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Answer:
![x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B20%20%2B%5Csqrt%7B454%7D%7D%7B18%7D%2C%20%5Cquad%20%5Cdfrac%7B20%20-%5Csqrt%7B454%7D%7D%7B18%7D)
Step-by-step explanation:
<u>Given functions</u>:
![p(x)=2x-4](https://tex.z-dn.net/?f=p%28x%29%3D2x-4)
![r(x)=\dfrac{6x-1}{9x+1}](https://tex.z-dn.net/?f=r%28x%29%3D%5Cdfrac%7B6x-1%7D%7B9x%2B1%7D)
Solve for p(x) = r(x):
![\begin{aligned}p(x) & = r(x)\\\implies 2x-4 & = \dfrac{6x-1}{9x+1}\\(2x-4)(9x+1)&=6x-1\\18x^2+2x-36x-4&=6x-1\\18x^2-40x-3&=0\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dp%28x%29%20%26%20%3D%20r%28x%29%5C%5C%5Cimplies%202x-4%20%26%20%3D%20%5Cdfrac%7B6x-1%7D%7B9x%2B1%7D%5C%5C%282x-4%29%289x%2B1%29%26%3D6x-1%5C%5C18x%5E2%2B2x-36x-4%26%3D6x-1%5C%5C18x%5E2-40x-3%26%3D0%5Cend%7Baligned%7D)
As the found quadratic equation cannot be factored, use the Quadratic Formula to solve for x:
<u>Quadratic Formula</u>
![x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D%5Cquad%5Ctextsf%7Bwhen%20%7D%5C%3Aax%5E2%2Bbx%2Bc%3D0)
Therefore:
![a=18, \quad b=-40, \quad c=-3](https://tex.z-dn.net/?f=a%3D18%2C%20%5Cquad%20b%3D-40%2C%20%5Cquad%20c%3D-3)
Substitute the values of a, b and c into the <u>quadratic formula</u> and solve for x:
![\begin{aligned}\implies x & =\dfrac{-(-40) \pm \sqrt{(-40)^2-4(18)(-3)} }{2(18)}\\\\& =\dfrac{40 \pm \sqrt{1816}}{36}\\\\& =\dfrac{40 \pm \sqrt{4 \cdot 454}}{36}\\\\& =\dfrac{40 \pm \sqrt{4}\sqrt{454}}{36}\\\\& =\dfrac{40 \pm2\sqrt{454}}{36}\\\\& =\dfrac{20 \pm\sqrt{454}}{18}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20x%20%26%20%3D%5Cdfrac%7B-%28-40%29%20%5Cpm%20%5Csqrt%7B%28-40%29%5E2-4%2818%29%28-3%29%7D%20%7D%7B2%2818%29%7D%5C%5C%5C%5C%26%20%3D%5Cdfrac%7B40%20%5Cpm%20%5Csqrt%7B1816%7D%7D%7B36%7D%5C%5C%5C%5C%26%20%3D%5Cdfrac%7B40%20%5Cpm%20%5Csqrt%7B4%20%5Ccdot%20454%7D%7D%7B36%7D%5C%5C%5C%5C%26%20%3D%5Cdfrac%7B40%20%5Cpm%20%5Csqrt%7B4%7D%5Csqrt%7B454%7D%7D%7B36%7D%5C%5C%5C%5C%26%20%3D%5Cdfrac%7B40%20%5Cpm2%5Csqrt%7B454%7D%7D%7B36%7D%5C%5C%5C%5C%26%20%3D%5Cdfrac%7B20%20%5Cpm%5Csqrt%7B454%7D%7D%7B18%7D%5Cend%7Baligned%7D)
Therefore, the solutions are:
![x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B20%20%2B%5Csqrt%7B454%7D%7D%7B18%7D%2C%20%5Cquad%20%5Cdfrac%7B20%20-%5Csqrt%7B454%7D%7D%7B18%7D)
Learn more about quadratic equations here:
brainly.com/question/27750885
brainly.com/question/27739892
Answer:
- <u>0.25</u>
- <u>0.85</u>
Step-by-step explanation:
P (Triangle or Square) :
- Area of Triangle + Area of Square / Area of Rectangle
- 1/2 x 3 x 4 (height is found by Pythagorean Theorem) + (3)² / 10 x 6
- 6 + 9 / 60
- 15/60
- <u>0.25</u>
<u></u>
P (Not the square) :
- Area of rectangle - Area of square / Area of rectangle
- 60 - 9 / 60
- 51/60
- 17/20
- <u>0.85</u>
You would have to Multiply 50 by 2 and then Multiply the answer to 300.
Answer:
C. and A.
Step-by-step explanation:
1/6 is a positive number so that is automatically greater than -0.33 and 0.3 is It's like, the bigger the number next to the negative sign, the MORE NEGATIVE it is, making it SMALLER.
Reward for answering question correctly:
So am I gonna get brainliest?