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2 years ago

Solve the system of equations: y= x^2 + 2x - 3 and y=3x+ 3.

Mathematics

1 answer:

Semenov [28]2 years ago

3 0

Answer:

(-2, -3)

(3, 12)

Step-by-step explanation:

To solve this, we're gonna get rid of the y's with substitution

x² + 2x - 3 = 3x + 3

Let's make this equation equal to zero

Subtract 3 from both sides

x² + 2x - 3 = 3x + 3

- 3 - 3

x² + 2x - 6 = 3x

Subtract 3x from both sides

x² + 2x - 6 = 3x

- 3x - 3x

x² - x - 6 = 0

Factor the equation

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

This means x can be -2 or 3

Let's solve it with -2 first, plug the new x in y = 3x + 3

y = 3(-2) + 3

y = -6 + 3 = -3

Do the same for x = 3

y = 3(3) + 3

y = 9 + 3 = 12

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Read 2 more answers

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Answer:

a) 0.033

b) 0.468

c) 100

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 105.3

Standard Deviation, σ = 8

The amount x of miraculin produced (measured in micro-grams per gram of fresh weight) had a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(x > 120)

$P( x > 120) = P( z > \displaystyle\frac{120 - 105.3}{8}) = P(z > 1.8375)$

$= 1 - P(z \leq 1.8375)$

Calculation the value from standard normal z table, we have,

$P(x > 120) = 1 - 0.967 = 0.033 = 3.3\%$

b) P(x between 100 and 110)

$P(100 \leq x \leq 110) = P(\displaystyle\frac{100 - 105.3}{8} \leq z \leq \displaystyle\frac{110-105.3}{8}) = P(-0.6625 \leq z \leq 0.5875)\\\\= P(z \leq 0.5875) - P(z \leq -0.6625)\\= 0.722 - 0.254 = 0.468 = 46.8\%$

$P(100 \leq x \leq 110) = 46.8\%$

c) P(x < a) = 0.25

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Calculation the value from standard normal z table, we have,

$P( z \leq -0.674) = 0.25$

$\displaystyle\frac{x - 105.3}{8} = -0.674\\\\x = -0.674\times 8 + 105.3 = 99.908 \approx 100$

3 0

2 years ago