Help solve the system of equations

Mathematics

2 answers:

Lady_Fox [76]3 years ago

7 0

2x + 4 = x^2 + x - 2
x^2 + x - 2 - 4 - 2x = 0
x^2 - x - 6 = 0
(x - 3)(x + 2) = 0

x - 3 = 0 y = 2x + 4
x = 3 y = 2(3) + 4
y = 10

x + 2 = 0 y = 2x + 4
x = -2 y = 2(-2) + 4
y = 0

solutions are : (3,10) and (-2,0) <===

liraira [26]3 years ago

7 0

Given,

y = 2x + 4

Also given,

y = x² + x - 2

Substituting the value of y from above,

2x + 4 = x² + x - 2

x² - x - 6 = 0

x² - 3x + 2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

(x + 2)(x - 3) = 0

x = -2 or 3

When x = -2,

y = 2x + 4 = (2 * -2) + 4 = -4 + 4 = 0

When x = 3,

y = 2x + 4 = (2 * 3) + 4 = 6 + 4 = 10

Hence, the two solutions are (-2, 0) and (3, 10).

Hence, the answer is C.

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Using the z-distribution, as we have a proportion, the 95% confidence interval is (0.2316, 0.3112).

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

In this problem, we have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.