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Blababa [14]
3 years ago
8

Two roots of a third degree polynomial function f(x) are –4 and 4. Which statement describes the number and nature of all roots

for this function?
f(x) has three imaginary roots.
f(x) has three real roots.
f(x) has two real roots and two imaginary roots.
f(x) has three real roots and one imaginary root.
Mathematics
2 answers:
Helen [10]3 years ago
7 0

Answer:

Three real roots

Step-by-step explanation:

marta [7]3 years ago
4 0

Answer:

Step-by-step explanation:

A third degree polynomial has a <em>total of three roots</em>, real and imaginary combined.

If it already has 2 real roots, -4 and +4, then it has to have three real roots because imaginary roots come in conjugate pairs, i.e. they come in even numbers.

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Park two has 12 more benches than Park one. If 2 benches were transferred from Park two to Park one, then Park two would have 2
marta [7]

Answer:

There were 6 benches in park 1 and 18 benches in park 2.

Step-by-step explanation:

Let x be the no of benches in Park 1 and y in park 2.

Given that there are 12 more benches in park 2 than 1

Writing this in equation form, we have y = x+12 ... i

Next is if 2 benches were transferred from park 2 to park 1, then we have

x+2 in park 1 and y-2 in park 2.

Given that y-2 = twice that of x+2

Or y-2 = 2x+4 ... ii

Rewrite by adding 2 to both sides of equation ii.

y = 2x+6 ... iii

i-iii gives 0 = -x+6

Or x =6

Substitute in i, to have y = 6+12 = 18

Verify:

Original benches 6 and 18.

18 = 6+12 hence I condition is satisfied

18-2 = 2(6+2)

II is also satisfied.

6 0
3 years ago
Read 2 more answers
The graph of a sinusoidal function intersects its midline at (0,5) and then has a maximum point at (\pi,6)
lesya692 [45]
First, let's use the given information to determine the function's amplitude, midline, and period. 

Then, we should determine whether to use a sine or a cosine function, based on the point where x=0.

Finally, we should determine the parameters of the function's formula by considering all the above.
     
                      Determining the amplitude, midline, and period 

The midline intersection is at y=5 so this is the midline. 

The maximum point is 1 unit above the midline, so the amplitude is 1. 

The maximum point is π units to the right of the midline intersection, so the period is 4 * π.
 
                            Determining the type of function to use 

Since the graph intersects its midline at x=0, we should use thesine function and not the cosine function. 

This means there's no horizontal shift, so the function is of the form -

a sin(bx)+d

Since the midline intersection at x=0 is followed by a maximumpoint, we know that a > 0.

The amplitude is 1, so |a| = 1. Since a >0 we can conclude that a=1. 

The midline is y=5, so d=5. 

The period is 4π so b = 2π / 4π = 1/2 simplified. 

f(x) = 1 sin ( \dfrac{1}{2}x)+5   <span>= Solution </span>
4 0
3 years ago
A line goes through the points (5, -1) and (7, -5). What is a possible equation to a new line that is perpendicular?
Leya [2.2K]

<em>Ok, so you are given an equation in standard form, 5x+4y=2, and a point, (7, 5). You are being asked to write the equation for a line that is parallel to the equation in standard from, and that includes the point (7, 5).  </em>

<em> </em>

<em> </em>

<em> </em>

<em>First, let's start by finding the slope of your new line. We know that it needs to have the same slope as 5x+4y=2, because parallel lines have the same slopes. To do that, we need to put the equation into slope-intercept form (y=mx+b), which means we need to isolate the "y."  </em>

<em> </em>

<em> </em>

<em> </em>

<em>  5x+4y=2 </em>

<em> </em>

<em>-5x     -5x  (subtract 5x from both sides to move it to the right side of your equation) </em>

<em> </em>

<em>4y = 2 - 5x </em>

<em> </em>

<em>/4  /4  /4 (divide all the terms by 4 to get "y" by itself) </em>

<em> </em>

<em>y = (1/2) - (5/4)x  ... I suggest leaving your slope as a fraction. </em>

<em> </em>

<em> </em>

<em> </em>

<em>Now, we know that our slope, m , is going to be -(5/4).  </em>

<em> </em>

<em> </em>

<em> </em>

<em>Next, we are going to use our slope, -(5/4), and point, (7, 5), to find the b-value (y-intercept) of your new line. Let's plug in what we know: </em>

<em> </em>

<em> </em>

<em> </em>

<em>y = 5 </em>

<em> </em>

<em>m = -(5/4) </em>

<em> </em>

<em>x = 7 </em>

<em> </em>

<em> </em>

<em> </em>

<em>y=mx+b </em>

<em> </em>

<em>5=(-5/4)(7) + b  -> I plugged in what we knew for y, m, and x.  </em>

<em> </em>

<em>5 = -(35/4) + b  -> I multiplied the numbers in the numerator (5 x 7) to get 35/4 </em>

<em> </em>

<em>20/4 = -(35/4) + b -> I converted 5 into a faction with a denominator of 4 by multiplying by (4/4) </em>

<em> </em>

<em>+(35/4) +(35/4)  -> I add (35/4) to both sides to isolate b </em>

<em> </em>

<em>55/4 = b ... or b = 13.74 </em>

<em> </em>

<em> </em>

<em> </em>

<em>Answer:  </em>

<em> </em>

<em>m = -(5/4) </em>

<em> </em>

<em>b = 13.75</em>

7 0
3 years ago
Please Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Oduvanchick [21]

Answer:

26:26

Step-by-step explanation:

I hope I've helped :)

4 0
3 years ago
I NEED HELP !!!! A taxi driver spends $105 every week on gas for 6 weeks. What integer represents the effect of buying $105 on g
aev [14]

.Answer:

-105

Step-by-step explanation:

Given

Gas = \$105 for 6 weeks

Required

Represent this as an integer

If the driver spends $105 on his taxi then it means that the money is debited from the driver's bank account.

Debit implies negative and it is represented by a negative symbon

Hence, the integer that represents this scenario is -105

7 0
3 years ago
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