Using the angle relationships, the sizes of the angles are:
a = 21°
b = 70°
c = 89°
<h3>What are Angle Relationships?</h3>
- Vertical angles are equal in measure.
- Two angles on a straight line are linear pair and are supplementary.
- All angles in a triangle will add up to the sum of 180 degrees.
Thus:
a = 21° (vertical angles).
b = 180 - 110 = 70° (linear pair).
c = 180 - (70 + 21) = 89° (triangle sum)
Therefore, using the angle relationships, the sizes of the angles are:
a = 21°
b = 70°
c = 89°
Learn more about angle relationships on:
brainly.com/question/12591450
First plugin 2y+4 for x
3(2y+4)+5y=32 distribute
6y+12+5y=32 combined like terms
11y+12=32 combined like terms
11y=20 divide
Y=1.818
Using a system of equations, it is found that:
- There are 8 chickens in the yard.
- There are 16 pigs in the yard.
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This question is solved using a system of equations. I am going to say that:
- x is the number of chickens.
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- A chicken has 1 head, as do a pig.
- There are 24 heads.
Thus:
![x + y = 24 \rightarrow y = 24 - x](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2024%20%5Crightarrow%20y%20%3D%2024%20-%20x)
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- A chicken has 2 feet.
- A pig has 4 feet.
- In total, there are 80 feet.
Thus:
![2x + 4y = 80](https://tex.z-dn.net/?f=2x%20%2B%204y%20%3D%2080)
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Number of chicken:
Since ![y = 24 - x](https://tex.z-dn.net/?f=y%20%3D%2024%20-%20x)
![2x + 4y = 80](https://tex.z-dn.net/?f=2x%20%2B%204y%20%3D%2080)
![2x + 4(24 - x) = 80](https://tex.z-dn.net/?f=2x%20%2B%204%2824%20-%20x%29%20%3D%2080)
![2x + 96 - 4x = 80](https://tex.z-dn.net/?f=2x%20%2B%2096%20-%204x%20%3D%2080)
![2x = 16](https://tex.z-dn.net/?f=2x%20%3D%2016)
![x = \frac{16}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B16%7D%7B2%7D)
![x = 8](https://tex.z-dn.net/?f=x%20%3D%208)
There are 8 chickens in the yard.
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Number of pigs:
![y = 24 - x = 24 - 8 = 16](https://tex.z-dn.net/?f=y%20%3D%2024%20-%20x%20%3D%2024%20-%208%20%3D%2016)
There are 16 pigs in the yard.
A similar problem is given at brainly.com/question/24104709
Hi there! The answers are B and E.
To find our answer we first need to work out the parenthesis.
![- 3.5(2 - 3n) - 2.5n =](https://tex.z-dn.net/?f=%20-%203.5%282%20-%203n%29%20-%202.5n%20%3D%20)
![- 7 + 10.5n - 2.5n](https://tex.z-dn.net/?f=%20-%207%20%2B%2010.5n%20-%202.5n)
Now we can collect terms.
![- 7 + 8n](https://tex.z-dn.net/?f=%20-%207%20%2B%208n)
Hence, B is correct and A and C are false.
To determine whether D or/and E is/are correct we need to work out the parentheses as well. When we do that we can see D ending up with a negative value of n and E with a positive value of n. Taking into account our previous results, E is correct and D is false.
Hence, B and E are correct.
Answer:
<h2>
![g(x) = \frac{1}{4} x - 3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%20%5Cfrac%7B1%7D%7B4%7D%20x%20-%20%203)
</h2>
Step-by-step explanation:
Since g(x) is the inverse of f (x) to find g(x) must first find f-¹(x)
To find f-¹(x) equate f(x) to y
That's
f(x) = y
y = 4x + 12
Next interchange the terms x becomes y and y becomes x
That's
x = 4y + 12
Next make y the subject
4y = x - 12
Divide both sides by 4
<h3>
![y = \frac{1}{4} x - 3](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B4%7D%20x%20-%203)
</h3>
Therefore
<h3>
![g(x) = \frac{1}{4} x - 3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%20%5Cfrac%7B1%7D%7B4%7D%20x%20-%20%203)
</h3>
Hope this helps you