With Khan Academy, there is a small trick that can be done to see answers, you just have to click the percentage before going back into the lesson and it shows the answers you have gotten wrong, and giving you the answer for them. Opening up two tabs allows a fluent work space. Hope this sort of helps. I’m not good at math.
RO divides the rectangle into two congruent right triangles.
The area of the one triangle is equal half area of the rectangle.
Calculate the area of rectangle:
![A_R=lw\\l=12,\ w=5\\\\A_R=12\cdot5=60](https://tex.z-dn.net/?f=A_R%3Dlw%5C%5Cl%3D12%2C%5C%20w%3D5%5C%5C%5C%5CA_R%3D12%5Ccdot5%3D60)
The area of right triangle:
![A_T=\dfrac{1}{2}A_R\to A_T=\dfrac{1}{2}\cdot60=30](https://tex.z-dn.net/?f=A_T%3D%5Cdfrac%7B1%7D%7B2%7DA_R%5Cto%20A_T%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot60%3D30)
Use the Pythagorean theorem to calculate the length of RO:
![|RO|^2=5^2+12^2\\\\|RO|^2=25+144\\\\|RO|^2=169\to|RO|=\sqrt{169}\to|RO|=13](https://tex.z-dn.net/?f=%7CRO%7C%5E2%3D5%5E2%2B12%5E2%5C%5C%5C%5C%7CRO%7C%5E2%3D25%2B144%5C%5C%5C%5C%7CRO%7C%5E2%3D169%5Cto%7CRO%7C%3D%5Csqrt%7B169%7D%5Cto%7CRO%7C%3D13)
The formula of an area of this right triangle is:
![A_T=\dfrac{1}{2}|RO||PA|](https://tex.z-dn.net/?f=A_T%3D%5Cdfrac%7B1%7D%7B2%7D%7CRO%7C%7CPA%7C)
Therefore we have the equation:
![\dfrac{1}{2}(13)|PA|=30\qquad|\cdot2\\\\13|PA|=60\quad|:13\\\\|PA|=\dfrac{60}{13}\\\\|PA|\approx4.62](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%2813%29%7CPA%7C%3D30%5Cqquad%7C%5Ccdot2%5C%5C%5C%5C13%7CPA%7C%3D60%5Cquad%7C%3A13%5C%5C%5C%5C%7CPA%7C%3D%5Cdfrac%7B60%7D%7B13%7D%5C%5C%5C%5C%7CPA%7C%5Capprox4.62)
Answer:
first number=2
second number=-5
Step-by-step explanation:
first number= a
second number= b
we have the following equations
7a+3b=-1 equation 1
a+b=-3 equation 2
using equation 2 we have
a=-3-b
using equation 1 we have
7(-3-b)+3b=-1
-21-7b+3b=-1
-4b=20
b=-20/4=-5 = second number
a+(-5)=-3
a-5=-3
a=-3+5
a=2= first number
Answer:
( 2x - 1 ) ( x + 3) / ( 2x - 3 ) ( x + 1 )
Step-by-step explanation:
(x - 2) / (x + 1) - 3(1 - 4x) / ( 2x - 3 ) ( x + 1 )
{ ( x - 2 ) ( 2x - 3) - 3 ( 1- 4x) } / ( 2x - 3 ) ( x + 1 )
{ 2x^2 - 7x - 3 + 12x} / ( 2x - 3 ) ( x + 1 )
{ 2x^2 + 5x - 3 } / ( 2x - 3 ) ( x + 1 )
( 2x - 1 ) ( x + 3 ) / ( 2x - 3 ) ( x + 1 )