Check the picture below.
so hmmm let's find the distance AC, which is the only one missing for the perimeter.
![\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{AC}\\ a=\stackrel{adjacent}{6}\\ b=\stackrel{opposite}{8}\\ \end{cases} \implies AC=\sqrt{6^2 + 8^2} \\\\\\ AC=\sqrt{100}\implies AC=10~\hfill \underset{Perimeter}{\stackrel{6~~ + ~~8~~ + ~~10}{\text{\LARGE 24}cm}} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Ctextit%7Busing%20the%20pythagorean%20theorem%7D%20%5C%5C%5C%5C%20c%5E2%3Da%5E2%2Bb%5E2%5Cimplies%20c%3D%5Csqrt%7Ba%5E2%20%2B%20b%5E2%7D%20%5Cqquad%20%5Cbegin%7Bcases%7D%20c%3D%5Cstackrel%7Bhypotenuse%7D%7BAC%7D%5C%5C%20a%3D%5Cstackrel%7Badjacent%7D%7B6%7D%5C%5C%20b%3D%5Cstackrel%7Bopposite%7D%7B8%7D%5C%5C%20%5Cend%7Bcases%7D%20%5Cimplies%20AC%3D%5Csqrt%7B6%5E2%20%2B%208%5E2%7D%20%5C%5C%5C%5C%5C%5C%20AC%3D%5Csqrt%7B100%7D%5Cimplies%20AC%3D10~%5Chfill%20%5Cunderset%7BPerimeter%7D%7B%5Cstackrel%7B6~~%20%2B%20~~8~~%20%2B%20~~10%7D%7B%5Ctext%7B%5CLARGE%2024%7Dcm%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=6\\ h=8 \end{cases}\implies A=\cfrac{1}{2}(6)(8)\implies A=\text{\LARGE 24}~cm^2](https://tex.z-dn.net/?f=%5Ctextit%7Barea%20of%20a%20triangle%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B1%7D%7B2%7Dbh%20%5Cbegin%7Bcases%7D%20b%3Dbase%5C%5C%20h%3Dheight%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20b%3D6%5C%5C%20h%3D8%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B1%7D%7B2%7D%286%29%288%29%5Cimplies%20A%3D%5Ctext%7B%5CLARGE%2024%7D~cm%5E2)
Answer:
8
Step-by-step explanation:
Hello,
This is related to ratios and proportions. We have a 12 foot tree that casts a 6 foot shadow, so now we are trying to figure out how tall is a tree that casts a 4 foot shadow.
We can set an easier method to get this.
12 = 6 (this means the 12 foot tree casts a 6 foot shadow)
x = 4 (this means how tall is the tree to cast a 4 foot shadow, the unknown height of the tree is denoted as x)
Then, we can cross multiply.
48 = 6x
Solve for x, which is the unknown height we are trying to figure out.
x = 8
Answer:
<u>x = 52°</u>
Step-by-step explanation:
The angles add up to 360°.
- x + 98 + x + 91 + x + 15 = 360
- 3x + 204 = 360
- 3x = 156
- <u>x = 52°</u>
The solution to the equation is x = 4
<h3>What are linear equations?</h3>
Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
<h3>How to determine the solution to the system?</h3>
A system of linear equations is a collection of at least two linear equations.
In this case, the equation is given as
(x + 20)/2 = 3x
Multiply both sides of the equation by 2
x + 20 = 6x
Subtract x from both sides of the equation
5x = 20
Divide both sides of the equation by 5
x = 4
hence, the solution to the equation is x = 4
Read more about equations at:
brainly.com/question/2972832
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