Answer:
The number of adult admissions was 12 and the the number of child admissions was 17
Step-by-step explanation:
Let
a ----> represent the number of adult admissions
c ----> represent the number of child admissions
we know that
A group of 29 people attending the zoo paid a total of $222 in admission fees
so
![a+c=29](https://tex.z-dn.net/?f=a%2Bc%3D29)
----> equation A
----> equation B
Solve using the substitution method
substitute equation A in equation B
![10(29-c)+6c=222](https://tex.z-dn.net/?f=10%2829-c%29%2B6c%3D222)
solve for c
![290-10c+6c=222\\4c=68\\c=17](https://tex.z-dn.net/?f=290-10c%2B6c%3D222%5C%5C4c%3D68%5C%5Cc%3D17)
Find the value of a
![a=29-17=12](https://tex.z-dn.net/?f=a%3D29-17%3D12)
therefore
The number of adult admissions was 12 and the the number of child admissions was 17
Answer:
rounded to nearest 10th is 30
Step-by-step explanation:
Divide Numerator by Denominator
Answer:
1. B (obtuse)
2. Obtuse
3. 20.92
Step-by-step explanation:
1.
We need to use the converse of the pythagorean theorem to solve this problem. Given that c is the longest side of a triangle, and a and b are the other two sides. The triangle is right triangle if ![c^2=a^2 +b^2](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%20%2Bb%5E2)
The triangle is acute triangle if ![c^2 < a^2 + b^2](https://tex.z-dn.net/?f=c%5E2%20%3C%20a%5E2%20%2B%20b%5E2)
The triangle is obtuse triangle if ![c^2 > a^2 + b^2](https://tex.z-dn.net/?f=c%5E2%20%3E%20a%5E2%20%2B%20b%5E2)
the longest side of this triangle is 47, so we check:
, and
![34^2 + 20 ^2 =1556](https://tex.z-dn.net/?f=34%5E2%20%2B%2020%20%5E2%20%3D1556)
Hence, c^2 is GREATER than a^2 + b^2, so the triangle is obtuse.
2. Using the points we showed above, we can again summarize:
- If
-- Right Triangle - if
-- Acute Triangle - if
-- Obtuse Triangle
This triangle's c (longest side) is 5. Let's check:
5^2 = 25, and
![(1.2)^2 + (4.6) ^2=22.6](https://tex.z-dn.net/?f=%281.2%29%5E2%20%2B%20%284.6%29%20%5E2%3D22.6)
Hence, c^2 is GREATER than a^2 +b^2, so the triangle is obtuse.
3.
The side opposite of the 90 degree angle is the <em>"hypotenuse"</em>, that is x. The side opposite the 35 degree angle is <em>"opposite"</em> side.
The trigonometric ratio that related "opposite" side to "hypotenuse" side is SINE. So we can write:
![Sin(35)=\frac{Opposite}{Hypotenuse}\\Sin(35)=\frac{12}{x}](https://tex.z-dn.net/?f=Sin%2835%29%3D%5Cfrac%7BOpposite%7D%7BHypotenuse%7D%5C%5CSin%2835%29%3D%5Cfrac%7B12%7D%7Bx%7D)
Now, cross multiplying and solving:
![Sin(35)=\frac{12}{x}\\x*Sin(35)=12\\x=\frac{12}{Sin(35)}\\x=20.92](https://tex.z-dn.net/?f=Sin%2835%29%3D%5Cfrac%7B12%7D%7Bx%7D%5C%5Cx%2ASin%2835%29%3D12%5C%5Cx%3D%5Cfrac%7B12%7D%7BSin%2835%29%7D%5C%5Cx%3D20.92)
Answer:
672
Step-by-step explanation:
If we call the number of non-fiction books as x, the number of fiction books would be 3x. Therefore: we can write the following equation:
3x - 120 = 2(x - 24) ← the 3x - 120 and x - 24 represents the new number of books
3x - 120 = 2x - 48
x - 120 = 48
x = 168 which means 3x = 3 * 168 = 504, therefore the total number of books is 168 + 504 = 672.