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3 years ago

-x + 3y = -23 -8x - 3y = -22 using elimination

Mathematics

2 answers:

Nikolay [14]3 years ago

8 0

There answer is x=5

Nikolay [14]3 years ago

4 0

72.00 with lend kids due is due I’d fue Uc fue. Cheh89 je 90

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write the slope-intercept form of the equation of the line passing through the point(-5,-2) and parallel to the line y=2x-2

Ivanshal [37]

Point- Slope form is
y - y1 = m (x - x1)
m = slope, (x1, y1) = point
Slope intercept form is y = mx + b
m = slope, b = y-intercept
In order for two lines to be parallel, they must have the same slope, so in this case our slope, m = 2. Now use point-slope form to insert the point and solve.
y--2 = 2 (x --5)
y + 2 = 2x + 10
y = 2x + 8

6 0

3 years ago

Line equations from point/slope

babunello [35]

Answer:

The answer is

$y = \frac{1}{4} x + 3$

Step-by-step explanation:

Plug in and solve the equation. We are trying to find the y-intercept:

$y= \frac{1}{4}x + b \\ 2 = \frac{1}{4} ( - 4) + b \\ 2 = - 1 + b \\ \frac{ + 1 = + 1 \: \: \: \: \: \: \: \: }{3 = b}$

We found the y-intercept, so now we plug it in it's right full spot in the formula.

$y = \frac{1}{4} x + 3$

8 0

2 years ago

Consider the function on the interval (0, 2π). f(x) = sin x + cos x (a) Find the open intervals on which the function is increas

Annette [7]

Answer:Increasing in x∈(0,π/4)∪(5π/4,2π) decreasing in(π/4,5π/4)

Step-by-step explanation:

given f(x) = sin(x) + cos(x)

f(x) can be rewritten as $\sqrt{2} [\frac{sin(x)}{\sqrt{2} }+\frac{cos(x)}{\sqrt{2} } ]..................(a)\\\\\ \frac{1}{\sqrt{2} } = cos(45) = sin(45)\\\\$

Using these result in equation a we get

f(x) = $\sqrt{2} [ cos(45)sin(x)+sin(45)cos(x)]\\\\= \sqrt{2} [sin(45+x)]..........(b)$

Now we know that for derivative with respect to dependent variable is positive for an increasing function

Differentiating b on both sides with respect to x we get

f '(x) = $f '(x)=\sqrt{2} \frac{dsin(45+x)}{dx}\\ \\f'(x)=\sqrt{2} cos(45+x)\\\\f'(x)>0=>\sqrt{2} cos(45+x)>0$

where x∈(0,2π)

we know that cox(x) > 0 for x∈[0,π/2]∪[3π/2,2π]

Thus for cos(π/4+x)>0 we should have

1) π/4 + x < π/2 => x<π/4 => x∈[0,π/4]

2) π/4 + x > 3π/2 => x > 5π/4 => x∈[5π/4,2π]

from conditions 1 and 2 we have x∈(0,π/4)∪(5π/4,2π)

Thus the function is decreasing in x∈(π/4,5π/4)

5 0

3 years ago

Domain of f(x)=3x+6,g(x)=x+1

sergey [27]

Here you have shared two separate functions, f(x) and g(x). You have not indicated how f and g interact. Is g supposed to be the input to f? or what?

The domains of f and g are "the set of all real numbers."

If you meant "find the domain of f(g(x))," then we're finding the domain of
3(x+1)+6, which happens to be the same as before: "the set of all real numbers."

Kindly check to ensure that you have shared ALL of the given problem.

7 0

3 years ago

The lifetime of a certain brand of battery is known to have a standard deviation of 9 hours. Suppose that a random sample of 150

Kobotan [32]

Answer:

The 90% confidence interval for the true mean lifetime of all batteries of this brand is between 39.3 hours and 41.7 hours. The lower limit is 39.3 hours while the upper limit is 41.7 hours.

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 Ztable as such z has a pvalue 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.

$M = 1.645\frac{9}{\sqrt{150}} = 1.2$

The lower end of the interval is the sample mean subtracted by M. So it is 40.5 - 1.2 = 39.3 hours

The upper end of the interval is the sample mean added to M. So it is 40.5 + 1.2 = 41.7 hours

The 90% confidence interval for the true mean lifetime of all batteries of this brand is between 39.3 hours and 41.7 hours. The lower limit is 39.3 hours while the upper limit is 41.7 hours.

7 0

3 years ago