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3 years ago

What two numbers can be multiplied to be -150 and added to be 5

1 answer:

8 0

Xy = -150
x + y = 5

x + y = 5
x - x + y = -x + 5
y = -x + 5

xy = -150
x(-x + 5) = -150
x(-x) + x(5) = -150
-x² + 5x = -150
-x² + 5x + 150 = 0
-1(x²) - 1(-5x) - 1(-150) = 0
  -1(x² - 5x - 150) = 0
-1 -1
x² - 5x - 150 = 0
x = -(-5) ± √((-5)² - 4(1)(-150))
  2(1)
x = 5 ± √(25 + 600)
2
x = 5 ± √(625)
2
x = 5 ± 25
2
x = 2.5 ± 12.5
x = 2.5 + 12.5 or x = 2.5 - 12.5
x = 15      or        x = -10

x + y = 5
15 + y = 5
- 15 - 15
y = -10
  (x, y) = (15, -10)

  or

x + y = 5
-10 + y = 5
+ 10 + 10
y = 15
  (x, y) = (-10, 15)

The two numbers that add up to 5 and multiply to -150 are 15 and -10.

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Answer:

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Step-by-step explanation:

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<h3>What is the z-score?</h3>

The z-score for this patient who takes 7 days to recover can be found as:

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The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.2 days and a standard deviation of 1.2 days.

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2 years ago

What is factorisation

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Factorization is a method of writing numbers as the product of their factors or divisors.

Solution:

Factorisation:

Factorization is a method of writing numbers as the product of their factors or divisors.

In other words we can say, Finding what to multiply together to get an expression.

It is like "splitting" an expression into a multiplication of simpler expressions.

Methods of factorisation:

Factoring out the GCF

The sum-product pattern

The grouping method

The perfect square trinomial pattern

The difference of squares pattern

Factoring out the GCF:

This methods means that factoring out common factors

For example:

$12x^2 + 3x = 3x(4x + 1)$

This can be used when each term in given expression shares a common factor

The sum-product pattern

A quadratic equation may be expressed as a product of two binomials

For example:

$x^2 + 7x + 12 = (x + 3)(x + 4)$

This method can be used for quadratic equations of form $ax^2 + bx + c = 0$

The grouping method

If the polynomial is of the form $ax^2 + bx + c$ and there are factors of ac that add up to b , we can use this method

For example:

$2x^2 + 7x + 3\\\\2x^2 + 6x + 1x + 3\\\\2x(x + 3) + 1(x + 3)\\\\(x + 3)(2x + 1)$

The perfect square trinomial pattern

If the first and last terms are perfect squares and the middle term is twice the product of their square roots , we can use this method

For example:

$x^2 + 10x + 25\\\\(x + 5)^2$

The difference of squares pattern

If the expression represents a difference of squares, we can use this method

Because $a^2 - b^2 = (a + b)(a - b)$

For example:

$x^2 - 25\\\\x^2 - 5^2\\\\(x + 5)(x - 5)$

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3 years ago