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A local water park found that if the price of admission was

\(10, the\ attendance\ was\ About\ 1150\ customers\ per\ day.\)

\( When\ the\ Price\ of\ Admission\ was\ dropped\ to \)

6,attendance increased to about 1900 per day.

Write a linear equation for the attendance in terms of the price,p. (A = mp+b)
 

\(A_2(6,1900)\\ A_1(10,1150)\)

\(m=\frac{y_2-y_1}{x_2-x_1}=\frac{750}{-4}\\ m=-187.5\)

\(A(p)=m(x-x_1)+y_1\\ A(p)=-187.5(p-10)+1150\)

\(A(p)=-187.5\ p+3025\)

  !

\(\displaystyle 9x^{4}+9x^{3}+27x+27 \\ = (9x^{4}+27x)+(9x^{3}+27) \\ =9x(x^{3}+3)+9(x^{3}+3) \\ = 9(x^{3}+3)(x+1).\)

This has no solution.  If a is positive the left hand side is negative.  If a is negative the left hand side is complex.  In neither case do they match the right hand side.

So at first, they both have x dollars. Then, keddy loses 22 and raj gains 22. so 5(x-22)=x+22, so 5x-5*22=x+22. rearranging, 4x=6*22, so x=33, in the end, raj has 33+22=55 dollars.

sorry I don't know how to typeset LaTeX.

If m1= (4x + 7), m2= (15x - 17), and m3 =(6x - 13)", thenfind the value of x.

An ambulance travels at 40 mph and can follow a 20-mile route making no stops to get to the hospital. A helicopter travels at one mile per minute, and the air route is 15 miles to get to the same hospital. However, the helicopter takes three minutes for takeoff and three minutes for landing. How many fewer minutes does it take for the helicopter to complete its trip (takeoff, flight and landing) than for the ambulance to complete its trip?

Hello Guest!

\(\Delta t=t_a-2\cdot 3\ min -t_h\)

\(t_a=\frac{20mls\cdot h}{40mls}\cdot \frac{60\ min}{h}\\ t_a=30\ min\)

\(t_h=\frac{15\ mls\cdot \ min}{1\ mls}\\ t_h=15\ min\)

\(\Delta t=t_a-2\cdot 3\ min -t_h\)

\(\Delta t=30\ min-2\cdot 3\ min -15\ min\)

\(\Delta t=9\ min\)

9 minutes many fewer does it take for the helicopter to complete its trip (takeoff, flight and landing) than for the ambulance to complete its trip.

  !

Thanks OlympusHero,

I suppose I would have guessed that, and maybe it is a normal thing these days that I should recognize,

But it just seems to me that the word 'area' should have been used.

Never mind, thanks for the info and the question answer.

2  4  5  8  10  16  20  25  32  40  50  64  80  100  125  128  160  200  250  256  320  400  500  512  625  640  800  1000  1024  1250  1280  1600  2000  2048  2500  2560  3125  3200  4000  4096  5000  5120  6250  6400  8000  8192  Total =  46 such integers.

hint:   9x - 3 = 109 - 5x

Factor by grouping: 9x^4+9x^3+27x+27

Hello Guest!

adoption \(x_1=-1\)

  (\(x^4\) +  \(x^3\)+3x+3) : (x+1) = \(x^3+3\)

  \(\underline{x^4+x^3}\)

             0 \(3x+3\)

                \(\underline{3x+3}\)

                          0

\(x^3+3=0\\ x_{2,3,4}=\sqrt[3]{-3} =-1.4422\)

Factor by grouping: \(9x^4+9x^3+27x+27\) = \(9\times (x+1)\times (x-\sqrt[3]{-3})^3\)

  !

I counted, and there are 28 integers that work.

The radius is r = 4/13.

By the property of telescoping sum, we have quite easily that \dfrac{1}{a_n} = 2-\sum_{k=0}^{n-1}\dfrac{1}{n+a_k}.

First we show that a_n<1 which is analogous to proving that \sum_{k=0}^{n-1}\dfrac{1}{n+a_k}<1. Now, we note that \{a_k\} is an increasing sequence, hence a_k\geq a_0 for all k\geq0. This gives \sum_{k=0}^{n-1}\dfrac{1}{n+a_k}\leq\dfrac{n}{n+a_0}=\dfrac{2n}{2n+1}<1 and thus we are done.

Now we prove the other part of the inequality. We note that \sum_{k=0}^{n-1}\dfrac{1}{n+a_k}\geq\dfrac{n}{n+a_n} because of increasing property of the sequence a_n. Now using the fact that \dfrac{1}{a_n}=2-\sum_{k=0}^{n-1}\dfrac{1}{n+a_k} we have, after some algebra that 2a_n^2+(n-1)a_n-n\geq0 implying, and keeping in mind that \{a_k\} is a positive sequence, a_n\geq\dfrac{-(n-1)+\sqrt{(n-1)^2+8n}}{4}. It remains to show that this huge quantity is greater than 1-\dfrac{1}{n}. By squaring both sides, and cancelling out terms, we come to 3n>2 which is true for any n. Hence, 1/(a_1 + 1) + 1/(a_2 + 1) + ... + 1/(a_n + 1) < 2.

The altitude of an equilateral triangle is the square root of 3 units. What is the area of the triangle, in square units? Express your answer in simplest radical form.

Hello Guest!

\(A=\frac{1}{2}ah\)

\(h=\sqrt{3}\)

\(a^2=(\frac{a}{2})^2+h^2\\ a^2-\frac{a^2}{4}=h^2\)

\(\frac{3}{4}a^2=3\\ a=\sqrt{\frac{3\cdot 4}{3}}\)

\(a=2\)

\(A=\frac{1}{2}ah\)

\(A=\frac{1}{2}\cdot 2\cdot \sqrt{3}\)

\(A=\sqrt{3}\)

  !

The angle just ABOVE 2a-9  is also 5a+14       and added together they equal 180 degrees

2a-9      +   5a+14       = 180     solve for a     then you can calculate the angles

Yes? vvvvvvvvvv...

:O

Yep, good point!   

T = all 4 tomato plants    b = basil plant

T bbb

bTbbb

bbTbb

bbbTb

bbbbT      5 ways

Two points    6, 255   and  9,255        just find a line as always

find slope, m

then       y-y1   = m(x-x1)           y is tix sold      x is price

The possible values of x + y + z are -3, -2 -1, 0, 1, 2, 3, so there are 7 possible values of x + y + z.

On Monday the stock increased by 20%. On Tuesday, it fell by: 1 - (1/1.20) =16 2/3 %

Arrows on lines are used to indicate that those lines are parallel. (Purplemath)

There are 400 such numbers beginning with: 2, 4, 6, 8, 12..........and ending  with: 992, 994, 996 and 998.

The distance is sqrt(58)

1 - 

-17 - 88 = - 105

-105 / 3 = 35 terms will appear before -17, which is the 36th term.

2 - The 23rd term = - 53