Therefore , the solution of the given problem of equation comes out to be a=1 and b =-1.
Define equation.An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.
Here,
y' = 3x2 = 3(1) (1) 2 = 3
As a result, the slope-point form of the necessary tangent line is: => y-yo = m. (x - xo) y-1=3(x-1)
The two slopes just need to match for y = x2 + ax + b to share a tangent line at the location (1, 1). (In this manner, the slope-point forms of the two tangent lines will be identical.)
Therefore, y = x2 + ax + b must meet the following two requirements:
It must go through (xo, yo) because: (1, 1).
At this point, it must have a slope (y') of 3.
These will provide us with the two unknowns for our two equations. With the first, we have y'= + axo + b.
⇒ 1 = (1)2 + a(1) + b
⇒ 0 = a + b
and the second one gives us
y=2x0+ a
=> 3 = 2(1) + a
=> a = 1
Looks like we know exactly what a is. All we need is to plug this value into the first equation and we'll find b:
a+b=0
b = -a
b = -1
Therefore , the solution of the given problem of equation comes out to be a=1 and b =-1.
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Which of the following statements correctly describes the graph? A. The graph represents a nonlinear function with a constant rate of change. B. The graph represents a nonlinear function with an increasing rate of change. C. The graph represents a linear function with a constant rate of change.
The statement that correctly describes the graph is given as follows:
C. The graph represents a linear function with a constant rate of change.
How to classify the functions as linear or non-linear?A function is classified as linear or non-linear depending on the rate of change of the function.
If the rate of change of the function is constant, that is, when x changes by one amount, y always changes by the same amount, then the function is classified as linear.
Conversely, if the rate of change of the function is different for different intervals, then the function is classified as non-linear.
As the graph presented at the end of the answer shows a linear function with constant slope, it has a constant rate of change, thus it is linear and option c is correct.
Missing InformationThe graph is given by the image presented at the end of the answer.
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Parabola Skate Rental rents skate boards for $4.50 per hour with a rental fee of $35. Arc Hawk Skate Rental rents skate boards for $5.25 per hour with a rental fee of $25.
Give an example when renting from Parabola's would be a better deal than renting from Arc of Hawk's? Justify your answer.
An example of when renting from parabolas would be a better deal than renting from Arc of Hawk's is when the rental period is 8 hours.
What is the rate?A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
The total cost of renting parabolas would be 8 × $4.50 + $35 = $43.
The total cost of renting from Arc Hawk's would be 8 × $5.25 + $25 = $45.75
So Parabola is cheaper by $2.75
In general, any rental period of 8 hours or less would be a better deal with Parabola's, as per hourly rate is cheaper and the rental fee is higher than Arc Hawk but still, the total cost is lesser.
As the rental period increases beyond 8 hours, the per-hour rate difference becomes negligible and Arc Hawk becomes cheaper.
It is important to compare the cost for the same rental period, to accurately determine which rental company offers a better deal.
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If a business discovered that changing the price of its muffins created an absolute value of .35 < 1, what did its price change mean
If a company found that raising the price of its muffins resulted in an absolute value of.35 < 1, then the demand for muffins is inelastic.
What is meant by mean?The mean is the set of two or more numbers' mathematical average. It is possible to calculate two different sorts of means: the arithmetic mean and the geometric mean. Add the numbers in a set together and divide by the total number of numbers in the set to find the arithmetic mean. To determine the mean, only numerical variables whether continuous or discrete can be employed.It is calculated by merely dividing the total number of values in a data collection by the sum of all the values in the data set. The mean, or average of the supplied numbers, is computed by dividing the total number of numbers by the sum of the given numbers.To learn more about mean, refer to:
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Perform the calculation then round to the appropriate number of significant digits
Answer:
315
Step-by-step explanation:
88.2 × 3.5742 = 315.24444
Answer: 315
How do you find the area of a isosceles triangle without the height?
Since an isosceles triangle has two equal sides, it has two equal angles and two equal heights. Therefore, if you know the length of two sides, you can use the formula A = (1/2)bh to calculate the area, where b is the length of the base and h is the length of the two equal heights.
An isosceles triangle is a triangle with two equal sides and two equal angles. Since the two equal sides also have two equal heights, we can use the formula A = (1/2)bh to calculate the area of the triangle without the height. The formula A = (1/2)bh requires the length of the base (b) and the length of the equal heights (h). Therefore, if you know the length of two sides, you can use the formula to calculate the area of the isosceles triangle without the height.
1. Determine the length of two sides of the triangle.
2. Calculate the area of the triangle using the formula A = (1/2)bh, where b is the length of the base and h is the length of the two equal heights.
3. Plug the known values into the formula and solve for the area.
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The length and the breadth of a rectangular room is in 3:2 and its area is 96m². Find the length and breadth of the room. [Ans: 12m, 8m]
Answer:12m,8m
Step-by-step explanation:BREAADTH
ADEF has coordinates D(2, 0), E(3, 3), and F(4, 1). What are the coordinates of AD E F if the original triangle is dilated by a scale factor of 4?
Option C is correct. The coordinates of ADE'F' after dilation by a scale factor of 4 are A'(8,0), D'(8,0), E'(12,12), and F'(16,4).
What are coordinates?Using one or more numbers, or coordinates, a coordinate system in geometry establishes a unique way to locate points or other geometrical objects on a manifold, such Euclidean space. The order of the coordinates is important, and they can sometimes be distinguished by their place in an ordered tuple or by a letter, such as "the x-coordinate." In simple mathematics, the coordinates are assumed to be real numbers, while they could also be complex numbers or components of a more abstract structure, such a commutative ring. Analytic geometry is based on the usage of coordinate systems, which make it possible to convert geometry-related problems into numerical problems and vice versa.
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A scuba diver is at a depth of -14 ft. Her
elevation changes -2 ft per second. How many
seconds will it take her to reach a depth of
79ft? Write and solve an equation.
On solving the provided question, we can say that - by the help of unitary method seconds will it take her to reach a depth of 79ft is = 39.5
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here,
scuba diver is at a depth of = -14 ft
elevation changes = -2 ft per second.
seconds will it take her to reach a depth of 79ft is = 39.5
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Which milk product will have approximately 15.36 grams of milk fat in an 80-gram serving? (Milk products and percent milk fat: Heavy Cream(36.7%), Light Cream(19.2%), Whole Milk(3.5%), Low-Fat Milk(1.5%), Skim Milk(0.05%)
The light cream milk product have approximately 15.36 grams of milk fat in an 80-gram serving.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Let n be the percentage of milk product to have approximately 15.36 grams of milk fat in an 80-gram serving.
Using percentage formula,
15.36 = n x 80 / 100
n = 1536 / 80
n = 19.2%
Therefore, the product is light cream milk.
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Write a system of linear inequalities represented by the graph.
Inequality 1:
Inequality 2:
By using the unitary approach to answer the given question, we may conclude that total 28 + 40 = $68.
Unitary method: what is it?The unit technique is a strategy for addressing issues that entails first figuring out the value of a single unit, then multiplying that value to figure out the needed value. Simply expressed, the unit technique is used to extract a single unit value from a multiple that is provided. For example, 40 pens would cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. something has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, mathematical analysis, or mathematics of matrices or operators.
One package of chicken costs = $7
steaks cost = $4 per pound.
cost of 4 chicken = 4 * 7 < $28
cost of 10 steaks = 4*10 < $40
total 28 + 40 > $ 68
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What is the remainder when f(x) = x^4 - 8x^2 + 10x + 22 is divided
B.2 by x + 3?
A. -107
B. -17
C. 61
D. 1
Answer:
Step-by-step explanation:
D. 1
Answer:
D) 1
Step-by-step explanation:
-3 | 1 0 -8 10 22
____-3_9_-3_-21_
1 -3 1 7 | 1
Hence, [tex]\frac{x^4-8x^2+10x+22}{x+3}= x^3-3x^2+x+7\,\,\,R1[/tex]
How do you find the missing side of a 30 60 90 triangle?
A 30-60-90 triangle is a right triangle where the three interior angles are 30°, 60°, and 90°.
Let, the shorter leg of a 30 60 90 triangle is equal to a. Then:
The second leg is equal to a√3;The hypotenuse is 2a;The area is equal to a²√3/2; andThe perimeter equals a(3 + √3).If we know the shorter leg length, we can find out that:
Longer leg= √3 times of shorter leghypotenuse= twice the shorter legIn the 30 60 90 triangles :
For angles, the ratio is 1:2:3 (30°: 60°: 90°)For sides, the ratio is 1 : √3: 2Read more about the right triangle:
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Find the height of a trapezium whoe area i 420 q. Cm and the um of the length of it parallel ide i 30 cm
The sum of length of the parallel sides of a trapezium exists 300 cm.
What is meant by trapezium?A trapezoid, which is often referred to as a trapezium, is a flat, closed object with four straight sides and one set of parallel sides. A trapezium's parallel bases and non-parallel legs are referred to as its bases and legs, respectively. Also possible are parallel legs on a trapezium.
Four sides, four corners/vertices, and four angles make up a trapezium, which is a closed shape or polygon. A trapezium has parallel sides on each of its opposing angles.
One set of the sides of a trapezium is parallel only. Since no trapezium is a rectangle, they are not all the same.
Area of trapezium = (a + b)/2 × h
where h is the perpendicular height, and a and b are parallel sides.
So, (a + b) exists sum of length of bases of a trapezium.
Let the equation be
Area of trapezium = (a + b)/2 × h
substitute the values in the above equation, we get
⇒ 4.2 × 100² = (a + b) / 2 × 280 {1 m = 100 cm}
simplifying the equation, we get
⇒ (84/280) × 10000 = a + b
⇒ a + b = 300 cm
Therefore, the sum of length of the parallel sides of a trapezium exists 300 cm.
The complete question is:
Find the sum of length of the parallel sides of a trapezium whose area is 4.2 m² and whose height is 280 cm.
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The sum of length of the parallel sides of a trapezium exists 300 cm.
What is meant by trapezium?A trapezoid, also known as a trapezium, is a closed, flat object with one pair of parallel sides and four straight sides. The parallel bases and the non-parallel legs of a trapezium are called the bases and the legs, respectively. A trapezium with parallel legs is another option.
A trapezium is a closed shape or polygon with four sides, four corners, and four angles. Each of the opposing sides of a trapezium has parallel sides.
A trapezium has only one set of parallel sides. They are not all the same since no trapezium is a rectangle.
Area of trapezium = (a + b)/2 × h
where h is the perpendicular height, and a and b are parallel sides.
So, (a + b) exists sum of length of bases of a trapezium.
Let the equation be
Area of trapezium = (a + b)/2 × h
substitute the values in the above equation, we get
⇒ 4.2 × 100² = (a + b) / 2 × 280 {1 m = 100 cm}
simplifying the equation, we get
⇒ (84/280) × 10000 = a + b
⇒ a + b = 300 cm
Therefore, the sum of length of the parallel sides of a trapezium exists 300 cm.
The complete question is:
Find the sum of length of the parallel sides of a trapezium whose area is 4.2 m² and whose height is 280 cm.
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How do you calculate seed multiplication ratio?
The number of seeds produced from a single seed when it is sown and harvested is referred to as the seed multiplication ratio.
What is Seed?A seed is an undeveloped plant embryo and food reserve that is encased in a protective outer covering in botany. More broadly, "seed" refers to anything that can be sown, which could include seed and husk or tuber.
Seeds are the result of a ripened ovule being fertilised by sperm from pollen, resulting in a zygote. The embryo within a seed develops from the zygote, forming a seed coat around the ovule and growing to a certain size within the mother plant before growth stops.
The formation of the seed is a step in the reproduction process of seed plants (spermatophytes). Other plants, such as ferns, mosses, and liverworts, do not have seeds and must reproduce through water-based means.
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(i) Six donkeys are each given 5 ml spoons of medicine three times each day.
Calculate the number of whole days a 2 L bottle of medicine will last.
pls I really need the answer
Hello there!
Answer:
33 days
Step-by-step explanation:
Every day you give 5 ml of medicine to 6 donkeys. So you spent 5 ml * 6 = 30 ml per day
1 L = 1000 ml
To find the answer you should volume of bottle divide by 30 ml per day:
1000 ml / 30 = 33.333...
It means that if will be possible to use the bottle 33 days but then it will be left
What is the sum of the greatest common factor of $3$ and $6$ and the least common multiple of $3$ and $6$?
The sum of the greatest common factor (HCF) and least common multiple (LCM) of 3 and 6 is 9.
Highest common factor (HCF) and Least common multiple(LCM)The H.C.F. defines the highest common factor present in between given two or more numbers, while L.C.M. defines the least common multiple number which is exactly divisible by two or more numbers.
factors of 3 are 1 and 3
factors of 6 are 1, 2, 3, and 6
3 = 1 × 3
6 = 2 × 3
LCM = 2 × 3
LCM = 6
HCF = 3
sum of HCF and LCM of 3 and 6 = 3 + 6
sum of HCF and LCM of 3 and 6 = 9
Therefore, 9 is the sum of the greatest common factor HCF least common multiple LCM of 3 and 6.
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Is N2 equal to Avogadro's number?
Yes, N2 equal to Avogadro's number. The symbol for Avogadro's number is N₂
What is Avogadro's number?Avogadro's number is a fundamental constant of physics and chemistry, defined as the number of atoms, ions or molecules in one mole of substance. It is approximately 6.022 x 10^23 and is used in many calculations in chemistry and physics, such as the number of atoms in a sample of an element, the number of ions in a salt, or the number of molecules in a gas sample. The constant is named after Amedeo Avogadro, an Italian scientist who first proposed the concept in 1811.
Yes, Avogadro's number is defined as the number of atoms, ions or molecules in one mole of substance, and is approximately 6.022 x 10^23. The symbol for Avogadro's number is N₂.
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The first 5 terms of a certain sequence are 6. 12, 24, 48, and 96.
Which two statements about this sequence are true?
This is a geometric sequence.
This is an arithmetic sequence.
The function f(n)2(6)"
The function f(7) = 6(2)"
The function f(n) = 6 -6(n
represetits this sequence, where is a positive whole
represents this sequence, where is a positive whole r
1) represents this sequence, where n is a positive wh
Answer:
see explanation
Step-by-step explanation:
there is a common ratio between consecutive terms, that is
12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 96 ÷ 48 = 2
this indicates the sequence is geometric
the nth term of a geometric sequence is
f(n) = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 6 and r = 2 , then
f(n) = 6 [tex](2)^{n-1}[/tex]
Select the correct answer.
What is the slope of the line that goes through the points (-1,4) and (14,-2)?
A. -15/6
B. -6/13
C. -5/2
D. -6/15
Slope = (-2 - 4)/(14 - (-1)) = -6/15
What are the two types of measurements of angles?
The two types of units that are used for the angle measurements are (d) degrees and radians .
The two types of Units of Measurements are Radians and Degrees ,
The unit Degrees is used to measure the direction and angle size. If the object is facing north, then the object is said to be at 0°. If the object turn the opposite direction to face south, then the object turned 180°.
A full circle comprises of 360 degree .
The Radian is an S.I. unit of measuring the angles , one radian is defined as angle made at center of a circle by an arc whose length is equal to radius of circle.
The value of 1 radian is approximately equal to 57.296 degree .
The given question is incomplete , the complete question is
What are two types of angle measurements ?
(a) metrics and radians
(b) radians and metrics
(c) degrees and metrics
(d) degrees and radians
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Daria chooses a paint color from 5 shades of blue, 2 shades of yellow, and 2 shades of purple to paint her room. She can choose either carpet or wood flooring. If each choice is equally likely, how much greater is the probability of her choosing a shade of blue and carpet than the probability of choosing a shade of yellow and wood flooring?
The probability of choosing a shade of blue and carpet is 1/6 greater than that of choosing a shade of yellow and wood flooring.
The total number of possible paint colors Daria can choose is 5 shades of blue + 2 shades of yellow + 2 shades of purple = 9 shades
The total number of flooring options Daria can choose from is carpet or wood = 2 options
The probability of choosing a shade of blue is 5/9 and the probability of choosing carpet is 1/2. So, the probability of choosing a shade of blue and carpet is (5/9) * (1/2) = 5/18.
The probability of choosing a shade of yellow is 2/9 and the probability of choosing wood flooring is 1/2. So, the probability of choosing a shade of yellow and wood flooring is (2/9) * (1/2) = 2/18
The probability of choosing a shade of blue and carpet is 5/18, and the probability of choosing a shade of yellow and wood flooring is 2/18. So, the probability of choosing a shade of blue and carpet is (5/18) - (2/18) = 3/18 or 1/6 greater than the probability of choosing a shade of yellow and wood flooring.
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Which One Doesn't Belong? Identify the linear expression that is not equivalent to the other three.
OA) (2x-1)+(-3x+7)
O B) (-5x + 3) + (4x + 3)
OC) (5x-6) + (-6x +12)
O D) (-5x-1)+(6x + 7)
The linear expression that is not equivalent to the other three is D) (-5x-1)+(6x + 7).
What is linear expression?A linear expression is an algebraic expression which is composed of constants, variables, and coefficients that are related by only addition and multiplication operations. It usually takes the form of ax + b, where 'a' and 'b' are constants and 'x' is a variable. Linear expressions can be used to describe various mathematical and physical phenomena, such as the slope of a line or the volume of a cylinder.
This linear expression is not equivalent to the other three because it does not have the same coefficient for the x terms and the constant terms. The other three expressions all have the same coefficients for the x terms and the constant terms, making them equivalent.
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suppose you and three friends are each dealt 13 cards from a shuffled deck, and you observe that you were dealt a single ace; what is then the probably that your three friends also each have an ace
The probability of each of your three friends having an ace is 32%.
The probability of each of your three friends having an ace is calculated using the Binomial Probability Formula. The formula is P(x) = nCr * p^x * (1-p)^(n-x). Here, n = 13 (number of cards dealt to each person) , r = 1 (number of aces you want to calculate the probability of), p = 4/52 (probability of getting an ace from a deck of 52 cards) and x = 1 (number of aces each of your three friends have).
Therefore, the probability of each of your three friends having an ace is P(x) = 13C1 * (4/52)^1 * (48/52)^(13-1) = 0.32.
This means that the probability of each of your three friends having an ace is 32%.
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Please Help! You Dont Have To do the Bottom Questions Just The Top!
Wastewater is filling barrels at the rate of 13 quarts per hour. The recycling facility picks up 96 full barrels on each trip, and each barrel holds 30 quarts of wastewater. How many days are between each pickup
If the recycling facility picks up 96 full barrels on each trip then there is 9 days gap between each pickup.
What is the recycling facility picks up?Recycling is the practice of reusing materials in existing products to create new ones. This can be accomplished in expected ways—such as using recycled paper as packaging material—or unexpected ways—such as using recycled glass to make artificial turf. Recycling helps to conserve limited resources, and—its proponents argue—it has other environmental benefits as well.
Since the recycling facility picks up 96 barrels on each trip
and each barrel contains 30 quarts of effluent.
Thus, the total volume of wastewater is 30 x 96, or 2880 quarts.
Each barrel is filled at a rate of 13 quarts per hour.
So 2880 quarts filled in hours.
We can now change 221.54 hours to days.
= 9.23 days
There are so 9 days in between pickups.
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How many solutions does the system y 3x 4 and 6x 2y 8 have?
The system y = 3x + 4 and 6x - 2y = 8 has no solutions.
A system of equations is a set of equations with multiple variables. To determine the number of solutions for a system of equations, one can use the following methods: graphing, substitution, or elimination. In this case, we can use the elimination method by adding or subtracting the equations to eliminate one of the variables.
If we add the two equations, we get y = 3x + 4 + 6x - 2y = 8, which results in 3x + 4 = 8. This is an inconsistent equation and does not have any solutions. Therefore, the system y = 3x + 4 and 6x - 2y = 8 has no solutions.
This shows that the system is inconsistent, which means that there's no solution that satisfies both equations.
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(look at photo)
iready level h compare functions quiz
Answer:
So I would say when the number of classes is lower fishing is less expensive and when the number of canoeing classes is lower it's less expensive
Step-by-step explanation:
You have to make sure to pay attention to the label and the points in the graph and the table
How do you solve 5t 35?
The answer to this question will t = 8. The first step to solving this equation is to combine the like terms by adding the two numbers together.
In this case, 5t + 35 = 40t. The next step is to divide both sides of the equation by the coefficient of the variable, which in this case is 5. When you do this, you get 40t/5 = t. Therefore, the answer to 5t + 35 is t = 8.
A coefficient is an integer that is either multiplied by the variable it is associated with or written alongside the variable. A coefficient is, in other words, the numerical factor of a term that contains both constants and variables. For instance, the coefficient in the expression 2x is 2.
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Mrs Anderson has 185 pieces of wood he sold 25 peacas of wood to his neighbor and distract the rest of the world into piles around his house each pile of wood contained 40 pieces of wood which equation can be used to find peat the number of piles of wood Mr. Anderson made?
Answer: Let x be the number of piles of wood that Mr. Anderson made.
We know that he sold 25 pieces of wood to his neighbor, and the rest of the pieces of wood were divided into piles around his house, with each pile containing 40 pieces of wood.
Therefore, we can set up the equation:
185 pieces - 25 pieces = x * 40 pieces
Simplifying the equation:
160 = x * 40
To find the value of x, we need to divide 160 by 40
160/40 = x
x = 4
Therefore, Mr. Anderson made 4 piles of wood after he sold 25 pieces of wood to his neighbor.
It's worth noting that this equation was used to find the number of piles of wood Mr. Anderson made after selling 25 pieces to his neighbor, and assuming that he didn't use the rest of the wood for anything else except for making the piles.
Step-by-step explanation:
10. Ashton walked into the restaurant and 4 employees were working registers. Use the trend line equation to predict how long he will wait to place his order.
On solving the provided question, we can have that by unitary method the answer will be total salary = 4 * 2340 = $ 9360
What is unitary method ?
The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
in a restaurant = 4 employees
salary of 1 = $ 2340
total salary = 4 * 2340 = $ 9360
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