Answers
The piecewise function f(x) = 1/2 |x| is equivalent to -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
What is a piecewise function?A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value function. Piecewise functions are implemented in the Wolfram Language as PiecewiseAdditional piecewise functions include the Heaviside step function, rectangle function, and triangle function.Given is the absolute value function -
f(x) = 1/2 |x|
We can write it as a piecewise function as follows. The given function is as follows :
f(x) = 1/2 |x|
The absolute value function is given as -
|x| = - x {x < 0}
|x| = x {x ≥ 0}
So, we can write the piecewise function as -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
Therefore, the piecewise function f(x) = 1/2 |x| is equivalent to -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
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Related Questions
Round 0.12406667 to the nearest hundredth
Answers
Answer:
Step-by-step explanation:
0.124
5. Mariel volunteers at the
animal shelter 3 times a month.
After 6 months, how many
times has she volunteered at
the animal shelter?
Answers
If m and n are positive integers, show that: 3 (m + n)! ≥ m! + n!
Answers
We can conclude the proof of inequality : 3 (m + n)! ≥ m! + n! below.
What is factorial?In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Mathematically, we can write -
[tex]$n! = n \times (n-1) \times \dots \times 1[/tex]
Given is the inequality -
3 (m + n)! ≥ m! + n!
We have -
3 (m + n)!
3 {(m + n)(m + n - 1)(m + n - 2) ....... (3)(2)(1)}
3 {m² + mn - m + nm + n² - n}(m + n + 2) ...... (3)(2)(1)
3 {m² + n² - m - n + 2mn}(m + n + 2) ........ (3)(2)(1)
3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1)
Now, for (m! + n!) --
(m! + n!) = m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)
It can be seen that -
3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1) ≥
m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)
Hence, it can be seen that -
3 (m + n)! ≥ m! + n!
Therefore, we can conclude that 3 (m + n)! ≥ m! + n!.
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3 Dylan needs to buy new contact lenses. His ophthalmologist sells 8-lens boxes in
packs of 2 for $52 and 10-lens boxes in packs of 4 for $120. Which option is the
better deal?
Answers
Answer:
Dylan should purchase the 10-lens boxes in packs of 4 for $120, as this is the better deal. This option provides 40 lenses for $120, which works out to be $3 per lens. The 8-lens boxes in packs of 2 for $52 only provides 16 lenses for $52, which works out to be $3.25 per lens Therefore, the 10-lens boxes in packs of 4 is the better deal.
Step-by-step explanation:
Answer:
he should buy the 10-lens boxes in packs of 4 for $120
Step-by-step explanation:
The crew on a fishing boat caught four fish that weighed a total of 1,032 pounds. The tarpon weighed twice as much as the amberjack and the white marlin weighed twice as much as the tarpon. The weight of the tuna was 5 times the weight of the amberjack.
Answers
Using equations, the weights of the four fish are as follows:
Amberjack = 86 poundsTarpon = 172 poundsWhite Marlin = 344 poundsTuna = 430 pounds.What are equations?Equations are mathematical statements showing the equality of two mathematical expressions.
Using the equation sign (=), equations depict that expressions are equal or equivalent.
The total weight of the four fish = 1,032
Let the weight of the Amberjack = x
Weight of the Tarpon = 2x
Weight of the White Marlin = 4x (2 x 2x)
Weight of the Tuna = 5x
x + 2x + 4x + 5x = 1,032
12x = 1,032
x = 86
Weights:Amberjack = 86 pounds (x)
Tarpon = 172 pounds (2x)
White Marlin = 344 pounds (4x)
Tuna = 430 pounds (5x)
Total weight = 1,032 pounds (86 + 172 + 344 + 430)
Thus, we solved the weight of each fish using equations.
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Question Completion:How much did each fish weigh?
whats 5x5? Maybe will mark brainiest
Answers
Answer:
25
Step-by-step explanation:
5x5 = 25
Answer:
25
Step-by-step explanation:
Let's go through our times tables really quick!
5x1 = 5 (5 + 0)
5x2 = 10 (5 + 5)
5x3 = 15 (5 + 5 + 5 [10 + 5])
5x4 = 20 (5 + 5 + 5 + 5 [15 (5x3) + 5)
As we can see, if we know 5x4, we can easily find 5x5! It's just 5x4 + 5
So, 5x5 is 25
Hope this helped!
How many ounces each of a 63% acid solution and a 33% acid solution must be mixed to produce 100 ounces of a 39% acid solution?
Answers
Answer:
20 ounces of the 63% solution and 80 ounces of the 33% solution.
Step-by-step explanation:
Let x = number of ounces of 63% solution.
Let y = number of ounces of 33% solution.
The total solution to be made is 100 oz.
x + y = 100
x ounces of 63% solution is 0.63x ounces of acid.
y ounces of 33% solution is 0.33y ounces of acid.
100 ounces of 39% solution is 39 ounces of acid
0.63x + 0.33y = 39
The system of equations is
x + y = 100
0.63x + 0.33y = 39
Multiply the both sides of the first equation by -0.33. Then add it to the second equation.
-0.33x - 0.33y = -33
+ 0.63x + 0.33y = 39
---------------------------------
0.3x = 6
x = 6/0.3
x = 20
x + y = 100
20 + y = 100
y = 80
Answer:
20 ounces of the 63% solution and 80 ounces of the 33% solution.
Calculate the volume of this cylinder, giving your answer to 1 decimal place.
14 cm ( diameter )
12 cm ( height )
Answers
22/7×14×14×12
the answer is 7392
please tell me how to solve!!
Answers
the equation in the form of slope interpretation is y = 1/3x -4.
What is a Linear equation?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation has the conventional form y = mx + c.
Given data in a table such as it makes a linear equation slope-intercept form of the given equation is y = mx +c
Where m is the slope
c is constant
The slope for the given data
m = (y₂ - y₁) / (x₂ - x₁)
m = (-5 + 6 )/ (-3 + 6)
m = 1/3
Hence, the equation would be
y = 1/3x + c
for constant we would satisfy the equation with other coordinates of the line.
Substituting ( 0, -4) in the above equation
-4 = 0 + c
c = -4
thus, the equation of the line is y = 1/3x -4
therefore, the linear equation of the given data is y = 1/3x -4.
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When Bashir commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 32 minutes and a standard deviation of 3 minutes. What percentage of his commutes will be shorter than 32 minutes, to the nearest 10th?
Answers
A percentage of Bashir's commute that would be shorter than 32 minutes, to the nearest 10th is 50%.
How to determine the required percentage?Mathematically, the z-score of a given sample size or data set can be calculated by using this formula:
Z-score, z = (x - μ)/σ
Where:
x is the sample score.σ is the standard deviation.μ is the mean score.Substituting the parameters into the z-score formula, we have;
Z-score, z = (32 - 32)/3
Z-score, z = 0/3
Z-score, z = 0
Since a commute of 32 minutes on a test has a z-score of 0, the percentage of Bahir's commute that would be shorter than 32 minutes can be calculated as follows:
P(x > 32) = P(z > 0)
P(z > 0) = 0.5
P(z > 0) = 50%.
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A women went to Shopping.First she spent 4/5th of all money she had in her purse, and then she lost 2/3 of what was remaining. Now she has 10$ left. How much money did she spent?
Answers
The amount of money that was spent is $120.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.
In this case, the women went to Shopping and first she spent 4/5th of all money she had in her purse, and then she lost 2/3 of what was remaining.
The fraction of money left will be:
= 1 - 4/5 - (2/3 × 1/5)
= 1 - 4/5 - 2/15
= 1/15
Since she had $10 left the original amount will be:
= $10 ÷ 1/15
= $10 × 15
= $150
The amount spent will be:
= 4/5 × $150
= $120
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the inaugural attendance of an annual film festival is 20,000. The attendance y increases by 5% each year
A. write a function that represents the attendance after t years.
B. about how many people will attend the festival in the fifth year?
Answers
A. A function that represents the attendance after t years can be written as y = 20,000(1 + 0.05t)
What does a math function mean?
a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
This function represents the initial attendance of 20,000, multiplied by 1 + 5% increase each year (0.05) times the number of years (t).
B. To find out about how many people will attend the festival in the fifth year, we can substitute t = 5 into the function.
y = 20,000(1 + 0.05 * 5)
y = 20,000(1 + 0.25)
y = 20,000(1.25)
y = 25,000
So, approximately 25,000 people will attend the festival in the fifth year.
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A group of friends went to lunch. The bill before sales tax and tip was $37.50. A sales tax of 8% was added. The group then tipped 18% on the amount after the sales tax was added. What was the amount, in dollars, of the sales tax?
What was the total amount the group paid, including tax and tip?
Answers
Sales Tax = $3.00
The total amount paid by the group was $48.15
The amount of the sales tax can be calculated by multiplying the pre-tax bill of $37.50 by the sales tax rate of 8%:
Sales tax = $37.50 * 8% = $3.00
The total amount paid including tax and tip can be calculated by adding the amount of the sales tax to the pre-tax bill and then calculating the tip on the new total:
Total = $37.50 + $3.00 + ($37.50 + $3.00) * 18% = $37.50 + $3.00 + $7.65 = $48.15
So the total amount paid by the group was $48.15.
At a baseball game, a vendor sold a combined total of 137 sodas and hot dogs. The number of sodas sold was 47 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Answers
Taking into account the definition of a system of linear equations, the number of sodas and hot dogs sold is 92 and 45 respectively.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
The values of the unknowns must be found, with which, when replaced, they must give the solution proposed in both equations.
Number of sodas and hot dogs soldIn this case, a system of linear equations must be proposed taking into account that:
"x" is the number of sodas sold."y" is the number of hot dogs sold.You know:
At a baseball game, a vendor sold a combined total of 137 sodas and hot dogs. The number of sodas sold was 47 more than the number of hot dogs sold.The system of equations to be solved is
x + y= 137
x= y + 47
To solve a system of equations by the substitution method, an unknown quantity must be solved in one of the equations. Substitute the expression of this unknown in the other equation, obtaining an equation with only one unknown and thus be able to solve it. The value obtained is substituted in the equation in which the unknown appeared. In this way, the two values obtained constitute the solution of the system.
In this case, substituting the second equation in the first one you get:
y + 47 + y= 137
Solving:
y+ y= 137 -47
2y= 90
y= 90÷2
y= 45
Replacing this value in the second equation, you get:
x= 45 + 47
x= 92
Finally, the number of sodas sold is 92 and the number of hot dogs sold is 45.
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solve the system by elimination. show steps so i can write down please i will mark brainliest thank you!! :)
Answers
Answer:
(-2,5), refer to the step-by-step. Feel free to comment any questions you may have!
Step-by-step explanation:
Given the system of equation, [tex]\left \{ {{x+6y=28} \atop {2x-3y=-19}} \right.[/tex], solve by elimination.
[tex]\left \{ {{-2(x+6y=28)} \atop {2x-3y=-19}} \right.[/tex] , multiply the top equation by -2.
We get, [tex]\left \{ {{-2x-12y=-56} \atop {2x-3y=-19}} \right.[/tex]
[tex]+ {{-2x-12y=-56} \atop {2x-3y=-19}} \right.[/tex], add the equations together.
We get, [tex]-15y=75[/tex], we just eliminated the variable, x, we can now solve this equation for y.
[tex]-15y=-75 = > y=\frac{-75}{-15}[/tex], [tex]y=\frac{75}{15} = > y=5[/tex]
We just found the value y, which is y=5. Now we can take this value and plug it into y for either of the two original equations and solve for x. I will take the top equation...
[tex]x+6y=28 = > x+6(5)=28 = > x+30=28[/tex], subtract the value, 30, from both sides. We get, [tex]x=-2[/tex].
We found the value x, x=-2.
Thus the solution to the given system of equations is (-2,5).
Answer:
(-2, 5)
Step-by-step explanation:
Given linear system of equations:
[tex]\begin{cases}x+6y=28\\2x-3y=-19\end{cases}[/tex]
To solve by the method of elimination, first multiply the first equation by -2:
[tex]\implies -2 (x+6y=28)[/tex]
[tex]\implies -2x-12y=-56[/tex]
Add this to the second equation to eliminate the term in x:
[tex]\begin{array}{lrcrcr}& 2x & - & 3y & = & -19\\+\vphantom{\dfrac12}&(-2x & - & 12y & = & -56\\\cline{2-6}&\vphantom{\dfrac12}&- & 15y & = &-75\end{array}[/tex]
Solve the expression for y:
[tex]\implies -15y=-75[/tex]
[tex]\implies y=5[/tex]
Substitute the found value of y into the expression for x and solve for x:
[tex]\implies x=28-6(5)[/tex]
[tex]\implies x=28-30[/tex]
[tex]\implies x=-2[/tex]
Check by substituting the found values of x and y into both equations.
Equation 1
[tex]\implies -2+6(5)=-2+30=28[/tex]
Equation 2
[tex]\implies 2(-2)-3(5)=-4-15=-19[/tex]
Hence proving that the solution (-2, 5) is true.
Can y’all pls help me solve this!!
Answers
Answer:
From left to right picture,
Scale factor = 2/3
x = 24
y = 12
z = 21
Step-by-step explanation:
Look at the two figures and identify the sides where both lengths are known.
That is the top right-hand side.
Scale factor is hence 18/27 = 2/3
Next, find x, y and z:
Bottom left-hand side: 16/x = 2/3
x = 3/2 x 16
x = 24
Bottom right-hand side: y/18 = 2/3
y = 18 x 2/3
y = 12
Top left-hand side: 14/z = 2/3
z = 3/2 x 14
z = 21
A rectangular playground area is 3,162 meters. The width is 51 meters. Find the length?
Answers
Work Shown:
area = length*width
length = area/width
length = 3162/51
length = 62 meters
A table and 4 chairs costs N82. If the table costs N25, what is the cost of each chair? Find the total cost of 2 tables and 6 chairs
Answers
Answer:
Step-by-step explanation:buordjkdkeek
Calculate the perimeter of a square with side 12cm
Answers
Answer: 48 cm
Step-by-step explanation:
12 + 12 + 12 + 12 = 48
Help asap PLSSS!! I’d really appreciate it. Thank you!!
Answers
The value of x and y in equations 17x - y = 40 and 2x + 4y = 50 are x = 3 and y = 11.
What is equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
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.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
17x - y = 40 ⇒ (1)
2x + 4y = 50 ⇒ (2)
(1)* 4
68x - 4y = 160
Adding equation (1) and (2)
68x - 4y = 160
2x + 4y = 50
⇒ 70 x = 210
x = 3
Substituting the value of x in equation (1)
17*3 - y = 40
51 - y = 40
-y = 40 - 51
-y = -11
y = 11
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PLEASE HELP ME RIGHT NOW DUE TOADY ASAP
Answers
Answer:
A 0.9102
Step-by-step explanation:
A correlation coefficient tells us the strength of the linear relationship between two variables. It is measured on a scale from +1 to -1.
The gradient is positive as it is going up the slope, so the correlation coefficient is positive. We can rule out B.
A correlation coefficient of 0 suggests there is no correlation, however, the scatter graph shows a positive correlation, so we can rule out C.
A correlation coefficient of 1 implies that there is a perfect positive correlation, so all the scatter points lie in a straight line. In the scatter graph given, the points do not all lie on a straight line, so we can rule out D.
Hence, the correlation coefficient is A, 0.9102
Write the two equations for each problem and explain please, thank you
1. Victoria has a total of 65 dimes and quarters worth $10.70. How many of each type of coin does she have?
2. Max has two part-time jobs. He makes $12 per hour mowing lawns and $15 per hour tutoring students. Over the
weekend he worked for a total of 14 hours and made a total of $192. How many hours did he work for each job?
Answers
Answer:
1) Let D be the number of dimes and Q be the number of quarters. We can set up the following system of equations to represent the given information:
D + Q = 65
0.1D + 0.25Q = 10.70
The first equation represents the total number of coins Victoria has, and the second equation represents the total value of those coins in dollars. Solving this system of equations will give us the number of dimes and quarters Victoria has.
2) Let M be the number of hours Max spends mowing lawns and T be the number of hours he spends tutoring. We can set up the following system of equations to represent the given information:
M + T = 14
12M + 15T = 192
The first equation represents the total number of hours Max worked over the weekend, and the second equation represents the total amount of money he made during that time. Solving this system of equations will give us the number of hours Max spent on each job.
The odometer of a car reads 35,467.219 the 5 stands for 5 x1,000 miles. Use expanded form to show what each of the other digits in the odometer reading means.
Answers
So the expanded form of the odometer reading 35,467.219 is:
5 x 1000 + 3 x 100 + 4 x 10 + 6 x 1 + 7 x 1/10 + 2 x 1/100 + 1 x 1/1000 + 9 x 1/10000
What is expanded form?A number is divided up into its place values, then expanded to represent the value of each digit. The enlarged form of 943 is shown as an example. 9 blocks of 100s Three blocks of ones, and four blocks of tens. Nine hundred increased to 4 tens, 3 ones. Form: 900 + 40 + 3.
Define Decimal Numbers.The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
In expanded form, the odometer reading of 35,467.219 can be broken down into the value of each digit in the number.
5 stands for 5 x 1,000 miles
3 stands for 3 x 100 miles
4 stands for 4 x 10 miles
6 stands for 6 x 1 miles
7 stands for 7 x 1/10 of a mile
2 stands for 2 x 1/100 of a mile
1 stands for 1 x 1/1000 of a mile
9 stands for 9 x 1/10000 of a mile
So the expanded form of the odometer reading 35,467.219 is:
5 x 1000 + 3 x 100 + 4 x 10 + 6 x 1 + 7 x 1/10 + 2 x 1/100 + 1 x 1/1000 + 9 x 1/10000
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the mean of 100 nummerical observations is 51.82
Answers
If the mean of 100 nummerical observations is 51.82 then the value of all 100 numbers is 5182.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that mean of 100 nummerical observations is 51.82
We need to find the sum of all the observations
The formula to find mean is mean=Sum of observations/ Number of observation
From given mean=51.82
Number of observations =100
Let us take x as sum of all 100 numbers
So 51.82=x/100
Now apply cross multiplication
x=51.82×100
x=5182
Hence, if the mean of 100 nummerical observations is 51.82 then the value of all 100 numbers is 5182.
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What is an equation for the linear function whose graph contains the points (9, 7) and (4, −8)?
Enter your answers in the boxes.
Answers
The line that passes through these two points is y=x-2
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here function whose graph contains the points (9, 7) and (4, −8)
Thus using the two point formula for a line we get the equation as y-7=(x-9)
y=x-2
Hence, The line that passes through these two points is y=x-2
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In the diagram below,
ZCAB≈ ZCDE. Solve for x. Round
your answer to the nearest tenth if
necessary.
14
A
D
X
с
18.7
E
9.3
B
Answers
Answer:14 a
Step-by-step explanation:
The explanation is that it is E
hello, i need helpw ith my math question
Answers
The three ways to purchase a vehicle include: (1) On lease (2) On hire purchased and (3) On cash basis
How to purchase a vehicle?A vehicle can be purchased on the following ways:
Lease: This involves granting the user access on the property over a period of time before he could make paymentHire purchase: In this method, the buyer deposits first initial money while he agrees with the seller to make the payment of the balance on installment basis Cash: In this method the buyer pays cash at prompt or on the point of purchaseAdvantages include:
It places the buyer on good life without cashHe enjoys the luxurious lifeDisadvantages:
He can run away with the vehicleThe seller looses in cash of accident taking the life of the buyerAdditional expenses include
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Please define the following: Revenue, Cost and Profit VS
Marginal Revenue, Marginal Cost and Marginal Profit.
Answers
The additional expense brought on by reducing the quantity is known as the cost. An additional expense "at the margin" is another name for this. The extra income that results from raising the supply is known as the marginal revenue.
What is Cost and Profit?
Profit is defined as the difference of revenue and cost (determined by deducting cost from revenue. when revenue exceeds operational expenses, the difference between them is called the operating profit.
The additional money "at the margin" is another name for this.The money left over after a corporation pays its bills and expenses is known as its profit. Costs are the out-of-pocket expenditures comes to making, producing, and marketing the company's goods and services.
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How to solve this problem?
Answers
The geometry object known as a line extends on both sides and is defined as an object with zero width. Any line without curves is said to be straight.
What is a straight line called?An object with zero width that extends on all sides is referred to as a line in geometry. Simply put, a straight line is an uncurved line. As a result, a straight line is one without any curves that stretches to infinity on both sides.
A line is a perfectly straight, one-dimensional shape that is endlessly long and thin in both directions. A line may be referred to as a straight line or, more formally, a right line (Casey 1893), to stress that there are no "wiggles" throughout its entire length.
y=mx+c
Definition. Y=mx+c is the formula for a straight line. m is the gradient and c is the height, commonly known as the y-intercept, at where the line crosses the y-axis in the equation y = m x + c.
[tex](b) $\because$ perpendicular makes an angle of $60^{\circ}$ with the line $x+y=0$.$\therefore$ the perpendicular makes an angle of $15^{\circ}$ or $75^{\circ}$ with $x$-axis.[/tex]
[tex]Hence, the equation of line will be $x \cos 75^{\circ}+y \sin 75^{\circ}=4$or $x \cos 15^{\circ}+y \sin 15^{\circ}=4$$(\sqrt{3}-1) x+(\sqrt{3}+1) y=8 \sqrt{2}$or $\quad(\sqrt{3}+1) x+(\sqrt{3}-1) y=8 \sqrt{2}$[/tex]
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A bill of $3400 was paid with $20 notes and $100 notes. Ninety notes were used. How many $20 notes were used?
Answers
Answer:
70
Step-by-step explanation:
for every 5 $20 notes is $100 70 notes is $1400 and the other 20 is $2000 which makes 3400