What is the solution to this system?

Mathematics

1 answer:

katovenus [111]3 years ago

6 0

The solution is where the two lines meet. From the the graph, it looks like
(1, -1)

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F(t)=t^2+19t+60 What are the zeros of the function and what is the vertex of the parabola?

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Answer: $-4,-15;\ \left(-\dfrac{19}{2},-\dfrac{121}{4}\right)$

Step-by-step explanation:

Given

Function is $F(t)=t^2+19+60$

Zeroes of the function are

$t^2+19t+60=0\\\\\Rightarrow t=\dfrac{-19\pm\sqrt{19^2-4\times 1\times 60}}{2\times 1}\\\\\Rightarrow t=\dfrac{-19\pm \sqrt{121}}{2}\\\\\Rightarrow t=\dfrac{-19\pm 11}{2}\\\\\Rightarrow t=-4,-15$

Using completing the square method

$y=t^2+2\times \dfrac{19}{2}t+\dfrac{19^2}{2^2}-\dfrac{19^2}{2^2}+60\\\\y=\left(t+\dfrac{19}{2}\right)^2+60-\dfrac{361}{4}\\\\y=\left(t+\dfrac{19}{2}\right)^2-\dfrac{121}{4}\\\\y+\dfrac{121}{4}=\left(t+\dfrac{19}{2}\right)^2\\\\\left(y-(-\dfrac{121}{4}\right)=\left(t-(-\dfrac{19}{2})\right)^2\\\\\text{The vertex is }\left(-\dfrac{19}{2},-\dfrac{121}{4}\right)$

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If you draw a net for a cylinder, such as a soup can, how many two-dimensional geometric shapes would this net have?

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please mark me brainlies :)

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Tony’s club is selling oranges to raise money. For every box they sell, they get 1 1/8 dollars profit. They have sold 75 boxes already. How many more boxes must they sell to raise 180 dollars?

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The amount of money Tony's club get for every box they sell $=1 \frac{1}{8} =1.125$ dollar