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3 years ago

Factor completely. 12x4+18x3+45x2 Enter your answer in the box.

Mathematics

1 answer:

lukranit [14]3 years ago

6 0

QUESTION 1

The given expression is

$12x^4+18x^3+45x^2$

The greatest common factor is $3x^2$ .

We factor to obtain;

$3x^2(4x^2+6x+15)$

QUESTION 2

The given quadratic equation is

$x^2+6x-72=0$

We split the middle term to obtain

$x^2+12x-6x-72=0$

Factor by grouping;

$x(x+12)-6(x+12)=0$

$(x+12)(x-6)=0$

Use zero product property;

$(x+12)=0\:\:or\:\:(x-6)=0$

$x=-12\:\:or\:\:x=6$

QUESTION 3

The given system of equation is

$3x+4y=-8$

$7x-3y=6$

If we multiply $3x+4y=-8$ by 3, we obtain;

$9x+12y=-24$

If we multiply $7x-3y=6$ by 4 we obtain;

$28x-12y=24$

Adding the last two equations will give us;

$37x=0$

The y-variable is eliminated.

Answer:Multiply 3x+4y=−8

by 3. Multiply 7x−3y=6 by 4. Add the resulting equations together.

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Answer:

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Step-by-step explanation:

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3 years ago

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A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n indepe

Naddik [55]

Answer:

P (X ≤ 4)

Step-by-step explanation:

The binomial probability formula can be used to find the probability of a binomial experiment for a specific number of successes. It does not find the probability for a range of successes, as in this case.

The range "x≤4" means x = 0 or x = 1 or x = 2 or x = 3 or x = 4, so there are five different probability calculations to do.

To to find the total probability, we use the addition rule that states that the probabilities of different events can be added to find the probability for the entire set of events only if the events are Mutually Exclusive. The outcomes of a binomial experiment are mutually exclusive for any value of x between zero and n, as long as n and p don't change, so we're allowed to add the five calculated probabilities together to find the total probability.

The probability that x ≤ 4 can be written as P (X ≤ 4) or as P (X = 0 or X = 1 or X = 2 or X = 3 or X = 4) which means (because of the addition rule) that P(x ≤ 4) = P(x = 0) + P(x = 1) + P (x = 2) + P (x = 3) + P (x = 4)

Therefore, the probability of x<4 successes is P (X ≤ 4)

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3 years ago

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Answer:

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3 years ago

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I need help! Will mark Brainliest for full answer!!!

Softa [21]

Answer:

Part a .............> x = 11

Part b .............> k = 57.2

Part c .............> y = 9.2

Explanation:

The three problems deal with inverse variation between two variables

An inverse variation relation between two variables means that when one of the variables increases, the other will decrease (and vice versa)

Mathematically, an inverse variation relation is represented as follows:

$y = \frac{k}{x}$

where x and y are the two variables and k is the constant of variation

Now, let's check the givens:

Part a:

We are given that y = 3 and k = 33

Substitute in the original relation and solve for x as follows:

$y = \frac{k}{x}\\ \\3 = \frac{33}{x}\\ \\x=\frac{33}{3}=11$

Part b:

We are given that y = 11 and x = 5.2

Substitute in the original relation and solve for k as follows:

$y=\frac{k}{x}\\ \\11=\frac{k}{5.2}\\ \\k=11*5.2=57.2$

Part c:

We are given that x=7.8 and k=72

Substitute in the original relation and solve for y as follows:

$y=\frac{k}{x}=\frac{72}{7.8}=9.2$ to the nearest tenth

Hope this helps :)

6 0

2 years ago