Answer:
[tex]a_{n}[/tex] = [tex]\frac{1}{2}[/tex] n + 15
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₆ = 18 and d = [tex]\frac{1}{2}[/tex] , then
a₁ + 5d = 18 , that is
a₁ + [tex]\frac{5}{2}[/tex] = 18 ( subtract [tex]\frac{5}{2}[/tex] from both sides )
a₁ = [tex]\frac{31}{2}[/tex]
Thus
[tex]a_{n}[/tex] = [tex]\frac{31}{2}[/tex] + [tex]\frac{1}{2}[/tex] (n - 1) = [tex]\frac{15}{2}[/tex] + [tex]\frac{1}{2}[/tex] n - [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] n + 15
A right-angled triangle has shorter side lengths exactly c^2-b^2 and 2bc units respectively, where b and c are positive real numbers such that cc is greater than b. Find an exact expression for the length of the hypotenuse (in appropriate units).
Answer: hypotenuse = [tex]c^{2} + b^{2}[/tex]
Step-by-step explanation: Pythagorean theorem states that square of hypotenuse (h) equals the sum of squares of each side ([tex]s_{1},s_{2}[/tex]) of the right triangle, .i.e.:
[tex]h^{2} = s_{1}^{2} + s_{2}^{2}[/tex]
In this question:
[tex]s_{1}[/tex] = [tex]c^{2}-b^{2}[/tex]
[tex]s_{2} =[/tex] 2bc
Substituing and taking square root to find hypotenuse:
[tex]h=\sqrt{(c^{2}-b^{2})^{2}+(2bc)^{2}}[/tex]
Calculating:
[tex]h=\sqrt{c^{4}+b^{4}-2b^{2}c^{2}+(4b^{2}c^{2})}[/tex]
[tex]h=\sqrt{c^{4}+b^{4}+2b^{2}c^{2}}[/tex]
[tex]c^{4}+b^{4}+2b^{2}c^{2}[/tex] = [tex](c^{2}+b^{2})^{2}[/tex], then:
[tex]h=\sqrt{(c^{2}+b^{2})^{2}}[/tex]
[tex]h=(c^{2}+b^{2})[/tex]
Hypotenuse for the right-angled triangle is [tex]h=(c^{2}+b^{2})[/tex] units
The expression for the length of the hypotenuse is [tex]c^2+ b^2 \ units[/tex].
Given that,
A right-angled triangle has shorter side lengths exactly [tex]c^{2} - b^{2}[/tex] and 2bc units respectively,
Where b and c are positive real numbers such that c is greater than b.
We have to determine,
An exact expression for the length of the hypotenuse?
According to the question,
The Pythagoras theorem states that the sum of the hypotenuse in the right-angled triangle is equal to the sum of the square of the other two sides.
A right-angled triangle has shorter side lengths exactly [tex]c^{2} - b^{2}[/tex] and 2bc units respectively,
Where b and c are positive real numbers such that c is greater than b.
Therefore,
The expression for the length of the hypotenuse is,
[tex]\rm (Hypotenuse)^2 = (c^2-b^2)^2+ (2bc)^2\\\\(Hypotenuse)^2 = c^4+ b^4 - 2c^2b^2 + 4c^2b^2\\\\(Hypotenuse)^2 = c^4+ b^4 +2c^2b^2 \\\\Hypotenuse = \sqrt{c^4+ b^4 +2c^2b^2}\\\\\ Hypotenuse = \sqrt{(c^2+ b^2)^2}\\\\ Hypotenuse = c^2+b^2 \ units[/tex]
Hence, The required expression for the length of the hypotenuse is [tex]c^2+ b^2 \ units[/tex].
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HELP PLZZ Which of the following choices will evaluate the function ƒ(x) = -(-x), when x = -3? 3 -1 -3 None of these choices are correct.
Answer:
-3
Step-by-step explanation:
[tex]F(x)=-\,(-x)\\f(-3)=-(-(-3))\\f(-3)=-3[/tex]
What’s the perimeter and surface area of this shape?
Please also show working out.
Answer: Perimeter = 8π ≈ 25.12
Area = 12π ≈ 37.68
Step-by-step explanation:
This is a composite of two figures.
The bigger figure is a quarter-circle with radius (r) = 8 cm
The smaller figure is a quarter-circle with diameter = 8 cm --> r = 4
Perimeter of a quarter-circle = [tex]\dfrac{1}{4}(2\pi r)[/tex] = [tex]\dfrac{\pi r}{2}[/tex]
Perimeter of composite figure = bigger - smaller figure
[tex]P_{bigger}=2\pi(8)\quad = 16\pi\\P_{smaller}=2\pi(4)\quad =8\pi\\P_{composite}=16\pi-8\pi \\.\qquad \qquad = \large\boxed{8\pi}[/tex]
Area of a quarter-circle = [tex]\dfrac{1}{4}\pi r^2[/tex]
[tex]A_{bigger}=\dfrac{1}{4}\pi (8)^2\quad =16\pi\\\\A_{smaller}=\dfrac{1}{4}\pi (4)^2\quad =4\pi\\\\A_{composite}=16\pi-4\pi\\.\qquad \qquad = \large\boxed{12\pi}[/tex]
if the second angle is 20% more than the first angle and the third angle is 20% less than the first angle in a triangle, then find the three angles of the triangle
Answer:
Step-by-step explanation:
If the second angle's measure is based on the first angle's measure, and the third angle's measure is also based on the first angle's measure, then the first angle is the main angle. We will call that x.
1st angle: x
2nd angle: x + 20%
3rd angle: x - 20%
By the Triangle Angle-Sum Theorem, all those angles will add up to 180, so:
x + (x + 20%) + (x - 20%) = 180 and
3x = 180 so
x = 60. That means that
2nd angle: 60 + (.2*60) which is
60 + 12 = 72 and
3rd angle: 60 - (.2*60) which is
60 - 12 = 48. Let's check those angles. If
∠1 = 60
∠2 = 72
∠3 = 48,
then ∠1 + ∠2 + ∠3 = 180 and
60 + 72 + 48 does in fact equal 180, so you're done!
The temperature in Chicago when the plane left was 22°F. When the plane arrived in Atlanta it was 46°F. What was the difference in temperature?
Answer:
24
Step-by-step explanation:
46 - 22 = 24
36 моля колкото по бързо може формулата е (X÷2)÷(x×3)=305,4
Answer:
Step-by-step explanation:
The quotient of two numbers is 305.4. Find the quotient if the divisor decreases 2 times and the divisor increases 3 times
x/y = 305.4
3x/(y/2) = 6x/y = 6*305.4 = 1832.4
Note that the question will be deleted soon because it is posted in a language other than English.
Обратите внимание, что вопрос будет удален в ближайшее время, потому что он размещен на языке, отличном от английского.
Mrs.joshi bought a saree for Rs 1750.she sold it at a profit of 4%.what would be her profit or loss percent ?
Answer: Rs 1820
Step-by-step explanation:
This is profit, thus is it a percentage increase of 4%. Thus, she sold the saree for 104% of what she bought it for, Rs 1750. Thus, simply do 1.04*1750 to get 1820.
Hope it helps <3
Simplify the following v^4*v^5*v
Answer:
v^10
Step-by-step explanation:
For this, we need to understand one important rule of exponents. For powers of like bases, you add the exponents when they are being multiplied. With this in mind let's continue.
In this problem, the base is v, each multiplied with different powers. So:
v^4 * v^5 * v = v^(4+5+1) = v^10
So the solution will be v^10.
An additional example would be 2^2 * 2^3.
For this we know it would be 2^2 * 2^3 = 2^(2+3) = 2^5 = 32.
We can verify by simply doing 2 * 2 * 2 * 2 * 2 = 32. Note both are 32, and this example shows the usefulness of exponent rules.
Hope this helps. Cheers.
Answer:
v10
Step-by-step explanation:
v^4*v^5*v=v^10
add exponents when multiplying since we have exponents 4,5, and 1
4+5+1=10
Each of four friends orders a sweatshirt from a catalog. There are 16 colors of sweatshirts, 7 of which are all cotton and 9 of which are a blend. Each one orders a different color (no repeats) at random. What is the probability that the friends order only cotton sweatshirts?
Answer:
here is your answer
Answer:hey guys just saying its 1/52
Step-by-step explanation:
a fish weighs 2 kg plus half of its weight. what is the total weight of the fish
Answer:
4kg
Step-by-step explanation:
...../...../
2kg + half of its weight
so half of its weight = 2kg
so 2kg + 2kg= 4kg the weight of the fish
Find the angle θ between the two sides of a triangle whose lengths are 5cm and 4cm , if its area is 5cm²
[tex] \Delta = \frac 1 2 a b \sin C[/tex]
[tex]\Delta=5, \quad a=5, \quad b=4[/tex]
[tex]\sin C = \dfrac{2 \Delta}{ab} = \dfrac{2 (5)}{5(4) } = \dfrac 1 2[/tex]
[tex]C=30^\circ \textrm{ or } C=150^\circ[/tex]
Answer: two possibilities, θ=30° or 150°
Which of these functions could have the graph shown below?
y
80
70-
60
50+
40+
30+
20
10
-5
-4 -3
-2 -1 0
1
2
3
4
х
O A. f(x) = 20e
O B. f(x) = 2020
O C. f(x) = 20%
O D. f(x) = e20x
Answer:
A
Step-by-step explanation:
[tex]f(x) = 20 {e}^{x} [/tex]
The function that could have the graph shown is:
f(x) = 20[tex]e^x[/tex]
Option A is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The function:
f(x) = 20[tex]e^x[/tex]
If we graph this function we get a similar graph that is shown.
The coordinates of f(x) = 20 [tex]e^x[/tex] are:
To find the coordinates, we need to plug in different values of x into the function and calculate the corresponding y-values.
For example, when x = 0, we have:
f(0) = 20e^0 = 20(1) = 20
So one coordinate on the graph is (0, 20).
Similarly, when x = 1, we have:
f(1) = 20e^1 = 20e = 20(2.71828) ≈ 54.6
So another coordinate on the graph is (1, 54.6).
We can find more coordinates by plugging in other values of x and calculating the corresponding y-values.
Now,
As x increases, the function f(x) grows exponentially, meaning the y-values will increase very rapidly.
Thus,
The function f(x) = 20[tex]e^x[/tex] could have the graph shown.
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A wheel rolling at a constant speed has a radius of 15 inches and takes 30
seconds to roll 100 feet along the ground. What is its angular velocity? Use
3.14 for (pie) , and solve to two decimal places
Answer:
152.87 degree/seconds
Step-by-step explanation:
1 rotation = Circumference of a circle = 2πr
r = 15 inches
1 rotation = 2 × 3.14 × 15
94.2 inches.
We are told in the question that it takes 30 seconds to roll 100 feet along the ground
Convert feet to inches
1 feet = 12 inches
100 feet =
100 × 12 = 1200 inches.
Hence, if
94.2 inches = 1 rotation
1200 inches = X
Cross multiply
94.2 × X = 1200 × 1
94.2X = 1200
X = 1200/94.2
X = 12.738853503 rotations
Formula for Angular velocity = Number of rotations × 2π/time in seconds
Time = 30 seconds
12.738853503 × 2 × 3.14/30
= 2.6666666667 rotations per second
Converting Angular velocity to degree per second
= 2.6666666667 × 180/ π
= 2.6666666667 × 180/3.14
= 152.86624204 degree/seconds
Approximately to 2 decimal places
= 152.87 degree/seconds
What the correct answer now
Answer:
[tex] Area = 1,309.0 in^2 [/tex]
Step-by-step explanation:
Given:
∆TUV
m < U = 22°
TV = u = 47 in
m < V = 125°
Required:
Area of ∆TUV
Solution:
Find the length of UV using the Law of Sines
[tex] \frac{t}{sin(T)} = \frac{u}{sin(U)} [/tex]
U = 22°
u = TV = 47 in
T = 180 - (125 + 22) = 33°
t = UV = ?
[tex] \frac{t}{sin(33)} = \frac{47}{sin(22)} [/tex]
Multiply both sides by sin(33)
[tex] \frac{t}{sin(33)}*sin(33) = \frac{47}{sin(22)}*sin(33) [/tex]
[tex] t = \frac{47*sin(33)}{sin(22)} [/tex]
[tex] t = 68 in [/tex] (approximated)
[tex] t = UV = 68 in [/tex]
Find the area of ∆TUV
[tex] area = \frac{1}{2}*t*u*sin(V) [/tex]
[tex] = \frac{1}{2}*68*47*sin(125) [/tex]
[tex] = \frac{68*47*sin(125)}{2} [/tex]
[tex] Area = 1,309.0 in^2 [/tex] (to nearest tenth).
how many ways can you order a hot dog with the choices below?
Answer:
8
Step-by-step explanation:
2 x 2 x 2 = 8
you have 2 choices each time, with or without
What the answer question
Answer:
TW = 3.18 yd (Approx)
Step-by-step explanation:
Given:
TV = 6 yd
∠TYW = 32°
∠TWV = 90°
Find:
TW
Computation:
Using trigonometry application.
TW / TV = Sin 32°
TW / 6 = 0.53
TW = 3.18 yd (Approx)
simplify. Remove all perfect squares from inside the square root. V180=
Answer:
6√5
Step-by-step explanation:
We have to solve the expression [tex]\sqrt{180}[/tex]
Break 180 into its factors which are in the perfect square form.
Since, 180 = 9 × 4 × 5
= 3² × 2² × 5
Therefore, [tex]\sqrt{180}=\sqrt{3^{2}\times 2^{2}\times 5}[/tex]
= [tex]\sqrt{3^2}\times \sqrt{2^{2}}\times \sqrt{5}[/tex] [Since [tex]\sqrt{ab}=\sqrt{a}\times \sqrt{b}[/tex]]
= 3 × 2 × √5
= 6√5
Therefore, solution of the given square root will be 6√5.
the point slope form of the equation of the line that passes through (-5,1 ) and (10,-7) is y +7= - 1/2 (x-10) what is the standard form of the equation for this line ?
Answer:
The standard form of the equation is y = -x/2 -2
Step-by-step explanation:
The standard form of equation of this line is expressing the line in the form;
y = mx + c
So let’s make a rearrangement to what we have at hand;
y + 7 = -1/2(x-10)
2(y + 7) = -1(x-10)
2y + 14 = -x + 10
2y = -x + 10 -14
2y = -x -4
divide through by 2
y = -x/2 -2
WILL GIVE BRAINLEST ANSWER IF ANSWERED IN THE NEXT 24 HRS Express the complex number in trigonometric form. -5i
Answer:
[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]
Step-by-step explanation:
If a complex number is z=a+ib, then the trigonometric form of complex number is
[tex]z=r(\cos \theta +i\sin \theta)[/tex]
where, [tex]r=\sqrt{a^2+b^2}[/tex] and [tex]\tan \theta=\dfrac{b}{a}[/tex], [tex]\theta[/tex] is called the argument of z, [tex]0\leq \theta\leq 2\pi[/tex].
The given complex number is -5i.
It can be rewritten as
[tex]z=0-5i[/tex]
Here, a=0 and b=-5. [tex]\theta[/tex] lies in 4th quadrant.
[tex]r=\sqrt{0^2+(-5)^2}=5[/tex]
[tex]\tan \theta=\dfrac{-5}{0}[/tex]
[tex]\tan \theta=\infty[/tex]
[tex]\theta=2\pi -\dfrac{\pi}{2}[/tex] [tex][\because \text{In 4th quadrant }\theta=2\pi-\theta][/tex]
[tex]\theta=\dfrac{3\pi}{2}[/tex]
So, the trigonometric form is
[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]
Answer:
in degrees the answer is 5 (cos 270 + i sin 270)
in radians the answer is 5 (cos (3pi/2) + i sin (3pi/2))
Step-by-step explanation:
The two lines graphed below are not parallel. How many solutions are
there to the system of equations?
Answer:
Step-by-step explanation:
Any non-parallel lines in the plane must intersect in one place; thus, there is one solution to the system of equations.
On the coordinate plane below, Point P, is located at (2,-3) and point Q is located at (-4,4). Find the distance between points, P and Q
Answer:
[tex]d = \sqrt{85}[/tex] or d ≈ 9.22
Step-by-step explanation:
Distance formula:
[tex]d = \sqrt{(2 - (-4))^2 + (-3- 4)^2} \\d = \sqrt{36+ 49}\\d = \sqrt{85} \\[/tex]
Indicate, in standard form, the equation or inequality that is shown by the graph.
Answer:
The equation is y = -x + 4
Step-by-step explanation:
This is a very trivial exercise:
The general equation of a line is given by:
y - y₁ = m(x - x₁)
where m = slope of the linear graph
From the given graph, it can be observed that the coordinate (x₁, y₁) and (x₂, y₂) are (0, 4) and (4, 0)
The slope, m = (y₂ - y₁)/(x₂ - x₁)
m = (0 - 4)/(4 - 0)
m = -4/4
m = -1
Substituting the values of (x₁, y₁) = (0, 4) and m = -1 into the general equation:
y - y₁ = m(x - x₁)
y - 4 = -1 (x - 0)
y - 4 = -x
y = -x + 4
Jack is counting days in his calendar by shading the block that represents each passing day. According to Jack’s calendar, how much time is shaded? Assume that 7 days equals 1 whole week. Check all that apply. 3 days 1 week + 3 days 1Three-sevenths weeks 1 week and 4 days 1 week and Four-sevenths of a week
Hi there,
I need help to solve the perimeter and the surface area of this shape.
Thanks!
Answer: Perimeter = 6π ≈ 18.84
Area = 15π ≈ 47.10
Step-by-step explanation:
This is a composite of a big semicircle with diameter of 10 --> radius (r) = 5
plus a medium semicircle with diameter of 6 --> r = 3
minus a small semicircle with diameter of 4 --> r = 2
Perimeter of a semicircle = [tex]\dfrac{1}{2}(2\pi r)=\pi r[/tex]
[tex]P_{big}=\pi (5)\quad =5\pi\\P_{medium}=\pi (3)\quad =3\pi\\P_{small}=\pi (2)\quad =2\pi\\P_{composite} =5\pi+3\pi -2\pi\\.\qquad \qquad =\large\boxed{6\pi}[/tex]
Area of a semicircle = [tex]\dfrac{1}{2}(\pi r^2)[/tex]
[tex]A_{big}=\dfrac{1}{2}\pi (5)^2\quad =12.5\pi\\\\A_{medium}=\dfrac{1}{2}\pi (3)^2\quad =4.5\pi\\\\A_{small}=\dfrac{1}{2}\pi (2)^2\quad =2\pi\\\\A_{composite} =12.5\pi+4.5\pi -2\pi\\\\.\qquad \qquad =\large\boxed{15\pi}[/tex]
How many solutions does this system have? y = 3 x minus 5. y = negative x + 4. one two an infinite number no solution
Answer:
One
Step-by-step explanation:
y = 3 x - 5.
y = -x + 4.
x=9/4 and y=7/4
1 solution (9/4 , 7/4)
For a system of the equation to be an Independent Consistent System, the system must have one unique solution. The system of the equation has only one solution. Thus, the correct option is A.
What is a System of equations?
Inconsistent System
For a system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.
Given the two equations y=3x -5 and y=-x+4. If the two of the equations are plotted on the graph. Then it can be observed from the graph that there is only one intersection between the two lines.
Hence, the system of the equation has only one solution. Thus, the correct option is A.
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Evaluate 3x2 - 4 when x = 2.
A. 12
B. 32
c. 2
D. 8
Answer:
8
Step-by-step explanation:
3x^2 - 4
Let x = 2
3 * 2^2 -4
Exponents first
3 *4 -4
Then multiply
12 -4
Now subtract
8
[tex]\text{Plug in and solve:}\\\\3(2)^2-4\\\\3(4)-4\\\\12-4\\\\8\\\\\boxed{\text{D). 8}}[/tex]
Need help i dont understand
Answer:
The answer is d
Step-by-step explanation:
Manuela solved the equation 3−2|0.5x+1.5|=2 for one solution. Her work is shown below. 3−2|0.5x+1.5|=2 −2|0.5x+1.5|=−1 |0.5x+1.5|=0.5 0.5x+1.5=0.5 0.5x=−1 x=−2 What is the other solution to the equation? x=−6 x=−4 x=2 x=4
Answer:
Step-by-step explanation:
We'll just work on solving both so you can see what's involved in solving an absolute value equation. Because an absolute value is a distance, we can have that distance being both to the right on the number line of the number in question or to the left. For example, from 2 on the number line, the numbers that are 5 units away are 7 and -3. Using that logic, we will simplify the equation down so we can set up the 2 basic equations needed to solve for x.
If [tex]3-2|.5x+1.5|=2[/tex] then
[tex]-2|.5x+1.5|=-1[/tex] What you need to remember here is that you cannot distribute into a set of absolute values like you would a set of parenthesis. The -2 needs to be divided away:
[tex]|.5x+1.5|=.5[/tex]
Now we can set up the 2 main equations for this which are
.5x + 1.5 = .5 and .5x + 1.5 = -.5
Knowing that an absolute value will never equal a negative number (because absolute values are distances and distances will NEVER be negative), once we remove the absolute value signs we can in fact state that the expression on the left can be equal to a negative number on the right, like in the second equation above.
Solving the first one:
.5x = -1 so
x = -2
Solving the second one:
.5x = -2 so
x = -4
We want to find the other solution of the given absolute value equation.
The other solution is x = -4
We know that:
3 - 2*|0.5*x + 1.5| = 2
It has one solution given by:
- 2*|0.5*x + 1.5| = 2 - 3 = -1
|0.5*x + 1.5| = 0.5
0.5*x + 1.5 = 0.5
0.5*x = 0.5 - 1.5 = -1
0.5 = -1/x
Then we have x = -2
To get the other solution we need to remember that an absolute value equation can be written as:
|x - a| = b
or:
(x - a) = b
(x - a) = -b
Then the other solution to our equation comes from:
|0.5*x + 1.5| = 0.5
(0.5*x + 1.5) = -0.5
0.5*x = -0.5 - 1.5 = -2
x = -2/0.5 = -4
The other solution is x = -4
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Wally rides his bicycle at an average speed of 13 miles per hour. How many miles will he travel in 4 1/2 hours? Please answer this quickly!
Answer:
58.5
Step-by-step explanation:
Distance = rate * time
so if it's 4.5 hours:
Distance = 13 mph* 4.5 hours
= 58.5 miles
Help please!! Thanks
Answer:
A
Step-by-step explanation:
First, let's label the variables:
[tex]\text{Let }x \text{ represent Kaylee's number of pens,}\\\text{Let }L \text{ represent Lou's number of pens,}\\\text{And let }I \text{ represent Ilene's number of pens.}[/tex]
The first and second sentence, Kaylee at the start has x pens. She gave half to Lou, who started out with two fewer than Kaylee.
In other words, the total Lou now has is:
[tex]L=(\frac{1}{2}x )+(x-2)[/tex]
The first term represents what Kaylee gave to Lou. The second term represents what Lou had originally (two fewer than Kaylee [x]).
Simplifying, we get:
[tex]L=\frac{3}{2}x-2[/tex]
Third sentence. Lou give half of his new total to Ilene, who started out with three fewer pens than Lou. Lou, remember, started with three fewer than Kaylee (x-2). In other words:
[tex]I=(\frac{1}{2}(\frac{3}{2}x-2) )+((x-2)-3)[/tex]
The left represents what is given to Ilene: one-third of Lou's new total. The right represents Ilene's original total: three fewer than Lou: or five fewer than Kaylee. Simplifying gives:
[tex]I=(\frac{3}{4} x-1)+(x-5)\\I=\frac{7}{4}x-6[/tex]
Finally, Ilene gives a third of this new amount to Kaylee, and Kaylee's final amount is 37. Thus:
[tex]37=x-\frac{1}{2}x+\frac{1}{3}(\frac{7}{4}x-6)[/tex]
The first term represents what Kaylee originally started with. The second term represents what she gave to Lou. And the third term represents what Ilene gave to Kaylee. Simplify:
[tex]37=\frac{1}{2}x+\frac{7}{12}x-2\\39=\frac{6}{12}x+\frac{7}{12}x \\39=\frac{13}{12}x\\ 468=13x\\x=36[/tex]