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3 years ago

Given the function f(x) =-x^2-1, find the value of f(1/3) in simplest form

Mathematics

1 answer:

Nimfa-mama [501]3 years ago

6 0

Answer:

$-1\frac{1}{9}\ or -\frac{10}{9}$

Step-by-step explanation:

To solve this, we have to plug in 1/3 for x:

$f(\frac{1}{3})=-(\frac{1}{3})^2-1=-(\frac{1^2}{3^2})-1=-\frac{1}{9}-1=-1\frac{1}{9}\ or -\frac{10}{9}$

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Solve for y<br> 20x + 5y = 30<br> y = 0<br> simplify

stepladder [879]

It should be 25xy that is the correct answer i did this today

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3 years ago

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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is four times

prohojiy [21]

Answer:

{36, 66, 78}

Step-by-step explanation:

Let the measures of the three angles be f, s and t, for first, second and third. Then s + t = 4f, t = 12 + s, and f + s + t = 180.

Subbing 12 + s for t in the first equation, we get s + 12 + s = 4f.

Subbing the same in the third equation, we get f + s + 12 + s = 180

This results in two equations in two unknowns (f and s):

2s - 4f = -12

2s + f = 168.

Let's eliminate s by subtracting the first of these two equations from the second. Doing so yields 5f = 180. Then the first angle, f, or x, is 36.

Then, from 2s + f = 168, we get 2s + 36 = 168, or 2s = 132. Thus, the second angle is s = y = 66.

The sum of the three angles must be 180. Thus, 36 + 66 + t = 180, or

102 + t = 180, or t = z = 78.

The three angles are

{36, 66, 78}.

3 0

3 years ago

What is the oposite of 42

o-na [289]

Step-by-step explanation:

i think its 24

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3 years ago

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The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees. If we want to be 90% c

siniylev [52]

Answer:

19 beers must be sampled.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.9}{2} = 0.05$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.05 = 0.95$ , so Z = 1.645.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees.

This means that $\sigma = 0.26$

If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample?

This is n for which M = 0.1. So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.1 = 1.645\frac{0.26}{\sqrt{n}}$

$0.1\sqrt{n} = 1.645*0.26$

$\sqrt{n} = \frac{1.645*0.26}{0.1}$

$(\sqrt{n})^2 = (\frac{1.645*0.26}{0.1})^2$

$n = 18.3$

Rounding up:

19 beers must be sampled.

7 0

3 years ago

Instructions: Find the measure of the indicated angle to the<br> nearest degree

Artemon [7]

Answer:

? = 57

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos ? = adj/ hyp

cos ? = 14/26

Taking the inverse cos of each side

cos ^-1 ( cos ?) = cos ^-1 ( 14/26)

? = 57.42102961

To the nearest degree

? = 57

5 0

3 years ago