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3 years ago

What is the solution of x2+x-6/x-7_<0

Mathematics

1 answer:

Katarina [22]3 years ago

5 0

Answer:

x < -3 or 2 < x < 7

Step-by-step explanation:

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Simplify the radical expression.

Ber [7]

$\bf \sqrt[4]{625x^{12}y^8}~~ \begin{cases} 625=&5\cdot 5\cdot 5\cdot 5\\ &5^4\\ x^{12}=&x^{3\cdot 4}\\ &(x^3)^4\\ y^8=&y^{2\cdot 4}\\ &(y^2)^4 \end{cases}\implies \pm\sqrt[4]{5^4(x^3)^4(y^2)^4}\implies \begin{array}{llll} \pm5x^3y^2\\\\ 5|x^3|y^2\\\\ |5x^3y^2| \end{array}$

8 0

3 years ago

As a town gets smaller, the population of its high school decreases by 8% each year. The senior class has 320 students now. In h

Semmy [17]

Answer:

in 13.95 years the senior class will have 100 students.

Step-by-step explanation:

P(h) = p(0.92)^t (equation for exponential change)

P(h) - population of highschool (or senior class) = 100

p - staring amount = 320

t = time in years

100 = 320(0.92)^t

1/3.2 = .92^t (divide both sides by 320)

log(1/3.2, .92) = t (log base 0.92 of 1/3.2 equals t)

13.9497 = t

6 0

3 years ago

What calculation can I use to find 498 after a 6.1% decrease?

Sergio039 [100]

Answer:

b is the answer

Step-by-step explanation:

i did some research

7 0

3 years ago

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For which function is f(x) equal to f^1(x) ( answer choices in picture )

Sonja [21]

Answer:

C. $f(x)=\frac{x+1}{x-1}$

Step-by-step explanation:

Let's find the inverse of each of the given options.

Option A:

$f(x)=\frac{x+6}{x-6}\\y=\frac{x+6}{x-6}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+6}{y-6}$

Rewrite in terms of 'y'. This gives,

$x(y-6)=y+6\\xy-6x=y+6\\xy-y=6x+6\\y=\frac{6x+6}{x-1}$

The given function $y=\frac{6x+6}{x-1}\ne y=\frac{x+6}{x-6}$

So, option A is incorrect.

Option B:

$f(x)=\frac{x+2}{x-2}\\y=\frac{x+2}{x-2}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+2}{y-2}$

Rewrite in terms of 'y'. This gives,

$x(y-2)=y+2\\xy-2x=y+2\\xy-y=2x+2\\y=\frac{2x+2}{x-1}$

The given function $y=\frac{2x+2}{x-1}\ne y=\frac{x+2}{x-2}$

So, option B is incorrect.

Option C:

$f(x)=\frac{x+1}{x-1}\\y=\frac{x+1}{x-1}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+1}{y-1}$

Rewrite in terms of 'y'. This gives,

$x(y-1)=y+1\\xy-x=y+1\\xy-y=x+1\\y=\frac{x+1}{x-1}$

The given function $y=\frac{x+1}{x-1}\ equals\ y=\frac{x+1}{x-1}$

So, option C is correct.

Option D:

$f(x)=\frac{x+5}{x-5}\\y=\frac{x+5}{x-5}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+5}{y-5}$

Rewrite in terms of 'y'. This gives,

$x(y-5)=y+5\\xy-5x=y+5\\xy-y=5x+5\\y=\frac{5x+5}{x-1}$

The given function $y=\frac{5x+5}{x-1}\ne y=\frac{x+6}{x-6}$

So, option D is incorrect.

Therefore, only option C is correct.

7 0

3 years ago

In a class of 34 students, 19 of them are girls.

Colt1911 [192]

Answer:

55.9%

Step-by-step explanation:

To find the percent that are girls, take the number of girls over the total number of students

19/34

.558823529

To change to percent form, multiply by 100%

55.8823529%

To 1 decimal place

55.9%

5 0

3 years ago

Read 2 more answers