Find the inverse of the function below. When typing your answer use the "^" key (shift+6) to indicate an exponent. For example, if we have x squared (x times x) we would type x^2. f(x)= \frac{5x+1}{2-5x}The numerator of f^{-1}(x) is Answer - AnswerThe denominator of f^{-1}(x) is Answer(Answer + Answer)
Answers
Answer:
[tex]\begin{gathered} \text{ The numerator of f}^{-1}(x)\text{ is 1-2x} \\ \text{ The denominator of f}^{-1}(x)\text{ is -5(x}+1) \end{gathered}[/tex]Step-by-step explanation:
To find the inverse of a function, replace f(x) by ''y'', then replace ''y'' with and x, and every x with a ''y''. Solve for y.
[tex]\begin{gathered} f(x)=\frac{5x+1}{2-5x} \\ Replace\colon\text{ f(x)}\rightarrow y \\ y=\frac{5x+1}{2-5x} \\ Replace\colon\text{ y}\rightarrow x\text{ x}\rightarrow y \\ x=\frac{5y+1}{2-5y} \\ \text{ Solve for y.} \\ x(2-5y)=5y+1 \\ 2x-5yx=5y+1 \\ -5yx=5y+1-2x \\ -5yx-5y=1-2x \\ y(-5x-5)=1-2x \\ y=-\frac{1-2x}{5x+5} \\ y=-\frac{1-2x}{5(x+1)} \end{gathered}[/tex][tex]\begin{gathered} Replacey\colon f^{-1}(x) \\ f^{-1}(x)=-\frac{1-2x}{5(x+1)} \end{gathered}[/tex]Related Questions
What is the degree of the polynomial, 105y75+125x5-100x10?
Answers
The degree of the polynomial is the largest of these three values, which is 75
What is polynomial ?Algebraic expressions called polynomials include constants and indeterminates. Polynomials can be thought of as a type of mathematics. Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.
Simply locate the highest exponent in the formula to determine the degree of the polynomial. The degree of the polynomial is seven because it is the highest exponent above.
There are multiple variables in the polynomial. The biggest sum of ALL of the exponents for ALL of the variables in a term is the polynomial's degree.
Given that := 105[tex]y^{75} + 125^{5} - 100x^{10}[/tex]
= 105[tex]y^{75} + 125^{5} - 100x^{10}[/tex]
To find the degree of a polynomial, simply find the highest exponent in the expression. As seven is the highest exponent above, it is also the degree of the polynomial.
The polynomial has more than one variable. The degree of the polynomial is the largest sum of the exponents of ALL variables in a term.
The first term is 105[tex]y^{75}[/tex]
The degree of this term is 75
The second term is 125[tex]x^{5}[/tex]
The degree of this term is 5.
The third term is 100[tex]x^{10}[/tex]
The degree of this term is 10.
The degree of the polynomial is the largest of these three values, which is 75
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can you help me on the part Drawing the Ace of Spades please
Answers
Solution
There is just one ace of spades
Therefore, the probability of drawing the ace of spade is;
[tex]\frac{1}{52}[/tex]find the volume specified. use 3.14 as the approximate value of pi, and round your answer to the nearest tenth.find the volume of a feed bin having the shape of a right circular cylinder of radius 5 ft and height 5 ft topped by a right circular cone of the same radius and height 3 ft Draw a picture to get started.
Answers
ANSWER
The volume of the bin is 471 cubic feet
EXPLANATION;
Given that;
The radius of the cylinder is 5ft
The height of the cylinderis 5 ft]
The height of the cone s 3ft]
To find the total volume of the bin, follow the steps below
Firstly, draw the structure of the bin
Secondly, Write the formula for calculating the volume of a cone and a cylinder
[tex]\begin{gathered} \text{ The volume of a cone = }\frac{1}{3}\pi r^2h \\ \text{ The volume of a cylinder = }\pi r^2h \end{gathered}[/tex][tex]\begin{gathered} \text{ The volume of the cone = }\frac{1}{3}\pi r^2h \\ \text{ where }\pi\text{ = 3.14} \\ \text{ The volume of the cone = }\frac{1}{3}\times\text{ 3.14 }\times\text{ 5}^2\text{ }\times\text{ 3} \\ \text{ The volume of the cone = }\frac{1}{3}\times\text{ 3.14 }\times\text{ 25 }\times\text{ 3} \\ \text{ The volume of the cone }=3.14\text{ }\times\text{ 25} \\ \text{ The volume of the cone = 78.5 ft}^3 \end{gathered}[/tex][tex]\begin{gathered} \text{ The volume of the cylinder = }\pi r^2h \\ \text{ }\pi\text{ = 3.14} \\ \text{ The volume of the cylinder = 3.14 }\times\text{ 5}^2\text{ }\times\text{ 5} \\ \text{ The volume of the cylinder = 3.14 }\times\text{ 25 }\times\text{ 5} \\ \text{ The volume of the cylinder = 392.5 ft}^3 \end{gathered}[/tex]Find the volume of the bin
[tex]\begin{gathered} \text{ Volume of the bin = volume of the cone + volume of cylinder} \\ \text{ Volume of the bin = 78.5 + 392.5} \\ \text{ Volume of the bin = 471 ft}^3 \end{gathered}[/tex]Hence, the volume of the bin is 471 cubic feet
Give the digits in the hundred thousands place and the ten thousands place.803,519
Answers
Given the number
[tex]803519[/tex]To get the digits in the hundred thousand places and the ten thousand place, we will first list out the values of all the digits
The Hundred thousands place is 8
For a card trick, Barry is using 14 cards from a deck if each suit he uses had 5 numbered cards and c face cards, which expression shows how many suits he is using.
A. 14 x 5 + c
B 14 divided by (5+c)
C 14 divided by 5+ C
D 14 x (5+c)
Answers
Answer:
b
Step-by-step explanation:
I NEED HELP ASP!! Which expression is equivalent to −2(5x + 3y)?
Answers
Answer:
-10x - 6y
Step-by-step explanation:
simplify - 2(5x + 3y): - 10x - 6y
-2(5x + 3y)
Apply the distributive law: a(b + c) = ab + ac
-2(5x + 3y) = -2 · 5x - 2· 3y
simplify -2 · 5x - 2· 3y : - 10x - 6y
therefore the answer is: = -10x - 6y
what is the median? -95, -94, -93, 95, 91, -92, -89, -92, -98
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Given the set of the data:
[tex]-95,-94,-93,95,91,-92,-89,-92,-98[/tex]Arranging the data in order from the least to the greatest:
[tex]-98,-95,-94,-93,-92,-92,-89,91,95[/tex]The number of the data = 9
so, the median is the number which is in the middle
It will be number (9+1)/2 = 10/2 = 5
so, the median = -92
The equation y = 11x represents the liters of water a baseball team drinks each practice. This equation shows that after two practices, the team will have consumed 22 liters of water.
Determine the constant of proportionality.
11
22
0.18
5.5
Answers
The constant of proportionality is equal to 11.
Constant of ProportionalityThe constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship. Other names for the constant of proportionality include the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
In this question, the constant of proportionality is that value that doesn't change or represents the number of players while x represented the number of games they played.
The constant of proportionality can be solved mathematically as
[tex]y = 11x\\x = 2\\22 = 11(2)\\22 = 22\\[/tex]
The constant of proportionality is the value that makes y = 11x and it is 11.
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Determine whether the variable is qualitative or quantitative.Favorite basketball playerIs the variable qualitative or quantitative?A. The variable is quantitative because it is an attribute characteristic.B. The variable is qualitative because it is a numerical measure.C. The variable is quantitative because it is a numerical measure.D. The variable is qualitative because it is an attribute characteristic.
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We have that favorite is a characteristic. It is a qualitative data. We cannot measure it at the weight, length, and other similar variables.
Therefore, the correct option is D:
eWhat are the zeros of the function f(x) = (2x+6)(x-4)?OA. x = 6 and x = -4OB. x=-6 and x = -4OC. x=3 and x = -4OD. x=-3 and x = 4
Answers
Hello there. To solve this question, we have to remember some properties about roots of polynomials.
Given the following function:
[tex]f(x)=(2x+6)\cdot(x-4)[/tex]We want to determine its roots.
For this, we want to determine the values of x such that
[tex]f(x)=0[/tex]Then we have that
[tex](2x+6)\cdot(x-4)=0[/tex]We know that a product of two values is equal to zero if and only if one of them is equal to zero.
So we have that
[tex]2x+6=0\text{ or }x-4=0[/tex]Subtract 6 on both sides of the first equation, we get
[tex]2x=-6[/tex]Divide both sides of the equation by a factor of 2
[tex]x=-3[/tex]Now for the second equation, add 4 on both sides of the equation
[tex]x=4[/tex]Hence we say that the roots of this function are
[tex]x=-3\text{ and }x=4[/tex]This is the answer contained in the last option.
I do not know how to find the information from a word question and would love some help
Answers
Explanation
Given
From the question, we can see that the bottom of the ferris wheel is 30 feet about the ground and also while rotating, it can move to a height of 550 feet off the ground. In essence the actual height the ferris wheel can attain is
[tex]h=550-30=520[/tex]The amplitude then becomes half of the height which is
[tex]A=\frac{h}{2}=\frac{520}{2}=260[/tex]The vertical shift the Ferris wheel undergoes becomes the sum of the amplitude and its distance above the ground.
[tex]D=260+30=290[/tex]Since it takes the Ferris wheel 15 minutes to move from bottom to top, it will take it twice that to complete one revolution which will be its period.
[tex]T=2\times15mins=30[/tex]Therefore, the frequency B, becomes;
[tex]B=\frac{2\pi}{T}=\frac{2\pi}{30}=\frac{\pi}{15}[/tex]We can then place in the above parameters to form the equation.
[tex]y=Acos(B(t+C))+D\Rightarrow260cos(\frac{\pi}{15}(t+C)+290[/tex]The last missing parameter is the phase shift C. At time t =0, the function (y) has a position at 30. Therefore,
[tex]\begin{gathered} 30=260cos(\frac{\pi}{15}C)+290 \\ 260cos(\frac{\pi}{15}C)=-290+30 \\ 260cos(\frac{\pi}{15}C)=-260 \\ divide\text{ both sides by 260} \\ \frac{\begin{equation*}260cos(\frac{\pi}{15}C)\end{equation*}}{260}=\frac{-260}{260} \\ cos(\frac{\pi}{15}C)=-1 \\ \frac{\pi}{15}C=cos^{-1}(-1) \\ \frac{\pi}{15}C=\pi \\ C=\frac{15\pi}{\pi} \\ C=15 \end{gathered}[/tex]Therefore, the function y becomes
Answer:
[tex]y=260cos(\frac{\pi}{15}(t+15)+290[/tex]The stemplot below displays the grades (out of 30) that 26 students received on a quiz.
A stemplot titled quiz grades has values 12, 14, 15, 16, 20, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 28, 28, 29, 29, 30.
Which of the following boxplots correctly displays the distribution of quiz grades?
Answers
If a stemplot as shown in the attachments attached alongside the question statement, display the grades (out of 30) that 26 students received on a quiz, and has values [12, 14, 15, 16, 20, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 28, 28, 29, 29, 30], then the boxplot (A) correctly displays the distribution of quiz grades.
As per the question statement, a stemplot as shown in the attachments attached alongside the question statement, display the grades (out of 30) that 26 students received on a quiz, and has values [12, 14, 15, 16, 20, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 28, 28, 29, 29, 30].
We are required to determine which one of the four boxplots provided in the attachments correctly displays the distribution of quiz grades.
To solve this question, first let us observe the distribution of the grades, where the grade 13, 17, 18, 19, 20 and 21 are missing. Hence, the set is a discontinuous one.
Looking at options (B) and (D), these boxplots have a straight continuous line from 12 upto 30, which means that the grades 13, 17, 18, 19, 20 and 21 are also included in the set. This is false, and hence, options (B) and (D) cannot be the correct answers.
Coming to Option (C), it has a continuous line from 15 to 30, which means, the grades [17, 18, 19, 20 and 21] are also included in the set, and this is also not true. Hence, option (C) is also not our correct answer.
Finally coming to option (A), It has four individual dots over 12, 14, 15 and 16, and then, a gap, and a continuous line from 20 to 30 after the gap. From our set, we can observe that, 12, 14, 15 and 16 are in-fact present in the set, each of them having occurrence once only, and thus the four individual dots over 12, 14, 15 and 16 correctly addresses this situation. Also, every number between 22 and 30 are present in the set, and the numbers of (23, 24, 25, 26 and 27) have the most occurrences, which the boxes on top of (23 - 27) again correctly address.
Hence, our correct answer is option (A).
Stemplot: In Statistics, a stem and leaf plot, or a stem plot, is a technique used to classify discrete or continuous variables, and used to organize data as they are collected. Since it looks something like a bar graph, and each number in the data is broken down into a stem and a leaf, it gets the name of Stemplot.Boxplot: In Statistics, a boxplot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum of a set of observations, and the name "box plot" comes from the fact that the graph looks like a rectangle with lines extending from the top and bottom.To learn more about Stemplots and Boxplots, click on the link below.
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Marco is driving to the Grand Canyon his distance from the Grand Canyon decreases 150 miles every three hours after four hours his distance from the Grand Canyon is 200 Mi Marcos distance from the Grand Canyon in Miles Y is a function of the numbers of the hours he drives what is the initial value fine markers distance from the Grand Canyon when he starts to drive
Answers
Answer:
-50
Step-by-step explanation:
The Rate of change is -50 and not 50. Don't get mixed.
Use equation below to find v, if u = 18, a=6, and t = 4. v=utat
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The given equation is
[tex]v=u\cdot t\cdot a\cdot t[/tex]Where, u=18, a=6, and t=4. Replacing these values, we have
[tex]v=18\cdot4\cdot6\cdot4=1,728[/tex]Therefore, the answer is 1,728.What is the equation for the translation of x2 + y² = 64 three units to the left and two units down
(x - 3)² + (y-2)² = 64
(x+3)2 + (y + 2)2 = 64
(x-3)² + (y + 2)² = 64
(x+3)² + (y-2)² = 64
Answers
The equation for the translation of [tex]x^{2} +y^{2}=64[/tex], three units to the left and two units down is option (b) [tex](x+3)^2+(y+2)^2=25[/tex]
The equation is [tex]x^{2} +y^{2}=64[/tex]
The standard form of the circle
[tex](x-h)^2+(y-k)^2=r^{2}[/tex]
Where r is the radius of the circle
(h,k) are the coordinates of the center of the circle.
The equation is [tex]x^{2} +y^{2}=64[/tex]
The center is (0,0)
Here the circle translated three units to the left
Therefore h = -3
The circle is translated two units down
k = -2
Substitute the values in the standard form of the circle
[tex](x--3)^{2}+(y--2)^{2}=25[/tex]
[tex](x+3)^2+(y+2)^2=25[/tex]
Hence, the equation for the translation of [tex]x^{2} +y^{2}=64[/tex], three units to the left and two units down is option (b) [tex](x+3)^2+(y+2)^2=25[/tex]
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Shannon's bicycle travels 50 feet for every 3 pedal turn. How many pedal turns are needed to travel one mile (1 mile=5280 feet)?
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Shannon's bicycle travels 50 feet for 3 pedal turn
He travels
[tex]50ft=3\text{ pedal turn}[/tex]Converting 1 mile to feet
[tex]1\text{mile}=5280ft[/tex]The number of pedal turns needed to travel a mile is
[tex]\begin{gathered} 50ft=3\text{ pedal turn} \\ For\text{ 1mile (5280ft)=}\frac{5280\times3}{50}=3168\text{ pedal turns} \end{gathered}[/tex]Hence, the answer is 3168 pedal turns
Gravel is piled in the shape of a cone. The circumference of the base is 221 ft. The slant height is 43 ft. Find the volume of gravel
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Answer:
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeee please
Answers
Answer:c
Step-by-step explanation:
Lacey’s bank account shows a balance of –$45.10. The next day, she deposits $65.00 and uses her debit card for a purchase of $23.75. What is her new balance?
Answers
Lacey's new balance in the account is -$3.85.
What is account balance?
The amount of funds held in a financial institution, for example, a savings or checks account, at any particular time is known as the account balance. The net amount, which includes all debits and credits, is always the account balance.In order for a company's accounts to balance, debits and credits must be employed in the bookkeeping process. Credits raise liability, revenue, or equity accounts while decreasing asset or expenditure accounts. Credits operate in reverse.Lacey’s bank account balance = –$45.10
she deposits = $65.00
Debit card for a purchase = $23.75
Updated balance = –$45.10+$65.00-$23.75= -$3.85
Lacey's new balance in the account is -$3.85.
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for the line of fit p = -26t + 5,649 , where t is the number of years since 1990 , what is the residual of the data point at t = 5?
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According to the problem, the equation of the line that best fit is
[tex]p=-26t+5649[/tex]To find the population when t = 5, we just have to evaluate the expression.
[tex]\begin{gathered} p=-26\cdot5+5649=-130+5649 \\ p=5519 \end{gathered}[/tex]Note that this value (p=5519) is different from the value assigned in the given table. In this way, the residual refers to the difference between these values.
[tex]r=5530-5519=11[/tex]It's important to know that the residual r=11 is positive because the value shown in the table (empirical data) is greater than the resulting value from the equation.
Therefore, the residual is 11.GI = 6, HI = 8, DT = 12, what is IE?a.12b.16c.8d.4
Answers
Since both chords passes through the point I the should be equal.
Now we know that GI=6 and HI=8, then GH=14; hence DE have to be equal to 14 too.
From this we conclude that IE should be 4.
What is the ratio of the areas of ΔABC to ΔA'B'C' ?
Answers
The first step is to find the scale factor relating ABC to A'B'C'. Since they are dilated, ABC is similar to A'B'C'. This means that the ratios of their corresponding sides are equal. Thus,
AB/A'B' = BC/B'C' = AC/A'C'
From the information given,
AB = 7
A'B' = 28
Thus,
ratio of ABC to A'B'C' = 7/28 = 1/4
Ratio of area of ABC to A'B'C' = (1/4)^2
Ratio of area of ABC to A'B'C' = 1/16
Graphthe line with slope 2/5 and y-intercept -3.
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1) As the line has a slope m=2/5 and a y-intercept = -3
Then we can write y=2/5x -3
2) Now let's plot that, setting a table with at least 3 values for that
x | y
0 -3
-1 -3.4
2 -2.2
With these points, we can trace a line.
Which of the following quadratic functions has a graph that opens downward? Check all that apply. A v=Bx2- 8x– 13 B. v= - (3+x? e. v=zx2 - 13x+5 O d. v=2r-
Answers
Ok, so
Remember that:
For any quadratic equation of the form:
[tex]y=ax^2+bx+c[/tex]- If the leading coefficient is greater than zero, the parabola opens upward, and
- If the leading coefficient is less than zero, the parabola opens downward.
So, here we have the following functions:
[tex]v=\frac{1}{3}x^2-8x-13[/tex]The leading coefficient is greater than zero, so this parabola opens upward.
Option B:
[tex]\begin{gathered} v=-(3+x^2) \\ v=-x^2-3 \end{gathered}[/tex]The leading coefficient is less than zero, so this parabola opens downward.
Option C:
[tex]v=\frac{2}{3}x^2-13x+5[/tex]The leading coefficient is greater than zero, so this parabola opens upward.
Option D:
[tex]v=2x-x^2[/tex]The leading coefficient is less than zero, so this parabola opens downward.
Therefore, the correct options are B and D.
0.0000235 in scientific notation
Answers
Answer:
2.35 × 10⁻⁵
Step-by-step explanation:
Scientific notation (also called "Standard form") is written in the form
a × 10ⁿ where 1 ≤ a < 10 and n is any positive or negative whole number.
To convert a number into scientific notation, move the decimal point to the left or right until there is one digit to the left of the decimal point.
The number of times you have moved the decimal point is the power of 10 (the value of n).
If the decimal point has moved to the left, n is positive.If the decimal point has moved to the right, n is negative.To convert 0.0000235 to scientific notation:
Move the decimal point 5 places to the right so that a = 2.35. As the decimal point has been moved 5 places the right, n = -5.Therefore, 0.0000235 = 2.35 × 10⁻⁵.
Estimate the sum or difference
76.81 + 2.17
Answers
The estimated sum of 76.81 and 2.17 is 79.
The first number given to us is 76.81.
The second number given to us is 2.17.
We need to find the estimated sum of the two numbers.
To find the estimated sum, we will round off the numbers to the nearest tenth.
Rounding a number implies simplifying it while retaining its value close to what it was. The end output is less precise but more usable.
After rounding, the first number becomes 76.8.
After rounding, the second number becomes 2.2.
The estimated sum is the addition of these rounded numbers.
The estimated sum is 76.8 + 2.2 = 79.
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create a non linear function that has a solution at (-2,6). Include a calculation that shows why this is a solution to your function.
Answers
In order to find a nonlinear function that has a solution at (-2,6) we need to choose first a parent function that is no linear in this case, we will use
[tex]y=x^2[/tex]in order to know that the solution is (-2, 6) so if I introduce the value of x coordinate which is -2 in the function we need to have as result 6
In this case, taken the parent function above and in order to have the desired result we have the next calculations
[tex]\begin{gathered} 6=(-2)^2+2 \\ 6=4+2 \\ 6=6 \end{gathered}[/tex]so the function that has a solution (-2,6) and is no linear is
[tex]y=x^2+2[/tex]Find the slope of the line that passes through the following points . Simplify your answer .
(-10, 10) and (-9, -10)
Answers
Answer:
-20 is the slope
Step-by-step explanation:
Using the slope formula y1-y2/x2-x1,
you get the slope of -20
Answer: -20/1
Step-by-step explanation:
1) Use the slope formula
y1-y
--------
x1-x
2) Substitute the numbers
-10-10
------
-9-(-10)
3) Solve
-20
------
1
-20/1
In a company, %90 of the workers are men . If 500 people work for the company who aren't , how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
Answers
90%=500x9=4500
4500+500=5000
or
90:10
9:1
4500:500=5000
5000 people
If the same number is added to the nunerator of 12/13 and subtract from the denominator, the new fraction is equal to 3/2. What is the number?
Answers
Answer:
x = 3
Step-by-step explanation:
If the same number is added to the numerator of 12/13 and subtract from the denominator, the new fraction is equal to 3/2. What is the number?
[tex]\frac{12+x}{13-x} =\frac{3}{2}[/tex]
multiply both sides by 13-x:
[tex](13-x)\frac{12+x}{13-x} =\frac{3}{2}(13-x)\\\\12+x = \frac{3(13-x)}{2} \\\\12+x = \frac{39-3x}{2} \\[/tex]
multiply both sides by 2:
[tex]2(12+x) = (\frac{39-3x}{2})\\\\24+2x = 39-3x[/tex]
subtract 24 from both sides:
24 + 2x - 24 = 39 - 3x - 24
2x = 15 - 3x
add 3 x to both sides:
2x + 3x = 15 - 3x + 3x
5x = 15
divide both sides by 5:
5x/5 = 15/5
x = 3
check:
[tex]\frac{12+x}{13-x} =\frac{3}{2}\\\\\frac{12+3}{13-3} =\frac{3}{2}\\\\\frac{15}{10} =\frac{3}{2}\\\\\frac{3}{2} =\frac{3}{2}[/tex]
