an object is translated by (x + 4, y - 2). If one point in the image has the coordinates (5 , -3), what would be the coordinates of it’s pre-image?

Answer:

\(h = \sqrt{72}in\)

Step-by-step explanation:

We have a right triangle with long side of 11in and smaller sides 14in/2=7in and h.

We know that

\(h^2 + (7in)^2 = (11in)^2\\h^2 = 121in^2 - 49in^2 = 72in^2\\h = \sqrt{72}in\)

Answer:

A

Hope you get it right!:)

The relation r = {(1,1),(1,2),(1,4),(2,1),(2,2),(3,3),(4,1),(4,4)} on the set a = {1,2,3,4} is not reflexive.

Reflexivity in a relation means that every element in the set is related to itself. In other words, for every element 'x' in the set, the pair (x,x) should be included in the relation.

In the given relation, the element 3 is in the set a = {1,2,3,4}, but there is no pair (3,3) in the relation. Therefore, the relation r is not reflexive.

To demonstrate reflexivity, we would need to have (x,x) pairs for each element x in the set. In this case, the pair (3,3) is missing, which violates the condition of reflexivity.

Hence, the reason why the relation r = {(1,1),(1,2),(1,4),(2,1),(2,2),(3,3),(4,1),(4,4)} is not reflexive is because it does not contain the required (x,x) pairs for all elements in the set a = {1,2,3,4}.

Learn more about set here:

https://brainly.com/question/30705181

#SPJ11

Answer:

Step-by-step explanation:

The inequalities are solved below

What is an inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. The notation a b indicates that an is less than b, while a > b indicates that an is more than b, among other distinct notations used to denote various types of inequalities. The notation a b indicates that a and b are not equal; this inequality is occasionally referred to as a type of stringent inequality. It doesn't even specify that a and b must be members of an ordered set, nor does it state that one is superior to the other.

The inequalities are

13y>9

or, y>9/13

and

2y-6>2

or, 2y>2+6

or, y>8/2

or, y>4

To know more about inequalities, click on the link

https://brainly.com/question/27640560

SPJ13

The given differential equations that describe the longitudinal motion of an airplane are

w = -2w +1790-278

Ö= -0.25w150 - 458

We have the state feedback control law n= ka

where k describes the vector r with gains k₁ and k₂ and is the state.

The gains k are chosen in such a way that the augmented system (after applying the control law) has a damping ratio of C = 0.5 and undamped natural frequency of wn = 20 rad/s.

First, we need to write the above differential equations in state space form.

Let us assume that x = [w, Ö]T.

Then,x' = [w', Ö']

T =[[-2 0.25][-150 -458]] [w Ö]T + [1790 0]

T = A[x]+ B[u]

where

A = [[-2 0.25][-150 -458]],

B = [1 0]T, u = kx is the input.

Then the eigenvalues of A + BK must have a damping ratio of 0.5 and an undamped natural frequency of 20 rad/s.

The desired characteristic equation is given by

λ² + 2ζωnλ + ωn² = (λ+ 20i)(λ - 20i) + (λ + 2i)(λ - 2i)

=λ²+18λ+404

Solving for k1 and k2So Given = desired

So,[[-2-k₁ 0.25-k₂][-150 -458-k₁]] = [[18 404][-1 18]]

k₁ = -20 and k₂ = -224

The final gains are k₁ = -20 and k₂ = -224.

To know more about  eigenvalues visit:

https://brainly.com/question/29861415

#SPJ11

Answer:

The formula is \(a_n = 3n-2\)

The 14th term is 40, in other words, \(a_{14} = 40\)

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

Explanation:

The given sequence is 1, 4, 7, 10, ...

Subtract each adjacent term:

This shows that each term is increasing by 3. This is the common difference, so d = 3.

The first term is \(a_1 = 1\)

The nth term of the arithmetic sequence is...

\(a_n = a_1 + d(n-1)\\\\a_n = 1 + 3(n-1)\\\\a_n = 1 + 3n-3\\\\a_n = 3n-2\\\\\)

As a check, let's plug in say n = 3 to find that:

\(a_n = 3n-2\\\\a_3 = 3(3)-2\\\\a_3 = 9-2\\\\a_3 = 7\\\\\)

The third term is 7, which matches with the sequence given to us. I'll let you confirm the other values.

-----------

We'll repeat this idea but now for n = 14 to find the 14th term of the sequence.

\(a_n = 3n-2\\\\a_{14} = 3(14)-2\\\\a_{14} = 42-2\\\\a_{14} = 40\\\\\)

The 14th term is 40.

You can make a table of values to help confirm the answer. In the first column you'll have the values of n (1,2,3,...) all the way up to 14. The second column will consist of the sequence 1, 4, 7, 10, ... each time going up by 3 until you reach the 14th term of 40.

To determine which expressions represent vectors, we need to understand the properties and characteristics of vectors. A vector is a mathematical object that has both magnitude and direction.

It can be represented geometrically as an arrow in space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

Based on this definition, we can identify the expressions that represent vectors:

1. → u: This expression represents a vector. The arrow symbol (→) indicates that it has both magnitude and direction.

2. → v: Similarly, this expression represents a vector. The arrow symbol (→) indicates that it has both magnitude and direction.

3. k → u: This expression also represents a vector. Multiplying a vector by a scalar (k) does not change its nature as a vector. It only scales the magnitude of the vector while keeping its direction intact.

4. → u + → v: This expression represents a vector. Adding two vectors together results in another vector with a magnitude and direction determined by the combination of the original vectors.

5. → u - → v: Similarly, this expression represents a vector. Subtracting one vector from another also results in a new vector with a magnitude and direction determined by the operation.

6. k(→ u + → v): This expression represents a vector. Here, we have both scalar multiplication (k) and vector addition (→ u + → v), which combine to produce another vector.

The expressions listed above all represent vectors because they possess both magnitude and direction, which are fundamental properties of vectors.

To know more about vectors refer here:

https://brainly.com/question/24256726#

#SPJ11

\(\dfrac{10}{1+2i}\\\\\\=\dfrac{10(1-2i)}{(1+2i)(1-2i)}\\\\\\=\dfrac{10-20i}{1 - (2i)^2}\\\\\\=\dfrac{10-20i}{1+4}~~~~~;[i^2 =-1]\\\\\\=\dfrac{10-20i}5\\\\=\dfrac{10}5 - \dfrac{20i}5\\\\=2-4i\)

First notice that angle C is a right angle, then:

Now, since this is a right triangle, we can find the measure of angle A using the trigonometric function sine:

In this case, we have the following:

Since the sum of the interior angles of a triangle equals 180, we can find the measure of angle B by solving the following equation:

therefore, angle A measures 48.6 degrees and angle B measures 41.4 degrees

Answer:

the answer is c

Step-by-step explanation:

The function that represents the given equation is:

f(x) = 3x + 8

The equation is -12x + 4y = 32. To solve for y as a function of x, we need to isolate y on one side of the equation.

Adding 12x to both sides, we get 4y = 12x + 32.

To solve for y, we divide both sides of the equation by 4. This gives us y = 3x + 8.

Hence, the function that expresses y as a function of x is:

f(x) = 3x + 8.

Using this function, we can determine the value of y corresponding to any given x value. For example, if we substitute x = 5 into the function, we have f(5) = 3(5) + 8 = 15 + 8 = 23. Therefore, when x is 5, y is 23 according to the function f(x) = 3x + 8.

In summary, the function f(x) = 3x + 8 represents the relationship between x and y in the given equation, allowing us to calculate the corresponding y value for any given x value.

Therefore, the function that represents the given equation is:

f(x) = 3x + 8

Learn more about function :

https://brainly.com/question/29633660

#SPJ11

Please find attached photograph for your answer.

Hope it helps.

Do comment if you have any query.

Answer:

-6, 6

Step-by-step explanation:

I hope this helps :)

Answer:

The independent variable is time.

Step-by-step explanation:

(Y=mx+b format)

Maddi's rental for the car costs $13 per hour so the x variable would be the hours (x=hour). This would be a Y= mx + b equation and in this case, Y=13x + 100. Independent means (mathmatically) a variable that does not depend on any other variable for its value. The costs is always changing being dependent on the time portion. The time isn't dependent on anything. Thus, the independent variable is time.

(If you need a starting point which is b, it would be the $100 as the processing fee.)

Answer:

its increases by 10 degrees

Step-by-step explanation:

The complete factor of the expression \(\rm x^3 + 4x^2 + 8x + 32\) is \(\rm (x^2 + 8)(x+ 4)\)correct option is A.

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The expression is \(\rm x^3 + 4x^2 + 8x + 32\).

To factorization the expression properly. Then we have

\(\rm x^3 + 4x^2 + 8x + 32 \\\\x^2(x+4) +8(x+ 4)\\\\(x+4)(x^2 + 8)\)

The factor is \(\rm (x^2 + 8)(x+ 4)\).

More about the factorization link is given below.

https://brainly.com/question/6810544

The cost of 15 litres of petrol ​ is rs. 516.7

From the question, we have the following parameters that can be used in our computation:

The cost of 9 litres of petrol is rs.310 .

This means that

Cost of 9 litres of petrol = rs.310

Multiply both sides of the equation by 5/3

So, we have the following representation

5/3 * Cost of 9 litres of petrol = 5/3 *  rs.310

Evaluate the products

Cost of 15 litres of petrol = rs. 516.7

Hence, the cost is rs. 516.7

Read more about rates at

https://brainly.com/question/19493296

#SPJ1

The correct answer is d. emergent.

An emergent leader is an individual who grows into the leadership role naturally, often due to circumstances or necessity. They are not appointed or assigned to the position of leadership but rather emerge from the group or organization based on their skills, qualities, or actions.

Emergent leaders may possess certain qualities or demonstrate their competence and ability to guide and influence others. They gain recognition and respect from their peers, leading to their emergence as leaders within the group or organization.

This type of leadership often occurs in situations where formal leadership structures may be absent or ineffective, and individuals step up to take charge based on their capabilities and the needs of the group.

 To learn more about group click here:brainly.com/question/14885504

#SPJ11

Then we add together

(6.42x\(10^{-23}\) )+ (3.3x

= 9.45 × \(10^{-24}\) kilograms

Therefore, combined mass in scientific notation can be written as 97.2× \(10^{-24}\) kg

Learn more at : https://brainly.com/question/1705769?referrer=searchResults

Answer:

97.2

Step-by-step explanation:

The denominators of two or more fractions must have a common factor, and the calculation can be defined as follows:

              \(\to\) \(\frac{2}{3} - \frac{3}{5}\\\\\)

              \(\to\) \(\frac{10-9}{15}\\\\\)

              \(\to\) \(\frac{10}{15} - \frac{9}{15}\\\\\)

So, the common denominator value by using the 15 is equal to

 \(\to \frac{2}{3} : \frac{10}{15} : \frac{3}{5}: \frac{9}{15}\)

Find out more about the common denominator here:

brainly.com/question/896263

Answer:

suppose length is x

breadth is y

now,

      x.y=18

      2(x+y)= 18

x= 3

y=6

Step-by-step explanation:

Answer:

Equation

1.95+1.6m ≤ 22

If solved

m ≤ 12.53

Step-by-step explanation:

SO we know the initial fee is 1.95

and for every mile driven, its $1.6

And we know that Shelly can spend less then or exactly the price of 22.

We know that m is miles driven

So we can make an equation

1.95+1.6m ≤ 22

1.95 can’t change since initial fee

1.6*m becuase its 1.6 for every mile driven and since “m” miles were driven, we multiply that by 1.6

Now it can’t go over 22 but it could be less than 22.

So this equation makes sense

If we solve it, it would be about  m ≤ 12.53 miles

The best prediction of the number of cards Glenalee can make in 13 hours is 46 cards.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope for the line of best fit;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (30 - 11)/(8 - 3)

Slope (m) = 18/5

Slope (m) = 3.8.

At data point (3, 8) and a slope of 3.8, a linear equation for the line of best fit can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 8 = 3.8(x - 3)

y = 3.8x - 10.8 + 8

y = 3.8x - 2.8

When x = 13 hours, the number of cards Glenalee can make in 13 hours can be calculated as follows;

y = 3.6(13) - 2.8

y = 46 cards.

Read more on point-slope here: brainly.com/question/24907633

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Jose will need 40.82 in² of paper to cover the stack of coins

The area in this scenario will be:

A = 2πr² + 2πrh

Where r and h represent the radius of the coins and the height of the coin stack respectively

Given: diameter of coin = 1 inch and thickness = 1/8 inch

radius(r) = diameter/2 = 1/2 inch

Substituting values gives:

A = 2×3.14 × (1/2)² + 2×3.14 ×(1/2)×(100 ×(1/8))

A = 40.82 in²

Note: the correct thickness of the coins should be 1/8 in

Therefore, the area of paper Jose will need to cover the stack of coins is 40.82 in²

Learn more about area of circle on:

https://brainly.com/question/15673093

#SPJ1

Answer:

Hypothesis: It is January

Conclusion:  There is snow

Step-by-step explanation:

COnditionals are in the form If p, then q.

P is the hypothesis.

Q is the conditional.

If (It is January), then (there is snow).

If and then are not included in the hypothesis and conclusion, respectively.

Hypothesis: It is January

Conclusion: There is snow

What is Hypothesis and Conclusion ?

The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement. The conclusion is the result of a hypothesis. Hypotheses followed by a conclusion is called an If-then statement or a conditional statement. This is noted as. p→q. This is read - if p then q. A conditional statement is false if hypothesis is true and the conclusion is false.

Conditionals are in the form if P, then Q.

P is the hypothesis.

Q is the conclusion.

If It is January, then there is snow.

Read more about Hypothesis and Conclusion at:

https://brainly.com/question/5497883

#SPJ2

Answer:

25 girls

Step-by-step explanation:

We Know

The ratio of boys to girls is 4:5. For every 4 boys, there are 5 girls.

To get from 4 to 20, we multiply by 5.

We Take

5 x 5 = 25 girls

So, there are 25 girls in class.

Answer: 25 girls are in the class

Step-by-step explanation: You can set up the ratio 4:5 as a fraction, \(\frac{4}{5}\) to find your answer. You are given the fact that 20 boys are in the class so now you can solve 2 ways.

Option 1 - Set up the equation algebraically as \(\frac{20}{x}\), where x = number of girls and set that equal to \(\frac{4}{5}\). This way allows you to see that the fraction must have the same ratio as 4:5. You can see that 4 x 5 = 20, so the multiple factor is 5. The variable x must equal 5 x 5, so x = 25.

Option 2 - Multiply the amount of boys given to you by the reciprocal of the ratio. Instead of using \(\frac{4}{5}\), you have to use \(\frac{5}{4}\) because there are more girls than boys in the class. This allows you to finish the problem by multiplying 20 x \(\frac{5}{4}\) to get the result of \(\frac{100}{4}\), which you may know simplifies into 25.