Answer:
![A_T=150cm^2](https://tex.z-dn.net/?f=A_T%3D150cm%5E2)
Explanation: We need to find the area of the triangle, We know that the area of any right triangle is:
![A_T=\frac{1}{2}(b\times h)](https://tex.z-dn.net/?f=A_T%3D%5Cfrac%7B1%7D%7B2%7D%28b%5Ctimes%20h%29)
Therefore in the information given we have the following:
![\begin{gathered} h=20\operatorname{cm} \\ b=15\operatorname{cm} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20h%3D20%5Coperatorname%7Bcm%7D%20%5C%5C%20b%3D15%5Coperatorname%7Bcm%7D%20%5Cend%7Bgathered%7D)
Therefore the Area of this triangle is as follows:
![\begin{gathered} A_T=\frac{1}{2}(b\times h) \\ \therefore\rightarrow \\ A_T=\frac{1}{2}(20cm\times15cm)=\frac{1}{2}(20\times15)cm^2 \\ A_T=\frac{1}{2}(300)cm^2=150cm^2 \\ \therefore\rightarrow \\ A_T=150cm^2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A_T%3D%5Cfrac%7B1%7D%7B2%7D%28b%5Ctimes%20h%29%20%5C%5C%20%5Ctherefore%5Crightarrow%20%5C%5C%20A_T%3D%5Cfrac%7B1%7D%7B2%7D%2820cm%5Ctimes15cm%29%3D%5Cfrac%7B1%7D%7B2%7D%2820%5Ctimes15%29cm%5E2%20%5C%5C%20A_T%3D%5Cfrac%7B1%7D%7B2%7D%28300%29cm%5E2%3D150cm%5E2%20%5C%5C%20%5Ctherefore%5Crightarrow%20%5C%5C%20A_T%3D150cm%5E2%20%5Cend%7Bgathered%7D)
Note! Units are centimeter-squared
<u>Solution</u><u>:</u>
The rationalisation factor for
is ![a + \sqrt{b}](https://tex.z-dn.net/?f=a%20%2B%20%5Csqrt%7Bb%7D%20)
So, let us apply it here.
![\frac{1}{5 - \sqrt{2} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B5%20-%20%20%5Csqrt%7B2%7D%20%7D%20)
The rationalising factor for 5 - √2 is 5 + √2.
Therefore, multiplying and dividing by 5 + √2, we have
![= \frac{1}{5 - \sqrt{2} } \times \frac{5 + \sqrt{2} }{5 + \sqrt{2} } \\ = \frac{5 + \sqrt{2} }{(5 - \sqrt{2})(5 + \sqrt{2} ) } \\ = \frac{5 + \sqrt{2} }{ {(5)}^{2} - ( \sqrt{2})^{2} } \\ = \frac{5 + \sqrt{2} }{25 - 2} \\ = \frac{5 + \sqrt{2} }{23}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B1%7D%7B5%20-%20%20%5Csqrt%7B2%7D%20%7D%20%20%5Ctimes%20%20%5Cfrac%7B5%20%2B%20%20%5Csqrt%7B2%7D%20%7D%7B5%20%2B%20%20%5Csqrt%7B2%7D%20%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B5%20%2B%20%20%5Csqrt%7B2%7D%20%7D%7B%285%20-%20%20%5Csqrt%7B2%7D%29%285%20%2B%20%20%5Csqrt%7B2%7D%20%29%20%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B5%20%2B%20%20%5Csqrt%7B2%7D%20%7D%7B%20%7B%285%29%7D%5E%7B2%7D%20-%20%28%20%5Csqrt%7B2%7D%29%5E%7B2%7D%20%20%20%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B5%20%2B%20%20%5Csqrt%7B2%7D%20%7D%7B25%20-%20%202%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B5%20%2B%20%20%5Csqrt%7B2%7D%20%7D%7B23%7D%20)
<u>Answer:</u>
<u>
</u>
Hope you could understand.
If you have any query, feel free to ask.
The difference between the mixed numbers is equal to 5/6.
<h3>How to perform the subtraction between the two mixed numbers?</h3>
A mixed number is a number that is written as a whole number plus an improper fraction, here we want to compute:
(2 + 1/2) - (1 + 2/3)
We can group the whole numbers and the fractions, so we get:
(2 - 1) + (1/2 - 2/3)
Now we can simplify this so we get:
(2 - 1) + (1/2 - 2/3)
= 1 + (3/6 - 4/6) = 1 - 1/6 = 6/6 - 1/6 = 5/6
We conclude that the difference between the mixed numbers is equal to 5/6.
If you want to learn more about mixed numbers:
brainly.com/question/1746829
#SPJ1
One bush costs $10 and One geranium costs $8. I believe this is the correct answer.
Answer:i think its c sorry if im wrong
Step-by-step explanation: