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4 years ago

Show a full solution to the inequality [(x+2)/(x-4)]

Mathematics

1 answer:

Papessa [141]4 years ago

3 0

Your sign chart is a bit off. The first two rows are correct. However keep in mind that you factored out a negative (when you factored -2x+14) so you need to negate the signs of the f(x) row.

Another thing to keep in mind: x = 4 is not allowed as its the vertical asymptote. However, x = 7 is valid. So you'll have an open circle at x = 4 and a close circle at x = 7

The answer in interval notation is (-infinity, 4) U [7, infinity)
which translates to this disjoint set of inequalities: x < 4 or x >= 7

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F(x+1)+f(x+2)=2x+3; f(x)=?

Rama09 [41]

Answer:

$F=\frac{-xf+f+2x}{x+1};\quad \:x\ne \:-1$

Step-by-step explanation:

$1. \mathrm{Subtract\:}f\left(x+2\right)\mathrm{\:from\:both\:sides}\\
F\left(x+1\right)+f\left(x+2\right)-f\left(x+2\right)=2x+3f-f\left(x+2\right)

$

$2. \mathrm{Simplify}\\
F\left(x+1\right)=-xf+f+2x\\
$

$3. \mathrm{Divide\:both\:sides\:by\:}x+1;\quad \:x\ne \:-1\\
\frac{F\left(x+1\right)}{x+1}=-\frac{xf}{x+1}+\frac{f}{x+1}+\frac{2x}{x+1};\quad \:x\ne \:-1$

$4. \mathrm{Simplify}\\
F=\frac{-xf+f+2x}{x+1};\quad \:x\ne \:-1$

Final Answer: $F=\frac{-xf+f+2x}{x+1};\quad \:x\ne \:-1$

4 0

3 years ago

Sarah's parents are filling their swimming pool. Her pool holds 22,000 gallons. it take 16 hours to fill . what unit would you s

Aneli [31]

The rate would be 22000 gallons per 16 hours or rate = 22000/16 = 1375 gallons/hr

8 0

3 years ago

Read 2 more answers

Please help will mark brainliest

NeX [460]

Answer: 145.8

Step-by-step explanation: you have to divide 45 and 25 to get 1.8, then you get 81 and you multiply 81 x 1.8 to get your answer.

7 0

3 years ago

Apples sell for $1.90 per pound, and bananas sell for $0.75 per pound. Troy bought some apples and some bananas. Together they w

matrenka [14]

Answer:

1.15p + 285 = 5.84

Step-by-step explanation:

This problem has two equations. Total cost and Total pounds. The cost and the pounds

p = apple pounds

b = banana pounds

Cost

1.90p + .75b = 5.84

Pounds

p + b = 3.8

Now we use the substitute method for system of equations to solve

p + b = 3.8

b = -p + 3.8

Now that we know what b equals, substitute is for b in the cost equation.

1.90p + .75b = 5.84

1.90p + .75(-p+3.8) = 5.84

distribute / multiply .75 by (-p+3.8)

1.90p + -.75p + 2.85 = 5.84

Combine the p values

1.15p + 285 = 5.84

4 0

3 years ago

A sample of 1000 college students at NC State University were randomly selected for a survey. Among the survey participants, 102

cupoosta [38]

Answer:

The upper endpoint of the 99% confidence interval for population proportion is 0.13.

Step-by-step explanation:

The confidence interval for population proportion is:

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

Given:

n = 1000

$\hat p$ = 0.102

$z_{\alpha /2}=z_{0.01/2}=z_{0.005}=2.58$

*Use the standard normal table for the critical value.

Compute the 99% confidence interval for population proportion as follows:

$CI=\hat p\pm z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.102\pm 2.58\times\sqrt{\frac{0.102(1-0.102)}{1000}}\\=0.102\pm0.0248\\=(0.0772, 0.1268)\\\approx (0.08, 0.13)$

Thus, the upper limit of the 99% confidence interval for population proportion is 0.13.

6 0

3 years ago