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Aleks [24]
3 years ago
11

Given the polynomial 6x3 + 4x2 - 6x - 4, what is the value of the coefficient 'k' in the factored form?

Mathematics
2 answers:
oksano4ka [1.4K]3 years ago
7 0
6 x³ + 4 x² - 6 x - 4 = 2 x² ( 3 x + 2 ) - 2 ( 3 x + 2 ) =
= ( 3 x + 2 ) ( 2 x² - 2 ) =
= 2 ( 3 x + 2 ) ( x² - 1 ) =
= 2 ( x + 1 ) ( x - 1 ) ( 3 x + 2 ) 
Answer: k = 1
Taya2010 [7]3 years ago
5 0

6 x³ + 4 x² - 6 x - 4 = 2 x² ( 3 x + 2 ) - 2 ( 3 x + 2 ) =

= ( 3 x + 2 ) ( 2 x² - 2 ) =

= 2 ( 3 x + 2 ) ( x² - 1 ) =

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

Answer: k = 1

hope this helps!!!

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A fair coin is tossed 5000 times. What can you say about getting the outcome of exactly 2500 tails
WINSTONCH [101]

Step-by-step explanation:

You can't expect to get exactly 2500 out of 5000 tosses more than a few times . You will come pretty close, but that's only good in horseshoes.

Of course I'm answering this on the basis of a computer language and not actually performinig this a million tmes, each part of a million consisting of 5000 tosses.

Simulations and not completely unbiased, but based on experience, 5000 is a very small number and getting 2500 more than a couple of times is unlikely

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Find The Difference.
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5 - 1 2/9 = 3 7/9

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3 years ago
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat
zavuch27 [327]

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

Step-by-step explanation:

We start by noticing that the expression on the left of the equal sign is a quadratic with leading term x^2, which means that its graph shows branches going up. Therefore:

1) if its vertex is ON the x axis, there would be one solution (root) to the equation.

2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:

We recall that the x-position of the vertex for a quadratic function of the form f(x)=ax^2+bx+c is given by the expression: x_v=\frac{-b}{2a}

Since in our case a=1 and b=5, we get that the x-position of the vertex is: x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}

This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).

We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the x_v=-\frac{5}{2}. Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

5 0
3 years ago
Thomas bought several paintbrushes for $4 each. He paid with a $20 bill. The expression 20 – 4n is used to determine how much ch
Tresset [83]

Answer:

the variable n represents how many of the product thomas bought

Step-by-step explanation:

20 dollars is the initial amount of money, and for every paintbrush, you have to subtract 4 dollars from thomas's initial amount, and the result of the subtraction is the amount of change he will recieve.

4 0
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