The correct values that create ordered pairs that are solutions to the solutions to the equation 3x - 5y = 20 are,
⇒ y₁ = - 1
⇒ x₂ = 10
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The equation is,
⇒ 3x - 5y = 20
Now, If (5, y₁) is the solution of above equation, then it satisfy the equation.
⇒ 3x - 5y = 20
⇒ 3 × 5 - 5y₁ = 20
⇒ 15 - 5y₁ = 20
⇒ 15 - 20 = 5y₁
⇒ - 5 = 5y₁
⇒ y₁ = - 1
And, If (x₂, 2) is the solution of above equation, then it satisfy the equation.
⇒ 3x₂ - 5y = 20
⇒ 3x₂ - 5×2 = 20
⇒ 3x₂ - 10 = 20
⇒ 3x₂ = 20 + 10
⇒ 3x₂ = 30
⇒ x₂ = 10
Thus, The correct values that create ordered pairs that are solutions to the solutions to the equation are,
⇒ y₁ = - 1
⇒ x₂ = 10
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A Ferris wheel is 45 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. How many minutes of the ride are spent higher than 35 meters above the ground?
If A Ferris wheel is 45 meters in diameter and boarded from a platform that is 1 meters above the ground. The number of minutes of the ride that are spent higher than 35 meters above the ground is: 2minutes.
How to find the number of minutes?Ferris wheel radius = 45/2
Ferris wheel radius = 22.5 meters
When the Ferris wheel is at the 12 o'clock position, the center of the wheel is at a height of 22.5 + 1 = 23.5 meters above the ground.
When the Ferris wheel is at the 3 o'clock position, the highest point on the wheel is at a height of (22.5 + 1) + (22.5) = 46 meters above the ground.
So the time spent higher than 35 meters is the time spent between 3 o'clock and 12 o'clock positions, which is a quarter of the full revolution time is:
Time spent higher than 35 meters = 8/4
Time spent higher than 35 meters = 2 minutes
Therefore the time spent higher than 35 meters is 2 minutes.
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List the members of the set {2< x < 5}
Answer:
3 and 4 or {3,4}
Step-by-step explanation:
3 and 4 are the only numbers greater than 2, but less than 5.
Ainsley works for the owners of a bookstore. Her starting salary is $24,500, and she gets a 3% raise each year.
a. Write an equation in function notation to represent Ainsley's salary as a function of the number of years she has been working at the bookstore.
b. What will Ainsley's salary be when she begins her fourth year working at the bookstore? Show your work.
The equation in function notation to represent Ainsley's salary is y = $24,500 * (1 + 0.03x) and Ainsley's salary will be $26,940 when she begins her fourth year working at the bookstore.
What is an equation in function notation?
An equation involving x and y, which is also a function, can be written in the form y = “some expression involving x”; that is, y = f ( x). This last expression is read as “ y equals f of x” and means that y is a function of x.
a. Let y be Ainsley's salary after x years of working at the bookstore.
The equation representing Ainsley's salary as a function of the number of years she has been working at the bookstore is y = $24,500 * (1 + 0.03x).
b. To find Ainsley's salary when she begins her fourth year working at the bookstore, we need to plug in x = 3 into the equation:
y = $24,500 * (1 + 0.03x)
y = $24,500 * (1 + 0.03 * 3)
y = $24,500 * 1.09
y = $26,940.
Hence, The equation in function notation to represent Ainsley's salary is y = $24,500 * (1 + 0.03x) and Ainsley's salary will be $26,940 when she begins her fourth year working at the bookstore.
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A phone company has a monthly cellular data plan where a customer pays a flat monthly fee of $40 and then $0.50 per megabyte (MB) of data used on the phone. Examine the problem and identify the variables in the situation.
The slope and the intercept of the linear function in this problem are given as follows:
Slope of $0.5, representing the cost per MB.Intercept of $40, representing the flat monthly fee.Hence the variables are given as follows:
Input variable x: number of MB of data used.Output variable y: total cost of the plan.What is a linear function?The linear function in slope-intercept format is given as follows:
y = mx + b
In which:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the intercept, representing the initial value assumed by the output variable.A phone company has a monthly cellular data plan where a customer pays a flat monthly fee of $40 and then $0.50 per megabyte (MB) of data used on the phone, hence the parameters are given as follows:
b = 40, m = 0.5.
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find n for which (5/6)^n is less than 0.00001
The n will be 12.175074 for which (5/6)^n is less than 0.00001.
We start by converting the target number to scientific notation: 0.00001 = 1 x 10^-5
Next, we take the logarithm base (5/6) of both sides:
n = log base (5/6) of (1 x 10^-5)
Using logarithm rules, we can simplify this to:
n = log base (5/6) of 1 - log base (5/6) of 10^-5
Using logarithm tables or a calculator, we find that:
log base (5/6) of 1 = 0
log base (5/6) of 10^-5 = -12.175074
So,
n = 0 - (-12.175074) = 12.175074
Therefore, n = 12.175074.
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how many grams of carbs in an ounce
One ounce of food contains average about 28 grams of carbs.
One of the three macronutrients that the body needs for energy, carbohydrates can be found in a wide variety of foods. Sugar, starch, and fiber are the three elements that make up carbohydrates. Weight is measured in ounces, which weigh 28.35 grams. As a result, one ounce of food contains about 28 grams of carbs. Carbohydrates are crucial for supplying the body with the 4 calories per gram of energy it needs to function, fuel physical activity, and help with digestion. Foods like fruits, vegetables, grains, nuts, and dairy products all naturally include ounces of carbs. It is crucial to remember that there are several kinds of carbs, some of which are healthier than others.
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The complete question is
How many grams of carbs in an ounce of food ?
Find the prelmage of the point (4, 3) under the given transformation.
A transformation T: (x,y) → (x-2, y + 3)
The prelmage of the point (4, 3) under the transformation is
How to determine the preimageFrom the question, we have the following parameters that can be used in our computation:
Image = (4, 3)
Transformation: (x,y) → (x-2, y + 3)
Using the above as a guide, we have the following:
(x-2, y + 3) = (4, 3)
So, we have
x - 2 = 4
y + 3 = 3
Evaluate
(x, y) = (6, 0)
Hence, the preimage is (6, 0)
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Use the graph that shows the solution f(x) = g(x)
F(x) = x^2 + 4x +2
G(x) (1/2)^2 + 1
What is the solution to f(x) = G(x)
A -1
B 0
C 2
D 3
The solution of both the functions, f(x) = g(x) = 2, is option(c).
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealised relationship between two changing quantities.
Given two functions,
f(x) = x² + 4x + 2
g(x) = [tex](1/2)^{x} + 1[/tex]
observe the graphs below
We are asked to find the solution of f(x) = g(x)
The solution that satisfies both functions is the intersecting point of both graphs.
From the graph, it is observed as (0,2)
Hence when x =0, the solution of both the functions f(x) = g(x) = 2, which is option(c).
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Mr. Anderson and Mrs. Brown both recorded the number of push-ups done by students in their class. They made line plots to display the data.
Select whether the value of each statistics is greater for Mr. Anderson's class, equal in both, or greater in Mrs. Brown's class based on the line plots.
1. Number of students who did push-ups :
2. Maximum number of push-ups :
3. Mean number of push-ups :
There were 37 pupils that completed push-ups. The maximum number of push-ups allowed is 32.
What is line plot?A line chart, also known as a curve chart, is a type of chart that presents information as a succession of data points called "markers" that are connected by straight line segments. It is a simple form of chart that is used in many disciplines. A line plot is a linear graph that displays data frequency distributions along a number line. It is useful for analyzing data with a single specified value. Line plots are sometimes known as dot plots. A line plot depicting the distance traveled by 17 turtles in one hour is shown below (we know it is 17 turtles because there are 17 dots on the line plot).
Here,
Mr. Anderson's class=20
Mrs. Brown's class=17
Number of students who did push-ups is 37. Maximum number of push-ups is 32.
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flinn started a campfire while his friends collected firewood. the wood pile had 5 sticks left over from yesterday, and flinn's friends added 7 sticks to the pile every minute. flinn took 3 sticks from the wood pile every minute and added tihem to the fire. how many minutes will it take the group to make a wood pile of 45 sticks?
It will take the group 10 minutes to make a wood pile of 45 sticks.
A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.
Ax+By=C is the typical form for linear equations in two variables. 2x+3y=5, for example, is a simple linear equation. It is rather simple to get both intercepts when an equation is stated in this way (x and y).
Let's call the number of minutes passed "t".
The total number of sticks in the wood pile after t minutes is given by the equation:
Woodpile = 5 + 7t - 3t = 5 + 4t
We want to find the time t it takes for the wood pile to have 45 sticks:
45 = 5 + 4t
Subtract 5 from both sides:
40 = 4t
Divide both sides by 4:
t = 10
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for what value(s) of a does the system have nontrivial solutions?
This equation has complex solutions and that means the system has no nontrivial solutions for real value of lambda.
[tex]\lambda = \frac{-6±\sqrt{-164} }{4} \\[/tex]
Now, According to the question:
Nontrivial Solutions of a System:
System of equations has a form:
AX = 0, X = (x , y, z)
System of equations has a nontrivial solutions if a determinant of a system is zero. If the determinant is not zero than the matrix has inverse and a nontrivial solution x=0. This can be said differently: The homogeneous system has the trivial solution if rank of A in the row reduced form of matrix is equal to the number of unknown variables. If rank of A is less than the number of variables then the system has nontrivial solutions.
λx + 2y + z = 0
x + 5y + 2z = 0
3x - λy + z= 0
So, we calculate and determinant :
[tex]\left[\begin{array}{ccc}\lambda&2&-1\\1&5&2\\3&-\lambda&1\end{array}\right][/tex] [tex]= \lambda det\left[\begin{array}{ccc}5&2\\-\lambda&1\end{array}\right][/tex] [tex]-2det\left[\begin{array}{ccc}1&2\\3&1\end{array}\right][/tex] [tex]det\left[\begin{array}{ccc}1&5\\3&-\lambda\end{array}\right][/tex]
[tex]=2\lambda^2+6\lambda+25=0[/tex]
This equation has complex solutions and that means the system has no nontrivial solutions for real value of lambda.
[tex]\lambda = \frac{-6±\sqrt{-164} }{4} \\[/tex]
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The given question is incomplete, complete question is :
For which values of ? does the following system have nontrivial solutions
λx + 2y + z = 0
x + 5y + 2z = 0
3x - λy + z= 0
We are going to fit together the 3 shapes below at point b
Will ABC make a straight line (YES or NO)?
Explain your answer
Answer:
ABC won't make a straight line.
Step-by-step explanation:
The sum of the angles is equal to 190°, which is greater than 180° (the measure of the straight angle).
Answer:
NO
Step-by-step explanation:
if the 3 shapes are placed together at point B to form ∠ ABC
if ABC make a straight line then the sum of the 3 vertices = 180°
63° + 95° + 32° = 190° ≠ 180°
then
ABC is not a straight line
if a1 = 3 and an = 4an - 1 - 4 then find the value of a3
Answer:
the value of a3 is 39.
Step-by-step explanation:
The given equation is a recursive formula for the sequence a(n) = 4a(n-1) - 1 - 4. This means that a(n) is defined in terms of the previous term in the sequence, a(n-1).
Given that a1 = 3, we can use this as the starting point and apply the recursive formula repeatedly to find the value of a3.
a2 = 4a1 - 1 - 4 = 4(3) - 1 - 4 = 11
a3 = 4a2 - 1 - 4 = 4(11) - 1 - 4 = 39
So the value of a3 is 39.
Answer:
28
Explanation:
Given that a1 = 3 and an = 4an-1 - 4
to find a3 we can substitute the value of a3 in terms of a2 and a1.
a3 = 4a2 - 4
and a2 = 4a1 - 4
substituting a2 and a1 in terms of their values we get
a3 = 4(4a1 - 4) - 4
substituting the given value of a1 we get
a3 = 4(4*3 - 4) - 4
a3 = 4(8) - 4 = 32 - 4 = 28
So the value of a3 is 28.
what does the entry of 1.00 indicate on the diagonal of the matrix?
Entry of 1.00 in the diagonal of the matrix indicate that it is a correlation matrix .
In the correlation matrix entries in the diagonal is equal to 1.00.In the table each random variable [tex]A_{i}[/tex] is correlated to the random variable [tex]A_{j}[/tex].They are related in the manner of value of A₁ : A₂ is same as the A₂ : A₁.For example :
A₁ A₂ A₃ A₄ A₅
A₁ 1
A₂ 2 1
A₃ 3 4 1
A₄ 5 6 7 1
A₅ 8 9 10 11 1
Diagonal values is always equal to 1 as the relation between A₁ to A₁ is always equal to one.
Therefore, the entry of one on the diagonal of the given matrix represents it is a correlation matrix.
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79% of 8400 + 66.66% of 4800 = 120% of 7200+ x% of 4784. what is the value of x?
(a) 33.33 (b) 25 (c) 11.11 (d) 20.13
The value of x = 25 % (option b) in 79% of 8400 + 66.66% of 4800 = 120% of 7200+ x% of 4784. by converting the percentages.
79% of 8400 = ( 79/100) x 8400
= 6636
66.66% of 4800 = (66.66/100)x4800
= 3199.68
120% of 7200 = (120/100)x7200
= 8640
x% of 4784 = (x/100) x 4784
we are given that, 79% of 8400 + 66.66% of 4800 = 120% of 7200+ x% of 4784. what is the value of x :
therefore, 6636 + 3199.68 = 8646 + (x/100) x 4784
(x/100) x 4784 = 6636 + 3199.68 - 8646
= 1189.68
(x/100) = 1189.68/4784
= 0.248
x = 0.248 x 100
therefore , the value of x is equals to 24.8 % or 0.248 which is approximated to 25 % that is option (b)
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3^-1 divided by 3^4 equals
3^-1 divided by 3^4 equals is 0.00411522633
What are fractions?An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters. There are three main fraction kinds in mathematics. They come in three varieties: proper fractions, incorrect fractions, and mixed fractions. Numerator and denominator terms are known as fractions. We define its types in light of these two words. There are seven different types of fractions: equivalent fractions, like fractions, mixed fractions, appropriate fractions, and fractions with the same numerator.Thus,
3^-1 divided by 3^4 equals is
0.00411522633
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The fraction of exponents 3⁻¹ divided by 3⁴ equals = 243.
What are fractions?An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters. There are three main fraction kinds in mathematics.
They come in three varieties: proper fractions, incorrect fractions, and mixed fractions. Numerator and denominator terms are known as fractions. We define its types in light of these two words. There are seven different types of fractions: equivalent fractions, like fractions, mixed fractions, appropriate fractions, and fractions with the same numerator.
Thus,
3-1 divided by 3^4 equals is
We know when base are same in division, we can factor the abse and subtract the exponent
[tex]3^{(4 -(-1))}[/tex]
= [tex]3^5[/tex]
= 243
Thus, 3⁻¹divided by 3⁴ equals = 243
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evaluate the integral. 1 (x2 4)e−x dx 0
After evaluating the integral of equation is ( x ^2+4)×e−x dx
=ex ^2+4e−dx
There are occasions when it is possible to perform an apparently difficult piece of integration
by first making a substitution. This has the effect of changing the variable and the integrand.
When dealing with definite integrals, the limits of integration can also change. In this unit we
will meet several examples of integrals where it is appropriate to make a substitution.
(x^2 + 4)e−x dx = 0
(x ^2+4)×e−x dx
Multiply the terms
e(x ^2+4)−x dx
Multiply the terms
Evaluate
x dx
Multiply the terms x^ 1+1 d
Add the terms
x ^2d
Multiply the terms dx ^2
e(x ^2+4)−dx ^2
Simplify
e(x ^2 +4)
Apply the distributive property
ex ^2+e×4
Multiply the terms
ex^ 2+4e
ex ^2+4e−dx ^2
After evaluating the integral of equation is(x ^2+4)×e−x dx =ex ^2+4e−dx ^2
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What proportion could you use to find the value of x?
A. 3/11=x/11
B. 3/x=x/11
C. 3+11/x=3/x
D. 11/x=x/11-3
The correct option: B. 3/x=x/11. is the proportion used to determine the the value of x.
Define the term proportion?Relationships among two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, each variable is consistently equal to the other's constant value. This "constant of proportionality" is the name of this constant.For the stated question:
The pair of sides x and 11 : as well as 3 and x are used to find the proportion.
Thus,
3/x = x/11
It is the correct relation to find the value of x.
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find the measure of each angle indicated
Answer:
90
Step-by-step explanation:
total is 360
so 360-120-2*75 =90
The ratio of runners to walkers in the fund raiser was 6 to 1. If there were 10 walkers, how many runners were there?
Answer:
If the ratio of runners to walkers in the fund raiser was 6 to 1, and there were 10 walkers, then there would have been 60 runners.
Answer:
60 runners
Step-by-step explanation:
1x10=10
6x10-60
a study of 1000 randomly selected flights of a major airline showed that 769 of the flights arrived on time. what is the probability of a flight will not arrive on time?
The probability of a flight will not arrive on time is 231/1000
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
Probability requested is equivalent to:
Flights arrive on time= 769
Total flights = 1000
P(arrive on time) = Flights arrive on time / Total flights
P(arrive on time) = 769/1000
P (not arrive on time) = 1 - 769/1000
P (not arrive on time) = (1000 - 769)/1000
P (not arrive on time) = 231/1000
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Please help me I’m desperate:(
Sammy's Bulk Store offers better buy.
The graph is for C = 0.4n.
How to determine which store offers the better buy for bottled water?A unit rate is defined as the rate for one of something. For example, if 10 oranges cost $50, the unit rate will be $50/10 = $5 i.e. $5 for one orange.
PART 1
In order to determine which store offers the better buy for bottled water, we need to calculated the unit rate for each store. That is:
Unit rate = price / number of items
In Value Market, $2.99 for 24 bottles:
Unit rate = $2.99/24 = $0.12
Sammy's Bulk Store, $3.96 for 36 bottles:
Unit rate = $3.96/36 = $0.11
Thus, Sammy's Bulk Store offers better buy
PART 2
For Hot dogs:
In Value Market, $3.19 for a pack of 8:
Unit rate = $3.19/8 = $0.4
C = 0.4n
Sammy's Bulk Store, $54.40 for a pack at 12:
Unit rate = $4.49/12 = $0.37
C = 0.37n
From the graph, we have point C = 4 and n = 10. Thus:
unit rate = C/n = 4/10 = 0.4
Thus, the graph is for C = 0.4n
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you are in charge of the cake for a child's birthday. you have decided the cake will have one candle for each year of their total age. they will only be able to blow out the tallest of the candles. count how many candles are tallest.
So normally, the way i am doing so is by moving from each place of the array comparing each other with two for cycles, the second cycle will count the iterate numbers, some people use Math.max imported function.
int birthdayCakeCandles(vector<int> candles) {
int count = 0;
int max = 0;
for(size_t i = 0; i < candles.size() ; i++)
{
int num = candles[i];
if (num > max)
{
max = num.
count = 1.
} else if (max == num)
{
count++.
}
}
return count.
}
This should be much clear, iterate through the array find max if max already exists again increase count, if some other element greater than max set it to max and reset count to 1.
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Factorise the following:
2x²-6x
Answer:
Step-by-step explanation:
5. Which of the following are empty sets?
(a) {0}
(b) {x: x is an integer and 2x - 1 = 10}
(c) (even prime numbers)
(d) {even factors of 21} -) (even numbers between 2 and 5)
The terms empty set, null set, and void set are all used to describe a set that is empty of any elements.
What is meant by empty sets?The empty set is the only set in mathematics that possesses no items; its size or cardinality is 0. While in other theories, its existence can be inferred, some axiomatic set theories guarantee the presence of the empty set by introducing an axiom of empty set.
An empty set is a set that contains no elements and can be represented by the symbol, which indicates that it is empty of elements. It has a definite number of elements since the finite set contains a countable number of items and the empty set has none. An empty set is a finite set since it has a cardinality of zero.
Therefore, the correct answer is option (c) (even prime numbers).
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On a piece paper, graph f(x)=2 x (0.5)^x. Then determine which answer choice matches the graph you drew.
For given function, Graph is provided in image.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
Graph for function f(x)=2*(0.5)^x is provided in image.
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Sue runs the 100-yd dash in 11.9 s, or
8.4 yd/s. If she could lower her time by
0.5 s, would she be better than average
for her age, which is 8.5 yd/s?
She needs to lower her head by 190 seconds by 0.5 seconds in order to go more quickly than the age-appropriate speed of 8.5 yards per second.
what is distance ?Distance is the broad, directionless movement of a moving object. Distance can be characterized as the amount of territory an object has covered, regardless of something like the originating or ending location. Distance is defined as the extent or size of the difference between two places. The space between two positions and the distance traveled between them are not the same thing, it should be emphasized. The distance traveled is the entire length of a path that connects two places. Distance is the actual travel distance of a body. It is also known as path length. For instance, OP = 360 m would be the length of the path for an object traveling from point O to point P.
given
V = D/t = 100/9.8 = 10.20 yd/sec is the speed with D = 100 yds, t = 9.8 s.
Convert the distance in yards for d = 100 meters, 1 yd/0.9144 m = 109.36 yds (1 yd = 0.9144 m d = 100 meters)
t=d/V=109.36 yards/10.20 yards per second = 10.72
The sprinter will finish the 100.0 meters in 10.72 seconds.
The sprinter's velocity is given by V = (10.20 yards per second)(0.9144 meters per yard) = 9.3 m/s.
Running 1.80 km in T = (1.80km * 1000m/1km)/9.33m/s will take 190 seconds.
She needs to lower her head by 190 seconds by 0.5 seconds in order to go more quickly than the age-appropriate speed of 8.5 yards per second.
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For each value of w determine whether it is a solution to 53=9w-1
-10
9
6
-1
Answer:
Hi.....Sorry bro...I can't understand...My bad, I am only 12 years old..
Answer:
6
Step by Step explanation:
If you replace the w with 6 you get 53.
How to Convert Grams to Moles and Vice Versa
The total atomic masses of a compound's constituent atoms, expressed in grams per mole, make up the compound's molar mass.
What is the difference between Grams and Moles?You must adhere to the grams to moles formula in order to accurately calculate the number of moles, n, of a substance with a given mass, m, (in grams): The molar mass of this substance is M, and n = m / M.
The atomic mass of an element is multiplied by the number of its atoms. Add the values once you've completed this for all the atoms to determine the amount of grams in a mole.
A compound's molar mass is determined by adding the atomic masses of all of its constituent atoms together in grams per mole. The number of moles in a compound cannot be measured physically, but we may connect its mass to the number of moles by utilizing the molar mass of the compound as a direct conversion factor.
To learn more about Grams and Moles refer to;
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[PLS HELP WILL GIVE BRAINLIEST!!]
Determine the value of x.
Answer:
The value of x is 8.1
Step-by-step explanation:
We can use SOH CAH TOA to find our answer.
In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse. S is for the SIN function. C is for the COS function. T is for the TAN function.
We can calculate the length of the string by using the COS function.
So we can say the tangent of angle [tex]\beta[/tex] is the opposite side divided by the adjacent side.
[tex]tan( \beta)=\frac{O}{A}[/tex]
We are given the angle and the opposite side. We are looking for the adjacent side.
Lets solve for [tex]A[/tex].
Take the reciprocal of both sides.
[tex]\frac{1}{tan(\beta)} =\frac{A}{O}[/tex]
Multiply both sides by [tex]O[/tex].
[tex]\frac{1}{tan(\beta)} *O=A[/tex]
We are given
[tex]\beta=56\textdegree \\O=12[/tex]
[tex]\frac{1}{tan(56)} *12=A[/tex]
[tex]A=8.0941022[/tex]
