Polygon WXYZ has vertices W(4, 2), X(6, 4), Y(2, 3), and Z(4, 5). If W′X′Y′Z′ is a dilation of WXYZ with center of dilation (0, 0) and vertex coordinates W′(2, 1), X′(3, 2), Y′(1, 1.5), and Z′(2, 2.5), find the scale factor.

Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

S-6. If the relative intensity of a quake is multiplied by 10, the Richter scale reading is increased by 1.

S-6. If the Richter scale reading of one quake is t units larger than that of a second quake, the relative intensity of the first quake is 10^(1.5t) times greater than that of the second quake.

S-7. If one sound has a relative intensity 1000 times that of another, their decibel levels differ by 30 dB, with the louder sound having a higher decibel level.

S-8. If one sound has a relative intensity one-tenth that of another, their decibel levels differ by -10 dB, with the louder sound having a higher decibel level.

S-9. One sound with a decibel reading of 5.5 has a relative intensity of 10^(5.5/10) = 3.16 times greater than another sound with a decibel reading of 7.5.

S-10. One sound with a decibel reading of 6.4 has a relative intensity of 10^(6.4/10) = 25.12 times greater than another sound with a decibel reading of 5.4.

S-11. log 1000 = 3, since 10^3 = 1000.

For more questions like intensity visit the link below:

https://brainly.com/question/2658053

#SPJ11

Answer:

40°

Step-by-step explanation:

The measure of the right angle is 90°.

The measures of the angles 10° and 2x add up to the measure of the right angle.

2x + 10° = 90°

2x = 80°

x = 40°

Answer:the answer is 240

Step-by-step explanation:the explanation 120-40 =80 80 divided by 2 = x  time by 80 =60 80 divide by 60 = 20 x = 20 20 x 8= 180 x by 20 = 240 so there fore the answe is 240

Answer:

x = \(\sqrt{164}\)

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² = 10² + 8² = 100 + 64 = 164 ( take square root of both sides )

x = \(\sqrt{164}\)

The surface area of the cone is 450π in². Therefore, the answer is option B.

The surface area of a cone can be represented as follows:

surface area of a cone = πr(r + l)

where

Therefore,

r = 9 inches

l = 41 inches

Hence,

surface area of a cone = π × 9(9 + 41)

surface area of a cone = 9π(50)

Therefore,

surface area of a cone = 450π inches²

learn more on cone here: https://brainly.com/question/23877107

#SPJ1

No, because intergers don't include fractions.

Answer:

No

Step-by-step explanation:

Integers cannot have any fractions.

If you simplify this to get 8/1 and then 8, 8 is an integer

Answer:

The answer is B

Step-by-step explanation:

Divide the distance by the time.

Answer:

y = mx + b    

Step-by-step explanation:

Substitute in the slope intercept formula

m = slope  

x = first number in the point

y = second number in the point  

and solve for b

Question 1

m=-1/2, x= -4  y=-2  substitute

-4 = -1/2(-4) + b

-4 = 2 + b

-4 -2 = 2 -2 + b

-6 = b

y=-1/2x -6

Answer: 274

7124 divided by 26 in decimal = 274

7124 divided by 26 in fraction = 7124/26

7124 divided by 26 in percentage = 27400%

Hope this helps

The value of y at x = 121.9 for the expression y = 3x - 245 will be 120.7.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that the expression is y = 3x - 245. The value of x is 121.9.

The solution for the value of y will be calculated as:-

y = 3x - 245

y = ( 3 x 121.9 ) - 245

y = 365.7 - 245

y = 120.7

Therefore, the value of y for the given expression will be 120.7.

To know more about an expression follow

https://brainly.com/question/28821943

#SPJ1

The complete question is given below.

Find the value of y for the expression y = 3x - 245 at x = 121.9.

Answer:

30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

LxW = Area

5*6 = 30

Area = 30

"Benefit pension plan" comes with a guaranteed retirement benefit at retirement.

What is retirement plan?

There are different types of retirement plans, and not all of them come with a guaranteed retirement benefit. However, one type of plan that typically does offer a guaranteed retirement benefit is a defined benefit pension plan.

With a defined benefit pension plan, an employer promises to pay a specific benefit amount to an employee upon retirement, based on a formula that takes into account the employee's years of service, salary, and other factors. The employer is responsible for funding the plan and managing its investments to ensure that it can meet its obligations to retirees.

In contrast, defined contribution plans, such as 401(k) plans, do not offer a guaranteed retirement benefit. Instead, these plans allow employees to contribute a portion of their salary to an investment account, and the value of the account at retirement will depend on the contributions made and the investment performance of the account.

To know more about pension, visit:

https://brainly.com/question/31215595

#SPJ1

Complete question is: "benefit pension plan" comes with a guaranteed retirement benefit at retirement.

Answer:

1/12

Step-by-step explanation:

2/3=8/12

2x4=8

3x4=12

1/4=3/12

1x3=3

4x3=12

8/12+3/12=11/12

1-11/12= 1/12

Answer:

(2, 5)

Step-by-step explanation:

Let the number of fancy throw pillows be x.

Let the number of plain throw pillows be y.

Hope spent a total of $131 on 7 throw pillows.

Fancy throw pillows  cost $28 and plain throw pillows cost $15.

These imply two things:

x + y = 7 _______  (1)

28x + 15y = 131 ___(2)

We have a linear system of equations.

From (1):

x = 7 - y

Substitute the value of f into (2):

28(7 - y) + 15y = 131

196 - 28y + 15y = 131

196 - 13y = 131

=> 13y = 196 - 131

13y = 65

y = 65 / 13

y = 5

This means that:

x = 7 - 5 = 2

Hope bought 2 fancy throw pillows and 5 plain throw pillows

Answer:

It would've costed $8 to buy these ribbons.

Step-by-step explanation:

Given:

(3 + 2) x 2 = Total cost

=> (5) x 2

= $10

Therefore, it would've costed $10 to buy these ribbons.

Hoped this helped.

Assuming that x ≥ 0 and y ≥ 0, the situation is infeasible: True.

In Mathematics, these rules are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a coordinate plane:

In this context, we can logically deduce that the given system of inequalities 5x+3y ≤ 15 and y ≥ 6 would not have a feasible solution set if they are subjected to x ≥ 0 and y ≥ 0:

Assuming the ordered pair (1, 2), we have:

y ≥ 6

2 ≥ 6 (False).

5x+3y ≤ 15

5(1) +3(2) ≤ 15

5 + 6 ≤ 15

11 ≤ 15 (True).

Therefore, it is not a feasible solution.

Read more on inequality here: brainly.com/question/27976143

#SPJ1

Missing information:

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

\(\huge\mathfrak\pink{Answer...}\)

+,- 17

\(\huge\mathfrak\purple{hope \: it \: helps..}\)

Answer:

301 plates

Step-by-step explanation:

For numbers between 0 and 9, 1 plate was used each.

This means that 10 plates were used.

For numbers between 10 and 99, 2 plates were used for each.

This means that the number of plates used will be:

2 * 90 = 180 plates

For numbers between 100 and 136, 3 plates were used for each.

This means that the number of plates used is:

3 * 37 = 111 plates

The total number of plates used is therefore:

10 + 180 + 111 = 301 plates

301 plates were used in total.

The number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.

What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]

Given, 6 people are to be selected from a group of 10, where the bride must be in the picture.
Following the statements in question, the bride since always there assists for filling five empty spaces using 9 people.
Since five positions are to be filled by nine people, the total number of ways possible = 9 × 8 × 7 × 6 × 5 = 15120
Thus, the number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.

To learn more about permutation and combination, tap on the link below:
https://brainly.com/question/11732255

#SPJ4

Answer:

0.25

Step-by-step explanation:

Following the law of segregation which states that only one of the two gene copies noticeable in an organism is diffused to each gamete (egg or sperm cell) and gene allocation is random.

A heterozygous gene for Q = Qq

If these two individuals mate and produce gametes by meiosis,

The probability that both the egg and sperm will carry the recessive allele is determined as follows:

Qq    ×    Qq

             Q              q

Q           QQ          Qq

q            Qq            qq

The probability that both the egg and sperm will carry the recessive allele qq is 25% or 0.25

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

Answer:

There were 12 people at the party

Answer:

Step-by-step explanation:

Other answers have already shown that there are  n=12  people at the party, either using combinatorial choose notation

(n2)=n!2!(n−2)!=66  

or by counting handshakes person by person, noting that each successive person has one fewer unique handshake than the prior (as the previously counted people are disregarded), and then using the sum-of-consecutive-integers formula to get

(n−1)+(n−2)+...+2+1=∑n−1k=1k=(n−1)n2=66  

and solving for n .

Here I will provide another method of arriving at n(n−1)2=66.

Instead of keeping track of unique handshakes from the start, note that each person shakes hands with  n−1  other people. As there are n  people at the party, this gives us n(n−1)  handshakes. However, notice that we counted each handshake twice; for example, if Alice and Bob shook hands, we counted that once for Alice, and then again for Bob. To account for the double-counting, we can divide by  2, which gives us the previously mentioned formula of n(n−1)2.

As a side note, if we did not previously know the sum formula, we could use this as a combinatorial proof to show that it works. Also, if we account for repeated counting by dividing by k! , the number of permutations of k  objects, a similar method can be used to derive the chosen formula  (nk)=n!k!(n−k)!.

If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113

To find the value of P(B|A), follow these steps:

Learn more about probability:

brainly.com/question/13604758

#SPJ11

In the transaction, he will receive $374 more in sales of buttered popcorn than caramel popcorn.

An operation, often known as an "operand" or "argument," is a function in mathematics that converts zero or more input values into a clearly defined output value. In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.

Given, Derek owns a snack shop where he sells tins of buttered and caramel popcorn. The table shows the number of each type of popcorn sold over w weeks.

Popcorn Sales     Popcorn Cost ($)      Number Sold Over w Weeks

Buttered                   11                                        8w+9

Caramel                    11                                        6w−1

After 12 weeks of total buttered popcorn, he will make the sale

= $11 * (8*12 + 9)

= 11 * (96 + 9)

= $1,155

After 12 weeks of total caramel popcorn, he will make the sale

= $11 * (6*12 - 1)

= $11* (71)

=$781

In the sale, he will get more sales in buttered popcorn than sales in caramel popcorn by 1,155 - 781 = $374

Therefore, He will make $374 more in sales of buttered popcorn than caramel popcorn during the sale.

Learn more about mathematical operations here:

https://brainly.com/question/20628271

#SPJ1

Answer:

Actually...It's really easy

Step-by-step explanation:

All you have to do is put the numbers in order like this

                422

            x     18

_________________

             7,596

There you go! Hope it helps!

The major variable in this statistics class is considered a nominal variable.

The major variable is considered a nominal level of measurement because it represents a categorical characteristic that cannot be ordered or measured in a quantitative manner.

In other words, the values assigned to different majors (e.g. Engineering, English, History) do not represent numerical quantities or differences.

The level of measurement of a variable determines the type of statistical analyses that can be conducted with that variable. In this case, the major variable is considered a nominal variable because it represents a categorical characteristic that cannot be ordered or measured in a quantitative manner.

Nominal variables are often used to categorize or group data based on non-numeric characteristics, such as gender, race, or occupation. By collecting data on both GPA and major, the statistics instructor can explore relationships between these variables, such as whether certain majors tend to have higher or lower GPAs.

In conclusion, the major variable in this statistics class is considered a nominal variable.

To know more about nominal variable visit:

brainly.com/question/30869438

#SPJ11

Answer:

3) Angle plus the angle will be the sum of the line making it 180 degrees.

4) X being the missing variable number to solve the final product of 180 with both angles missing a variable number. With angle 1 being 11x-6 and angle 2 being 4x+21

5) This is the after work when 11x and 4x was combined giving 15x and 21 and -6 combined giving 15 which combines both angles helping to find the sum in which will be 180

6) The after work, after 180 was subtracted with 15 giving it 165

7) The after work, after 165 was divided by 15 giving it 11, with 11 being the missing value of x

Step-by-step explanation:

There may or may not exist a basis for mathbb{R}^2 consisting of eigenvectors for matrix A. Whether or not such a basis exists depends on the matrix A itself. If matrix A is diagonalizable, then it has a basis consisting of eigenvectors. However, not all matrices are diagonalizable. For example, a matrix with only one eigenvalue may not be diagonalizable. Therefore, it is not possible to say for certain whether or not a basis for mathbb{R}^2 consisting of eigenvectors for A exists without more information about A.

If something went wrong in part (b) of the question, it may be due to the fact that the matrix A is not diagonalizable and therefore does not have a basis consisting of eigenvectors. In such cases, the Jordan normal form can be used to find a generalized basis consisting of eigenvectors and generalized eigenvectors. This may be more complicated than simply finding a basis consisting of eigenvectors, as it involves finding additional vectors to complete the basis. If the problem in part (b) assumed that a basis for mathbb{R}^2 consisting of eigenvectors for A exists, then it would not be a valid assumption if A is not diagonalizable.

To learn more about eigenvectors : brainly.com/question/31043286

#SPJ11

Answer:

x=2 is incorrect

Step-by-step explanation:

Y(2)=(3/4)*x^2=(3/4)*4=3