We are given coordinates of three points RST and are asked to prove that it forms a Right Triangle.
We kn
How many kilometers could the red car travel in 12 hours? Write an equation to show your work.
The kilometers that the red car travel in 12 hours is 2604 kilometers.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
From the diagram, it should be noted that the red car has a speed of 217 km per hours.
Therefore, the distance traveled in 12 hours will be:
Distance = Speed × Time
= 217 × 12
= 2604 km
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Which expressions are equivalent to the one below? Check all that apply. 9x 36* D A Св. х5 B. | * c. c. 36 D D. 9.9X+1 36 DE E. LASSE F. 9.9x-1
To answer this question we will use the following properties of exponents:
[tex]\begin{gathered} (\frac{a}{b})^x=\frac{a^x}{b^x}, \\ a^x*a^y=a^{x+y}. \end{gathered}[/tex]Now, notice that:
[tex]9=\frac{36}{4}.[/tex]Therefore:
[tex]9^x=(\frac{36}{4})^x.[/tex]Using the first property we get that:
[tex]9^x=\frac{36^x}{4^x}.[/tex]Now, notice that x=1+x-1, then:
[tex]9^x=9^{1+x-1}=9*9^{x-1}.[/tex]Answer: Options A, E, and F.
Find y if the point (5,y) is on the terminal side of theta and cos theta = 5/13
For this problem we have a point given (5,y) and we know that this point is on a terminal side of an angle, we also know that:
[tex]\cos \theta=\frac{5}{13}[/tex]If we know the cos then we can find the sin on this way:
[tex]\sin \theta=\frac{y}{13}[/tex]Then we can apply the following identity from trigonometry:
[tex]\sin ^2\theta+\cos ^2\theta=1[/tex]Using this formula we got:
[tex](\frac{5}{13})^2+(\frac{y}{13})^2=1[/tex]And we can solve for y:
[tex]\frac{y^2}{169}=1-\frac{25}{169}=\frac{144}{169}[/tex]And solving for y we got:
[tex]y=\sqrt{169\cdot\frac{144}{169}}=\sqrt{144}=\pm12[/tex]And the two possible solutions for this case are y=12 and y=-12
Solve the system by the addition method x + 2y = - 26x + 3y = - 30
We are asked to solve the following system of equations via the addition method:
x + 2 y = - 2
6 x + 3 y = - 30
so via the addition method we will try to eliminate one of the variables by multiplying for the appropriate factor that would ease tha process. We notice that if wemultiply the whole first eqaution by the factor (-6), we will be able to in the second step eliminate the term in "x" by combining both equations term by term.
So we do that: Multiply the whole first equation by "-6":
(-6) (x + 2 y ) = (-6) (-2)
- 6 x - 12 y = 12
now we combine this with the second equation term by term to eliminate the term in x:
- 6 x - 12 y = 12
+
6 x + 3 y = - 30
_______________
0 - 9 y = - 18
Now divide both sides by "-9" to isolate y:
y = - 18 / (-9)
y = 2
Now we use y = 2 in the very first equation to solve for the variable x:
x + 2 y = - 2
x + 2 (2) = -2
x + 4 = - 2
subtract 4 from both sides:
x = - 2 - 4
x = - 6
In one month, Jason eams $32.50 less than twice the amount Keyin earns, Jason earns $212.50write and solve an equation to solve for the amount of money that kevin earns
Let the amount Kevin earns be represented with K
Let the amount Jason earns be represented with J
Jason earns $32.50 less than twice Keyin earns can be represented by
J = K - 32.5 ----- equation 1
Jason earns $ 212.5
J = 212.5 ----- equation 2
From equation 1, we can write the equation to solve for what Kevin earns
J = K - 32.5
Making K the subject of the formula
K = J + 32.5
Putting J = 212.5 into the equation above
K= $ 212.5 + $ 32.5
K = $ 245
Kevin earns $245
Tell whether x and y show direct variation, inversevariation, or neither. Explain your reasoning.X 24.68y -5 -11 -17 -23The products xy areThe ratios Y areХSo, X and y show
Neither
1) Firstly, we can start filling in the blanks.
2) The products xy are:
[tex]xy=-10,-44,-102,-184[/tex]We're simply multiplying each x-entry by its output y.
The ratios y/x are:
[tex]\frac{y}{x}=-\frac{5}{2},-\frac{11}{4},-\frac{17}{6},-\frac{23}{8}[/tex]So, x and y show:
Note that xy is not constant, for their product differs. So it is not an
inverse variation.
On the other hand, y/x is not constant as well. So it is not a direct variation.
3) Hence, it's neither direct nor inverse.
which of the triangles cannot be proved congruent? so a different tutor gave me the answer which is D. But he told me to ask another tutor to tell me how to type out how I got the answer.
The triangles that cannot be proved congruent are the triangles in option D. We are not told that the other side is congruent to the corresponding side of the other triangle.
To prove they are congruent, we need to know the other side is congruent and prove this using the SSS postulate.
In the other cases, we can be proved they are congruent by:
• Case A ---> SAS postulate.
,• Case B ---> ASA postulate.
,• Case C ---> SSS postulate (the triangles share a common side)
In summary, we only have that the triangles in D cannot be proved congruent since we have two corresponding congruent sides, and one angle (vertical angle) to be congruent corresponding parts. It would be an SSA method. However, this method is not Universal, and it is not enough to demonstrate they are congruent.
convert r= 5/ 1+3sinθ to a rectangular equation
Given:
[tex]r=\frac{5}{1+3\sin \theta}[/tex]Find: Rectangular equation.
Sol:
[tex]r^2=x^2+y^2[/tex][tex]\begin{gathered} y=r\sin \theta \\ \sin \theta=\frac{y}{r} \end{gathered}[/tex][tex]\begin{gathered} r=\frac{5}{1+3\sin \theta} \\ r=\frac{5}{1+\frac{3y}{r}} \end{gathered}[/tex][tex]\begin{gathered} r=\frac{5r}{r+3y} \\ r+3y=5 \\ r=5-3y \\ r^2=(5-3y)^2 \end{gathered}[/tex]Put the value in rectangular equation:
[tex]\begin{gathered} x^2+y^2=r^2 \\ x^2+y^2=(5-3y)^2 \end{gathered}[/tex]Find the area of the figure. (Sides meet at right angles.)4 m5 m15 m5 m5 m4 m4 m
The area of the figure will be the area of the rectangle of the top, plus the area of the rectangle of the bottom:
The area of the rectangle of the top is:
[tex]A1=w1\cdot h1=5\cdot4=20m^2[/tex]The area of the rectangle of the bottom is:
[tex]A2=w2\cdot h2=14\cdot4=56m^2[/tex]so, the total area is:
[tex]A=A1+A2=20m^2+56m^2=76m^2[/tex]Write a word problem that involves a proportional relationship and needs more than one step to solve.Show how to solve the problem
To write a word problem that involves a proportional relationship:
Sam bought 4kg of apples for $12. How many kilograms of apples, he can buy for $30?
Sam bought 4kg of apples for $12.
So, cost of 1 kg of apples is,
[tex]\frac{12}{4}=3[/tex]Let x be the number of kg apples.
Therefore, He can buy 3x kg apples for $30.
So,
[tex]\begin{gathered} 3x=30 \\ x=\frac{30}{3} \\ x=10 \end{gathered}[/tex]Therefore, He can buy 10 kg apples for $30.
I would like to know if I answered the question correctly
INFORMATION:
We have the next system of equations:
[tex]\begin{cases}{x-5y=-16} \\ {9x+9y=72} \\ {4x-6z=-8}\end{cases}[/tex]And we need to determine if (4, 4, 4) is a solution of the system.
STEP BY STEP EXPLANATION:
To know if the ordered triple is a solution of the system, we need to that (4, 4, 4) means x = 4, y = 4 and z = 4.
Then, to know if it is a solution we must replace the values on each equation to verify if the values are solutions
We have three equations:
1. x - 5y = -16
Replacing x = 4 and y = 4, we obtain
[tex]\begin{gathered} 4-5\cdot4=-16 \\ 4-20=-16 \\ -16=-16 \\ \text{ TRUE} \end{gathered}[/tex]2. 9x + 9y = 72
Replacing x = 4 and y = 4, we obtain
[tex]\begin{gathered} 9\cdot4+9\cdot4=72 \\ 36+36=72 \\ 72=72 \\ \text{ TRUE} \end{gathered}[/tex]3. 4x - 6z = -8
Replacing x = 4 and z = 4, we obtain
[tex]\begin{gathered} 4\cdot4-6\cdot4=-8 \\ 16-24=-8 \\ -8=-8 \\ \text{ TRUE} \end{gathered}[/tex]Finally, since the three equations are true when x = 4, y = 4 and z = 4, the ordered triple is a solution
ANSWER:
Yes
Steven flew from Boston to Orlando with a stop in Atlanta to switch planes. His first flight leftBoston at 12:00 P.M. and was 3 hours and 45 minutes long. Steven was in Atlanta for 2 hours and 30 minutes, and his flight from Atlanta to Orlando was 1 hour and 30 minutes long. Whattime was it when Steven landed in Orlando?
Answer:
07:45 pm
Explanation:
Steven landed in Orlando after the sum of the following time
3 hours and 45 minutes
2 hours and 30 minutes
1 hour and 30 minutes
If we add the hours and the minutes, we get:
3 hours + 2 hours + 1 hour = 6 hours
45 minutes + 30 minutes + 30 minutes = 105 minutes
But 1 hour = 60 minutes, so
6 hours and 105 minutes = 7 hours and 45 minutes
because
105 - 60 = 45
Since the flight left Boston at 12:00 pm, it was 07:45 pm when Steven landed in Orlando.
Find d and then find the 20th term the sequence. Type the value of d (just the number) in the first blank and then type the 20th term(just the number) in the second blank.a1=6 and a3=14
We have that an arithmetic sequence can be defined by the following explicit formula:
[tex]a_n=a_1+(n-1)\cdot d[/tex]where n represents the index of each term in the sequence and d represents the common difference beteen each term. a1 is the first term of the sequence.
In this case we have that the first term is a1 = 6, and also we have that a3=14. We can use the formula to find the common difference:
[tex]\begin{gathered} a_3=a_1+(3-1)d \\ \Rightarrow a_3=a_1+2d \\ \Rightarrow14=6+2d \end{gathered}[/tex]solving for d, we get:
[tex]\begin{gathered} 2d+6=14 \\ \Rightarrow2d=14-6=8 \\ \Rightarrow d=\frac{8}{2}=4 \\ d=4 \end{gathered}[/tex]therefore, the value of d is d = 4.
We have now the explicit formula for the sequence:
[tex]\begin{gathered} a_n=6_{}+4(n-1) \\ \end{gathered}[/tex]then, for the 20th term, we have to make n = 20 on the formula, and we get the following:/
[tex]\begin{gathered} a_{20}=6+4(20-1)=6+4(19)=6+76=82 \\ \Rightarrow a_{20}=82 \end{gathered}[/tex]therefore, the 20th term is 82
The hypotenuse of a right triangle is 1 centimeter longer than the longer leg. The shorter leg is 7 centimeters shorter than the longer leg. Find the length of the shorter leg of the triangle.
Answer:
[tex]\text{Shorter leg= 5cm}[/tex]Step-by-step explanation:
As a first step to go into this problem, we need to make a diagram:
Let x be the measure of the longer leg.
Now, understanding this we can apply the Pythagorean theorem to find x, it is represented by the following equation:
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{where,} \\ a=\text{longer leg} \\ b=\text{shorter leg} \\ c=\text{hypotenuse } \end{gathered}[/tex]Substituting a,b, and c by the expressions corresponding to its sides:
[tex]\begin{gathered} x^2+(x-7)^2=(x-1)^2 \\ \end{gathered}[/tex]apply square binomials to expand and gather like terms, we get:
[tex]\begin{gathered} x^2+x^2-14x+49=x^2-2x+1 \\ 2x^2-x^2-14x+2x+49-1=0 \\ x^2-12x+48=0 \end{gathered}[/tex]Now, factor the quadratic equation into the form (x+?)(x+?):
[tex]\begin{gathered} (x-4)(x-12)=0 \\ x_1=4 \\ x_2=12 \end{gathered}[/tex]This means, the longer leg could be 4 or 12, but if we subtract 7 to 4, we get a negative measure for the shorter leg, that makes no sense.
Therefore, the long leg is 12 cm.
Hence, if the shorter leg is 7 centimeters shorter than the longer leg:
[tex]\begin{gathered} \text{Shorter leg=12-7} \\ \text{Shorter leg=}5\text{ cm} \end{gathered}[/tex]Which of the following graphs represents the equation 2x - 8y = 32?
Answer:
C
Step-by-step explanation:
2x-8y = 32
2/2 x - 8/2 y = 32/2
x - 4y = 16
if x = 0
-4y = 16
-4/-4 y = 16/-4
y = -4
If x = 16
16-4y = 16
-4y = 0
-4/-4 y = 0/-4
y = 0
Lesson 6.02: Finn's fish store has 5 tanks of goldfish; each tank holds 40 fish. He collects andinspects 5 fish from each tank and finds that 4 fish have fin rot. Find the estimated numbergoldfish in the store that have fin rot. SHOW ALL WORK!
Answer:
Explanation:
We are told that of each 5 fish inspected in the tank, 4 have fin rot, therefore, the probability o getting a fin rot is
[tex]\frac{4}{5}\times100\%=80\%[/tex]This means 80% of the fish in a tank have fin rot.
Now, for one tank 80% of 40 fish is
[tex]\frac{80\%}{100\%}\times40=32[/tex]Now, since there are 5 fish tanks in the store and 32 fish in each have fin rot; therefore, the total number of fish that have fin rot will be
[tex]32fish\times5=160\text{fish}[/tex]Hence, the estimated number of fish with fish rot in the store is 160.
i am not sure what I am doing wrong here
We know that segment RS is a diameter of the circle, this means that arcs RS an RST measure 180°. Now that we know that an using the ratio for arcs RT and TS given we have:
[tex]\begin{gathered} RT+5RT=180 \\ 6RT=180 \\ RT=\frac{180}{6} \\ RT=30 \end{gathered}[/tex]Now, we know that an angle inscribed in a circle is half its intercepted arc, then we have:
[tex]m\angle RST=\frac{30}{5}=15[/tex]Therefore, we have that arc RT is 30° and angle RST is 15°
The number of newly reported crime cases in a county in New York State is shown inthe accompanying table, where x represents the number of years since 2006, and yrepresents number of new cases. Write the linear regression equation that representsthis set of data, rounding all coefficients to the nearest tenth. Using this equation,estimate the calendar year in which the number of new cases would reach 767.Years since 2006 (x) New Cases (y)099619232882389248405813
Solution
For this case we have the following data:
x y
0 996
1 923
2 882
3 892
4 840
5 813
sum xi = 15
sum yi = 5346
sum xi yi = 12788
sum xi^2 = 55
And we want to find and equation like this one:
y= mx+ b
So then we can estimate the slope using least squares and we have:
[tex]m=\frac{n\sum ^n_{i=1}x_iy_i-\sum ^n_{i=1}x_i\sum ^n_{i=1}y_i}{n(\sum ^n_{i=1}x^2_i)-(\sum ^n_{i=1}x_i)^2}[/tex]Replacing we have:
[tex]m=\frac{6\cdot12788-(15\cdot5346)}{6(55)-(15)^2}=\frac{-3462}{105}=-32.971[/tex]m= -32.971
And the intercept would be:
[tex]b=\frac{\sum^n_{i=1}y_i}{n}-m\cdot\frac{\sum^n_{i=1}x_i}{n}=\frac{5346}{6}-(-32.971)\cdot\frac{15}{6}=973.429[/tex]b= 973.428
Then the equation would be:
y= -32.971x+ 973.428
And we can find the value of x for y = 767 and we got::
767 = -32.971x+ 973.428
Solcing for x we have:
767- 973.428 = -32.971 x
x= 6.26
Regression Equation: y= -32.9x + 973.4
Final Answer: 2012
rogers flight took off at 9:27 am. the flight is scheduled to land at 1:05 pm. if the flight lands on schedule , how long is the flight?
We need to calculate the time of thr flight, so we have to calculate the different between the landing time and the take off time:
[tex]\begin{gathered} 1\colon05pm=13\text{hours 5minutes} \\ 9\colon27\text{ am = 9hours 27 minutes} \\ \Delta t=1\colon05pm-9\colon27am=(13-9)\text{hours (5-27)minutes} \\ \Delta t=4hours\text{ (-22)minutes=3hours (60-22)minutes} \\ \Delta t=3\text{ hours 38 minutes} \end{gathered}[/tex]The flight is 3 hours 38 minutes long.
Team Arrow shoots an arrow from the top of a 1600-foot building on Earth-51. The arrow reaches a maximum height of 1840 feet after 4 seconds.Write an equation for the height of the arrow, h, in feet as a function of the number of seconds, t, since the arrow was shot.Round to 3 decimal places as needed. After how many seconds will the arrow reach the ground?Round to 3 decimal places as needed.
We will have the following:
***First:
[tex]h=h_0+v_0\cdot t+\frac{1}{2}g\cdot t^2[/tex]Now, we will determine the value for the speed:
[tex]1840=1600+v_0\cdot(4)+\frac{1}{2}(-32.17)\cdot(4)^2\Rightarrow240=4v_0-\frac{25736}{25}[/tex][tex]\Rightarrow\frac{31736}{25}=4v_0\Rightarrow v_0=\frac{7934}{25}\Rightarrow v_0=137.36[/tex]So, the equation for the height of the arrow (h) in feet as a function of the number of seconds t is:
[tex]h=1600+317.36t+\frac{1}{2}gt^2[/tex]Here "g" is the gravitational pull of earth.
***Second:
We will determine how much time it would take for the arrow to hit the ground as follows:
[tex]0=1600+317.36t+\frac{1}{2}(-32.17)t^2\Rightarrow-\frac{3217}{200}t^2+317.36t+1600=0[/tex][tex]\Rightarrow t=\frac{-(317.36)\pm\sqrt[]{(317.36)^2-4(-\frac{3217}{200})(1600)}}{2(-\frac{3217}{200})}\Rightarrow\begin{cases}t\approx-4.163 \\ t\approx23.893\end{cases}[/tex]So, afeter 23.893 seconds the arrow would hit the ground.
What is the solution to 2x + 2 (x – 5)= 6 ? Show your work. explainhow you solved the equation.
Step 1
eliminate the parenthesis, use distributive property
[tex]\begin{gathered} 2x+2(x-5)=6 \\ 2x+2x-10=6 \end{gathered}[/tex]Step 2
add similar terms
[tex]\begin{gathered} 2x+2x-10=6 \\ 4x-10=6 \end{gathered}[/tex]Step 3
add 10 in both sides
[tex]\begin{gathered} 4x-10=6 \\ 4x-10+10=6+10 \\ 4x=16 \end{gathered}[/tex]Step 4
divide each side by 4
[tex]\begin{gathered} 4x=16 \\ \frac{4x}{4}=\frac{16}{4} \\ x=4 \end{gathered}[/tex]so, the answer is x=4
what are the unit prices for 100 sheets for $.99 and 500 sheets for $4.29
Answer:$.0099/sheet; $.00858/sheet;500 sheets
Step-by-step explanation:
Answer please the picture scanner deal won’t scan over this and i don’t know how to type it out
Solution
We are given the arithmetic sequence
[tex]\begin{gathered} a_1=5 \\ a_n=a_{n-1}-4 \end{gathered}[/tex]To find an explicit formula
[tex]\begin{gathered} First\text{ }Term=5 \\ a=5 \end{gathered}[/tex]From the second recursive formula
[tex]\begin{gathered} a_n-a_{n-1}=-4 \\ Common\text{ }Difference=-4 \\ d=-4 \end{gathered}[/tex]The nth term of an Arithmetic sequence is given by
[tex]\begin{gathered} a_n=a+(n-1)d \\ a_n=5+(n-1)(-4) \end{gathered}[/tex]Therefore, the answer is
[tex]a_{n}=5+(n-1)(-4)[/tex]A parabola can be drawn given a focus of (-7,3) and a directrix of x = 9. What canbe said about the parabola?
The focus of a parabola is given by:
[tex]F(h,k+p)[/tex]and the directrix is given by:
[tex]y=k-p[/tex]since the directrix is x = 9, we can conclude it is a horizontal parabola, so:
[tex]\begin{gathered} x=9=k-p \\ so\colon \\ k=9+p \end{gathered}[/tex][tex]\begin{gathered} F(-7,3)=(h,k+p) \\ h=-7 \\ k+p=3 \\ 9+p+p=3 \\ 9+2p=3 \end{gathered}[/tex]solve for p:
[tex]\begin{gathered} 2p=3-9 \\ 2p=-6 \\ p=-\frac{6}{2} \\ p=-3 \end{gathered}[/tex][tex]\begin{gathered} k=3-p \\ k=3-(-3) \\ k=6 \end{gathered}[/tex]We can write the parabola in its vertex form:
[tex]\begin{gathered} x=\frac{1}{4p}(y-k)^2+h \\ so\colon \\ x=-\frac{1}{12}(y-6)^2-7 \end{gathered}[/tex]It is a horizontal parabola that opens to the left, and has vertex located at (-7,6)
hi, need help how the graph looks like for this [tex]y \ \textless \ \frac{1}{2} x - 2[/tex][tex]y \leqslant - 2x + 4[/tex]
Solution:
Given:
[tex]\begin{gathered} y<\frac{1}{2}x-2 \\ y\leq-2x+4 \end{gathered}[/tex]Using a graph plotter, the graph of the two inequalities is shown;
Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the unknowns.six subtracted from a number
Tim is building a model of a castle with small wooden cubes. So far Tim has constructed part of a security world castle,as shown below. Each wooden cube has a side length of 1/8ft
From the given model, the length of the wall is 9/8 ft, the width of the walk is 1/2 ft, and the height of the wall is 11/8. The volume of the portion of security wall that Tim has constructed so far is 99/128 cu ft.
What is the Volume of the Block?From the given image of the building model we see that part of a security world castle is shown.
We see that the length has 9 blocks.
Since the length has a total of 9 blocks and each side length is 1/8 ft, then we say that;
Length = 9*(1/8) = 9/8 ft
We also observe that the height has 11 blocks and as such;
height = 11*(1/8) = 11/8 ft
Meanwhile the width will have a length of: 1/2 ft
Formula for volume is;
Volume = length * height * width
Thus;
Volume = (9/8) * (11/8) * (1/2)
Volume = (9 * 11 * 1)/(8 * 8 * 2)
Volume = 99/128 cu ft
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Complete question is;
Tim is building a model of a castle with small wooden cubes. So far Tim has constructed part of a security world castle,as shown below. Each wooden cube has a side length of 1/8ft
Based on the model,the length of the wall is ___ft, the width of the walk is 1/2 ft, and the height of the wall is ___. The volume of the portion of security wall that Tum has constructed so far is ___ cu ft.
Find the area of the parallelogram. 6.5 cm 3.1 cm 3 cm O 9.3 cm^2 O 19.5 cm^2 O 20.15 cm^2 O 60.45 cm^2
Data
length = 6.5 cm
height = 3 cm
side = 3.1 cm
Formula
Area = base x height
Substitution
Area = (6.5 x 3)
Result
Area = 19.5 cm^2
Next
The right answer is the second choice
12 + 1.5x >= 20
write an equation to represent"three consecutive integers is 12 less than 4 times the middle integer'
Consider that the three consecutive integers are:
least integer = n
middle integer = n + 1
greatest integer = n + 2
THe expression "three consecutive integers is 12 less than 4 times the middle integer" can be written as follow:
n + (n + 1) + (n + 2) = 4(n +1) - 12
In order to find the numbers, proceed as follow:
n + (n + 1) + (n + 2) = 4(n +1) - 12 cancel parenthesis
n + n + 1 + n + 2 = 4n + 4 - 12 simplify like terms
3n + 3 = 4n - 8 subtract 4n and 3 both sides
3n - 4n = - 8 - 3
-n = -11
n = 11
Hence, the three consecutive integers are:
n = 11
n + 1 = 12
n + 2 = 13
If a golden rectangle has a length of 1 cm, what is its width (shorter side) rounded to the NEAREST TENTH?
In any golden rectangle the following poreperty should hold:
[tex]\frac{a+b}{a}=\frac{a}{b}[/tex]where a+b is the length and a is the width. We know that the length of the rectangle is 1, then:
[tex]\begin{gathered} a+b=1 \\ b=1-a \end{gathered}[/tex]Plugging this values in the first equation we have:
[tex]\frac{1}{a}=\frac{a}{1-a}[/tex]Solving this equation for a:
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