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3 years ago

What is the roots of the quadratic equation? 6x^2+5x-4=0

Mathematics

2 answers:

Rama09 [41]3 years ago

4 0

x = $\frac{1}{2}$ or x = - $\frac{4}{3}$

consider the factors of the product 6 × - 4 = - 24 which sum to the coefficient of the x- term ( + 5)

the factors are + 8 and - 3 ( split the middle term using these factors

6x² - 3x + 8x - 4 = 0 ( factor by grouping )

3x(2x - 1) + 4(2x - 1 ) ( take out common factor of (2x - 1) )

= (2x - 1)(3x + 4) = 0

equate each factor to zero and solve for x

2x - 1 = 0 ⇒ x = $\frac{1}{2}$

3x + 4 = 0 ⇒ x = - $\frac{4}{3}$

mariarad [96]3 years ago

3 0

6x² + 5x - 4 = 0

Multiply the first and last term (6x² * -4) to get -24x². Now find two factors of -24x² whose sum is the middle term (5x). -3x + 8x Replace 5x with -3x + 8x, then factor and solve.

6x² - 3x + 8x - 4 = 0

3x(2x - 1) +4(2x - 1) = 0

(3x + 4) (2x - 1) = 0

3x + 4 = 0 or 2x - 1 = 0

x = $-\frac{4}{3}$ or x = $\frac{1}{2}$

Note: you can also use the quadratic formula to find the foots.

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Assume that the Poisson distribution applies and that the mean number of aircraft accidents is 9 per month. Find P(0), the prob

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Answer: 0.0001

It is unlikely to have a month with no aircraft accidents .

Step-by-step explanation:

Given : Mean number of aircraft accidents = 9 per month

The Poisson distribution formula :-

$\dfrac{e^{-\lambda}\lambda^x}{x!}$ , where $\lambda$ is the mean of the distribution.

If X = the number of aircraft accidents per month, then the probability that in a month, there will be no aircraft accidents will be :-

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3 years ago

Nima uses 2/3 cup peanuts, 1/2 cup cashews, 3/4 cups pecans, and some raisinsin a recipe that makes 2 1/4 cups of trail mix. How

Lesechka [4]

Answer:

8/27 cups

Step-by-step explanation:

Nima uses 2/3 cups of peanuts to make a recipe of 2 1/4 = 9/4 cups of trail mix. If we want to find how many cups of peanuts are there per cup of trail mix, we can do a rule of three:

If 9/4 cups of trail mix need 2/3 cups of peanuts, 1 cup of trail mix need X cups of peanuts:

9/4 cups of trail mix -> 2/3 cups of peanuts

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3 years ago

What is the common denominator of (5/x^2-4) - (2/x+2) in the complex fraction (2/x-2) - (3/x^2-4)/(5/x^2-4) - (2/x+2)

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Answer:

common denominator: (x² -4)
simplified complex fraction: (2x +1)/(9 -2x)

Step-by-step explanation:

It is helpful to remember the factoring of the difference of squares:

a² -b² = (a -b)(a +b)

Your denominator of (x² -4) factors as (x -2)(x +2). You will note that one of these factors is the same as the denominator in the other fraction.

It looks like you want to simplify ...

$\dfrac{\left(\dfrac{2}{x-2}-\dfrac{3}{x^2-4}\right)}{\left(\dfrac{5}{x^2-4}-\dfrac{2}{x+2}\right)}=\dfrac{\left(\dfrac{2(x+2)}{(x-2)(x+2)}-\dfrac{3}{(x-2)(x+2)}\right)}{\left(\dfrac{5}{(x-2)(x+2)}-\dfrac{2(x-2)}{(x-2)(x+2)}\right)}\\\\=\dfrac{2(x+2)-3}{5-2(x-2)}=\boxed{\dfrac{2x+1}{9-2x}}$

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2 years ago

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