Students have received the marks for their Mathematics quiz. Ali found out that Ahmad's marks is five more than double of his marks. If the total of their marks is 125, what is Ali's marks and what is Ahmad's marks?​

Answers

Answer 1

Answer:

Ali's mark= 40

Ahmad's mark= 85

Step-by-step explanation:

Let x be Ali's mark and y be Ahmad's mark.

y=2x+5

x+y=125

x+2x+5=125

3x=120

x=40

y=85


Related Questions

determine whether each relationship is proportional by graphing on a coordinate plane. explain your reasoning.

Answers

This answer states that when graphing a linear relationship (y = 2x) on a coordinate plane, the points form a straight line, indicating that the relationship is proportional. However, when graphing a non-linear relationship (y = x2) on a coordinate plane, the points form a parabolic curve, indicating that the relationship is not proportional.

A: Relationship 1:

The relationship between x and y is y = 2x.

When graphed on a coordinate plane, the points (0,0), (1,2), (2,4), (3,6), and (4,8) form a straight line, indicating that the relationship is proportional.

Relationship 2:

The relationship between x and y is y = x2.

When graphed on a coordinate plane, the points (0,0), (1,1), (2,4), (3,9), and (4,16) form a parabolic curve, indicating that the relationship is not proportional.

This answer states that when graphing a linear relationship (y = 2x) on a coordinate plane, the points form a straight line, indicating that the relationship is proportional. However, when graphing a non-linear relationship (y = x2) on a coordinate plane, the points form a parabolic curve, indicating that the relationship is not proportional.

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A bird of species ​ A, when diving, can travel 5 times as fast as a bird of species B top speed. If the total speeds for these two birds is 222 miles per ​ hour, find the fastest speed of the bird of species A and the fastest speed of the bird of species B.

Answers

The fastest speed of the bird of species A is 185 mph and the fastest speed of the bird of species B is 37 mph

What is an equation?

An equation is an expression showing the relationship between numbers and variables.

Let a represent the top speed of bird A and b represent the top speed of bird B.

A bird of species ​ A, when diving, can travel 5 times as fast as a bird of species B top speed, hence:

a = 5b

a - 5b = 0     (1)

If the total speeds for these two birds is 222 miles per hour, hence:

a + b = 222    (2)

To solve by elimination method, subtract equation 2 from 1, hence:

-6b = -222

Dividing by -6:

b = 37

Put b = 37 in equation 2:

a + 37 = 222

a = 185

The speed of the bird are 185 miles per hour and 37 miles per hour

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Help plss i don’t know an easy way to do this

Answers

Answer:   2

See the diagram below.

=================================================

Explanation:

Pick two points on this diagonal line. I'll go for (0,-3) and (1,-1)

Apply the slope formula to those coordinates.

[tex](x_1,y_1) = (0,-3) \text{ and } (x_2,y_2) = (1,-1)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-1 - (-3)}{1 - 0}\\\\m = \frac{-1 + 3}{1 - 0}\\\\m = \frac{2}{1}\\\\m = 2\\\\[/tex]

A slope of 2, aka 2/1, means "move up 2, then right 1".

This "up 2, right 1" motion allows us to move from (0,-3) to (1,-1) as shown in the diagram below.

Use the method of successive differences to determine the next number in the given sequence 3, 7, 17, 33, 55, 83, 117

Answers

The next number in the sequence is 151.

What is the successive differences?

The method of successive differences involves finding the differences between consecutive terms in a sequence and using that information to predict the next term in the sequence.

To use this method for the sequence 3, 7, 17, 33, 55, 83, 117:

Find the differences between consecutive terms:

7 - 3 = 4

17 - 7 = 10

33 - 17 = 16

55 - 33 = 22

83 - 55 = 28

117 - 83 = 34

Check if the differences are constant. In this case, they are increasing by 6 each time.

Use this information to predict the next term in the sequence:

117 + 34 = 151

So, the next number in the sequence is 151.

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−4≤−2(y−1)<2
Step 1 of 2 : Solve the inequality and express your answer in interval notation. Use decimal form for numerical values.

Answers

The inequality is solved to and represented in interval notation as follows

(-∞, 3] [0, ∞)

How to find the values of y in the inequality

The inequality is made of two sets and can be separated as

−4 ≤ −2(y − 1)

−2(y − 1) < 2

solving the first

−4 ≤ −2(y − 1)

−4 ≤ −2y + 2

−4 - 2 ≤ −2y

-6 ≤ −2y

divide through by -2

y ≤ 3

solving the second

−2(y − 1) < 2

−2y + 2 < 2

−2y < 2 - 2

−2y < 0

divide through by -2

y > 0

the inequality in interval notation is

(-∞, 3] [0, ∞)

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A probability experiment is conducted in which the sample space of the experiment is S={ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, event F={5, 6, 7, 8, 9}​, and event G={9, 10, 11, 12}. Assume that each outcome is equally likely. List the outcomes in F or G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule.
List the outcomes in F or G. Select the correct choice below​and, if​ necessary, fill in the answer box to complete your choice.
A. F or G = { _____ }
​(Use a comma to separate answers as​ needed.)

Answers

F or G = { 5,6,7,8,9,10,11,12 } is probability  P(F or G) using the general addition rule.

What are examples and probability?

The likelihood that something will happen is called the probability. the total number of conceivable outcomes.

                                   For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). P(heads) = 12 is what we write.  the forerunners of the contemporary mathematical theory of probability (for example the "problem of points").

S={ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14},

event F={5, 6, 7, 8, 9}​, and

event G={9, 10, 11, 12}.

F or G = { 5,6,7,8,9,10,11,12 }

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5 of 5
Find the 8th term of the sequence below.
Tn = 2n²-3n - 6
T8 =
Sorry again I don’t understand how to do this :(

Answers

Answer:

8th term = 98

Step-by-step explanation:

Given equation,

→ Tn = 2n² - 3n - 6

Now the 8th term will be,

→ Tn = 2n² - 3n - 6

→ T8 = 2(8)² - 3(8) - 6

→ T8 = 2(64) - 24 - 6

→ T8 = 128 - 30

→ [ T8 = 98 ]

Hence, the 8th term is 98.

Rewrite (2+3)+4 using the Associative Law of Addition

Answers

Answer:

9 is correct

Step-by-step explanation:

2+3=5+4=9 , believe

pt2 , ANSWER ASAP

At a bakery, one customer pays $5.67 for 3 bagels and 4 muffins. Another customer pays $6.70 for 5 bagels and 3 muffins. Let x be the cost (in dollars) of a bagel and let y be the cost (in dollars) of a muffin. Use the system of equations below to determine the cost of 1 bagel and 1 muffin?

3x+4y =5.67

5x+3y=6.7


A. $0.75 for a bagel and $0.89 for a muffin

B. $0.89 for a bagel and $0.75 for a muffin

C. $1.49 for a bagel and $0.23 for a muffin

D. $0.23 for a bagel and $1.49 for a muffin

Answers

The answer is B because 3x0.89+0.75x4

Let L represent the number of workers hired by a firm, and let Q represent that firm's quantity of output. Assume two points on the firm's production function are (L = 12, Q = 122) and (L = 13, Q = 132). Then the marginal product of the 13th worker isa.) 8 units of output.b.) 10 units of output.c.) 122 units of output.d.) 132 units of output.

Answers

The amount  of marginal product of the 13th worker is 10 units of output, which is the difference between the quantity of output when L = 12 (122) and when L = 13 (132).

The marginal product of the 13th worker can be calculated as follows:

Marginal product = Quantity of output for L = 13 - Quantity of output for L = 12

Marginal product = 132 - 122

Marginal product = 10 units of output

The marginal product of the 13th worker is the additional output created by hiring one additional worker. This is calculated by taking the difference between the quantity of output when the number of workers is 12 and when it is 13. In this case, the quantity of output when L = 12 is 122, and when L = 13 it is 132, so the marginal product is 10 units of output. This calculation shows that the 13th worker is adding 10 units of output to the firm's total production. This is an important concept in production economics, as it helps firms determine the optimal number of workers to hire in order to maximize their output and profits.

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All of the quadrilaterals in the shape below are squares. Find the area of the shaded region.

Answers

45 units squared- 5+7=12, 12 squared=144. 144-49-50=45.

suppose 3 1.a+b
2.a-b
3.ab
4.a/b

Answers

The range of values for each expression is given as follows:

1. 8 ≤ a+b ≤ 16

2. -6 ≤ a - b ≤ 2

3. 15 ≤ ab ≤ 63

4. 1/3 ≤ a/b ≤ 7/5.

How to obtain the values?

For the maximum values, we have that:

Sum and multiplication: a and b have maximum values.Subtraction and division: maximum a, minimum b.

For the minimum values, we have that:

Sum and multiplication: a and b have minimum values.Subtraction and division: minimum a, maximum b.

Missing Information

The problem asks for the range of values for each expression, considering 3 < a < 7 and 5 < b < 9.

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given that angle A is congruent to angle C and A E equals E C, which of the following can be used to show that triangle A O B is congruent to triangle C E D?

Answers

Two angle and an include side are congruent, hence by the ASA postulate triangle AEB congruent to triangle CED.

ASA similarity theorem: Two triangles are similar if two corresponding angles of one triangle are congruent to the two corresponding angles of another triangle. Also, the corresponding sides are proportional. ASA similarity is mostly known as the AA similarity theorem.

Statement: Line segments AE and EC are equal.

Reason: Given

Statement: angle A is congruent to angle B.

Reason: Given

Statement: Angles AEB & CED are equal.

Reason: vertically opposite angles are equal.

Hence, two angle an include side are congruent.

Triangles AOB & CED are congruent.

Reason: ASA Postulate.

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Fin volunteers at the local pet shelter with his friends Conor and Tiah. His friends each volunteer 1.5 hours longer than Fin. The three friends volunteer for a combined total of 12 hours. Let x represent the number of hours that Fin volunteers. Which is the equation that would answer this question?
x+ 2x +1.5 = 12
x+x+x+1.5 = 12
x+ 2(x+1.5) = 12
x+ (2x +1.5) = 12

Answers

The equation that would answer this question is x + (2x + 1.5) = 12. where x is the number of hours that Fin volunteers, and 2x + 1.5 represents the number of hours that each of his friends volunteers.

How to find the equation?

In this scenario, you can set up an equation that represents the total amount of time Fin and his friends volunteer. Let 'x' be the number of Finn's volunteer hours. His friends volunteer 1.5 hours more than Finn, so the number of hours each friend volunteers can be represented by x + 1.5. The total number of hours that all three friends volunteered can be expressed as:

x + (x + 1.5) + (x + 1.5) = 12

Expansion of the 2nd and 3rd terms:

x + x + 1.5 + x + 1.5 = 12

Combining the same terms:

3x + 4.5 = 12

Subtract 4.5 from both sides:

3x = 7.5

Divide both sides by 3:

x = 2.5

So Fin volunteers his 2.5 hours. 

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David is 1 year old and he climbs off a couch that is 2 feet high and lands on the floor. It takes him 1 second to get off the couch.

Assuming David’s height off the floor is continuous and differentiable, which of the following is true?

The Mean Value Theorem applies; the average rate of change is: f(1)−f(0)1=11=1ft/secThe Mean Value Theorem applies; the average rate of change is: f ( 1 ⁢ ⁢ ) − f ( 0 ⁢ ) 1 = 1 1 ⁢ = 1 ⁢ f t ⁢ / sec ⁡ ,

The Mean Value Theorem does not apply.
The , Mean Value Theorem, does not apply.

The Mean Value Theorem applies; the average rate of change is: f(1)−f(0)1=21=2ft/secThe Mean Value Theorem applies; the average rate of change is: f ( 1 ⁢ ⁢ ) − f ( 0 ⁢ ) 1 = 2 1 ⁢ = 2 ⁢ f t ⁢ / sec ⁡ ,

The Mean Value Theorem applies; the average rate of change is: f(1)−f(0)2=12ft/sec

Answers

Assuming David’s height off the floor is continuous and differentiable, the statement that is true is: B. The Mean Value Theorem does not apply.

Does the mean value theorem that applies or not?

Based on the details we can vividly states that the Mean Value Theorem does not apply based on the fact that the function that help to described David's height off the floor is not continuous and differentiable.

This  function would only be differentiable if David's movement off the couch and landing on the floor could be described by a mathematical function, which is highly unlikely.

Therefore the correct option is B.

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Joseph has a bag filled with 2 red, 4 green, 15 yellow, and 9 purple marbles. Determine P(not purple) when choosing one marble from the bag.

A. 70%
B. 50%
C. 30%
D. 20%

Answers

The probability of randomly selecting a marble that is not purple is 70%, so the correct option is A.

How to find the probability?

We know that there are:

2 red marbles4 green marbles15 yellow marbles9 purple marbles

For a total number of 2 + 4 + 15 + 9 = 30

There are a total of 30 marbles on the bag, the probability of randomly selecting a marble that is not purple, is equal to the quotient between the number of marbles that are not purple and the total number of marbles.

21 marbles are not purple, then the probability is:

P = (21/30)*100%

P = 0.7*100%

P = 70%

The correct option is a.

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decide whether each proposed multiplication or division of measurements is possible. if it is possible, write the result in the last column of the table.

Answers

1. The unit g/cm³ is valid. So, division of measurements is possible.

2. The unit mm is valid. So, division of measurements is possible.

3. The unit L² is not valid. So, multiplication of measurements is not possible.

What are measurement units?

The group of units used to quantify different physical quantities collectively known as the units of measurement. Since ancient times, we have measured these things using many units, including length, mass, volume, current, and temperature.

1. 63g/7cm³ = 9 g/cm³

The density of a substance indicates how dense it is in a given area. Mass per unit volume is the definition of a material's density. In essence, density is a measurement of how closely stuff is packed. It is a particular physical characteristic of a specific thing.

The unit g/cm³ is a unit for measuring density.

Therefore, the division of measurements is possible.

2. The m or mm must be converted so that the units are the same.  

1 m = 1000 mm.

Convert the meters to mm:  

0.080 m = 80 mm.

480 mm²/80 mm = 6 mm

The word "area" refers to a free space. A shape's length and width are used to compute its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc.

The mm² is a unit for measuring area.

The m is a unit for measuring length or width.

Therefore, the division of measurements is possible.

3.  (4.5 dL) × (0.70 L)

Liquid volume is a term used to describe how much 3-D space a given amount of liquid takes up.

Volume of a liquid is measured in litres (L).

Squaring Litres doesn't make any sense.

Therefore, the multiplication of measurements is not possible.

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the sum of two numbers is 51. the larger number is 21 more than the smaller number. what are the numbers ?
larger number: ?
smaller number: ?

Answers

The smaller number is 15 and the larger number is 36.

Let x and y be the smaller and larger numbers, respectively.

From the given information, we know:

y = x + 21 (because the larger number is 21 more than the smaller number)

x + y = 51 (because the sum of the two numbers is 51)

We can substitute the first equation into the second equation to find the value of x:

x + (x + 21) = 51

x + x + 21 = 51

2x = 30

x = 15

Now that we know the value of x, we can use the first equation to find the value of y:

y = x + 21

y = 15 + 21

y = 36

So the smaller number is 15 and the larger number is 36.

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pls help first to answer all will get brainliest!!

Answers

Answer:To show that Lorenz curves are always concave up on the interval [0, 1], we can use the definition of a Lorenz curve, which is L(x) = xp. Taking the second derivative of L(x) with respect to x gives us L''(x) = p. Since p is always greater than 0, L''(x) is always greater than 0. This means that L(x) is always concave up on the interval [0, 1].

Table of Lorenz values for p = 1.2, 1.5, 2.1, 2.5, 3, and 5:

a. The value of p that corresponds to the most equitable distribution of wealth is 1, as this would mean that the proportion of wealth held by each portion of the population is equal.

b. The value of p that corresponds to the least equitable distribution of wealth is 5, as this would mean that a small portion of the population holds a large proportion of the wealth.

The Gini Index is a measure of income inequality, where a value of 0 represents perfect equality (everyone has the same income) and a value of 1 represents perfect inequality (one person has all the income). The Gini Index is calculated as the ratio of the area between the Lorenz curve and the line of equality to the total area beneath the line of equality.

To find A and B for the Gini index we can use the following integral:

A = ∫(L(x) - x) dx from 0 to 1

B = ∫(x - L(x)) dx from 0 to 1

We can then solve the integral for each specific function of L(x) = xp to find the specific value of A and B.

Step-by-step explanation:

Answer:....

Step-by-step explanation:

4:5=___:35 fill in the missing value

Answers

Answer: 28:35

Step-by-step explanation: The missing number is 28, here's how to solve it:

So, if we know both components of the first ratio AND the second component of the 2nd ratio, we need to divide the 2nd components from each ratio. So, 35 / 5 = 7. Now, we need to multiply 7 by 4. We get 28. So, the 2nd ratio is 28:35. I hope this helps!

(Look at the attachment for a better idea)

A neighbor charges $10 to mow your lawn plus $20 per hour. Write a function rule for the total cost of hiring your neighbor (y) for a certain amount of hours (x).

Answers

The value of function showing the total cost of hiring your neighbor (y) for a certain amount of hours (x) is,

⇒ y = 10 + 20x

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.

We have to given that;

A neighbor charges $10 to mow your lawn plus $20 per hour.

Let the total cost of hiring your neighbor = y

And, Number of amount of hours = x

Hence, We can formulate;

The function which showing the total cost of hiring your neighbor (y) for a certain amount of hours (x) is,

⇒ y = 10 + 20x

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it is possible to have a function with an infinite number of critical points. also, it is possible to have a function where every point is a critical point. g

Answers

A function with an infinite number of critical points can be expressed as a continuous function with a derivative that is equal to zero at every point in its domain.

For example, the function f(x) = 0 has an infinite number of critical points since its derivative f'(x) = 0 for every x in its domain. Alternatively, a function that has every point as a critical point can be expressed as a function with a derivative that is always equal to zero. For example, the constant function f(x) = c has a derivative f'(x) = 0 for every x in its domain, and thus every point in its domain is a critical point.

In addition, an example of a function with every point as a critical point is the constant function, f(x) = c, where c is a constant. The derivative of this function is f'(x) = 0, which means that the derivative is zero for all values of x. Therefore, every point of the constant function is a critical point.

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River is surfing off Cocoa Beach. The depth of the water at various distances from the shore, point

are shown in the diagram. When he is

feet (ft) from the shore a point

, the dept of the water is

ft. He continued to point

about

ft away from the shore.

Answers

The depth of the water RF is, 18 ft.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

We have to given that;

⇒ ΔSML ≅ ΔSRF

⇒ SM = 10

⇒ ML = 6

⇒ SR = 30

Since, Both triangles SML and SRF are similar.

Hence, We get;

⇒ SM / ML = SR / RF

Substitute all the values, we get;

⇒ 10 / 6 = 30 / RF

⇒ RF = 30 × 6 / 10

⇒ RF = 3 × 6

⇒ RF = 18 ft

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Which of the following types of words must be capitalized? (5 points) a A government position when it comes before a specific name b Time of year when mentioned in a general way c The last word in a narrative sentence d Every word in a book title

Answers

The types of words must be capitalized is

A) A government position when it comes before a specific name

What is Word Capitalization?

In writing systems with a case distinction, capitalization (American English) or capitalisation (British English) refers to writing a word with its initial letter as a capital letter (uppercase letter) and the other characters in lower case. The phrase could also be used to describe the choice of text case.

Given:

In English, the initial word of a phrase and all proper nouns are written in capital letters (words that name a specific person, place, organization, or thing).

The initial word in a quotation and the first word following a colon may occasionally both need to be capitalized.

So, the types word can be capitalized is a government position when it comes before a specific name like President Obama.

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ANSWER ASAP
At the produce store, 6 bananas are the same cost as 9 apples. You buy 4 bananas and 2 apples. The purchase cost $8. This scenario is modeled by the given system. Choose the correct description below that connects the meaning of the solution (1, 1.5) to the context of this scenario.

6y=9x
2x+4y=8

A. Each apple costs $1.50 and each banana costs $1.
B. You purchased 1 apple and 1.5 bananas.
C. You purchased 1.5 apples and 1 banana.
D. Each apple costs $1 and each banana costs $1.50.

Answers

The solution (1, 1.5) denotes:

Each apple costs $1.

Each banana costs $1.50.

Option D is the correct answer.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

6y = 9x _____(1)

2x + 4y = 8 ______(2)

From the equation,

x is the cost of an apple.

y is the cost of a banana.

Now,

(1, 1.5) = (x, y)

This means,

The cost of an apple = $1.

The cost of a banana = $1.5

Thus,

The solution (1, 1.5) denotes that the cost of an apple is $1 and a banana is $1.5.

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Find the indefinite integral of each of the following by using [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n #1
(a) e^x (3 - e^x)^4 dx
(b) 3e^2x √(1 + e²x) dx
(c) 3e^-2x / (1 + e^-2x)^3 dx
(d) 4 cos 2x sin³ 2x dx
(e) sec² 3x tan³ 3x dx
(f) 2+tan ² x / cos² x dx​

Answers

Answer:

a) e^x (3 - e^x)^4 dx

Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,

we have:

e^x (3 - e^x)^4 dx = (e^x)^5 (3 - e^x)^4 / 5 + c

= (e^5x - 4e^4x + 6e^3x - 4e^2x + e^x) / 5 + c

b) 3e^2x √(1 + e²x) dx

Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,

we have:

3e^2x √(1 + e²x) dx = (3e^2x)^2 * (1 + e²x)^(3/2) / 2 + c

= (9e^4x + 3e^2x) / 2 + c

c) 3e^-2x / (1 + e^-2x)^3 dx

Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,

we have:

3e^-2x / (1 + e^-2x)^3 dx = -(3e^-2x)^2 / (1 + e^-2x)^2 + c

= -(9e^-4x) / (e^-4x + 2e^-2x + 1) + c

d) 4 cos 2x sin³ 2x dx

Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,

we have:

4 cos 2x sin³ 2x dx = -4 cos 2x (sin 2x)^4 / 4 + c

= -(cos 2x) (1 - cos 4x)^2 / 2 + c

e) sec² 3x tan³ 3x dx

Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,

we have:

sec² 3x tan³ 3x dx = -sec² 3x (tan 3x)^4 / 4 + c

= -sec² 3x (sec² 3x - 1)^2 / 4 + c

f) 2+tan ² x / cos² x dx

Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,

we have:

2+tan ² x / cos² x dx = ln|sec x| + c

It's worth noting that all these integrals are indefinite, which means that the constant c is arbitrary, and the actual antiderivative depends on the problem context.

Step-by-step explanation:

May you please help me? I need help, asap. It's missing ;l

Answers

Answer:

g(f(- 4)) = 40

Step-by-step explanation:

to evaluate g(f(- 4)) , evaluate f(- 4) and substitute the value obtained into g(x)

f(- 4) = (- 4)² + 3(- 4) + 6 = 16 - 12 + 6 = 4 + 6 = 10 , then

g(10) = 5(10) - 10 = 50 - 10 = 40

Let A be a 5 by 7 , B be a 7 by 6 and C be a 6 by 5 matrix. How to determine the size of the following matrices ? O AB, BA, O A^TB, BC, O ABC , CA ,O B^TA , BC^T

Answers

The matrices matrix A be a 5 by 7 , matrix B be a 7 by 6 and matrix C be a 6 by 5 matrix.

now, we need to determine the size of the matrices

AB = [tex](AB)_{5*6}[/tex]

BA is undefined

[tex]A^{T}[/tex]B  is undefined

BC = [tex](BC)_{7*5}[/tex]

ABC = [tex](ABC)_{5*5}[/tex]

CA = [tex](CA)_{6*7}[/tex]

[tex]B^{T}[/tex]A is undefined.

B[tex]C^{T}[/tex] is undefined.

given that

matrix A is [tex]A_{5*7}[/tex]

matrix B is [tex]B_{7*6}[/tex]

matrix C is [tex]C_{6*5}[/tex]

now, we need to determine the size of the matrices

AB multiplication of two matrices

multiplication of two matrices is possible only when B has the same number of columns as rows in A,

[tex]A_{m*n}[/tex]and [tex]B_{n*p}[/tex]

If it is defined as above, then the matrix AB will have m rows and p columns, i.e., A must have n columns and B must have n rows in order for AB to be defined.

[tex](AB)_{m*n}[/tex]

In addition, a matrix gets transposed when columns turn into rows and vice versa.

Thus, if

[tex]A_{m*n}[/tex]⇒[tex](AT)_{m*n}[/tex]

So, for this particular question, we have:  [tex]A_{5*7}[/tex],  [tex]B_{7*6}[/tex] , [tex]C_{6*5}[/tex]

According to the aforementioned idea, AB is therefore [tex](AB)_{5*6}[/tex] in size.

Additionally, BA and [tex]A^{T}[/tex]B are not defined.

[tex](BC)_{7*5}[/tex]

ABC=(AB)C=A(BC) because matrix multiplication is associative,

[tex](ABC)_{5*5}[/tex]

[tex](CA)_{6*7}[/tex]

[tex]B^{T}[/tex]A is undefined. because they don't have same number of columns in matrix B and rows in matrix A

B[tex]C^{T}[/tex] is undefined. because they don't have same number of columns in matrix B and rows in matrix C

To learn more about matrices:

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The graph of h(x) is shown.

What are the intercepts and asymptote(s) of h(x)? Explain how to find these using the graph.

Answers

The intercepts and the asymptotes of h(x) using the graph is  x-intercept -4 and y-intercept =-1

What is y-intercept?

The y-intercept of a function y = f(x) is a point where its graph would meet the y-axis and is obtained by substituting x = 0. Understand the y-intercept and its formula with derivation

From the given graph

Y-intercept is the point where the curves crosses the y-axis

From the graph, the coordinate of the y-intercept is (0, -1)

X-intercept is the point where the curves crosses the x-axis

From the graph, the coordinate of the x-intercept is (-4, 0)

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Answer:

The vertical asymptote is -5

Step-by-step explanation:

You basically have to set it to 0 and then solve the equation. You should get x= -5

Choose the graph that represents the equation below: y = 8x + 4

Answers

Answer: Go up 8 and to the right 1 starting at the point (0,4)

Step-by-step explanation: y=mx+b where m=8 (your slope) and b= 4 (your y-intercept)

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