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3 years ago

8

A prime polynomial cannot be written as a product of lower-degree polynomials. Which polynomial is prime? a)8x2 – 10x – 3 b)8x2

+ 2x – 3 c)8x2 – 6x – 3 d)8x2 + 23x – 3

2 answers:

Basile [38]3 years ago

10 0

As already described above, the prime polynomial is that which can no longer be factored to yield a much simpler terms. From the given choices, that which cannot be factored is letter C.

otez555 [7]3 years ago

10 0

Answer:

The correct option is c.

Step-by-step explanation:

Option a,

$8x^2-10x-3$

$8x^2-12x+2x-3$

$4x(2x-3)+(2x-3)$

$(2x-3)(4x+1)$

A prime polynomial cannot be written as a product of lower-degree polynomials. Therefore option a is not prime.

Similarly find the factors of other expressions.

$8x^2+2x-3$

$8x^2-6x+4x-3$

$2x(4x-3)+(4x-3)$

$(2x+1)(4x-3)$

Therefore option b is not prime.

$8x^2-6x-3$

This polynomial factored further and cannot be written as a product of lower-degree polynomials. Therefore it is prime and option c is correct.

$8x^2+23x-3$

$8x^2+24x-x-3$

$8x(x+3)-(x+3)$

$(8x-1)(x+3)$

Therefore option d is not prime.

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the end of the road is 15/16 of a mile away. Luke walked 7/8 of a mile down the road. How much further did he need to walk

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Answer:

1/16 of a mile left to walk to reach the end of the road

Step-by-step explanation:

The total distance to be walked = 15/16 miles

already walked= 7/8 miles = 14/16 miles

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2 years ago

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat

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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.

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3 years ago

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stich3 [128]

<u>Answer-</u>

<em>A. strong negative correlation.</em>

<u>Solution-</u>

<u>Direction of a relationship</u>

Positive- If one variable increases, the other tends to also increase. If one decreases, the other tends to also. It is represented by positive numbers(i.e 0 to 1).
Negative- If one variable increases, the other tends to decrease, and vice-versa. It is represented by negative numbers(i.e 0 to -1)

<u>Strength of a relationship</u>

Perfect Relationship- When two variables are linearly related, the correlation coefficient is either 1 or -1. They are said to be perfectly linearly related, either positively or negatively.
No relationship- When two variables have no relationship at all, their correlation is 0.

As in this case, correlation coefficient was found to be -0.91, which is negative and close to -1, so it is a strong negative correlation.

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Answer:

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<u />

<u>Compound Interest Formula</u>

$\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}$

where:

A = final amount
P = principal amount
r = interest rate (in decimal form)
n = number of times interest applied per time period
t = number of time periods elapsed

Given:

A = $17,474.00
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$\implies \sf \dfrac{17474}{7790}=\left(1.0125}\right)^{12t}$

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$\implies \sf \ln\left(\dfrac{17474}{7790}\right)=12t \ln \left(1.0125}\right)$

$\implies \sf t=\dfrac{\ln\left(\frac{17474}{7790}\right)}{12 \ln \left(1.0125}\right)}$

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