Treat x^4 as the square of p: x^4 = p^2.

Then x^4 - 5x^2 - 36 = 0 becomes p^2 - 5p - 36 = 0.

This factors nicely, to (p-9)(p+4) = 0. Then p = 9 and p = -4.

Equating 9 and x^2, we find that x=3 or x=-3.
Equating -4 and x^2, we see that there's no real solution.

Show that both x=3 and x=-3 are real roots of x^4 - 5x^2 - 36 = 0.

6 0

3 years ago

You are conducting a left-tailed test of a claim about a population mean when sigma is unknown with a sample size of 7.

Artyom0805 [142]

<h3>Answer: -3.71</h3>

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Explanation:

You'll need to use a T table to answer this question. Your stats textbook should have such a table in the back appendix section.

If your textbook doesn't have the proper table, or you don't have your textbook with you, then I recommend searching online for "t table" and you should have tons of free options to choose from.

In the table you'll look for the degrees of freedom row 6, since the degrees of freedom are equal to n-1. In this case, n = 7.

In this row, locate the column labeled "alpha = 0.005" and you'll be looking at "one tail". The value in this row and column is roughly 3.707

Since we're doing a left tailed test and we want P(t < C) = 0.005, where C is the critical value we're after. This must mean C < 0. So C = -3.707 approximately. Round this to two decimal places and we end up with -3.71

4 0

3 years ago

In triangle abc shown below side ab is 6 and side ac is 4

kaheart [24]

Question is Incomplete, Complete question is given below:

In Triangle ABC shown below, side AB is 6 and side AC is 4.

Which statement is needed to prove that segment DE is parallel to segment BC and half its length?

Answer

Segment AD is 3 and segment AE is 2.

Segment AD is 3 and segment AE is 4.

Segment AD is 12 and segment AE is 4.

Segment AD is 12 and segment AE is 8.

Answer:

Segment AD is 3 and segment AE is 2.

Step-by-step explanation:

Given:

side AB = 6

side AC = 4

Now we need to prove that segment DE is parallel to segment BC and half its length.

Solution:

Now AD + DB = AB also AE + EC = AC

DB = AB - AD also EC = AC - AE

Now we take first option Segment AD is 3 and segment AE is 2.

Substituting we get;

DB = 6-3 = 3 also EC = 4-2 =2

From above we can say that;

AD = DB and EC = AE

So we can say that segment DE bisects Segment AB and AC equally.

Hence From Midpoint theorem which states that;

"The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side."

Hence Proved.

7 0

3 years ago

For the graphed function f(x) = −(5)x − 3 + 2, calculate the average rate of change from x = 3 to x = 4.

azamat

Answer:

-4 is the average rate of change from 3 to 4

Step-by-step explanation:

Average rate of change is defined as the fraction of change in f(x) value to change in x value.

Here we have x values as 3 and 4.

To find the average rate of change from x=3 to x=4

Average rate of change = change in f(x)/change in x

f(4) = -5^{4-3} +2 = -3\\f(3) = 1\\f(4)-f(3) = -3-1 =-4

Change in x = 4-3 =1

6 0

3 years ago

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