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Snezhnost [94]
3 years ago
8

What are the solutions of the following system? -2x^2 + y=-5 y=-3x^2+5

Mathematics
2 answers:
Ray Of Light [21]3 years ago
8 0

Answer:

c

Step-by-step explanation:

Doss [256]3 years ago
5 0
\begin{cases}-2x^2+y=-5\\y=-3x^2+5\end{cases}\\\\\\
-2x^2+(-3x^2+5)=-5\\\\
-2x^2-3x^2+5=-5\quad|-5\\\\-5x^2=-10\quad|:(-5)\\\\x^2=2\\\\
\boxed{x=-\sqrt{2}\qquad\vee\qquad x=\sqrt{2}}\\\\\\
y=-3x^2+5\qquad\vee\qquad y=-3x^2+5\\\\
y=-3(-\sqrt{2})^2+5\qquad\vee\qquad y=-3(\sqrt{2})^2+5\\\\
y=-3\cdot2+5\qquad\vee\qquad y=-3\cdot 2+5\\\\
y=-6+5\qquad\vee\qquad y=-6+5\\\\
\boxed{y=-1\qquad\vee\qquad y=-1}\\\\\\
\begin{cases}x=-\sqrt{2}\\y=-1\end{cases}\qquad\vee\qquad\begin{cases}x=\sqrt{2}\\y=-1\end{cases}

Answer C.
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3 years ago
What is a35 for the arithmetic sequence presented in the table below?
Kryger [21]

Answer: choice B) a35 = -118

=====================================================

Explanation:

When n = 5, an = 32 as shown in the first column of the table. This means the fifth term is 32. Plug in those values to get

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a1 = 32-4d

We'll plug this in later

Turn to the second column of the table. We have n = 10 and an = 7. Plug those values into the formula

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Now substitute in the equation in which we solved for a1

7 = a1+9d

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--------------

The nth term formula is therefore

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To check this result, plug in n = 5 to find that a5 = 32. Similarly, you'll find that a10 = 7 after plugging in n = 10. I'll let you do these checks.

--------------

Replace n with 35 to find the 35th term

an = -5n + 57

a35 = -5(35) + 57

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