The Triangle and square shown below have the same perimeter What is the length of one side of the square

a. 240 students were surveyed in all. b. 60 students chose blue. c. The number of students who chose purple is 7, green is 10, others is 7 students.

In mathematics, a proportion is a statement that two ratios or fractions are equal. A proportion can be expressed as an equation of the form:

a/b = c/d

where a, b, c, and d are numbers, and b and d are not equal to zero. This equation can also be written in the form of a cross product:

ad = bc

This equation means that the product of the numerator of one fraction and the denominator of the other fraction is equal to the product of the denominator of the first fraction and the numerator of the second fraction.

a. If 20% of the students surveyed chose yellow and 48 students chose yellow, we can set up the following proportion to find the total number of students surveyed (let "x" be the total number of students):

20/100 = 48/x

Solving for x, we get:

x = 240

Therefore, 240 students were surveyed in all.

b. 25% of the students surveyed chose blue, so the number of students who chose blue is:

25/100 x 240 = 60

Therefore, 60 students chose blue.

c. We are given that 3% of the students surveyed chose purple, and 4% chose green. To find the number of students who chose purple or green, we can add the two percentages and find the corresponding portion of the total number of students:

3/100 + 4/100 = 7/100

So 7% of the students surveyed chose purple or green. The number of students who chose purple is:

3/100 x 240 = 7.2 (rounded to the nearest whole number, this is 7)

Similarly, the number of students who chose green is:

4/100 x 240 = 9.6 (rounded to the nearest whole number, this is 10)

We are also given that 3% of the students surveyed chose "other". Therefore, the number of students who chose "other" is:

3/100 x 240 = 7.2 (rounded to the nearest whole number, this is 7)

So 7 students chose "other".

To know more about surveyed visit:

https://brainly.com/question/28656803

#SPJ1

Yes, dog will catch the frisbee. The coordinates of the point or points where they meet are (0,6) and (6,18). So, option(a) is correct answer for this question.

I have a training your dog to catch a frisbee. The path equation of frisbee is y= –x² + 8x + 6 --(1)

and the path equation of the dog is modeled by

y = 2x + 6 --(2)

We have to check dog catch the frisbee or not and also determine the coordinates. The dog will catch the frisbee, when both equations are intersect to each other. That is intersection point of equation (1) and (2) are the required coordinates. Now, we determine the intersection points between the equation (1) and (2).

Substituting the value of y from equation (2) to equation (1), y = 2x + 6 in y = - x² + 8x + 6

=> 2x + 6 = -x² + 8x + 6

Simplify, x² - 8x + 2x = 6-6

=> x² - 6x = 0

=> x( x - 6) = 0

either x = 0 or x -6 = 0

=> x = 0, x= 6

from equation (1), y = 2(0) + 6 = 6

when x = 6, y = 2(6) + 6 = 18

Hence, required coordinates are (0,6) and (6,18).

For more information about intersection points, visit :

https://brainly.com/question/25723413

#SPJ4

Complete question:

You are training your dog to catch a frisbee. You are playing in a large field, and you are standing next to your dog when you throw the frisbee. If the path of the frisbee is y= –x² + 8x + 6 and the path of the dog is modeled by y = 2x + 6, will the dog catch the frisbee? If so, what are the coordinates of the point or points where they meet?

a) Yes, they intersect at the coordinates (0, 6) and (6, 18)

b) Yes, they intersect at the coordinates (1, 13) and (2, 10)

c) Yes, they intersect at the coordinates (2, 18) and (3, 12)

d)No, the paths do not cross

Answer:

(c+1)(c+2)

Step-by-step explanation:

you need to find the two numbers that get 2 when you multiply them and get 3 when you add them. those two numbers are 2 and 1 and c times c is c^2

you can check the answer by using foil like this:

(c+1)(c+2)

first: c times c= c^2

second: 2 times c= 2c

third: 1 times c= 1c

last: 1 times 2= 2

and all that together you get c^2+2c+1c+2

simply and get C^2+3c+2

Sharon worked 49 hours to earn $749.

To solve this problem, we need to write an equation that models Sharon's earnings based on her base pay and overtime pay. The equation is as follows:

Earnings = (Base pay x Regular hours) + (Overtime pay x Overtime hours)

Since Sharon earns a base pay of $14 per hour and time and a half for overtime, her overtime pay is $14 x 1.5 = $21 per hour. We can plug these values into the equation:

$749 = ($14 x 40) + ($21 x Overtime hours)

Solving for the overtime hours, we can rearrange the equation and isolate the variable on one side:

$749 - $560 = $21 x Overtime hours

$189 = $21 x Overtime hours

Overtime hours = 9

Therefore, Sharon worked 9 hours of overtime in addition to her regular 40 hours, for a total of 49 hours.

To know more about Base pay click on below link:

https://brainly.com/question/5690738#

#SPJ11

The forecasted sales volume is 34.116 thousand Euro if the investment volume is planned to be 30 thousand Euro.

Let's solve this problem step by step:

Calculate the correlation coefficient (r) using the formula:
r = (ΣXY - (ΣX)(ΣY)/n) / sqrt([(ΣX^2 - (ΣX)^2/n)(ΣY^2 - (ΣY)^2/n)])

Plug in the given values into the formula:
r = (126.54 - (22)(66)/12) / sqrt([(45.8 - (22)^2/12)(369.94 - (66)^2/12)])

Simplify the formula and solve for r:
r = (126.54 - 121) / sqrt([(45.8 - 40.333)(369.94 - 363)])
r = 5.54 / sqrt[(5.467)(6.94)]
r = 5.54 / 4.967
r = 1.115

Make conclusions about the closeness of the linear relationship based on the value of r:
Since the value of r is close to 1, this indicates a strong positive linear relationship between the investments (X variable) and the main product's sales (Y variable).

Find the linear regression from variable Y to the X using the formula:
Y = a + bX

Calculate the slope (b) using the formula:
b = (ΣXY - (ΣX)(ΣY)/n) / (ΣX^2 - (ΣX)^2/n)

Plug in the given values into the formula and solve for b:
b = (126.54 - (22)(66)/12) / (45.8 - (22)^2/12)
b = 5.54 / 5.467
b = 1.013

Calculate the intercept (a) using the formula:
a = (ΣY - b(ΣX))/n

Plug in the given values into the formula and solve for a:
a = (66 - 1.013(22))/12
a = 44.714/12
a = 3.726

Plug in the values of a and b into the linear regression formula:
Y = 3.726 + 1.013X

Forecast the sales volume if the investment volume is planned to be 30 thousand Euro by plugging in the value of X into the linear regression formula:
Y = 3.726 + 1.013(30)
Y = 3.726 + 30.39
Y = 34.116

Therefore, the forecasted sales volume is 34.116 thousand Euro if the investment volume is planned to be 30 thousand Euro.

Learn more about Sales

brainly.com/question/29857652

#SPJ11

Answer: To find the area of the white part of the billboard, we first need to find the area of the entire billboard and then subtract the area of the non-white part.

The area of a triangle can be found using the formula:

Area = (1/2) x base x height

In this case, the white part of the billboard is a right-angled triangle with a height of 4 ft and a base of 2.5 ft (half of the total base of 4.5 ft).

The area of the entire billboard is:

Area = (1/2) x base x height

Area = (1/2) x 4.5 ft x 4 ft

Area = 9 ft²

The area of the non-white part of the billboard is:

Area = (1/2) x base x height

Area = (1/2) x 2.5 ft x 4 ft

Area = 5 ft²

Therefore, the area of the white part of the billboard is:

Area of white part = Total area - Area of non-white part

Area of white part = 9 ft² - 5 ft²

Area of white part = 4 ft²

So the area of the white part of the billboard is 4 square feet.

Step-by-step explanation:

We can use the formula for compound interest to find the amount in the account after 5 years:

A = P(1 + r/n)^(nt)

where:

A = the amount in the account after 5 years

P = the principal (initial amount) = $200.00

r = the annual interest rate as a decimal = 0.09

n = the number of times the interest is compounded per year = 1 (compounded annually)

t = the time in years = 5

Plugging in the values, we get:

A = $200.00(1 + 0.09/1)^(1*5)

A = $200.00(1.09)^5

A = $200.00(1.538624)

A = $307.72

Therefore, there will be $307.72 in the account after 5 years.

The solution of the system of equations by substitution method is 3x + 4(2x - 7) = 16, The correct option is D.

To solve the system of equations {y=2x-7, 3x+4y=16} using substitution, we can solve the first equation for y in terms of x (or x in terms of y) and substitute this expression into the second equation.

Solving the first equation y=2x-7 for y, we get:

y = 2x - 7

We can substitute this expression for y into the second equation 3x+4y=16, replacing y with 2x-7, to get:

3x + 4(2x - 7) = 16

Therefore, the expression after substituting the value of y is 3x + 4(2x - 7) = 16.

To know more about substitution methods follow

https://brainly.com/question/22340165

#SPJ9

Answer:

x=6x³-5x²-66x-40

Step-by-step explanation:

Please mark as brainliest

The point on Π that is closest to A is (3,-2,0).

(a) The distance between the plane Π and the point A is 3. To find this, we need to find the equation of the plane Π. The equation of the plane is given by:

Ax + By + Cz + D = 0

where (A, B, C) is the normal vector to the plane, which is perpendicular to the line that passes through points A and B. Since the normal vector of the plane is perpendicular to the line, the normal vector (A, B, C) is equal to the cross product of the two vectors of the line AB, given by:

A=(3,0,-2), B=(-1,1,0)

A x B = (A2B3-A3B2, A3B1-A1B3, A1B2-A2B1) = (-5,3,3)

Therefore, the equation of the plane Π is:

-5x + 3y + 3z + D = 0

To find D, we need to plug in the coordinates of the point (1,2,3). Therefore,

-5(1) + 3(2) + 3(3) + D = 0
-5 + 6 + 9 + D = 0
D = -20

Therefore, the equation of the plane Π is:

-5x + 3y + 3z - 20 = 0

To find the distance between the plane Π and the point A, we need to calculate the shortest distance between the plane and the point A. We can do this using the distance formula, given by:

d = |Ax + By + Cz + D|/sqrt(A^2 + B^2 + C^2)

Substituting the equation of the plane Π and the coordinates of point A into the distance formula, we get:

d = |-5(3) + 3(0) + 3(-2) - 20|/sqrt(-5^2 + 3^2 + 3^2)
d = |-15 - 20|/sqrt(34)
d = |-35|/sqrt(34)
d = 3

Therefore, the distance between the plane Π and the point A is 3.

(b) The point on Π that is closest to A is (3,-2,0). To find this, we need to solve the system of equations given by:

-5x + 3y + 3z - 20 = 0
x - 3 = 0
y - 0 = 0
z + 2 = 0

Solving this system of equations, we get x = 3, y = -2, and z = 0. Therefore, the point on Π that is closest to A is (3,-2,0).

Learn more about vectors

brainly.com/question/29740341

#SPJ11

Answer:

g(x) = f(x + 2) = 2^(x + 2) + 2

Step-by-step explanation:

To shift the function f(x) = 2^x + 2 two units to the left, we need to replace x with (x + 2) in the equation. This will shift the graph horizontally to the left by two units.

So, the new function g(x) that represents the shifted graph is:

g(x) = f(x + 2) = 2^(x + 2) + 2

By answering the above question, we may state that The circle's radius is  radius 8.5 feet as a result.

In more modern use, a circle's or sphere's length is equal to its radius, and it is one of the line segments connecting the object's centre and circumference. The phrase is derived from the Roman word circle, which also describes a waggon wheel's spokes. The radius of a circle is the separation of any points on its circumference from its centre. Often, it is denoted by "R" or "r". A line segment with one termination in the centre and one on the circle's perimeter is called a radius. Radius = circular diameter A circle's diameter is the portion that passes through its centre and has ends on the circle.

The formula for calculating a circle's circumference is:

C = 2πr

When r denotes the radius, C denotes the circumference, and denotes a mathematical constant roughly equal to 3.14159.

We are informed that the circle's diameter is 17 feet. We may solve for r by setting this equal to the circumference formula:

17π = 2πr

By multiplying both sides by 2, we obtain:

r = 17π / (2π)

The units are cancelled, leaving:

r = 17 / 2

Examining this expression results in:

r = 8.5 ft

The circle's radius is 8.5 feet as a result.

To know more about radius visit:

https://brainly.com/question/28946570

#SPJ1

The Big Ideas or Focal Points in the mathematics curriculum in grade 5 are:
1. Number Sense and Algebraic Thinking. 2. Geometry and Spatial Sense. 3. Data Analysis and Probability. 4. Measurement and Estimation. 5. Problem Solving

1. Number Sense and Algebraic Thinking - understanding numbers, relationships between numbers, and operations;
2. Geometry and Spatial Sense - understanding, representing, and reasoning with two- and three-dimensional shapes;
3. Data Analysis and Probability - understanding, organizing, and interpreting data;
4. Measurement and Estimation - understanding units of measurement and making reasonable estimates;
5. Problem Solving - applying appropriate strategies to solve mathematical problems.


These Big Ideas or Focal Points are important because they help students to develop a deeper understanding of mathematical concepts and to build a strong foundation for further learning in mathematics. By focusing on these key concepts, students are able to gain a better understanding of how mathematics works and how it can be applied in real-world situations.

Know more about Focal Points here:

https://brainly.com/question/30761313

#SPJ11

1. The population in 2005 was 5000

2. when t is -2, it indicates that 1250 the population before 2 years was 1250

3. For t  - -2 population was more than 1000

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal.

a. To find the population of the fish species in 2005, we need to plug in t = 0 into the equation:

p = 5,000 .2^t

p = 5,000 .2^0

p = 5,000

Therefore, the population of the fish species in 2005 was 5,000.

b. When t is -2, it means we are two years before 2005, the year when the fish population in the lake was first surveyed. In other words, we are trying to find the population of the fish species two years before 2005. To do this, we plug in t = -2 into the equation:

p = 5,000 .2^t

p = 5,000 .2^-2

p = 5,000 .25

p = 1,250

Therefore, the population of the fish species two years before 2005 was 1,250.

c. The fish population at t = -2 is more than 1,000. We know this because we calculated that the population was 1,250, which is greater than 1,000.

To know more about Equation check:

https://brainly.com/question/1529522

#SPJ9

The correct option would be s must be less than 35.

Option (A) is correct.

What is inequality?

In mathematics, an inequality is a mathematical statement that compares the values of two expressions or quantities using a relational symbol such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).

A. s must be less than 35.

The inequality s < 35 means that the speed s must be less than 35 miles per hour, which is the speed limit on the neighborhood road. Therefore, statement A is true. Statement B is false because the least possible value of s is zero, not 35. Statement C is false because the greatest possible value of s is infinite, although there may be practical limits to how fast a vehicle can go on a neighborhood road. Statement D is false because s cannot be greater than 35 if the speed limit is 35 miles per hour.

Hence, the correct option would be s must be less than 35.

Option (A) is correct.

To learn more about inequalities, visit:

https://brainly.com/question/24372553

#SPJ1

The correct answer is option A, counter clockwise 90°, for the needle to lean on the outline section, the wheel must be turned counter clockwise 90°. Any other turn of the wheel will not result in the needle leaning on the outline section.

Counterclockwise is an adjective used to describe motion or rotation that is in the opposite direction of a clock's hands. For example, when a person swims in a pool, they may swim counterclockwise around the perimeter of the pool. This is the opposite direction of the way a clock's hands move. Counterclockwise rotation is also known as anti-clockwise rotation.

When an object is placed on a flat surface and the wheel is turned, it will rotate in the same direction as the motion of the wheel. If the needle is leaning on the outline section, the wheel must be turned counter clockwise 90°. This is because when the wheel is turned counter clockwise, the needle will be forced to move in the same direction and end up leaning on the outline section.

When the wheel is turned clockwise, the needle will move in the opposite direction and it will not end up leaning on the outline section. Therefore, a clockwise turn of 120° or 180° is not the correct answer. Similarly, turning the wheel counter clockwise by 180° is also not the correct answer. This is because the needle will end up pointing in the same direction it was pointing before the wheel was turned.

In conclusion, for the needle to lean on the outline section, the wheel must be turned counter clockwise 90°. Any other turn of the wheel will not result in the needle leaning on the outline section.

For more questions related to direction

https://brainly.com/question/28336821

#SPJ9

Answer:

A. counter clockwise 90°.

Step-by-step explanation:

Given that diameter of a circle is 7 ft, its area to the nearest tenth is 38.5 square feet.

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2 where r is the radius of the circle.

To find the radius, we can divide the diameter by 2: r = d/2 = 7/2 = 3.5 ft

Now we can plug this into the formula for the area:

A = πr^2

A = π(3.5)^2

A ≈ 38.48

Therefore, rounding to the nearest tenth, the area of the circle is approximately 38.5 square feet.

Read more about area

brainly.com/question/25292087

#SPJ1

Tyler takes 32 minutes to read 24 pages.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Tyler reads 3/4 pages per minute. Then the ratio of pages to minutes is given as,

Ratio = (3/4)/1

Ratio = 3:4

If he read 16 minutes, then the number of pages is calculated as,

(3/4) x 16

3 x 4

12 pages

Tyler has to read 24 pages for homework. Then the number of minutes is given as,

24 / (3/4)

24 x (4/3)

8 x 4

32 minutes

Therefore, it takes 32 minutes to read 24 pages.

To learn more about the ratio visit:

brainly.com/question/13419413.

#SPJ1

Answer:

First, we need to calculate the total cost of Lisa's and Tracy's lunches before tax and tip.

Lisa's lunch = $6

Tracy's lunch = $7

Total before tax and tip = $6 + $7 = $13

Now we need to add the 5% sales tax:

$13 x 0.05 = $0.65

Total after tax = $13 + $0.65 = $13.65

Finally, we need to add the 15% tip:

$13.65 x 0.15 = $2.05

Total bill = $13.65 + $2.05 = $15.70

Therefore, the total bill, including tax and tip, is $15.70.

Answer:

Step-by-step explanation:

6 + 7 = 13

Now for the sales tax and tip, we need to add 15 and 5 together which is 20. So now we need to multiply 13 times the decimal equivalent of 20%. So, 0.20 x 13 = 2.6

2.6 + 13 = 15.6

The answer is 15.6

Answer:

I think you forgot a picture

An οdd number squared is always an οdd number, and we have prοved it fοr the case οf (2n+1)².

An integer is a whοle number that can be either pοsitive, negative, οr zerο. It dοes nοt have a fractiοnal οr decimal cοmpοnent.

Tο prοve that an οdd number squared is an οdd number, we can start by expressing an οdd number as 2n+1, where n is an integer.

Then, we can square this expressiοn tο get:

(2n+1)² = (2n+1)(2n+1)

Expanding the right side οf the equatiοn using the distributive prοperty, we get:

(2n+1)² = 4n² + 2n + 2n + 1

Simplifying the expressiοn by cοmbining like terms, we get:

(2n+1)² = 4n² + 4n + 1

Nοw we can see that the first twο terms, 4n² and 4n, are bοth even since they cοntain a factοr οf 2. Adding twο even numbers always results in an even number.

Therefοre, the sum οf 4n² and 4n is even.

Adding 1 tο an even number results in an οdd number.

Therefοre, we have shοwn that:

(2n+1)² = 4n² + 4n + 1 = (2n² + 2n) + 1 = 2n(n+1) + 1

Since 2n(n+1) is even, the sum οf 2n(n+1) and 1 is οdd.

Hence, an οdd number squared is always an οdd number, and we have prοved it fοr the case οf (2n+1)².

To learn more about integers from the given link.

https://brainly.com/question/1768254

#SPJ1

The volume of the Nestle Cremora Carton container is 400 m³

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The volume of a cuboid is given as:

Volume = Length * Width * Height

The question is incomplete. Let us assume that the container dimensions are as follows:

The Nestle Cremora Carton container is in the shape of a cuboid. Hence:

Volume of container = length * width * height = 10 m * 8 m * 5 m = 400 m³

The volume is 400 m³

Find more on equation at: https://brainly.com/question/2972832

#SPJ1

Tracy's total investment is $4,940. The Option A is correct.

An investment basically means the process of exchanging income during one period of time for an asset that is expected to produce earnings in future periods.

To find Tracy's total investment, we need to calculate the cost of buying 150 shares of Upton Group and 100 shares of WHI Health.

For 150 shares of Upton Group:

Total cost = number of shares × offer price

Total cost = 150 × $18.96

Total cost = $2,844

For 100 shares of WHI Health:

Total cost = number of shares × offer price

Total cost = 100 × $20.96

Total cost = $2,096

Tracy's total investment is the sum of these two costs:

Total investment = $2,844 + $2,096

Total investment = $4,940.

Read more about investment

brainly.com/question/29547577

#SPJ1

A. My sister is a graduate of Polytechnic University and a border services officer who lives in North Delta.
B. Yesterday, Jasmine left to visit her friend in Alberta.
A. They listened to relaxing music while they did their homework, which helped them concentrate.
B. To help them focus on their homework, they listened to relaxing music.

Combining sentences is a useful writing technique that helps make sentences concise and easy to read. Combining two or more sentences into one sentence can also help to create smoother transitions between ideas. When combining sentences, it is important to make sure the sentence remains grammatically correct, and to retain important information from the original sentences.

Another way to combine sentences is to delete certain words or phrases. For example, in the sentence “Yesterday, Jasmine left to visit her friend in Alberta”, the phrase “yesterday” can be removed without changing the meaning of the sentence.

You can also combine sentences by changing the order of the words. For example, in the sentence “They listened to relaxing music while they did their homework, which helped them concentrate”, the order of the words can be changed to “They did their homework while they listened to relaxing music, which helped them concentrate”.

Finally, it is important to make sure that the sentence remains grammatically correct. When combining sentences, it is important to make sure that the sentence still has a subject and verb, and that the verb is still in the correct tense.

For more about Polytechnic University:

https://brainly.com/question/28067175

#SPJ11

The inequality to represent the given scenario is b≥ [tex]22\frac{2}{3}[/tex]. Therefore, option A is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, at Dublin International Airport if your luggage weighs more than  [tex]22\frac{2}{3}[/tex] kilograms, you will be charged an additional baggage fee for the overweight luggage.

So, the inequality is b≥ [tex]22\frac{2}{3}[/tex]

Therefore, option A is the correct answer.

To learn more about the inequalities visit:

https://brainly.com/question/20383699.

#SPJ1

The given statement is true for all matrices A.

1) For any 2x2 matrices A and B, (AB)2 = A2B2 - False. A counter-example to this claim would be if A and B are non-invertible matrices, such as A = [1, 0; 0, 0] and B = [1, 0; 0, 1]. (AB)2 = [1, 0; 0, 0], but A2B2 = [1, 0; 0, 1].

2) For any 2x2 matrices A, B, and C, if AB = AC, then B = C - True. This statement is true, as long as A is an invertible matrix. This can be seen from the properties of matrix multiplication; if AB = AC, then B = A-1AC = C.

3) For any 2x2 matrix A, if A2 = A, then either A = 0 or A = I - False. A counter-example to this claim would be if A = [1, 0; 0, 0], then A2 = A = [1, 0; 0, 0], but A ≠ 0 and A ≠ I.

1) Counter-example:Let the matrices A and B be given by\[A=\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}, B=\begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}\].Now,\[(AB)^2=\begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}^2=\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}\].and\[A^2B^2=\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}^2\begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}^2=\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}=\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}\]Hence\[(AB)^2\ne A^2B^2\]2) Let AB=AC. Then, we need to show that B=C. Let A, B and C be given as follows:\[A=\begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}, B=\begin{pmatrix} 3 \\ 4 \end{pmatrix}, C=\begin{pmatrix} 5 \\ 6 \end{pmatrix}\].Now, AB=\[\begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}\begin{pmatrix} 3 \\ 4 \end{pmatrix}=\begin{pmatrix} 11 \\ 4 \end{pmatrix}\]and AC=\[\begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}\begin{pmatrix} 5 \\ 6 \end{pmatrix}=\begin{pmatrix} 11 \\ 6 \end{pmatrix}\]Thus,\[AB=AC\]But, B=\[\begin{pmatrix} 3 \\ 4 \end{pmatrix}\]and C=\[\begin{pmatrix} 5 \\ 6 \end{pmatrix}\].Therefore,\[B\ne C\]Thus, AB=AC does not imply that B=C.3) True.According to the given statement, \[A^2=A\]Then,\[A^2-A=0\]⇒\[A(A-I)=0\]Either A=0 or A=I. Thus, the given statement is true for all matrices A.

Learn more about invertible matrix

brainly.com/question/18187793

#SPJ11

By answering the above question, we may state that  The two lines intersect at the point (1, -2), so the system of linear equations has one solution at (1, -2).

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A formal statement that proves the equality of two calculations is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two phrases that are inscribed on opposite sides of a letter. Frequently, the logo and indeed the particular software are identical. like in 2x - 4 = 2, for example.

The two lines intersect at the point (1, -2), so the system of linear equations has one solution at (1, -2).

Therefore, the answer is: One solution at (1, −2).

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

The median, Q₁, Q₃, lower fence and upper fence of the given data set are 82, 75, 83, 63 and 95.

What is Inter quartile range?

In a range of values, from lowest to highest, the IQR denotes the median 50% of values. Find the median (middle value) of the lower and higher half of the data first, then use that number to calculate the interquartile range (IQR). The first quartile (Q1) and third quartile (Q3) of these values (Q3). What separates Q3 from Q1 is known as the IQR.

Given data set : 72, 81, 82, 83, 83, 85, 100, 54, 75, 81, 83

Firstly, we will arrange the data into ascending order.

we get, 54, 72, 75, 81, 81, 82, 83, 83, 83, 85, 100.

Here, no. of terms is 11

So, Median = (n+1)/2 th = (11+1)/2 = 6th term

So, Median = 82.

Q₁ = (n+1)/4 th term = (11+1)4 th = 3rd term

                                                 = 75

Q₃ = 3(n+1)/4 th term = 9th term = 83

Inter-quartile range = Q₃ - Q₁

                                  = 83 - 75 = 8.

Now, Lower fence = Q₁ - 1.5*IQR

                              = 75 - 1.5× 8

                              = 75 - 12 = 63

       Upper fence = Q₃ + 1.5*IQR

                              = 83 + 1.5×8

                              = 83 + 12

                              = 95.

To learn more about Median and Outliers, visit the link:

https://brainly.com/question/26177250

#SPJ1

The polynomial function will be x³ + (3-√2)x² - 3√2x = 0.

What is a polynomial function?

A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable.

The simplest straightforward and typical mathematical equation is one with polynomial functions. It can be described using a polynomial. The polynomial function is modelled by a polynomial equation. A polynomial is typically written as P. (x). The degree of a polynomial is the largest exponent of the variable P(x). Understanding a polynomial's degree is crucial since it explains how function P(x) behaves as the value of x increases. Polynomial functions only apply to real numbers in their domain (R).

Given : zeros of polynomial = 0, -3 and √2

So, the polynomial function can be found :

  = (x-0) (x+3)(x-√2)

  = x (x+3) (x-√2)

  = (x²+3x) (x-√2)

  = x³ -√2x² + 3x² - 3√2x

  = x³ + (3-√2)x² - 3√2x

To learn more about Polynomial, visit the link:

https://brainly.com/question/2833285

#SPJ1

Answer:

B. 3:1

Step-by-step explanation:

45 : 15

Divide both side by 15

= 3 : 1