All categories

3 years ago

Solve the following equation and show all the steps to solving.

1 answer:

8 0

$\bf \cfrac{x}{x-2}+\cfrac{x-1}{x+1}=-1\impliedby LCD\to (x-2)(x+1)\\\\
-------------------------------\\\\
\cfrac{x(x+1)+(x-1)(x-2)}{(x-2)(x+1)}=-1
\\\\\\
x^2+x+x^2-3x+2=-1(x-2)(x+1)
\\\\\\
2x^2-2x+2=-1(x^2-x-2)\implies 2x^2-2x+2=-x^2+x+2
\\\\\\
3x^2-3x=0\implies 3x(x-1)=0\implies 
\begin{cases}
3x=0\implies &x=0\\
x-1=0\implies &x=1
\end{cases}$

You might be interested in

Find the volume of this square based pyramid. 5ft 6 fi

sweet [91]

This answers I believe is 30 ft

4 0

3 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Y = (4/9) x

frez [133]

Answer:

V = 8.06 cubed units

Step-by-step explanation:

You have the following curves:

$y_1=\frac{4}{9}x^2=f(x)\\\\y_2=\frac{13}{9}-x^2=g(x)$

In order to calculate the solid of revolution bounded by the previous curves and the x axis, you use the following formula:

$V=\pi \int_a^b [(g(x))^2-(f(x))^2]dx$ (1)

To determine the limits of the integral you equal both curves f=g and solve for x:

$f(x)=g(x)\\\\\frac{4}{9}x^2=\frac{13}{9}-x^2\\\\\frac{4}{9}x^2+x^2=\frac{13}{9}\\\\\frac{13}{9}x^2=\frac{13}{9}\\\\x=\pm 1$

Then, the limits are a = -1 and b = 1

You replace f(x), g(x), a and b in the equation (1):

$V=\pi \int_{-1}^{1}[(\frac{13}{9}-x^2)^2-(\frac{4}{9}x^2)^2]dx\\\\V=\pi \int_{-1}^1[\frac{169}{81}-\frac{26}{9}x^2+x^4-\frac{16}{81}x^4]dx\\\\V=\pi \int_{-1}^1 [\frac{169}{81}-\frac{26}{9}x^2+\frac{65}{81}x^4]dx\\\\V=\pi [\frac{169}{81}x-\frac{26}{27}x^3+\frac{65}{405}x^5]_{-1}^1\\\\V\approx8.06\ cubed\ units$

The volume of the solid of revolution is approximately 8.06 cubed units

8 0

4 years ago

In a school with 2,000 students, a random sample of 120 students were asked which fruit is their favorite. Their responses are s

ki77a [65]

We know that

Out of 120 students----------> 34 chose orange as the favorite fruit
Find the percentage
percentage=34/120------> 17/60-----> 0.2833------> 28.33%

for 2,000 students
0.2833*2000=566.67-----------> about 567 students

the answer is
about 567 students

3 0

4 years ago

Read 2 more answers

4. x = a. 20° b. 240 C. 28° (5x) 120° d. 30°

MaRussiya [10]

An exterior angle equals the sun of the two opposite inside angles:

5x = 120 + x

Subtract 1 x from both sides:

4x = 120

Divide both sides by 4:

X = 30

The answer is D. 30

6 0

3 years ago

Betsy and Marie both got their haircut on the same day bed she gets her haircut every 28 days and Mary gets her haircut every 35

makkiz [27]

Answer:

140 days until they both get their haircut on the same day again

Step-by-step explanation:

When two events, A and B, happen every x and y days, respectively, they will happen on the same day in each lcm(x,y) days. lcm(x,y) is the lesser common multiple of x and y which is not 0.

In this question:

Betsy every 28 days.

Mary every 35 days.

Multiples of 28: {0,28,56,84,112,140,...}

Multiples of 35: {0,35,70,105,140,...}

So the lesser common multiple between 28 and 35 is 140.

140 days until they both get their haircut on the same day again

3 0

3 years ago

Read 2 more answers