Answer: 14/45
explanation:
Answer:
<h2>
<em>x</em><em>=</em><em>3</em></h2>
<em>Sol</em><em>ution</em><em>,</em>
<em>Theorem</em><em>:</em>
<em>The</em><em> </em><em>angle</em><em> </em><em>bisector</em><em> </em><em>theorem</em><em> </em><em>states </em><em>that</em><em> </em><em>if</em><em> </em><em>a</em><em> </em><em>ray </em><em>bisects</em><em> </em><em>an</em><em> </em><em>angle</em><em> </em><em>of</em><em> </em><em>a</em><em> </em><em>triangle,</em><em>then</em><em> </em><em>it</em><em> </em><em>divides</em><em> </em><em>the</em><em> </em><em>oppos</em><em>ite</em><em> </em><em>side</em><em> </em><em>into</em><em> </em><em>two </em><em>segments</em><em> </em><em>that</em><em> </em><em>are</em><em> </em><em>proportional</em><em> </em><em>to</em><em> </em><em>other</em><em> </em><em>two</em><em> </em><em>sides</em><em>.</em>
<em>By</em><em> </em><em>the</em><em> </em><em>theorem</em><em>,</em>
<em>
</em>
<em>hope</em><em> </em><em>this</em><em> </em><em>helps</em><em>.</em><em>.</em><em>.</em>
<em>Good</em><em> </em><em>luck</em><em> on</em><em> your</em><em> assignment</em><em>.</em><em>.</em>
The r% of a quantity x is computed by dividing x in 100 parts, and considering r of such parts. So, the r% of the male is
![30\times\cfrac{r}{100} = 0.3 r](https://tex.z-dn.net/?f=%2030%5Ctimes%5Ccfrac%7Br%7D%7B100%7D%20%3D%200.3%20r%20)
and similarly, the r% of female is
![20\times\cfrac{r}{100} = 0.2 r](https://tex.z-dn.net/?f=%2020%5Ctimes%5Ccfrac%7Br%7D%7B100%7D%20%3D%200.2%20r%20)
The number of males decreased by this quantity, so now it is
![30 - 0.3r](https://tex.z-dn.net/?f=%2030%20-%200.3r%20)
and the number of female increased by this quantity, so now it is
![20+0.2r](https://tex.z-dn.net/?f=%2020%2B0.2r%20)
we know that these two new counts are the same number, so we can build and solve the equality
![30 - 0.3r = 20+0.2r](https://tex.z-dn.net/?f=%2030%20-%200.3r%20%3D%2020%2B0.2r%20)
Subtract 20 and add 0.3r from both sides:
![10 = 0.5r](https://tex.z-dn.net/?f=%2010%20%3D%200.5r%20)
Divide both sides by 0.5 to solve for r:
![r = 20](https://tex.z-dn.net/?f=%20r%20%3D%2020%20)
Let's check the answer
The 20% of 30 is
, while the 20% of 20 is 4. So, we are stating that
which is true because both expressions evaluate to 24.
Answer:
![p:y = 3x-10](https://tex.z-dn.net/?f=p%3Ay%20%3D%203x-10)
Step-by-step explanation:
We are given the following in the question:
A(1, 1), B(2, 4), C(4, 2)
i) Slope of AB
![A(1, 1), B(2, 4)\\\\m = \dfrac{y_2-y_1}{x_2-x_1}\\\\m = \dfrac{4-1}{2-1}=3](https://tex.z-dn.net/?f=A%281%2C%201%29%2C%20B%282%2C%204%29%5C%5C%5C%5Cm%20%3D%20%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%5C%5Cm%20%3D%20%5Cdfrac%7B4-1%7D%7B2-1%7D%3D3)
Thus, slope of AB is 3.
ii) Point slope form
The point slope form of a line can be written as:
![y - y_1 = m(x - x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%20%3D%20m%28x%20-%20x_1%29)
The point intercept form of line can be written as:
![y = mx + c](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20c)
The line is parallel to AB and contains point C(4, 2). Since line p is parallel to AB, line p will have the same slope as line AB
Putting values, we get,
![y - 2 = 3(x-4)\\y = 3x-12+2\\y = 3x-10](https://tex.z-dn.net/?f=y%20-%202%20%3D%203%28x-4%29%5C%5Cy%20%3D%203x-12%2B2%5C%5Cy%20%3D%203x-10)
which is the required slope intercept equation of line p.