Solve the system of equations:

Mathematics

1 answer:

iVinArrow [24]3 years ago

5 0

$(-1,-2) \: \: \: \: \: and \: \: \: \: \: (3,6) \\ Answer: A$

Step-by-step explanation:

$y = 2x \\ y = {x}^{2} - 3 \\ \\ 2x = {x}^{2} - 3 \\ {x}^{2} - 2x - 3 = 0 \\ (x + 1)(x - 3) = 0 \\ x + 1 = 0 \: \: \: \: \: or \: \: \: \: \: x - 3 = 0 \\ x = - 1 \: \: \: \: \: or \: \: \: \: \: x = 3$

When x = -1

Substitute x = -1 into y = 2x

y = 2(-1)

y = -2

( -1, -2)

When x = 3

Substitute x = 3 into y = 2x

y = 2(3)

y = 6

( 3, 6)

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Null hypothesis: $H_0:\; \mu = 48\; ^\circ\rm F$ .

Alternative hypothesis: $H_1:\; \mu \ne 48\; \rm ^\circ F$ .

Step-by-step explanation:

In hypothesis testing, the alternative hypothesis $H_1$ represents the claim that is being tested. According to the claim in this question, the true (population) mean $\mu$ is "incorrect," or not equal to (" $\ne$ ") the proposed value of $48\; \rm ^\circ F$ . Hence, the alternative hypothesis for this question would be $H_0:\; \mu \ne 48\; \rm ^\circ F$ .

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