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2 years ago

Solve the system of equations y=x^2+3x-4 and y=2x-4

Mathematics

1 answer:

laila [671]2 years ago

4 0

Answer:

Step-by-step explanation:

Given the 2 equations

y = x² + 3x - 4 → (1)

y = 2x - 4 → (2)

Substitute y = x² + 3x - 4 into (2)

x² + 3x - 4 = 2x - 4 ( subtract 2x - 4 from both sides )

x² + x = 0 ← in standard form

x(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x = 0

x + 1 = 0 ⇒ x = - 1

Substitute these values into (2) for corresponding values of y

x = 0 → y = 2(0) - 4 = 0 - 4 = - 4 ⇒ (0, - 4 )

x = - 1 → y = 2(- 1) - 4 = - 2 - 4 = - 6 ⇒ (- 1, - 6 )

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What is the equation of a sine function with an amplitude of 2 and a period of 4

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Now that we know the standard form and the components, we know that we can forget about k and plug in 0 for h. This would leave us with $y=asin[b(x)]$ . We know that the amplitude is 2, therefore, a=2. To find the period, you divide 2π by the given period. $\frac{2\pi }{b} =\frac{2\pi }{4\pi } =\frac{2}{4} =\frac{1}{2}$ , therefore, b=1/2.

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2 years ago

Zara has forgotten her 4-digit PIN code. She knows the first digit is a factor of 20 and the 4 digits make a number divisible by

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Answer:

800 different sets of digits.

Step-by-step explanation:

Since the first digit is a factor of 20, the factors of 20 are 1,2,4,5,10,20. We only need the single digit factors which are 1,2,4 and 5. These 4 numbers can be permuted in 1 way for the first digit, so we have ⁴P₁.

For the second digit, we have 10 digits permuted in 1 way, ¹⁰P₁ and also for the third digit, we have 10 digits permuted in 1 way, ¹⁰P₁ and for the last digit, which is divisible by 5, it is either a 0 or 5, so we have two digits permuted in 1 way, ²P₁.

So, the number of different 4 digit number that Zara'2 4-digit PIN code could be is ⁴P₁ × ¹⁰P₁ × ¹⁰P₁ × ²P₁ = 4 × 10 × 10 × 2 = 800 different sets of digits

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