Answer:
The missing angle is 24 degrees
Step-by-step explanation:
The two angles form a straight line so they add to 180 degrees
x+156 = 180
Subtract 156 from each side
x+156-156 = 180- 156
x = 24
The missing angle is 24 degrees
Answer:
7/9 and 6
Step-by-step explanation:
Coefficients are intergers that are parted with a variable.
7/9 and 6 are the coefficients
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Answer:
<em>The base is 24 cm long.</em>
Step-by-step explanation:
<u>Equations</u>
Let's call
b= base of the triangle
h=height of the triangle
The base is 9 cm longer than the height, thus:
b = h + 9
The area of the triangle is:
![\displaystyle A=\frac{bh}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%3D%5Cfrac%7Bbh%7D%7B2%7D)
![\displaystyle A=\frac{(h+9)h}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%3D%5Cfrac%7B%28h%2B9%29h%7D%7B2%7D)
And its value is 180:
![\displaystyle \frac{(h+9)h}{2}=180](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B%28h%2B9%29h%7D%7B2%7D%3D180)
Multiplying by 2:
![(h+9)h=360](https://tex.z-dn.net/?f=%28h%2B9%29h%3D360)
Operating:
![h^2+9h-360=0](https://tex.z-dn.net/?f=h%5E2%2B9h-360%3D0)
Factoring:
![(h-15)(h+24)=0](https://tex.z-dn.net/?f=%28h-15%29%28h%2B24%29%3D0)
The only valid positive solution is:
h = 15 cm
And b = h + 9 = 24
b = 24 cm
The base is 24 cm long.
Answer:
The weight of cat is <u>14 pounds</u> and the weight of kitten is <u>4 pounds</u>.
Step-by-step explanation:
Given:
Callie has a new kitten. It can weigh 3 pounds less than half the weight of Callie‘s cat. Together the cat and kitten weigh 18 pounds.
Now, to find the weight of each animal:
Let the cat's weight be ![x.](https://tex.z-dn.net/?f=x.)
And the kitten weight = ![\frac{x}{2} -3](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%20-3)
Total weight of cat and kitten = 18 pounds.
Now, to set an equation to get the weight of each animal:
![(x)+(\frac{x}{2}-3)=18](https://tex.z-dn.net/?f=%28x%29%2B%28%5Cfrac%7Bx%7D%7B2%7D-3%29%3D18)
![x+\frac{x}{2} -3=18](https://tex.z-dn.net/?f=x%2B%5Cfrac%7Bx%7D%7B2%7D%20-3%3D18)
![\frac{2x+x-6}{2} =18](https://tex.z-dn.net/?f=%5Cfrac%7B2x%2Bx-6%7D%7B2%7D%20%3D18)
![\frac{3x-6}{2} =18](https://tex.z-dn.net/?f=%5Cfrac%7B3x-6%7D%7B2%7D%20%3D18)
<em>Multiplying both sides by 2 we get:</em>
<em />
<em />
<em>Adding both sides by 6 we get:</em>
<em />
<em />
<em>Dividing both sides by 3 we get:</em>
<em />
<em />
<em>The weight of cat = 14 pounds.</em>
Substituting the value of
to get the kitten's weight:
![\frac{x}{2} -3\\\\=\frac{14}{2}-3\\\\=7-3\\\\=4.](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%20-3%5C%5C%5C%5C%3D%5Cfrac%7B14%7D%7B2%7D-3%5C%5C%5C%5C%3D7-3%5C%5C%5C%5C%3D4.)
<em>The kitten's weight = 4 pounds.</em>
Therefore, the weight of cat is 14 pounds and the weight of kitten is 4 pounds.