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3 years ago

Use the discriminant to determine how many X intercepts the graph of the equation has

1 answer:

7 0

<span> The quadratic formula says that any quadratic equation of the form ax^2 + bx + c, then
x=(-b ± √(b^2 - 4ac))/2a, and so because of the square root, theres obviously going to be no x-intercepts if b^2 - 4ac is negative, one x-intercept if its zero, or two if its positive. So to calculate the discriminant, which is whether it has an intercept, no intercepts or two intercepts is:
∆=b^2 - 4ac, where delta, the greek equivalent of D, is used to represent the discriminant.
In the above equation a=-4, b=3 and c=-2, so
∆=3^2 - 4*-4*-2=9 - 32=-23, so because the discriminant is negative, then there are no x-intercepts.

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Please please help me!!!! :)

kifflom [539]

Answer:

Measure of ∠5 is 142°

Step-by-step explanation:

We are given that, Lines L and M are parallel.

As, the third line is intersecting both line L and M.

<em>We know that, 'The opposite angles formed by the intersecting lines are equal'.</em>

Since, the sum of the four angles formed by the third line and M is 360°.

So, we get,

∠1 + ∠6 + ∠7 + 38 = 360°

i.e. 2∠1 + 2×38° = 360°

i.e. 2∠1 = 360° - 76°

i.e. 2∠1 = 284°

i.e. ∠1 = 142°

Thus, ∠1 = ∠7 = 142°

Since, L and M are parallel.

So, ∠3 = ∠5 = 142°

Hence, we get that measure of ∠5 is 142°.

3 0

3 years ago

A machine, when working properly, produces 5% or less defective items. Whenever the machine produces significantly greater than

vovikov84 [41]

Answer:

The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.

Step-by-step explanation:

A machine, when working properly, produces 5% or less defective items.

This means that the null hypothesis is:

$H_0: p \leq 0.05$

Test if the percentage of defective items produced by this machine is greater than 5%.

This means that the alternate hypothesis is:

$H_a: p > 0.05$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.05 is tested at the null hypothesis:

This means that $\mu = 0.05, \sigma = \sqrt{0.05*0.95}$

A random sample of 300 items taken from the production line contained 27 defective items.

This means that $n = 300, X = \frac{27}{300} = 0.09$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.09 - 0.05}{\frac{\sqrt{0.05*0.95}}{\sqrt{300}}}$

$z = 3.18$

Pvalue of the test:

Testing if the mean is greater than a value, which means that the pvalue of the test is 1 subtracted by the pvalue of Z = 3.18, which is the probability of a finding a sample proportion of 0.09 or higher.

Looking at the Z-table, Z = 3.18 has a pvalue of 0.9993

1 - 0.9993 = 0.0007

5 0

3 years ago

A store manager is accepting applications for part-time workers. he can hire no more than 14 people. so far,he has hired 9 peopl

Lorico [155]

The manager already hired 9 people. Let $x$ be the number of people he still can hire. Since these people will add to the 9 he already hired, when the hiring campaign will be over he will have hired $9+x$ people. We know that he can't hire more than 14 people, so the number of people hired must be less than or equal to 14:

$9+x \leq 14$

If we subtract 9 from both sides, we have

$x \leq 14-9=5$

so, the manager can hire at most 5 other people

6 0

3 years ago

Pls help me with this <br>ans should be well explained

Snezhnost [94]

Let's observe

#1st column

3+2+1+4=10

10th alphabet=J

#2nd

5+9+4+6=24

24th alphabet=X

#3rd

2+1+3+3=9

9 th Alpha bet=I

#4th

8+4+9+5=26

26th Alphabet=Z

#5th

7+3+1+2=13

13 th alphabet=M

Option B is correct

5 0

3 years ago

The number of men and women participating in the Winter Olympic Games has been steadily increasing in recent years. In the 19th

Montano1993 [528]

Using a system of equations, it is found that the correct option is:

A) 1389x+1660y=787x+1121y.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, considering the amounts in each olympics(1389 men and 787 women participated on the 19th, 1660 men and 1121 women in the 22th), the system is:

A) 1389x+1660y=787x+1121y.

More can be learned about a system of equations at brainly.com/question/24342899

6 0

2 years ago