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2 years ago

State the property that justifies the statement: If 4x + 9 = 15 and X=2y + 1,

Mathematics

1 answer:

GREYUIT [131]2 years ago

6 0

Answer:

Substitution property of equality

Step-by-step explanation:

Given

$4x + 9 = 15$ and $x = 2y + 1$

Then

$4(2y + 1) + 9 = 15$

Required

State the property

From the list of options, (d) answers the question.

This is so because:

Substitution property of equality states that

If $a = b$ then $b = a$

In other words, both can replace one another.

So if $x = 2y + 1$ , then 2y + 1 can be substituted for x in $4x + 9 = 15$

So:

$4x + 9 = 15$ becomes

$4(2y + 1) + 9 = 15$

<em>Hence, it is substitution property of equality</em>

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What two numbers multiply to -126 and add up to -65

Airida [17]

Xy = -126
x + y = -65

$xy = -126$
$\frac{xy}{x} = \frac{-126}{x}$
$y = \frac{-126}{x}$

$x + y = -65$
$x + \frac{-126}{x} = -65$
$\frac{x^{2}}{x} + \frac{-126}{x} = -65$
$\frac{x^{2} - 126}{x} = -65$
$-65x = x^{2} - 126$
$0 = x^{2} + 65x - 126$
$x = \frac{-(65) \+ \sqrt{(65)^{2} - 4(1)(-126)}}{2(1)}$
$x = \frac{-65 \± \sqrt{4225 + 504}}{2}$
$x = \frac{-65 \± \sqrt{4729}}{2}$
$x = \frac{-65 \± 68.8}{2}$
$x = \frac{-65 + 68.8}{2}$ $or$ $x = \frac{-65 - 68.8}{2}$
$x = \frac{3.8}{2}$ $or$ $x = \frac{-133.8}{2}$
$x = 1.9$ $or$ $x = -66.9$

x + y = -65
  1.9 + y = -65
- 1.9   - 1.9
y = -66.9
  (x, y) = (1.9, -66.9)

or

  x + y = -65
  -66.9 + y = -65
+ 66.9 + 66.9
y = 1.9
  (x, y) = (-66.9, 1.9)

The two numbers that add up to -65 and can multiply to -126 are the numbers -66.9 and 1.9.

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The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

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The probability mass function for the Binomial distribution is given as:

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Where (nCx) means combinatory and it's given by this formula:

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$P(X \geq 2)$

And we can use the complement rule and we got:

$P(X \geq 2) = 1-P(X$

And we can find the individual probabilities using the probability mass function and we got:

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