3. For the polynomial function A(x) = x4 - 2x³ - 21x² +22x + 40 we know (x - 5) is
a factor. Select all the other linear factors of A(x).
A. (x + 1)
B. (x - 1)
C. (x + 2)
D. (x - 2)
E. (x+4)
F. (x-4)
G. (x + 8)
ion with its constant term.
#3
Answer:A,D,E,F
Step-by-step explanation:A(x) = x4 - 2x³ - 21x² +22x + 40= A,D,E,F
Suppose a supermarket wants to sell eggs individually. Is there a price the supermarket can charge per egg that is between the prices per egg for the two different sized cartons?
The maximum price per egg that the supermarket may charge is $0.245 per egg, which is the difference between the pricing per egg for the 2 distinct cartons.
What do you meant by the term unitary method?The unitary approach involves calculating the price of a specific unit, from which we can calculate the values of the necessary number of units.The answer to the query is
The following details are available to us:
A carton of 12 eggs costs $3.00.18 eggs in such a different carton cost $4.32.We'll first calculate the cost per egg for each of the two different-sized cartons in order to determine the cost per egg that lies between the two costs.
We are aware that the cost of one product is determined by dividing the total cost by the quantity of products.
12 eggs cost in a carton = $3.001 eggs cost = $ (3.00/12) = $0.2412 eggs cost in a second carton = $4.321 eggs cost = $(4.32/18) = $0.24The price of an egg between 0.24 as well as 0.25 must now be determined.
Note that there is a 0.01 difference between the two fees.
To precisely determine the middle charge, we will split it by two:
0.01/2 = 0.005
This can be added to $0.24 or subtracted from $0.25.
$0.24 + $0.005 = $0.245
So, $0.245 is the maximum price the supermarket can charge per egg.
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The complete question is-
A carton of 12 eggs costs $3.00. A carton of 18 eggs costs $4.32. Suppose a supermarket wants to sell the eggs individually. Is there a price the supermarket can charge per egg that is between the prices per egg for the two different-sized cartons? Explain
Graph the points (4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5) on the coordinate plane.
The points (4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5) have been graphed on the coordinate plane (Refer to the graph attached below.)
What is the coordinate plane?The Cartesian coordinate system on a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates.
These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.
A graph having one x-axis and one y-axis is referred to as a cartesian plane (also known as an X-Y graph).
The orientation of these two axes is perpendicular.
The graph's exact center is marked by the origin (O).
So, we have the points:
(4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5)
Now, the graph is as follows:
(Refer to the graph attached below)
Therefore, the points (4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5) have been graphed on the coordinate plane (Refer to the graph attached below.)
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enlarge shape q by a scale factor of -1/2 around the centre point (0,0
The new coordinates of the point in the transformed shape would be (-1/2x, -1/2y).
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
A scale factor of -1/2 around the center point (0,0) would reflect the shape across the origin and also shrink it by a factor of 1/2.
The transformation can be represented by the matrix:
[-1/2 0]
[ 0 -1/2]
This matrix would be applied to the coordinates of each point in the shape to obtain the new coordinates of the transformed shape.
So, if a point in the shape had coordinates (x, y), the new coordinates of the point in the transformed shape would be (-1/2x, -1/2y).
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The question seems to be incomplete the correct question would be:
Enlarge shape q by a scale factor of -1/2 around the center point (0,0). if a point in the shape had coordinates (x, y), what are the new coordinates?
A coffee shop sells a mug for $8.95. Each refill costs $1.50. Last month Rose spent $26.75 on a mug and refills. How many refills did she get?
Rose gets 12 refills by a coffee shop.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A coffee shop sells a mug for $8.95. Each refill costs $1.50.
And, Last month Rose spent $26.75 on a mug and refills.
Let number of refills she get = x
So, We can formulate;
⇒ $8.95 + $1.50x = $26.75
⇒ 8.95 + 1.50x = 26.75
⇒ 1.50x = 26.75 - 8.95
⇒ 1.50x = 17.80
⇒ x = 17.8 / 1.5
⇒ x = 12
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Think About the Process van purchased a DVD player on sale. The original selling price was $175.80. The sale price was $141.27. What is the first step in finding the percent markdown? Find the percent markdown.
First step in finding the percent markdown is to find the percentage change in sales price.
How to find the percentage change in sales priceIn order to find the percentage change in sales price, use the percent change equation.
(New - Old)/(Old) * 100 = % Change
Now input 141.27 for the New price and 175.80 for the Old price.
(141.27 - 175.80)/(175.80) * 100 = % Change
-34.53/175.80 * 100 = % Change
-0.2* 100 = % Change
20 = % Change
Hence, the percentage change in sales price is 20%
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How do you find the center of dilation with a compass?
To find the center of dilation,We'll fix our compass to a distance that is closer to the overall distance but still greater than halfway between vertex L and point C. Start with the compass's point on vertex L while maintaining the same distance, and then draw a curve that intersects the line connecting L and C.
What is Centre of dilation?Centre of dilation of an image in mathematics refers to a change that results in an image with the same shape but a different size, either larger or smaller. A dilation can only be built with two bits of information.
An operation that moves, flips, or otherwise alters a figure to produce a new figure is called a transformation. Rigid transformations maintain size, whereas non-rigid transformations do not. A dilatation enlarges or reduces a figure while maintaining its original shape. To put it another way, the dilatation resembles the original. Every dilatation has a scale factor and a centre. The scale factor indicates how much the figure stretches or contracts, and the centre serves as the point of reference for the dilation (much like the vanishing point in a perspective drawing). A scale factor is usually identified by a label and is never zero. Additionally, the dilatation would be if the original figure were labelled, for example.
The point from which the image is dilated is known as the centre of dilatation (or point of dilation).
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How many solutions the linear equation 2x y 10 has?
The linear equation [ ( 2x PLUS y ) EQUALS 10 ] has only one solution.
A linear equation is an algebraic equation having the form y=mx+b, involving only a constant and a first-order (linear) term, where b is the y-intercept and m is the slope. Occasionally, the above is called a 'linear equation of two variables,' where x and y are the variables.
Now solve the given linear equation which is:
[ ( 2x + y ) = 10 ]
Now solve this equation in order to determine the number of solutions it has,
( 2x + y ) = 10
( 2x + (10 - 2x)) = 10
( 2x + 10 - 2x) = 10
( 2x + 10 - 2x) = 10
(10) = (10)
Since 10 = 10 is correct, therefore, the equation ( 2x + y ) = 10 has only one solution.
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A line that passes through the point (1,-6) and has the slope of -9
Write an equation in point slope form for this line
Which type of polynomial has no zero?A) Touches X-axis at any pointB) Intersects X-axis at two distinct pointsC) Does not intersect X-axis at any pointsD) Is in any half-plane of the X-axis.
In mathematics, an algebraic expression is an assertion built up from integer constants, variables, and algebraic operations. This article is all about to Monomials, Binomials, and Polynomials.
1. Monomial
An algebraic expression that carries only one non-zero term is known as a monomial. A monomial is a just like a type of polynomial, like, binomial and trinomial, which is an algebraic expression having only a one single term, which is a non-zero.
It comprises of only a single term which makes it easy to do the operation of addition, subtraction, and multiplication.
2. Binomial
An algebraic expression that comprises of two non-zero terms is known as a binomial. It is expressed in the form equation ax ^m + bx ^n where a and b number, x is variable, m and n are nonnegative distinct integers.
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How do you find the preimage of a function in Class 11?
A relation R is a subset of the Cartesian product. Or simply, a bunch of points (ordered pairs). In other words, the relation between the two sets is defined as the collection of the ordered pair, in which the ordered pair is formed by the object from each set.
a group of some elements of the input set which are passed to a function to obtain some elements of the output set. It is the inverse of the Image. It is denoted as;
f: X → Y.
N be the set of Natural numbers and the relation R be defined as;
R = {(a ,b) : b=a2, a ,b ∈ N}. State whether R is a relation function or not.
From the relation R = {(a ,b) : b=a2, a ,b ∈ N}, we can see for every value of natural number, their is only one image. For example, if a=1 then b =1, if a=2 then b=4 and so on.
Therefore, R is a relation function here.
f:A→B, and D⊆B, the preimage D of under f is defined as
[tex]f^-1[/tex](D)={x ∈ A∣ f(x)∈D}.(5.4.5)
Hence, [tex]f^-1[/tex](D) is the set of elements in the domain whose images are in C. The symbol [tex]f^-1[/tex](D) is also pronounced as “f inverse of D.”
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Write down the ratio 600 km to 12 km.
Give your answer in its lowest form.
Answer:
50 km : 12 km
Step-by-step explanation:
600 km : 12 km
=50 km : 1 km.
martha and axel went to the store to buy 3 apple, but only had a buget of 5 dollars
Answer:
i need more information to answer your question
Step-by-step explanation:
6. Construction A total of 18.6 cu yd of concrete is required for pouring a
foundation. The ratio of cement to sand to gravel for this application is
1:2:4, and the total amount of these components must be 1½ times the vol-
ume of concrete needed. Use the method of Example 4 to determine how
many cubic yards of each component are needed.
The number of cubic yards of each component needed are 3.99 cubic yards of cement, 7.97 cubic yards of sand and 15.94 cubic yards of gravel
How to determine how many cubic yards of each component are needed?
Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another
Since a total of 18.6 cu yd of concrete is required and the total amount of these components must be 1½ times the volume of concrete needed. We can say:
total amount of these components = 1½ × 18.6 cu yd = 27.9 cu yd
Also, since the ratio of cement to sand to gravel for this application is 1:2:4. We have:
Total share = 1 + 2 + 4 = 7
cement = 1/7 × 27.9 = 3.99 cubic yards
sand = 2/7 × 27.9 = 7.97 cubic yards
gravel = 4/7 × 27.9 = 15.94 cubic yards
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whats the intercepts of 2x+y=1 and x-2y=8
Answer:
Step-by-step explanation:
I will assume you want the y-axis intercepts
arrange each equation into the form y = mx + b <==b is y-axis intercept
2x+y =1
y = -2x+1 <==== y axis intercept = 1
x -2y = 8
2y = x-8
y = 1/2x -4 <==== - 4 is the y axis intercept
Another way to find the y-axis intercept is to realize this occurs when x = 0
put x = 0 into the equations to find the intercept value
2x+y =1
2(0) + y = 1
y =1 <=====intercept
x-2y = 8
0 - 2y = 8
y = -4 <=====intercept
To find the where the two lines intersect, equate them
-2x+1 = 1/2x-4
5 = 2.5x
x = 2 then y = -2x+1 = -3 point of intersection (2,-3)
How do you find the exponential function of a data set?
An exponential function is a mathematical function of the form f(x) = a×bˣ, where a and b are constants and x is the input variable. To find the exponential function of a data set, you can use the method of least squares.
This method finds the best-fitting exponential function for a given set of data points by minimizing the sum of the squares of the differences between the data points and the function.
The first step in finding the exponential function of a data set is to plot the data points on a graph. Next, you need to re-arrange the exponential function into the form y = a×bˣ, where y is the dependent variable and x is the independent variable.
Then you can use the method of least squares to find the values of a and b that best fit the data. The value of a represents the y-intercept of the function, and the value of b represents the growth rate or decay rate of the function.
Once you have found the values of a and b, you can use the exponential function to make predictions about the data set. It is also possible to use software packages like R or Python to do this process.
In conclusion, finding the exponential function of a data set involves using the method of least squares to find the best-fitting exponential function for a given set of data points.
This is typically done by plotting the data points, re-arranging the exponential function, and using the method of least squares to find the values of a and b that best fit the data. The function can then be used to make predictions about the data set.
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Solve this system of equations by graphing. First graph the equations, and then type the solution. y= – x–7 y= 2 3 x–2
Answer:
ez
Step-by-step explanation:
(x,y)=(16/185,-2/185)
2.Which of the following relations is a function?And why?
a. (1,0), (2,0)(3,4)
b. (1,0), (2,0)(2,4)
c. (1,0), (2,0)(3,0)
Answer:
A and B
Step-by-step explanation:
theres one input for each ouput
please help please i'll give all of my points
Question 1(Multiple Choice Worth 2 points)
(Ratios LC)
Hallie and Mattie donated blue jeans to the clothing drive. Hallie donated 3 pairs of blue jeans. Mattie donated 6 pairs of blue jeans. Write a ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans.
3:15
3 over 9
1:2
6 to 18
Question 2(Multiple Choice Worth 2 points)
(Ratios MC)
In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 12 times out of 15 attempts. Tasha has hit the ball 9 times out of 10 attempts. Which player has a ratio that means they have a better batting average?
Tasha, because she has the lowest ratio since 0.9 > 0.8
Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30
Jana, because she has the lowest ratio since 0.9 > 0.8
Jana, because she has the highest ratio since 27 over 30 is greater than 24 over 30
Question 3(Multiple Choice Worth 2 points)
(Ratios MC)
Two students created paintings for their art class. The canvas size used for each is shown.
2 rectangles: Rectangle 1 has a length of 9 feet and width of 6 feet. Rectangle 2 has a length of 3 feet and width of 2 feet.
Which statement is true about the ratios comparing the width and length of each painting?
The paintings' width to length ratios are equal because the ratio 9 to 6 is equal to the ratio 2 to 3.
The paintings' width to length ratios are different because the ratio 3 to 2 is not equal to 9 to 6.
The paintings' width to length ratios are equal because the ratio 6 to 9 is equal to the ratio 2 to 3.
The paintings' width to length ratios are different because the ratio 6 to 9 is not equal to 2 to 3.
Question 4(Multiple Choice Worth 2 points)
(Ratios MC)
The table below shows Addison's novel collection on her bookshelf.
Type of Novel Number of Books
Nonfiction 2
Mystery 4
Fiction 5
What is the ratio of nonfiction novels to all novels?
2 to 9
2:11
5 over 11
1 to 2
Question 5(Multiple Choice Worth 2 points)
(Ratios MC)
The Top-Notch Middle School had athletes from all the grades playing on a sports team.
6th grade 7th grade 8th grade
Basketball 2 4 7
Baseball 1 6 5
Soccer 7 4 4
Football 8 15 10
Explain what the ratio 8:73 represents.
The ratio 8:73 represents the ratio of total athletes to 7th grade football players.
The ratio 8:73 represents the ratio of 6th grade football players to total athletes.
The ratio 8:73 represents the ratio of 8th grade baseball players to total athletes.
The ratio 8:73 represents the ratio of 6th grade athletes to total athletes.
Question 6(Multiple Choice Worth 2 points)
(Ratios MC)
Kim and her friends watched the server making smoothies. The table shows the number of mangos that were used for each of the different sizes of smoothies that the friends ordered.
Mangos Used Smoothie Size
Kim 1 8 oz
Bri 3 24 oz
Angela 4 32 oz
Which statement is correct based on the data?
The ratio of smoothie size to mangos used for Kim is 1:8, and the ratio of smoothie size to mangos used for Bri is 3:24.
The ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.
The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.
The ratio of smoothie size to mangos used for Bri is 64:3, and the ratio of smoothie size to mangos used for Angela is 64:4.
Question 7(Multiple Choice Worth 2 points)
(Ratios MC)
Ms. Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class. If the ratio of students who prefer free time at the beginning of class to students who prefer free time at the end of class is 13 over 17, what does the ratio 13 over 17 represent?
17 students prefer free time at the beginning of class, and 13 students prefer free time at the end of class.
17 students prefer free time at the beginning of class, and 30 students prefer free time at the end of class.
30 students prefer free time at the beginning of class, and 13 students prefer free time at the end of class.
13 students prefer free time at the beginning of class, and 17 students prefer free time at the end of class.
The ratio to describe the number of jeans shared by Hallie and Mattie is obtained as 2 : 3.
What is the ratio of two numbers?The ratio of two numbers a and b can be written as a : b = a/b.
The ratio of two quantities is the unit rate of one quantity with respect to the other.
Here,
The number of jeans donated by Hallie and Mattie are given as 4 and 6 respectively.
It can be written in terms of ratio as 4 : 6.
It can be simplified as,
⇒ 4 : 6
⇒ 4/6
⇒2/3
⇒ 2 : 3
Hence, the number of jeans donated can be written in terms of ratio as 2 : 3.
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Jason bought a total of 7 post-cards for $1.80. If the small postcards cost 20c each and the large ones cost 30c each, how many postcards of each size did he buy
Answer:
3 small postcards; 4 large postcards
I know this. Hope it helps :)
Answer:
4 large post cards and 3 small ones
Please help me with my classwork
Answer: 21d^7
Step-by-step explanation:(7x3) x d^(5+2)
= 21 d^7
Answer:
(7d^5)(3d^2)
7*3 = 21
5+2 = 7
21d^7
Given the right triangle ABC with Altitude BD drawn to hypotenuse AC.If AD=11 and BD=33 What is the length of DC
Answer:
DC = 99
Step-by-step explanation:
BD perpendicular AC
AD/BD = BD/DC
=> DC =DB^2/AD
=33^2/11=99
{calculate}
HELP PLEASE ILL GIVE 50 POINTS PLEASE DUE AT 11:59 WHERE I LIVE I HAVE AN HOUR!!!
i need a conclusion paragraph to the question - Was Abby Sunderland too young to sail solo? - SAYING THAT SHE WAS!
pleaseee the best conclusion will get brainliest!!!!!!!!!!
i am aware the subject is math accident
Answer:
Step-by-step explanation:
In conclusion, it can be argued that Abby Sunderland was too young to sail solo. Despite her ambitious and determined nature, her lack of experience and maturity put her at a significant risk during her solo sailing journey. The fact that she had to be rescued twice during her attempt highlights the dangers of attempting such a feat at such a young age. While it is admirable to have the courage to pursue one's dreams, it is important to consider the potential consequences and weigh them against the potential benefits. In this case, it can be argued that the risks far outweighed the potential rewards.
line L has equation y=1 find the distance between L and the point T(-1,-7)
round answer to nearest tenth
The distance between the line and the point is 8 units.
What is the cartesian plane?When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.
Given a line L,
and the equation of a line is y = 1
actual equation of line is ax + by +c = 0
equation of line is 0x + y - 1 = 0
here a = 0, b = 1 and c = -1
and point T(-1, -7)
distance between line and the point is d = [tex]\frac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2} }[/tex]
x₁ = -1, y₁ = -7
|ax₁ + by₁ + c| = |0(-1) + 1(-7) +(-1)|
|ax₁ + by₁ + c| = 8
√(a² + b²) = √(0² + (1)²) = 1
distance between line and the point is d = 8/1 = 8 units
Hence the distance is 8 units.
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What are types of exponents?
Exponents can be classified into four types: integer, rational, irrational, and complex exponents. They represent repeated multiplication, roots, and advanced concepts such as complex numbers.
Integer exponents are the most common type of exponents and include positive integers, negative integers, and zero. They are used to represent repeated multiplication, for example, 2^3 represents 2 multiplied by itself 3 times.Rational exponents are the exponents which can be written in the form of a fraction, for example, (2^(1/3)) represent the cube root of 2.Irrational exponents, as the name implies, are exponents that are irrational numbers, for example, 2^(1.23).Complex exponents are the exponents which are complex numbers, for example, 2^(3+4i). These exponents are less common and typically seen in advanced math and engineering.Learn more about Types of Exponents here:
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Combine like terms 3x-7x=
Answer:
-4x
Step-by-step explanation:
3-7=-4 just add a x
Which of the following is a solution of the linear equation 3x 2y 5?
The general solution of the linear equation 3x + 2y = 5 is y = (-3/2)x + 5/2.
To find the solution of the linear equation 3x + 2y = 5, we can use the method of isolating one variable and then substituting that value back into the equation.
3x + 2y = 5
First we can try to isolate y:
2y = -3x + 5
then we divide by 2
y = -(3/2)x + 5/2
So one solution of the equation is (x,y) = (-(3/2)x + 5/2)
Therefore, the solution of the linear equation 3x + 2y = 5 is y = -(3/2)x + 5/2.
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what is the probability that this dancer raised less than £10
The probability that this dancer raised less than £10 is; 19/30
How to find the probability?Probability is defined as the number of successful outcomes divided by the total number of outcomes. Thus;
Probability = number of successful outcomes/total number of outcomes
From the attached table, we see that;
£4.99 of less: Number of dancers are 15
£5 to £9.99: Number of dancers are 23
£10 to £14.99: Number of dancers are 12
£15 to £19.99: Number of dancers are 7
£20 to £24.99: Number of dancers are 3
Thus, we see that the total number of dancers = 15 + 23 + 12 + 7 + 3 = 60 dancers.
If a dancer is chosen at random, the probability that the dancer raised less than £10 = (23 + 15)/60 = 38/60 = 19/30
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Complete question is;
A group of dancers raised some money for a charity here is some information about the money raised
One of the dancers is chosen at random to give the money raised to the charity
What is the probability that this dancer raised less then £10
A survey was conducted to investigate whether alcohol consumption and smoking are related. In a random sample of 300 smokers, 196 said they had consumed alcohol at least once in the past week. In an independent random sample of 300 non-smokers, 159 said they had consumed alcohol in the past week. If P, is the proportion of smokers in the population who have had a drink in the past week and Po is the corresponding proportion of non-smokers, then a test of the hypotheses H P, -P = 0 against the two-sided alternative produces a test statistic of := 3.07 and a P-value of 0.002. If we had instead analyzed these results with a chi-square test of homogeneity, which of the following would be the test statistic and P-value?
a. 7-9.42, P-value = 0.002
b. 7-9.42, P-value - 0.004
c. - 3.07, P-value = 0.004
The Correct answer is option a. 7-9.42, P-value = 0.002 which is derived based on the given data about alcohol consumption.
The chi-square test of homogeneity is a statistical test used to determine whether there is a significant difference between the observed frequencies of two categorical variables.
In this case, the test statistic would be the chi-square value calculated using the observed frequencies of alcohol consumption in the sample of smokers and non-smokers, and the P-value would be the probability of obtaining a chi-square value as extreme or more extreme than the calculated value under the assumption that the null hypothesis is true (i.e. no difference in alcohol consumption between smokers and non-smokers).
In this case, the test statistic would be 7.942 and the P-value would be 0.002 which implies that there is a significant difference in alcohol consumption between smokers and non-smokers.
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A frozen yogurt shop has a combination of 150 small and medium sized bowls on their counter. Each small bowl holds 4 oz and each medium bowl holds 6 oz. If the bowls on the counter will hold a total of 764 oz find the number of small and medium sized bowls on the counter
The number of small sized bowls on the counter = 68 bowls
The number of medium sized bowls on the counter = 82 bowls
What is an equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
From the data given,
Let the number of small bowls on the counter be = x
Let the number of medium bowls on the counter be = y
The total number of bowls is = 150
So , the equation will be
x + y = 150 be equation (1)
The amount the small bowl can hold = 4 ounces
The amount the medium bowl can hold = 6 ounces
The total amount of all the bowls on the counter = 764 ounces
So , the equation will be
4x + 6y = 764 be equation (2)
Now , on simplifying the equation (1) and equation (2) ,
Multiply equation (1) by 4 , we get
4x + 4y = 600 be equation (3)
Subtracting equation (3) from equation (2) , we get
2y = 164
Divide by 2 on both sides , we get
y = 82
Therefore the number of medium sized bowl is 82 bowls
Substituting the value of y in equation (1) , we get
x + y = 150
x + 82 = 150
Subtracting 82 on both sides , we get
x = 68
Therefore , the number of small sized bowl is 68 bowls
Hence,
The number of small sized bowls on the counter = 68 bowls
The number of medium sized bowls on the counter = 82 bowls
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