The period of the function is 48 minutes if the periodic function goes through 5 complete cycles in 4 min.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
A periodic function goes through 5 complete cycles in 4 min
From the question:
f = 5/4 cycles per minutes
f = 5/240 cycles per seconds [1 minutes = 60 seconds]
f = 1/48
Period = 1/f
Period = 48 minutes
Thus, the period of the function is 48 minutes if the periodic function goes through 5 complete cycles in 4 min.
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The period of the given periodic function is 48 sec.
What is periodic function?
A periodic function is a function which returns same values at regular intervals. Let f be a periodic function then
f( x +P ) = f(x) , for every x in the domain of f and P is some non zero constant
P is the regular interval or period after which a periodic function returns same values.
P=[tex]\frac{1}{f}[/tex]
where [tex]f[/tex] is the frequency of the periodic function
or [tex]f[/tex] = no of cycles per unit time
Given that a periodic function goes through 5 cycles in 4 min
therefore frequency for this periodic function , f is given by
[tex]f=\frac{5}{4}[/tex] cycles per min
or
[tex]f=\frac{5}{4*60} \\f=\frac{5}{240} \\[/tex]
[tex]f=\frac{1}{48}[/tex] cycles per sec
Thus,
Period of the given periodic function , P =[tex]\frac{1}{f}=1/\frac{1}{48}=48[/tex] sec
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the characteristics and properties of a linear equation
The graph of a linear function is a straight line. One independent variable and one dependent variable make up a linear function.
What are the characteristics of a linear function?
The graph of a linear function is a straight line. One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables.What are the properties of equation?
The properties of the relationship of equality, reflexivity, symmetry, transitivity, and the properties of operations are employed to solve an equation.A mathematical relationship (function) that can be graphically represented as a straight line is said to be linear.Learn more about linear function
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A high school decided to spend $ 750 on student academic achievement awards. At least 5 awards will be given, they should be equal in value, and each award should not be less than $ 50 . Write and sketch a function that models the relationship between the number a of awards and the cost c of each award. What are the domain and range of the function?
b. What information can you use to determine the domain and range?
Following is domain and range for given function -
A)The function's range is -5≤ a≤50.
The function's range is -50≤c≤150.
B) The information we got from equation of the function is used to determine domain and range.
Given,
The whole amount spent is $750.
As a result, our equation is
ca = 750
calculating c,
c = 750 / a
The function's domain and range are:
a ≤ 5
Each prize now needs to be under 50.
= 50 ≤ c
Using the formula, ac = 750
A's maximum value is 75.
we can say that domain is
5 ≤ a ≤ 50
Finally, by substituting a = 5 we can see that the maximum for c is 150.
This gives range for c as -
50 ≤ c ≤ 150
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What is the volume of the cuboid in cm3 ?
What is the volume of the cuboid in mm3
Answer:
3150mm
Step-by-step explanation:
1cm is 10mm you convert it then times it together l x b x h will equal 3150
pls pls help whoever gets it right gets a crown
Answer:
[tex] \sf \: x=0.4[/tex]
Step-by-step explanation:
-0.5x-3.69=x-1.9-2.39
Step 1: Simplify both sides of the equation.
−0.5x−3.69=x−1.9−2.39
−0.5x+−3.69=x+−1.9+−2.39
−0.5x−3.69=(x)+(−1.9+−2.39)(Combine Like Terms)
−0.5x−3.69=x+−4.29
−0.5x−3.69=x−4.29
Step 2: Subtract x from both sides.
−0.5x−3.69−x=x−4.29−x
−1.5x−3.69=−4.29
Step 3: Add 3.69 to both sides.
−1.5x−3.69+3.69=−4.29+3.69
−1.5x=−0.6
Step 4: Divide both sides by -1.5.
−1.5x/−1.5 = −0.6/−1.5
x=0.4
The value of x will be 0.4.
What is an equation?In mathematics, an equation is a connection of two expressions that is expressed as an equality on all sides of the corresponding sign. A statement that uses the equal sign to show that both of the expressions possess the same value is called an equation. Mathematical equations are made up of figures, an equal sign, and an optional variable in the position of an unknowable value.
-0.5x-3.69=x-1.9-2.39
-0.5x - x = -1.9 - 2.39+3.69
Simplifying the given equation:
-1.5 x = - 0.6
x = 0.6 / 1.5
x = 0.4
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HELP................................
Answer: Letter C
Step-by-step explanation:
just look at the problem a little closely
Can u help me figure this out
Step-by-step explanation:
what is it you need help in?
Which of the following is the solution to | x | +9 ≤7?
A. No solution
B. All values are solutions
C. x≤-2
D. x≤-2 and x> -16
The solution for the inequality | x | + 9 ≤ 7 is (option d) x ≤ -2 and x > -16
You can solve an inequality by: adding the same amount to each side; taking the same amount away from each side; multiplying or dividing each side by the same positive amount. The inequality symbol needs to be turned around if either side is multiplied or divided by a negative number. Therefore, the answer is x > 1.
Given,
The expression: | x | + 9 ≤ 7
If | x | ≤ a ⇒ -a ≤ x ≤ a
Then,
-7 ≤ | x | + 9 ≤ 7
⇒ -7 - 9 ≤ x ≤ 7 - 9
⇒ -16 ≤ x ≤ -2
That is x ≤ -2 and x > -16.
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is the expression (17)/(2)g-(9)/(2)h the same as (9)/(2)h-(17)/(2)g ? Explain.
The fraction expression (17)/(2)g - (9)/(2)h is not the same as (9)/(2)h-(17)/(2)g.
How to subtract fractions?
We are given the fraction expression;
(17/2)g - (9/2)h
Now, the fraction (17/2) is greater than (9/2) and as such the result of the subtraction of the fractions will be positive.
Now, if we change the order of the subtraction to be;
(9/2)h - (17/2)g
This means that the result will now be negative since (9/2) is less than (17/2).
Thus, we can conclude that the expression (17)/(2)g - (9)/(2)h is not the same as (9)/(2)h-(17)/(2)g.
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Find the result graphically. Click and drag the arrows to represent each term. Type in the result.
3+(-10)
The arrow is in -7 on the number line since 3 + (-10) = -7.
What is a number line?A number line is a pictorial representation of numbers on a straight line.
It is a horizontal line that has equally spread number increments.
We have,
3 + (-10)
This can be written as:
= 3 - 10
= -7
We can draw a number line to represent graphically:
<↓-------(subtracting 10)-------------->
< ---------(-9)-(-8)-(-7)-(-6)-(-5)-(-4)-(-3)-(-2)-(-1)-0-1-2-3-4-5-6-7-8------------->
Thus the equation can be represented graphically with an arrow in -7 on the number line since 3 + (-10) = -7.
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Question attached below.
Using linear functions, we have that:
a) The rate of change for Job A is of $14, while the rate of change for Job B is of $17, and these are the hourly pay for each job.
b) The slope represent the hourly pay for each job.
c) The intercepts represent the fixed salary for each job.
d) The pay will be the same on both jobs after 25 hours, of $425, as given by the intersection point on the graph.
e) For 40 hours, the payment on Job A is of $635 and on Job B of $680, hence, due to the higher payment, Tommy should accept Job B.
What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For this problem, the two functions are given as follows:
A(h) = 75 + 14h. (slope of 14 as when x changes by 2 y changes by 28).B(h) = 17h. (slope of 17 as when x changes by 2 y changes by 34).The functions are graphed at the end of the answer.
Hence:
a) The rate of change for Job A is of $14, while the rate of change for Job B is of $17, and these are the hourly pay for each job.
b) The slope represent the hourly pay for each job.
c) The intercepts represent the fixed salary for each job.
The pay will be equal when:
A(h) = B(h)
Hence:
75 + 14h = 17h
3h = 75
h = 25.
d) The pay will be the same on both jobs after 25 hours, of $425, as given by the intersection point on the graph.
For 40 hours, the payments are given as follows:
A(40) = 75 + 14 x 40 = $635.B(40) = 17 x 40 = $680.Hence:
e) For 40 hours, the payment on Job A is of $635 and on Job B of $680, hence, due to the higher payment, Tommy should accept Job B.
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Solve each equation. Check your answers.
1.1+ln x²=6
After solving the equation 1.1+ln x²=6, the value of x is equal to [tex]\sqrt{e^{4.9}}[/tex]
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
We have been asked to find x in 1.1+ln x²=6
⇒ 1.1+ln x²=6
⇒ ln x² = 6 - 1.1
⇒ ln x² = 4.9
⇒ x² = [tex]e^{4.9}[/tex]
⇒ x = [tex]\sqrt{e^{4.9}}[/tex]
Thus, x = [tex]\sqrt{e^{4.9}}[/tex] in 1.1+ln x²=6
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Molly is making a punch for the school picnic. The recipe calls for 3/4 quart of lemonade, 3 cups of cranberry juice, 4 cans of orange juice concentrate, and 5 cups of water. If Molly uses 1(2/5) quarts of lemonade, how many cups of cranberry juice will she need?
She will need 5 3/5 cups of cranberry juice to make a punch for the school if Molly uses 1 2/5 quarts of lemonade.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
To make the recipe,
3/4 quart of lemonade and 3 cups of cranberry juice
The ratio of cranberry juice to a quart of lemonade
⇒ 3/(3/4) = 4
To make the same recipe with 1(2/5) quarts of lemonade the ratio of cranberry juice to a quart of lemonade must be maintained.
So,
4 = cranberry juice / 1(2/5)
(5/7) × cranberry juice = 4
Cranberry juice = 28/5 ⇒ 5 (3/5).
Hence "She will need 5 3/5 cups of cranberry juice to make a punch for the school if Molly uses 1 2/5 quarts of lemonade".
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Stefan and Kendrick both walk to work each day. It takes them the same amount of time, even though Stefan lives farther away. One morning, they decide to meet at a coffee shop. The coffee shop is the same distance from each of their apartments. Who will likely get to the coffee shop in less time?
Answer:
Stefan
Step-by-step explanation:
Stefan
What is the solution of the equation x²-24 x+144=0 ?
The solution of the equation x² - 24 x + 144 = 0 is x = 12 .
It is a quadratic equation , it will have 2 roots .
Using factorisation ,
x²-24 x+144=0
( [tex]x^{2}[/tex] - 12 x - 12 x + 144 ) = 0
x ( x - 12 ) - 12 ( x - 12 ) = 0
( x - 12 ) * ( x - 12 ) = 0
x = 12
Both roots are same and are equal to 12 .
Hence , the solution of the equation x² - 24 x + 144 = 0 is 12 .
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x+y+z=−42x+3y−2z=10−x+2y−3z=−12
Enter your answer, in the form (x,y,z), in the boxes in simplest terms.
Answer:
x = 13
Step-by-step explanation:
Suppose there are 6 pennies on a meter stick so that the mean position is the 50
centimeter mark and the mad is 10 centimeters.
1. find possible locations for the 6 pennies.
2. find a different set of possible locations for the 6 pennies.
Using the mean absolute deviation concept, it is found that:
1. One set of possible locations is given as follows: (40, 40, 40, 60, 60, 60).
2. Another set of possible locations is given as follows: (39, 40, 41, 59, 60, 61).
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.Hence, for a mean of 50 and a mean absolute deviation of 10, with 6 pennies, we want data-sets with these following characteristics:
Sum of 50 x 6 = 300.Sum of the differences of the observations and 50 of 6 x 10 = 60.Hence:
1. One set of possible locations is given as follows: (40, 40, 40, 60, 60, 60).
2. Another set of possible locations is given as follows: (39, 40, 41, 59, 60, 61).
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Simplify each expression.
ln e⁴/8
We will get Ine⁴/8 after simplifying the given expression ln · e⁴/8.
What exactly is an expression?An expression in mathematics is a sentence that contains at least two numbers or variables and at least one mathematical operation.Math operations include addition, subtraction, multiplication, and division.The structure of an expression is as follows: An expression is (Number/variable, Math Operator, Number/variable).So,
Given: ln · e⁴/8
Then,
ln · e⁴/8Ine⁴/8Therefore, we will get Ine⁴/8 after simplifying the given expression ln · e⁴/8.
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What is the slope of the line through (-1,8)(−1,8)left parenthesis, minus, 1, comma, 8, right parenthesis and (3,-4)(3,−4)left parenthesis, 3, comma, minus, 4, right parenthesis?
Choose 1 answer:
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{-12}{3 +1}\implies \cfrac{-12}{4}\implies -3[/tex]
!!! HELP QUICKLY PLEASE !!! 40 POINTS!
Find the correct standard form for the expanded forms listed.
A. 500 + 20 + 5 + 0.3 + 0.04
B. 10 + 2 + 0.8 + 0.006
C. 7 + 0.2 + 0.09 + 0.004
D. 30 + 1 + 0.5 + 0.02
All you need to do is answer the questions you don't have to explain the answers, answer all of the questions for brainiest, full star, and of course a thanks!!!
A. 525.34
B. 12.086
C. 7.294
D. 31.52
Hope it helps ^^
Find the value of x
(3x + 2)
(6x - 118)
Answer:
+ x = 116/9
- x = 40
* x = -2/3 and x = 59/3
/ x = -2/3
Step-by-step explanation:
Since it's unclear what operations here are all of them, plus, minus, multiply and divide. If you need Steps, let me know.
A line with slope 12 passes through the point (-6,14)
Answer:
y = 12x + 86
Step-by-step explanation:
y = mx + b
slope is 12 so m = 12
Using (-6,14) then
14 = 12(-6) + b
14 = -72 + b
b = 72 + 14 = 86
I NEEDDDD HELPPPP ASAPPPP
Answer:
24
Step-by-step explanation:
the angle should be the same on the other side so wouldn't it be 120 divided by 5 which is 24. I could def be wrong tho sorry hun
1. I look like this _ _ _ _ . _
2. all of my digits are odd.
3. my thousands digit is equal to the sum of my tens, ones, and tenths digit.
4. my tenths and ones digits are equal
5. the product of my tenths and ones is more than my tens digit
6. my hundreds digit is larger than my thousands digit
Answer:
I think the answer could be 7913.3
Step-by-step explanation:
Using clue number 2 we know that all the numbers in this are odd so that mean the only numbers that can be there are 1,3,5,7 and 9 Using clues 3 and 4 there are a few combinations some of which can be 1 + 1 + 3 = 5 , 1 + 1 + 7 = 9, 1 + 1 + 5 = 7, and 3 + 3 + 1 = 7 With clue 5 in being mentioned the dights in the ones place can't be 1 and 1 because it would equal one and any other dight besides it would be greater then that so I went with 3 and 3 as the tenths and ones dights since 3 × 3 = 9 and 1 being in the tenths place is less then 1The only other clue is clue 6 which means that the hundreds dights has to be a odd number greater than 7 and 9 is the only option that's greater than 7. The number is 7,913.3
Simplify each radical expression. Use absolute value symbols when needed. ∛125 x⁶ y⁹
The simplified form is [tex]5x^{3} y^{9}[/tex].
Simplify is to make something less complicated or much less cluttered. An instance of simplification is when you provide an explanation for a difficult math idea in truly smooth phrases for a kid to understand. An example of simplifying is whilst you chop out a whole lot of the activities that were making you busy and careworn. To turn out to be less difficult.
The phrase simplifies the approach to make something simpler to do or understand. So, by lowering or simplifying the fractions approach we make the fraction as simple as viable. We do this by dividing the numerator and the denominator via the biggest range that may divide into each number precisely.
Factoring the number,
[tex]125=5^{3}[/tex]
[tex]\sqrt[3]{5^{3} x^{6} y^{9} }[/tex]
Applying radical rule,
[tex]\sqrt[3]{5^{3} } =5^{9}[/tex]
[tex]5x^{3} y^{9}[/tex]
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Express y^-9 using a positive exponent
Answer:
[tex]\frac{1}{y^9}[/tex]
Step-by-step explanation:
Exponent rule → [tex]a^{-b}=\frac{1}{a^b}[/tex]
Using exponent rule → [tex]y^{-9}=\frac{1}{y^9}[/tex]
Final result → [tex]=\frac{1}{y^9}[/tex]
The concentration of hydrogen ions in household dish detergent is 10⁻¹² . What is the pH level of household dish detergent?
If the concentration of hydrogen ions in household dish detergent is 10⁻¹² , then the calculated pH level of household dish detergent is 12.
Given that the concentration of hydrogen ions in household dish detergent is 10⁻¹² .
We are told to find the pH level of household dish detergent.
pH is basically a measure of how acidic/basic water is. The range of pH ranges from 0 - 14, with 7 being neutral.
We have to find the negative value of log value of concentration level to find pH of the solution.
pH=-log ([tex]10^{-12}[/tex])
pH=-(-12)log (10) [We know that [tex]log a^{b}[/tex]=b log a]
pH=12*1
pH=12
Hence if the concentration of hydrogen ions in household dish detergent is 10⁻¹² , then the calculated pH level of household dish detergent is 12.
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pls solve the the question above
In mathematics, a variable is a symbol and placeholder for any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set
While multiplying two integer numbers, the rule is simple.
If both the integers have the same sign, then the result is positive.
If the integers have different signs, then the result is negative.
For example,
(+2) x (+3) = +6
(+3) x (-4) = – 12
The major Properties of Integers are:
Closure Property
Associative Property
Commutative Property
Distributive Property
Additive Inverse Property
Multiplicative Inverse Property
Identity Property
According to the distributive property of integers, if a, b and c are integers, then:
a x (b + c) = a x b + a x c
Example: Prove that: 3 x (5 + 1) = 3 x 5 + 3 x 1
LHS = 3 x (5 + 1) = 3 x 6 = 18
RHS = 3 x 5 + 3 x 1 = 15 + 3 = 18
Since, LHS = RHS
Hence, proved.
1) (a-b)+c
a= 0.5 , b= 2, c= -1
(0.5- 2)+-1
=-1.5-1
=-2.5
2) a= 3 . b=-4, c=-2
(3-(-4)+-2
= (3 +4)+2
= 9
3) a= -8, b= 5, c= 3
(-8+5)+3
=-3+3
= 0.
-(a-b)-c
1) a=0.5 , b= 2, c=-1
-(o.5-2)-(-1)
=-0.5+2+1
= 2.5
2) a= 3, b= -4, c=-2
-(3-(-4)-(-2)
-(3+4)+2
-3-4+2
= -5
3) a= -8, b=5 ,c=3
-(-8-5)-3
=(8+5)-3
= 13-3
= 10.
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What is the product of -15 and -3
Answer:
45
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{Guide to follow:}[/tex]
[tex]\large\text{The word \boxed{\rm{difference}} means subtraction/subtract.}[/tex]
[tex]\large\text{The word \boxed{\rm{product}} means addition/add.}[/tex]
[tex]\large\text{The word \boxed{\rm{quotient}} means division/divide.}[/tex]
[tex]\large\text{The word \boxed{\rm{product}} means multiplication/multiply.}[/tex]
[tex]\large\text{Also guide to follow:}[/tex]
[tex]\large\text{2 negatives gives you a positive}[/tex]
[tex]\large\text{2 positives gives you a positive as well}[/tex]
[tex]\large\text{1 negative \& 1 positive gives you a negative}[/tex]
[tex]\large\text{1 positive \& 1 negative gives you a negative as well}[/tex]
[tex]\large\textsf{So, in this particular question we're doing multiplication because the}\\\large\textsf{key term in the word phrase is \boxed{\textsf{product}}. }[/tex]
[tex]\large\text{Now, that we have that information out of the way we can answer}\\\large\text{your given question.}[/tex]
[tex]\large\text{The product of }\large\text{-15 and -3 is translated to \boxed{\rm{-}\large\text{15 }\times\ -\large\text{3}}}[/tex]
[tex]\large\text{Equation: }\rm{-15\times-3}[/tex]
[tex]\large\text{Simplify the equation we have gathered above and you should have}\\\large\text{pverall answer.}[/tex]
[tex]\large\text{We have received was 45}[/tex]
[tex]\huge\text{Therefore, your answer should be \boxed{\mathsf{45}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Problem (PLEASE HELP AND EXPLAIN)
Jamar wants to hire a plumber to fix his shower. The plumber informs him that 1 shower job requires 3 hours of work. The plumber charges $25 per hour, but he will only accept British Pounds as payment. Every British Pound is worth $1.62. How many British Pounds will Jamar need to pay the plumber for the shower job?
Which two units canceled?
Why is it important to cancel units when solving problems with multiple units? Use at least 2 complete sentences.
Answer:
[tex] \sf \fbox{46.296 British Pounds}[/tex]
Step-by-step explanation:
1 shower job requires 3 hours of work,
plumber will fix only 1 shower that means he will work for 3 hours,
Charges of 1 hour = 25$
Charges of 3 hour = 25× 3 = 75$
The currency that plumber accept is British pound (£),
1 British pound (£) = 1.62 dollar ($)
x British pound = 75 dollar
[tex] \frac{1}{x} = \frac{1.62}{75} [/tex]
taking reciprocal both the side,
[tex] \frac{x \cancel £}{1\cancel£} = \frac{75 \: \cancel\$ }{1.62 \:\cancel \$} [/tex]
[tex]x = 46.296[/tex]
Jamar need to pay 46.296 British Pounds to plumber for the shower job.
The two units that were cancelled was Dollar & Pound.
It is required to cancel units because, mathematical operation does not work for different units. For e.g. If I have given two measurement one is volume(cm³) & another is length(cm) so I cannot add them.
[tex] \sf Volume + Length = Not \: possible [/tex]
Same thing happens with division Operation of two different units, the magnitude gets cancelled but unit still remains there.
[tex]\sf \small \pink{Thanks }\: \green{for} \: \blue{joining} \: \orange{brainly } \: \red{community}![/tex]
A football team has P points.
P= 3W + D
Wis the number of wins.
D is the number of draws.
a) A team has 5 wins and 3 draws.
How many points does the team have?
b) After 35 games a different team has 50 points.
14 games were draws.
How many games has this team lost?
Answer:
a)18 points
Step-by-step explanation:
a)
[tex]p = 3(w) + d[/tex]
therefore
[tex]p = 3(5 \: wins ) + 3 \: draws [/tex]
find the product of 5 and 3
[tex]p = 15 + 3[/tex]
[tex]p = 18[/tex]
B) how many games lost
[tex]3x + 14 = 50[/tex]
[tex]3x + 14 - 14 = 50 - 14[/tex]
[tex]3x = 36[/tex]
[tex] \frac{3x}{3} = \frac{36}{3} [/tex]
[tex]x = 12 \: games \: won| [/tex]total Games= Games won + games drawn + games lost
[tex]35 = 12 + 14 + x[/tex]
[tex]35 - 26 = 26 - 26 + x[/tex]
[tex] \times = 18 \: games \: lost[/tex]