C%5Cy%3D-4)
the answer as an ordered pair is:
![(\frac{1}{2},-4 )](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%2C-4%20%29)