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3 years ago

Solve the following equation. show all your work x/x-2+x-1/x+1=-1

Mathematics

2 answers:

Andru [333]3 years ago

6 0

Answer:

X=1

Step-by-step explanation:

dmitriy555 [2]3 years ago

3 0

We hates fractions, yess precious, nasty fracitons

multiply both sides by (x-2)(x+1) to clea fractions
x(x+1)+(x-1)(x-2)=(-1)(x-2)(x+1)
distribute
x^2+x+x^2-3x+2=-x^2+x-2
add like terms
2x^2-2x+2=-x^2+x+2
add x^2 to both sdes
3x^2-2x+2=x+2
minus x from both sides
3x^2-3x+2=2
minus 2 both sides
3x^2-3x=0
factor
(3x)(x-1)=0
set to zero

3x=0
x=0

x-1=0
x=1

x=0 or 1

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A normal distribution curve, where x = 70 and σ = 15, was created by a teacher using her students’ grades. What information abou

alexira [117]

The correct answer is:

We can conclude that 68% of the scores were between 55 and 85; 95% of the scores were between 40 and 100; and 99.7% of the scores were between 25 and 100.

Explanation:

The empirical rule tells us that in a normal curve, 68% of data lie within 1 standard deviation of the mean; 95% of data lie within 2 standard deviations of the mean; and 99.7% of data lie within 3 standard deviations of the mean.

The mean is 70 and the standard deviation is 15. This means 1 standard deviation below the mean is 70-15 = 55 and one standard deviation above the mean is 70+15 = 85. 68% of data will fall between these two scores.

2 standard deviations below the mean is 70-15(2) = 40 and two standard deviations above the mean is 70+15(2) = 100. 95% of data will fall between these two scores.

3 standard deviations below the mean is 70-15(3) = 25 and three standard deviations above the mean is 70+15(3) = 115. However, a student cannot score above 100%; this means 99.7% of data fall between 25 and 100.

4 0

3 years ago

Read 2 more answers

P(x) = x + 1x² – 34x + 343 d(x)= x + 9

Feliz [49]

Answer:

$x=\frac{9}{d-1},\:P=\frac{-297d+378}{\left(d-1\right)^2}+343$

Step-by-step explanation:

Let us start by isolating x for dx = x + 9.

dx - x = x + 9 - x > dx - x = 9.

Factor out the common term of x > x(d - 1) = 9.

Now divide both sides by d - 1 > $\frac{x\left(d-1\right)}{d-1}=\frac{9}{d-1};\quad \:d\ne \:1$ . Go ahead and simplify.

$x=\frac{9}{d-1};\quad \:d\ne \:1$ .

Now, $\mathrm{For\:}P=x+1x^2-34x+343, \mathrm{Subsititute\:}x=\frac{9}{d-1}$ .

$P=\frac{9}{d-1}+1\cdot \left(\frac{9}{d-1}\right)^2-34\cdot \frac{9}{d-1}+343$ .

Group the like terms... $1\cdot \left(\frac{9}{d-1}\right)^2+\frac{9}{d-1}-34\cdot \frac{9}{d-1}+343$ .

$\mathrm{Add\:similar\:elements:}\:\frac{9}{d-1}-34\cdot \frac{9}{d-1}=-33\cdot \frac{9}{d-1}$ > $1\cdot \left(\frac{9}{d-1}\right)^2-33\cdot \frac{9}{d-1}+343$ .

Now for $1\cdot \left(\frac{9}{d-1}\right)^2 > \mathrm{Apply\:exponent\:rule}: \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c} > \frac{9^2}{\left(d-1\right)^2} = 1\cdot \frac{9^2}{\left(d-1\right)^2}$ .

$\mathrm{Multiply:}\:1\cdot \frac{9^2}{\left(d-1\right)^2}=\frac{9^2}{\left(d-1\right)^2}$ .

Now for $33\cdot \frac{9}{d-1} > \mathrm{Multiply\:fractions}: \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c} > \frac{9\cdot \:33}{d-1} > \frac{297}{d-1}$ .

Thus we then get $\frac{9^2}{\left(d-1\right)^2}-\frac{297}{d-1}+343$ .

Now we want to combine fractions. $\frac{9^2}{\left(d-1\right)^2}-\frac{297}{d-1}$ .

$\mathrm{Compute\:an\:expression\:comprised\:of\:factors\:that\:appear\:either\:in\:}\left(d-1\right)^2\mathrm{\:or\:}d-1 > This\: is \:the\:LCM > \left(d-1\right)^2$

$\mathrm{For}\:\frac{297}{d-1}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:d-1 > \frac{297}{d-1}=\frac{297\left(d-1\right)}{\left(d-1\right)\left(d-1\right)}=\frac{297\left(d-1\right)}{\left(d-1\right)^2}$

$\frac{9^2}{\left(d-1\right)^2}-\frac{297\left(d-1\right)}{\left(d-1\right)^2} > \mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}> \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$\frac{9^2-297\left(d-1\right)}{\left(d-1\right)^2} > 9^2=81 > \frac{81-297\left(d-1\right)}{\left(d-1\right)^2}$ .

Expand $81-297\left(d-1\right) > -297\left(d-1\right) > \mathrm{Apply\:the\:distributive\:law}: \:a\left(b-c\right)=ab-ac$ .

$-297d-\left(-297\right)\cdot \:1 > \mathrm{Apply\:minus-plus\:rules} > -\left(-a\right)=a > -297d+297\cdot \:1$ .

$\mathrm{Multiply\:the\:numbers:}\:297\cdot \:1=297 > -297d+297 > 81-297d+297 > \mathrm{Add\:the\:numbers:}\:81+297=378 > -297d+378 > \frac{-297d+378}{\left(d-1\right)^2}$

Therefore $P=\frac{-297d+378}{\left(d-1\right)^2}+343$ .

Hope this helps!

5 0

3 years ago

What is 30+234567654567

prohojiy [21]

The answer would be 234,567,654,597

5 0

3 years ago

Read 2 more answers

The diagonal length of a rectangle is 25 inches, and the length of the rectangle is 9 inches.

diamong [38]

Answer:

Option C is the right answer.

Step-by-step explanation:

Given that:

Length of diagonal = 25 inches

Length of rectangle = 9 inches

Width of rectangle will be one of the two legs of right angled triangle and the diagonal will be the hypotenuse.

Using Pythagorean theorem;

$a^2+b^2=c^2\\(9)^2+w^2=(25)^2\\81 + w^2 = 625 \\w^2 = 625-81\\w^2 = 544$

Taking square root;

$\sqrt{w^2}=\sqrt{544}\\w=23.3$

Therefore,

Option C is the right answer.

3 0

3 years ago

Hi i am Grace and i realllyyyyyy need help on this. If you could please help that would be great.

uranmaximum [27]

The probability of picking a black ball first is $\dfrac{4}{5}$ , because there are 4 black balls and 1 white ball which is 5 balls in total. After picking the first ball, 4 balls remain - 3 black and 1 white, so the probability of picking a white ball is $\dfrac{1}{4}$ .
So, the probability of picking a black ball first followed by a white ball is $\dfrac{4}{5}\cdot\dfrac{1}{4}=\dfrac{1}{5}$

7 0

3 years ago