Simplify (3x-9) / (x^2-x-6)

9514 1404 393

Answer:

  2/3

Step-by-step explanation:

The slope is found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -(-7))/(4 -(-5)) = 6/9 = 2/3

The slope of the line is 2/3.

_____

The attached graph shows the equation of the line in point-slope form.

This is quite an interesting problem. I am not sure how high you are in math, but I am going to use calculus I techniques to solve it. First, we need to model an equation. Let P be the total profit and x be every time you increase the cost by $10. If you think about it hard enough you come up with the equation

[tex]P(x)=(200-5x)(250+10x)[/tex]

(200-5x) is the amount of plots you will be able to sell, and (250+10x) is the amount you charge for. So, at x =0

[tex]P(0)=(200-5(0))(250+10(0))=(200)(250)=$50,000[/tex]

This is the initial condition where if we sell 200 plots at $250/plot.

So, this equation makes sense.

Now, let's maximize using the first derivative of the function.

Let's get it into an easily differentiable form.

[tex]P(x)=(200-5x)(250+10x)=-50x^2+2000x-1250x+50000\\=-50x^2+750x+50000[/tex]

From here, differentiate the problem.

[tex]P'(x)=-100x+750[/tex]

Now, set it equal to zero and solve for x.

[tex]P'(x)=-100x+750=0\\x=7.5[/tex]

This a critical point of the function. Let's plug back into the original equation to see what it gives us.

[tex]P(7.5)=(200-5(7.5))(250+10(7.5))=(162.5)(325)=52,812.50[/tex]

You cant sell half a plot, so we need to see what happens if we sell 162 plots and 163 plots, and then compare which one gives us more money.

In order to sell 162 plots

[tex]200-5x=162\\x=7.6[/tex]Plug back into P(x) to see the profit

[tex]P(7.6)=(200-5(7.6))(250+10(7.6))=(162)(326)=52,812[/tex]

Now, do the same for 163 plots

[tex]200-5x=163\\x=7.4\\P(7.4)=(200-5(7.4))(250+10(7.4))=(163)(324)=52,812[/tex]

As we can see, they are the same. So, you can charge either $324 or $326 in rent. But, if your teacher is not looking for a logical answer and you can somehow sell half a plot, you can charge $325 in rent for the maximum profit.

Answer:

Step-by-step explanation:

Step-by-step explanation:

yes, if your teacher meant to include the default factors of every positive integer number : 1 and the number itself.

these are the 2 positive integer factors.

if a positive number can only be divided without remainder by 1 or by itself (with result 1), then it is per definition a prime number.

if the number can be divided without remainder by another number, then we are not dealing with a prime number.

but if your teacher did not have these default factors in mind, then no :

example : 15

15 has only 2 factors : 3 and 5.

both are positive integer numbers.

and yet 15 is not a prime number.

but back to my first point, 15 also has formally the factors 1 and 15. so, if we count them too, then we have suddenly 4 factors. and the original statement fits again.

Answer:What would be the interest cost(simple interest) for a $3000 loans with a 8% rate for nine months of a years? [Simple interest= Principal Rate Time. In this case, time is 9/12(for 0.75 of a year).

Step-by-step explanation: The cost to borrow the money, expressed as a percentage of the loan. After you enter the details, the auto loan payment calculator automatically ...A finance charge is the dollar amount that the loan will cost you. Lenders generally charge what is known as simple interest. The formula to calculate ...

It takes Brian 1.5 hours to get home from school

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

Let d represent the distance from their school to the house and t represent the time (hours) it takes Brian to teach home.

For Brian:

4 = d/t

d = 4t

For Scott:

6 = d / (t - 1/2)

d = 6t - 3

4t = 6t - 3

2t = 3

t = 1.5 hours

Therefore it takes Brian 1.5 hours to get home from school

Find out more at: https://brainly.com/question/22889670

Answer:

13:7

Step-by-step explanation:

This ratio would be 13 laptop computers for every 7 desktop computers; 13:7

26:100

..............................

26 percent in simplest form is the fraction 13/50. Since 'percent' means 'per hundred,' 26 percent would be equivalent to the fraction 26/100.

Take the unknown number as 'y'.

=》33% = 33/100

=》1.45 = 145/100

33/100 × y = 1.45

33/100 × y = 145/100

33y = 145/100 × 100/1

33y = 145

y = 145/33

y = 4.39

______

RainbowSalt2222 ☔

4,39

I'm sorry if I'm wrong

Answer:

C would be the answer

Hope this helps!

Answer:

1) No solution

2) Infinitely many solutions

Step-by-step explanation:

1) No solution

0=2 is false.

2) Infinitely many solutions

2=2 is true because both sides are equal, hence, it is an infinite solution.

Hope this helps :)

Using the normal distribution, it is found that Sue will get a letter grade of B.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, Sue got a grade of 0.85, hence [tex]z = 0.85[/tex].

A similar problem is given at https://brainly.com/question/25745464

Answer:

26°

Step-by-step explanation:

90°+64°+x°=180° (Sum of all the angles in a right angled triangle=180°)

154°+x°=180°

x°=180-154°

x°=26°

Answer:

20.5

Step-by-step explanation:

Use Pythagorean theorem,

[tex]x^2 = 14^2 +15^2 \\\\\implies x^2 =421\\\\\implies x =\sqrt{421}\\\\\implies x =20.5[/tex]

Answer:

27pi in^3

Step-by-step explanation:

the volume for a cone is (1/3)pi*r^2*h. r=3in, h=9in. so the volume is (1/3)*pi*3^2*9=27pi

Answer:

  D, A, B

Step-by-step explanation:

The sign of the leading coefficient always tells you the end behavior on the right: positive = rises; negative = falls.

The degree of the polynomial tells you how the left- and right-end behaviors compare: even = they are the same; odd = they are opposites.

__

A) negative leading coefficient, even degree:

__

B) positive leading coefficient, odd degree:

__

C) negative leading coefficient, odd degree

Answer:

1.2!

Step-by-step explanation:

The value of the numerical expression 0.90 ÷ 0.75 in the decimal form will be 1.20.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numbers are given below.

0.90 and 0.75

Then the division between the numbers 0.90 and 0.75 will be given by putting a division sign between them. Then we have

⇒ 0.90 ÷ 0.75

⇒ 0.90 / 0.75

⇒ 1.20

The worth of the mathematical articulation 0.90 ÷ 0.75 in the decimal structure will be 1.20.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Let [tex]x = \arcsin(y)[/tex], so that

[tex]\sin(x) = y[/tex]

[tex]\tan(x)=\dfrac y{\sqrt{1-y^2}}[/tex]

[tex]dx = \dfrac{dy}{\sqrt{1-y^2}}[/tex]

Then the integral transforms to

[tex]\displaystyle \int_{x=0}^{x=\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \int_{y=\sin(0)}^{y=\sin\left(\frac\pi2\right)} \frac{y}{\sqrt{1-y^2}} \ln(y) \frac{dy}{\sqrt{1-y^2}}[/tex]

[tex]\displaystyle \int_{x=0}^{x=\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy[/tex]

Integrate by parts, taking

[tex]u = \ln(y) \implies du = \dfrac{dy}y[/tex]

[tex]dv = \dfrac{y}{1-y^2} \, dy \implies v = -\dfrac12 \ln|1-y^2|[/tex]

For 0 < y < 1, we have |1 - y²| = 1 - y², so

[tex]\displaystyle \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy = uv \bigg|_{y\to0^+}^{y\to1^-} + \frac12 \int_0^1 \frac{\ln(1-y^2)}{y} \, dy[/tex]

It's easy to show that uv approaches 0 as y approaches either 0 or 1, so we just have

[tex]\displaystyle \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy = \frac12 \int_0^1 \frac{\ln(1-y^2)}{y} \, dy[/tex]

Recall the Taylor series for ln(1 + y),

[tex]\displaystyle \ln(1+y) = \sum_{n=1}^\infty \frac{(-1)^{n+1}}n y^n[/tex]

Replacing y with -y² gives the Taylor series

[tex]\displaystyle \ln(1-y^2) = \sum_{n=1}^\infty \frac{(-1)^{n+1}}n (-y^2)^n = - \sum_{n=1}^\infty \frac1n y^{2n}[/tex]

and replacing ln(1 - y²) in the integral with its series representation gives

[tex]\displaystyle -\frac12 \int_0^1 \frac1y \sum_{n=1}^\infty \frac{y^{2n}}n \, dy = -\frac12 \int_0^1 \sum_{n=1}^\infty \frac{y^{2n-1}}n \, dy[/tex]

Interchanging the integral and sum (see Fubini's theorem) gives

[tex]\displaystyle -\frac12 \sum_{n=1}^\infty \frac1n \int_0^1 y^{2n-1} \, dy[/tex]

Compute the integral:

[tex]\displaystyle -\frac12 \sum_{n=1}^\infty \frac1n \int_0^1 y^{2n-1} \, dy = -\frac12 \sum_{n=1}^\infty \frac{y^{2n}}{2n^2} \bigg|_0^1 = -\frac14 \sum_{n=1}^\infty \frac1{n^2}[/tex]

and we recognize the famous sum (see Basel's problem),

[tex]\displaystyle \sum_{n=1}^\infty \frac1{n^2} = \frac{\pi^2}6[/tex]

So, the value of our integral is

[tex]\displaystyle \int_0^{\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \boxed{-\frac{\pi^2}{24}}[/tex]

[tex]\displaystyle \int \limits_{0}^{ \frac{ \pi}{2} } \tt\tan (x) \ln ( \sin (x))\\ \\\displaystyle \sf{ \implies \: I = \int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin \left( \dfrac{\pi}{2} - x \right) \right) \: dx } \\ \\\displaystyle \sf{ \implies \: I = \int^{ \frac{\pi}{2} }_{0} \: \ln \left( cos(x) \right) \: dx } \\ \\\displaystyle \sf{ \implies \:2I =\int^{ \frac{\pi}{2} }_{0} \:\ln \left( sin(x) \right) \: dx + \int^{ \frac{\pi}{2} }_{0} \: \ln \left( cos(x) \right) \: dx } \\ \\\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin(x) \right) +\ln\left( cos(x) \right) \: dx }[/tex]

[tex]\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin(x) \: cos(x) \right) \: dx } \\ \\\displaystyle\sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( \dfrac{sin(2x)}{2}\right) \: dx } \\ \\\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \:\ln \left( sin(2x) \right)\:dx-\ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx}[/tex]

[tex]\displaystyle\sf{ \implies \: 2I = \dfrac{1}{2} \int^{ \pi}_{0} \: \ln \left( sin(t) \right) \:dt - \ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx} \\ \\\displaystyle\tt{ \implies \: 2I = \dfrac{1}{2} \cdot2 \int^{ \frac{\pi}{2}}_{0} \: \ln \left( sin(t) \right) \: dt - \ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx}[/tex]

[tex]\displaystyle \tt{ \implies \: 2I =\int^{ \frac{\pi}{2}}_{0} \: \ln \left( sin(t) \right) \: dt - \ln(2)\int^{ \frac{\pi}{2} }_{0} \: dx} \\ \\ \displaystyle \tt{ \implies \: 2I = I - \ln(2) \left[x \right] ^{ \frac{\pi}{2} }_{0} } \\ \\ \displaystyle \tt{ \implies \: I = -\ln(2)\left[ \dfrac{\pi}{2} - 0 \right] }[/tex]

[tex]\displaystyle \sf{ \implies \: I = - \dfrac{\pi}{2} \ln(2) }[/tex]

☞︎︎︎Apologies,if incorrect.

Answer:

12% increase compared to last years

Step-by-step explanation:

Given that-

√(0.09×0.09×x) = 0.09×0.09×√z

On squaring both sides then

⇛[√(0.09×0.09×x) ]² = (0.09×0.09×√z)²

⇛ 0.09×0.09×x= (0.09)²×(0.09)²×(√z)²

⇛ (0.09)² × x = (0.09)²×(0.09)²×z

⇛ (0.09)² × x/z = (0.09)²×(0.09)²

⇛x/z = (0.09)²×(0.09)²/(0.09)²

⇛x/z = (0.09)²

⇛x/z = 0.09×0.09

⇛x/z = 0.0081

Answer:- Hence the value of x/z will be 0.0081 r respectively.

Using the independence between an individual's party affiliation and his support of full-body  scans, it is found that:

a) 57 Republicans would be expected to not support the use of full-body scans.

b) 305 Democrats would be expected to support the use of full-body scans.

c) 18 Independents would be expected to not know or not answer.

The independence between an individual's party affiliation and his support of full-body  scans means that no matter the political party, the proportions for each option would be the same.

In the sample, there are 318 + 369 + 450 = 1137 people.

Item a:

[tex]\frac{170}{3} = 56.67[/tex]

Rounding, 57 Republicans would be expected to not support the use of full-body scans.

Item b:

264 + 299 + 351 = 914 people support the use of full-body scans, hence:

[tex]\frac{914}{3} = 304.67[/tex]

Rounding, 305 Democrats would be expected to support the use of full-body scans.

Item c:

16 + 15 + 22 = 53 people do not know or do not answer, hence:

[tex]\frac{53}{3} = 17.67[/tex]

Rounding, 18 Independents would be expected to not know or not answer.

A similar problem is given at https://brainly.com/question/24372153

Answer:

You: 3, 6, 9, 12

Friend:4, 8, 12, 16

Step-by-step explanation:

You/Friend ratio is 3/4

Missing numbers:

Numbers:

You      3, 6, 9, 12

Friend  4, 8, 12, 16

Answer: 32 hours

Step-by-step explanation: 51/6 = 8.5

So, Erica makes 8.5 dollars per hour. 272/8.5 = 32. Thus, Erica will need 32 hours.

Brainliest?

i guess you have copied the wrong question.. it should be somewhat like if tan theta + sec theta = p then find tge value of sin theta...

secθ+tanθ=P

⇒(secθ+tanθ)² = P²

⇒sec² θ+tan² θ+2tanθsecθ=P²

⇒2tan²θ + 1 + 2 sinθ/cos θ = P²

⇒2 sin²θ+ cos²θ+ 2 sinθ total by cos²θ = P²

Applying componendo and dividendo

=> 2sin²θ+ cos²θ+ 2sinθ- cos²θ/ 2sin²θ+ cos²θ+ 2sinθ- cos²θ = p²-1 / p²+1

⇒2sinθ(sinθ+1)/ 2(sinθ+1) = p²-1 / p²+1

=> sinθ = p²-1/ p²+1

Answer:

Equation 2 represents the greatest value of x!

Step-by-step explanation:

Let's solve each equation for x.

Equation 1; x = 4.1 (about)

Equation 2: x = 5 (about)

Equation 3: x = 4 (exact)

Equation 4: x = 3 (exact)

Hope this helps. :)

Answer:

We need to find how much more or less the ratio becomes

1.61 / 23 = 0.07

we multiply 0.07 with 1 to make the ratio even and get your answer

1 x 0.07 = 0.07 on the map

Hope this helps

Step-by-step explanation:

Answer:

yshannmm

Step-by-step explanation:

yes