Equation of parallel line is y = x + 5
What in math is a coordinate?
a pair of numbers that utilize the horizontal and vertical breakups from the two reference axes to define a point's location on a coordinate plane. generally expressed by the x-value and y-value pair (x,y).
Step-by-step explanation:
If there is a constant distance between each point and the two lines never cross, they are considered to be parallel. If two lines have the same slope, they are said to be parallel.
By above statement we concluded that y = x should be same as its but we can change its intercept part
Hence Equation parallel to y = x + 6 is y = x + 5
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PLEASE HELP FAST!!!! ILL GIVE BRAINLIEST!!!!
A linear function contains the following points.
What are the slope and y-intercept of this function?
A. The slope is 11/2
The y-intercept is (0, -5).
B. The slope is 2/11
The y-intercept is (0, -5).
C. The slope is 11/2
The y-intercept is (-5, 0).
D. The slope is 11.
The y-intercept is (0, -5).
a wooden artifact from an ancient tomb contains 25 percent of the carbon-14 that is present in living trees. how long ago, to the nearest year, was the artifact made? (the half-life of carbon-14 is 5730 years.)
The artifact was created 11,460 years ago.
Given
that,25% of the carbon-14 found in living trees can be found in a wooden artifact from an ancient tomb and the half-life of carbon-14 is 5730 years Half Time [tex]t_{1/2}[/tex] = 5730 yearsln 2 / k = 5730k = 5730 / ln 2Let Po = 100P(t) =25 after t yearsP(t) = Po e^ -kt25 = 100 e ^ -(5730t / ln 2)5730t / ln 2 = ln 4
By applying
we get,t = 5730 * log⁴₂t = 11460 years Hence, the artifact was made 11,460 years ago.
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What was the cost of full coverage insurance in female in her 50s as a percentage of the same insurance in a male in his 30s if female cost $819. 73 and male cost $1192. 64
the cost of full coverage insurance in female in her 50s as a percentage of the same insurance in a male in his 30s if female cost $819. 73 and male cost $1192. 64 was $ 68.73
We have the insurance coverage amount for men of 30 years and for women of 50 years. Therefore, to find the percentage that represents the cost of coverage of the 50-year-old woman based on the cost of coverage of the man, we need to perform the following operation:
Xw= Cw/Cm * 100%
Where:
Cw: cost of coverage for a woman of 50 years.
Cm: coverage cost for a 30-year-old man.
Xw= 819.73/1192.64 *100%
= 68.73
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A certain airline charges a service fee of 7% for each plane ticket purchased. What is the total price the airline charges for a $320 plane ticket?
Answer: $342.40
Step-by-step explanation:
There are two ways you can solve this problem:
Simply turning the percentage to a decimal and multiplying it to the $320.
In the picture provided the method at the top represents you multiplying $320 x .07, You might be wondering “why .07 instead of 7%?” Well, if you were turning this number from a percent to a decimal you would shift the decimal point over to the left 2 times.
And so multiplying $320 x .07 = 22.4 or 22.40. Either way works but without the zero is the way you should write it. And you would add 22.4 to $320 and get $342.40.
Also in the picture provided I used the method of proportions.
Where the total is $320 in this case which you would put next to 100% as 100% means complete or the total. And you would put 7% above 100%. Then, proceed to cross multiply $320 by 7 and it will give you, 2240. Then, you divide it by 100. When you divide it you get 22.40. Then you would add it to $320 and get 342.40.
Point G is the centroid of right triangle ABC with hypotenuse AB=18in. Find CG.
Since Point G is the centroid of right triangle ABC with hypotenuse AB=18in. Then CG is 6 in.
What guidelines govern a right triangle?The area of the square whose side is the hypotenuse (the side across from the right angle) in any right triangle equals the sum of the areas of the squares whose sides are the two legs, according to the Pythagorean theorem.
Note that from the question, A triangle's centroid, G, is located 2/3 of the way down one of its medians. We tend must determine the median C's length in order to find CG.
We require the use of Thale's Theorem to get the median length at C. According to this, a right triangle ABC can be encircled by a semicircle with the hypotenuse acting as the diameter.
Therefore, the median C is a point on the semicircle that connects to the diameter of the hypotenuse AB. Since it is connected to the center, median C is a radius. Half of its length, or 18/2, or 9 inches, makes it.
So:
CG is 2/3 down the median, which is:
9 x 2/3 = 6 inches.
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Graph f(z)=-0.25z +4.
The graph of the function f(z) = - 0.25z + 4 is drawn.
What is a Graph?Drawing the graph (curve) of the appropriate function is the process of graphing a function. Although graphing simple functions like linear, quadratic, cubic, etc. is very straightforward, complicated functions like rational, logarithmic, etc. need some expertise and an understanding of certain mathematical principles.
Drawing a function's representation as a curve on a coordinate plane is known as graphing. Every point on a curve (or graph) that represents a function satisfies the function equation.
A collection of edges that are ordered pairings of vertices (also known as directed edges, directed links, directed lines, arrows, or arcs) is displayed
The graph of the function is drawn. On the x-axis, the z-variable variables and on the y-axis the f(z) values are shown.
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1. (a) What does probability convey about an event's
occurrence? (b) What is the probability of a
random event based on?
a) In any given experiment or trial, there is a probability that either an event occurs or it does not. The probability of the occurrence of an event lies between 0 and 1.
The event E of a sample space S is said to have occurred if the outcome ω of the experiment is such that ω ∈ E. However if the outcome ω is such that, ω ∉ E we say that the event has not occurred.
Let us take the example of playing cards. Here the event E is drawing a face card. If you draw a king of spades, we say the event E has occurred. However, if you draw an eight of clubs, we say the event E has not occurred.
b) The probability of an event is equal to the events relative frequency in the population of possible events that can occur.
An event’s relative frequency is a number between 0 and 1, so the event’s probability is from 0 to 1.
For example, when someone says that the probability it raining today is high, you understand that they mean that there is a high chance that it will rain.
But what if someone says that the probability of something happening is very low? You understand that the person means that the event may not occur at all. In mathematics, we define probability in a similar sense.
What is Probability?
Probability is the measure of uncertainty of any event (any phenomenon happened or bound to happen).
What is event?
In probability, the set of outcomes from an experiment is known as an Event.
What is random events?
An event with a probability of occurrence determined by some probability distribution.
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The cost of mailing a package is proportional to the weight of the package. The proportional relationship can be represented with the equation c = 0.8w, where c represents the total cost and w represents weight in ounces. A graph for the equation is shown. graph with x axis labeled weight in ounces and y axis labeled cost in dollars, with a line from 0 comma 0 going through 2 comma 1.6 Which of the following statements is true about the graph shown?
The correct statement regarding the proportional relationship c = 0.8w is given as follows:
The equation c = 0.8w is correctly represented by the graph.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.
When the two variables x and y are direct proportional, the output variable y is obtained as the multiplication of the input variable x by the constant of proportionality k, as follows:
y = kx.
In this problem, the equation is given as follows:
c = 0.8w.
In which:
c is the cost in dollars -> output -> y-axis of the graph.w is the weight in ounces -> input -> x-axis of the graph.For a input of 2, the output is given as follows:
c = 0.8 x 2 = 1.6.
Hence point (1,0.8) is in the graph, along with point (2,1.6).
Missing InformationThe statements are given as follows:
The equation c = 0.8w is correctly represented by the graph.The graph is incorrect and the line should go through the point (0.8, 1).The x-axis and y-axis are labeled incorrectly.The graph does not show a proportional relationship.More can be learned about proportional relationships at https://brainly.com/question/10424180
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Enter the equation of the graph in vertex form?
The equation of the given graph is y = (x + 4)² -5.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
The vertex form of a parabola is y = (x - h)² + k which is opened upward direction and vertex is (h, k).
From the graph, the vertex of the quadratic equation is (-4, -5)
Thus h = -4 and k = -5.
Putting h = -4 and k = -5 in y = (x - h)² + k
y = (x - (-4))² + (-5)
y = (x + 4)² -5
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What is 150 rounded to the nearest 10th divided by 4
The value of 150/4 to the nearest tenth is 37.50
What are fractions?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. . In a proper fraction, the numerator is less than the denominator. In improper fraction, the denominator is smaller to the numerator.
The value of 150/4 = 75/2= 37 1/2
1/2 in decimal is 0.5
Therefore 150/4= 37+ 0.5= 37.5
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g with normalcdf if 15% of adults in a certain country work from home, what is the probability that fewer than 60 out of a random sample of 500 adults will work from home?
The probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03
In the given probability case we have;
What is the likelihood that, out of a random sample of 500 persons, fewer than 60 will work from home if 15% of adults in a particular country do so?
Let,
P = 15% = 0.15
n = 500
By considering the binomial distribution case the formula is given by
P( X = x ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ
P( X ≤ 60 ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ
= ⁶⁰∑ₓ=₀ (⁵⁰⁰Cₓ) (0.15)ˣ (1 - 0.15)⁵⁰⁰⁻ˣ
= 0.031
≅ 0.03
Hence, the probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03
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A quadratic function f has a vertex at (6, −2).
a. Explain what it means for a function to have a vertex at this point.
b. How can you determine if this vertex is a maximum or minimum? Explain.
c. Explain how the values of f(2) and f(10) compare to the value of ƒ (6).
d. Compare the values f(2) and f(10).
Considering the vertex of the quadratic function at point (6,-2), it is found that:
a) The meaning is that the turning point of the function is at point (6,-2).
b) If the parabola is concave down, then the vertex is a maximum. If the parabola is concave up, then it is a minimum.
c) If the parabola is concave down, then f(2) = f(10) < f(6). If the parabola is concave up, then f(2) = f(10) > f(6).
d) f(2) = f(10).
What is the vertex of a quadratic equation?A quadratic equation is defined by the rule presented as follows:
y = ax² + bx + c.
The vertex can represent either a maximum point or a minimum point, depending on the coefficient a, as follows:
Maximum: a < 0. -> concave down parabola.Minimum: a > 0. -> concave up parabola.The vertex is also the turning point of the graph of the parabola.
In this problem, the coordinates of the vertex are (6,-2), hence:
If the parabola is concave down, all the values are lesser than f(6).If the parabola is concave up, all the values are greater than f(6).When two points are equidistant from the vertex, they have the same numeric value, hence:
f(2) = f(6).
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(x+2)(x+3)(x+4) can be written in the form [tex]x^{3}[/tex] + a[tex]x^{2}[/tex] + bx c where a, b and c are positive integers.
Work out the values of a, b and c.
a = (Answer here) (1)
b = (Answer here) (1)
c = (Answer here) (1)
Answer:
a = 9 ; b = 26 ; c = 24
Step-by-step explanation:
(x^2+3x+2x+6)(x+4)
(x^2+5x+6)(x+4)
x^3+5x^2+6x+4x^2+20x+24
x^3+9x^2+26x+24
What is the sum of all the even numbers between 105 and 351?
What is the difference between the sum of all the even numbers between 305 and
609 and the sum of all the odd numbers between 304 and 608?
The sum of even numbers between 105 and 351 is 28,044 .
What is arithmetic progression ?An additive or arithmetic sequence is a sequence of numbers such that the difference between consecutive terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15 ... is an exponent plus the common difference of 2.
Calculationeven numbers between 105 and 351
the series will start like
106 , 108 , 110 , .................................. , 346 , 348 , 350
this is a arithmetic progression
a = 106 d = 2 l = 350
we need to find n
350 = 106 + ( n - 1 ) 2
350 - 106 = (n -1 ) 2
244/2 = n -1
n = 123
now sum = 123/2 ( 106 + 350)
= 28,044
so the sum of even numbers between 105 and 351 is 28,044 .
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Which table represents an exponential function of the form y = b when 0
Second table represents an exponential function of the form y = b when 0
Define exponential function.A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered. In addition to many other applications, exponential functions are used to estimate populations, carbon date artefacts, assist coroners in determining the time of death, compute investments, and many more. Three of the most popular applications—population expansion, exponential decay, and compound interest—will be covered in this session.
Given,
Second table represents an exponential function of the form y = b when 0
Function: y = bˣ
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(25x^2+4-30x)-(9x^2+4-12x)
Answer:
16x² - 18x
Step-by-step explanation:
(25x² + 4 - 30x) - (9x² + 4 - 12x) ← distribute this parenthesis by - 1
= 25x² + 4 - 30x - 9x² - 4 + 12x ← collect like terms
= (25x² - 9x²) + (4 - 4) + (- 30x + 12x)
= 16x² + 0 + (- 18x)
= 16x² - 18x
Dominique uses a car service company to travel to work and back home. She uses the same route each way. The company charges a ride fee of $3.00 and $1.25 per mile. Dominique pays $11.75 for transportation each way. Select all of the equations that model the total amount of money Dominique spends on travel each day if her route to work is x miles long.
The equation that model the total amount of money Dominique spends on travel each day if her route to work is x miles long is 3 + 1.25x = 11.75.
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.
In this case, Dominique uses a car service company to travel to work and back home.
The company charges a ride fee of $3.00 and $1.25 per mile. The appropriate equation will be:
3 + 1.25(x) = 11.75
where x = number of miles
3 + 1.25(x) = 11.75
3 + 1.25x = 11.75
This illustrates the equation.
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A store manager instructs some new trainees that a barbecue grill priced at $700 winds up costing a customer $714 once the sales tax is included. What is the sales tax percentage?
Write your answer using a percent sign (%).
Answer:
0.02 or 2%
Step-by-step explanation:
$700(x)=$714
$700(0.02)=14
700+14=714
What is the answer to this question?
We get the values when x is -8 y is 62, when y is -73 x is 7 and when x is 3 y is -37 for the linear equation y=-9x-10.
Given that,
The linear equation is y=-9x-10.
We have to fill the table given in the question.
First,
Taking x value is -8
We get y value as,
y=-9(-8)-10 (multiply -9 and -8)
y=72-10 (Subtracting 72 and 10)
y=62
When x is -8 y is 62.
Taking y value is -73
We get x value as,
-73=-9x-10
-73+10=-9x
-63=-9x
63=9x
x=63/9
x=7
When y is -73 x is 7.
Taking x value is 3.
We get y value as,
y=-9(3)-10
y=-27-10
y=-37
When x is 3 y is -37.
Therefore, We get the values when x is -8 y is 62, when y is -73 x is 7 and when x is 3 y is -37 for the linear equation y=-9x-10.
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DUE TOMORROW PLS HELP!!
does anyone know how to solve the area and perimeter for this parallelogram pls help!!! In details !!!
Answer:
The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all four sides. x is in this case the length of the rectangle while y is the width of the rectangle. The area is a measurement of the surface of a shape. for example
You are able to find the perimeter of the rectangle by adding length and width and multiplying by two because the opposite sides of a rectangle are equal in length. Both lengths of the rectangle are the same, and both widths are the same. For example, P = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17.3 in).
Step-by-step explanation:
pLS HURRY!!!This area model shows the quotient of 1/5+4
What is the quotient?
Enter your answer as a fraction in simplest from by
filling in the boxes.
The quotient of the fraction is 0.05 and the fraction in its simplest form is 1/20
How find the quotient of a fraction?The quotient of a fraction is the whole number that is obtained when you simplify the fraction. If the simplification of a fraction is not a whole number, the quotient is the decimal form of the fraction
Given: 1/5÷4
1/5÷4 = 1/5 × 1/4 (Note: If ÷ change to ×, 4 will change to 1/4 )
= 1/20 = 0.05
Therefore, the quotient of the fraction is 0.05 and 1/20 should be filled in the box
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Find the values of the variables. Then find the side length of the square 
Answer:
x = 4y = 8side length = 4Step-by-step explanation:
You have a square with sides labeled (y-4), (3x-8), (2y-12), and you want to know the values of the variables as well as the side length.
SetupAll sides of the square are the same length. Equating two different y-expressions, we get ...
y -4 = 2y -12
We can use the solution to that to find x:
y -4 = 3x -8
SolutionAdding 12-y to the first of these equations gives us ...
8 = y
Using this value in the second equation, we have ...
8 -4 = 3x -8
12 = 3x . . . . . . add 8
4 = x . . . . . . . . divide by 3
The side length is ...
y -4 = 8 -4 = 4
The values of the variables are x = 4, y = 8, and the side length of the square is 4.
Simplify. (4i+1)^2
show all work
(4i+1)² can be simplified to 8i-15
What is Complex number?A complex number is a number of the form a + bi, where a and b are real numbers
Given expression is (4i+1)²
four times of i plus one whole square.
(4i+1)² can be expanded by using algebraic identity
(a+b)²=a²+b²+2ab
(4i+1)²
Now put a as 4i and b as 1
(4i+1)²=16i²+1+2(4i)(1)
Where i²=-1
=-16+1+8i
=8i-15
Hence (4i+1)² can be simplified to 8i-15
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Peggy is planting a garden. The garden is 103 feet wide by 7 feet long. What is the area of the garden?
Answer: 721 ft
Step-by-step explanation:
formula for area is a=l*w
Given: w=103, length=7
103*7=721
Answer: The answer 721. When you are finding an area of something you must multiply the length and the width so the information given.
103 x 7 = 721 feet long
Here is the real problem:
It's sloppy as long as you understand the concept : )
Study each equation, then solve.
8) 5 + r = 6 - r
9) z - 16 = - 16
10) 7n - 7 = 0
The solution for r in equation 5 + r = 6 - r, r =1/2
The solution for z in equation z - 16 = - 16, z= 0
The solution for n in equation 7n - 7 = 0 , n= 1
(8) 5 + r = 6 - r
Step 1: Rearrange the equation by collecting the like terms
r +r=6-5
Step 2: Simplify r +r=6-5
2r = 1
Step 3: Divide both sides by 2
2r/ 2 =1/2
r =1/2
9) z - 16 = - 16
Step 1; Add 16 to both sides
z-16 +16 = -16 +16
z= 0
10) 7n - 7 = 0
To solve for n
Step 1: Add 7 to both sides
7n - 7 +7 = 0+7
7n =7
Step 2: Divide both side by 7
7n/7 =7/7
n= 1
Therefore, the solution for r in equation 5 + r = 6 - r, r =1/2
The solution for z in equation z - 16 = - 16, z= 0
The solution for n in equation 7n - 7 = 0, n= 1
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Write the equation of the circle in standard form that has the following: Center (-5,7) and Radius = 4
Answer:
[tex](x+5)^{2}+(y-7)^{2} =16[/tex]
Step-by-step explanation:
The Standard Form of Circle Equation whose Center is at ( h , k) and Radius of r is given by
[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]
So for our Question
we have ( h , k ) = ( -5 , 7 ) and r = 4
By substitution
[tex](x-(-5))^{2}+(y-7)^{2} =4^{2}[/tex]
Simplify [tex](x+5)^{2}+(y-7)^{2} =16[/tex]
graph each function for the given domain 2x-y=3; d: (-2,0,1,3)
The range values for the domain of the functions are as follows
x y
-2 7
0 3
1 1
3 -3
How to complete the tables for the graphThe domain are the input values of the graph the output values are solved using the given functions
The given function 2x-y=3
rearranging gives
y = 3 - 2x
solving for the range values using the domain values: (-2,0,1,3)
= 3 - 2x = 3 - 2 * -2 = 7
= 3 - 2 * 0 = 3
= 3 - 2 * 1 = 1
= 3 - 2 * 3 = -3
The graph is attached
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you are constructing a cardboard box from a piece of cardboard with the dimensions 4 m by 8 m. you then cut equal-size squares from each corner so you may fold the edges. what are the dimensions (in m) of the box with the largest volume?
The dimensions (in m) of the cardboard box with the largest volume is obtained as 2 m length.
Define the term largest volume?Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc. Volume is sometimes referred to as capacity.Dimensions of piece of cardboard;
Length = 8 mWidth = 4 m.Let the corner cut length be 'x',
New dimensions;
Length = 8 - 2x Width = 4 - 2xHeight = xVolume = length x width x height
Put the values;
V = ( 8 - 2x ) (4 - 2x) x
Find the solution of the obtained quadratic equation by quadratic formula.
x = 0, 2 and 4.
As, x ≠ 0 and 4.
Thus, x = 2.
Thus, the dimensions (in m) of the box with the largest volume is obtained as 2 m length.
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Rewrite the point-slope form equation into slope-intercept form.
y+4= -3(x-5)
The slope-intercept form of the equation is
(Type an equation. Use integers or fractions for any numbers in the equation.
The point slope and the intercept form is y = -3x + 11
What is the slope intercept form?One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).
This written in the form of y = ax + b
where a is the slope and b is the intercept
We have the equation as
y + 4 = - 3 ( x - 5 )
we would have to open the bracket and then take the like term
this is going to be
y + 4 = -3x + 15
From here we would get the like term
y = -3x + 15 -4
y = -3x + 11
The slope is -3 and the intercept is 11.
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Answer each question below, showing all work.
A local movie theater is showing a new movie this weekend. The theater sold 144 tickets. Adult
tickets cost $9.00 each and a child's ticket costs $6.00 each. The theater collected $1164.00 from these
ticket sales. How many adult tickets and how many children's tickets were sold? Only an algebraic
solution will be accepted.
Answer:
a=100, c=44
Step-by-step explanation:
# of adult tickets is represented by a
# of child tickets is represented by c
C+A=144
9a+6c=1164
system of equations is solved by solving 1 equation for 1 variable first.
c=144-a
plug in c in the second equation
9a+6(144-a)=1164
9a+864-6a=1164
combine like terms
3a=300
a=300/3
a=100
now we know a is 100 we can plug it into the original equation of c=a=144
c+100=144
c=144-100
c=44