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3 years ago

What are the key features of a graph of a quadratic equation with only complex solutions

Mathematics

1 answer:

dybincka [34]3 years ago

4 0

Answer:

If D< 0, the roots of the quadratic equation will b complex.

Step-by-step explanation:

Let $ax^{2} + bx + c =0$ is the given quadratic equation.

So, if the Discriminant (D) = $b^{2} - 4ac < 0$ , the the equation will have only complex solutions.

Complex roots are represented in the form of $(x \pm iy)$

1. x represents the X axis (real) co ordinate,

y represents the Y axis (imaginary) coordinate

2. Also, the graph of the with equation D < 0 NEVER CROSSES the X - axis, as there are no real roots of the equation, only complex roots.

3. Here. roots are always identical but are opposite in signs. Such pair or roots with opposite sign are called CONJUGATE PAIRS.

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Yolanda made $192 for 12 hours of work. At the same rate, how many hours would she have to work to make $272?

denpristay [2]

Answer:

17 hours

take $192 and divide it by 12 so you know how much they make per hour

$192 / 12 = 16

then you're going to take $272 and divide it by what you know now - how much they make per hour (this will get you how many hours they worked)

$272 / 16 = 17

6 0

2 years ago

A 12 foot board is cut so that one piece is 5 times as long as the other. Find the length of each piece.

sveta [45]

Answer:

2 and 10

Step-by-step explanation:

Let x be length of the small piece and y the length of the big one.

● y = 5x

Since the big piece is 5 times longer than the short one.

The total length is 12 ft

● y + x = 12

● 5x + x = 12

● 6x = 12

Divide both sides by 6

● 6x/6 = 12/6

● x = 2

So the length of the two pieces are 2 ft and 10 ft (5×2)

4 0

3 years ago

Your state is considering raising the legal age for consumption of alcoholic beverages to 21 years old. How large a sample size

julsineya [31]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.01$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

For this case we can use as estimator for the proportion $\hat p =0.5$ , since we don't have any other previous info. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

8 0

3 years ago

4. Find the value of 8 + 12 + 4 + 6 x 1 + 2. Guys I am doing a test and I need help!!

skelet666 [1.2K]

32 is the correct answer I believe if using PEMDAS method

6 0

2 years ago

Nancy found that x=1 is one solution to the quadratic equation (x 2)2=a. what is the value of a? -9 -3 3 9

AlladinOne [14]

The value of the a, in the provided quadratic equation for which Nancy found one solution as x=1 is 9.

<h3>What is the solution of equation?</h3>

The solution of the quadratic equation is the solution of the variable of the equation, for which the equation satisfies.

Nancy found that x=1 is one solution to the quadratic equation. The quadratic equation is,

$(x +2)^2=a$

For this equation, one solution is x=1. Put this value in the above equation to get the value of a,

$(1 +2)^2=a\\(3)^2=a\\9=a\\a=9$

Thus, the value of the a, in the provided quadratic equation for which Nancy found one solution as x=1 is 9.

Learn more about the solution of the equation here;

brainly.com/question/21283540

5 0

2 years ago

Read 2 more answers