Hello!
For a:
How I would do this, is I would first say if all 46 animals (heads) were chickens, how many legs would there be? Each chicken has 2 legs, so 46 * 2 = 92. The total amount of legs is 96 as stated in the question, so if all of the animals were chickens, the farmer would be 4 legs short.
Now to add rabbits into the equation. Rabbits have 4 legs, and chickens have 2. You want to find the difference between the two, because as you add rabbits to the animals the farmer has, then you have to take away chickens at the same time. 4-2 = 2, so for each rabbit you replace, you add 2 legs.
Since the farmer is 4 legs short with all chickens, then you just divide that 4 by the 2 legs you add by replacing a chicken with a rabbit.
4 / 2 = 2 rabbits
So that means there are 2 rabbits. Since there are 46 heads in total, if 2 are rabbits, that means there are 44 chickens.
So there are 44 chickens and 2 rabbits.
b)
You can follow the same steps: I'm assuming all are child tickets for now:
3.05 * 100 = $305
And now you find how much money short you are.
498.6 - 305 = 193.6
Next, you find the difference in the ticket costs.
5.25 - 3.05 = 2.20
And you divide to find the number of adult tickets.
193.6 / 2.2 = 88
Since 100 tickets were sold, and 88 adult tickets were sold, that means 12 child tickets were sold.
List the GCF of 18 and 28
18: 1, 2, 3, 6, 9, 18
28: 1, 2, 4, 7, 14, 28
So 2 is the GCF because it is the greatest number that can divide by both numbers
Answer:
x = -1,5
Step-by-step explanation:
2x² - 8x - 10
2x² - 10x + 2x - 10
2x(x - 5) + 2(x - 5)
(x - 5)(2x + 2)
x = 5 x = -2/2
x = -1,5
To find the area of his exclusion zone you would need to understand that a triangle with dimensions of 3, 4, and 5 represent a right triangle.
This means the exclusion zone would be applied to the base and the height of the triangular space.
You would add 2 km to the 3 km, and 2 km to the 4 km to create a new height of 5 km and a new base of 6 km.
Please see the attached picture to understand this.
You will find the area of the total space created by the new triangle and subtract the space represented by the original triangle to find the area of the exclusion zone.
(1/2 x 6 x 5) - (1/2 x 4 x 3)
15 km² -6 km² equals 9 km².
The exclusion space is 9 km².