Write the following sets using the "roster method". That is, write the sets in list form. (a) A = {: is a natural number and x appears in the decimal expansion of 313/999} (b) B = {x:x is an odd integer smaller than 1} 2. List the next element in each of the following sets. (a) {1,1/4,1/16,1/64,...} (b) (3,3,6,9,15,24,...} 3. Answer either TRUE or FALSE to each of the statements (a) through (d). A = {3,6,9, ..., 96, 99} B = {1,0, 1, 2, 3, 4, 5, 6} (a) 66 € A ___
(b) 0 € C ___ (c) {4} € B ___ (d) C C A ___

Answer: x = 12

Step-by-step explanation:
To find the value of x, you're gonna need to know that all the angles of a triangle put together should equal 180 degrees.


We should start by adding the two angles we do have: 67 + 70 = 137.
Now that we know the amount of angle space we DO have, we need to subtract 137 from 180.
180 - 137 = 43
We now know that our missing angle has a total of 43 degrees.

Solving for x:
Now, we need to write out our problem, and we need to solve for x.
3x + 7 = 43

To solve for x, we need to get rid of the 7 first, using the inverse of addition: subtraction.
3x + (7 - 7) = (43 - 7)

The two 7s cancel out, and 43 - 7 is 36.
3x = 36

To get rid of the 3, and get x alone, we need to do the opposite of multiplication: division.
(3 ÷ 3) x = (36 ÷ 3)

Finish solving:
x = 12

Checking your work:
Implant the new value for x back into the main equation:

3(12) +7 = 43
36 + 7 = 43
43 = 43

Hope this helps you!

To find the coordinates of point R, we can use the concept of proportionality in the line segment PQ.

The proportionality states that if a line segment is increased or decreased by a certain percentage, the coordinates of the new point can be found by extending or reducing the coordinates of the original points by the same percentage.

Given that line segment PQ is increased by 200%, we can calculate the change in the x-coordinate and the y-coordinate separately.

Change in x-coordinate:

[tex]\displaystyle \Delta x=200\%\cdot ( 1-3)=-4[/tex]

Change in y-coordinate:

[tex]\displaystyle \Delta y=200\%\cdot ( 3-4)=-2[/tex]

Now, we can add the changes to the coordinates of point Q to find the coordinates of point R:

[tex]\displaystyle x_{R} =x_{Q} +\Delta x=1+(-4)=-3[/tex]

[tex]\displaystyle y_{R} =y_{Q} +\Delta y=3+(-2)=1[/tex]

Therefore, the coordinates of point R are [tex]\displaystyle (-3,1)[/tex].

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Box R's coordinates, after a 200% increase from PQ in its lengths, are (-3, 1) as determined by multiplying PQ's x and y displacement by three and adding those to the original coordinates of P.

To solve this problem, we can use the concept of vectors and displacement. We know the line segment PQ x-displacement (x2 - x1) = 1 - 3 = -2 and its y-displacement (y2 - y1) = 3 - 4 = -1. Noting that the point R is generated by increasing the length of PQ by 200%, the displacement from P to R would be three times the displacement from P to Q. Therefore, Rx = 3*(-2) = -6 and Ry = 3*(-1) = -3. Since these displacements are measured from initial point P(3,4), the coordinates of R would be (3 + Rx, 4 + Ry) = (3 - 6, 4 - 3) = (-3, 1).

https://brainly.com/question/36266415

#SPJ11

If we find the square of a negative number, say -x, where x > 0, then (-x) × (-x) = x 2. Here, x 2 > 0. Therefore, the square of a negative number is always positive.

The answer is:

below

Work/explanation:

The square of a negative number is always a positive number :

[tex]\sf{(-a)^2 = b}[/tex]

where b = the square of -a

The thing is, the square of a positive number is equal to the square of the same negative number :

[tex]\rhd\phantom{333} \sf{a^2 = (-a)^2}[/tex]

So if we take the square root of a number, let's say the number is 49 - we will end up with two solutions :

7, and -7

This was it.

The solution to the equation -10x - 2(8x + 5) = 4(x - 3) is x = 1/15.

To solve the equation: -10x - 2(8x + 5) = 4(x - 3), we can start by simplifying both sides of the equation:

-10x - 2(8x + 5) = 4(x - 3)

-10x - 16x - 10 = 4x - 12

Next, let's combine like terms on both sides of the equation:

-26x - 10 = 4x - 12

To isolate the variable x, we can move the constants to one side and the variables to the other side of the equation:

-26x - 4x = -12 + 10

-30x = -2

Finally, we can solve for x by dividing both sides of the equation by -30:

x = -2 / -30

x = 1/15

Know more about equation here:

https://brainly.com/question/29538993

#SPJ11

The standard deviation of the data set is 3.66.

The mean of the data set:

= (10 + 12 + 10 + 6 + 18 + 11 + 18 + 14 + 10) / 9

= 109 / 9

= 12.11

The difference between each data point and the mean:

(10 - 12.11), (12 - 12.11), (10 - 12.11), (6 - 12.11), (18 - 12.11), (11 - 12.11), (18 - 12.11), (14 - 12.11), (10 - 12.11)

Square each difference:

[tex](-2.11)^2, (-0.11)^2, (-2.11)^2, (-6.11)^2, (5.89)^2, (-1.11)^2, (5.89)^2, (1.89)^2, (-2.11)^2[/tex]

Calculate the sum of the squared differences:

[tex]= (-2.11)^2 + (-0.11)^2 + (-2.11)^2 + (-6.11)^2 + (5.89)^2 + (-1.11)^2 + (5.89)^2 + (1.89)^2 + (-2.11)^2\\= 120.46[/tex]

Divide the sum by the number of data points:

[tex]= 120.46 / 9\\= 13.3844[/tex]

The standard deviation:

[tex]= \sqrt{13.3844}\\= 3.66.[/tex]

Read more about standard deviation

brainly.com/question/475676

#SPJ4

The standard deviation of the given data set is approximately 3.60.

To find the standard deviation of a set of data, you can follow these steps:

Calculate the mean (average) of the data set.

Subtract the mean from each data point and square the result.

Calculate the mean of the squared differences.

Take the square root of the mean from step 3 to obtain the standard deviation.

Let's calculate the standard deviation for the given data set: 10, 12, 10, 6, 18, 11, 18, 14, 10.

Step 1: Calculate the mean

Mean = (10 + 12 + 10 + 6 + 18 + 11 + 18 + 14 + 10) / 9 = 109 / 9 = 12.11 (rounded to two decimal places)

Step 2: Subtract the mean and square the differences

(10 - 12.11)^2 ≈ 4.48

(12 - 12.11)^2 ≈ 0.01

(10 - 12.11)^2 ≈ 4.48

(6 - 12.11)^2 ≈ 37.02

(18 - 12.11)^2 ≈ 34.06

(11 - 12.11)^2 ≈ 1.23

(18 - 12.11)^2 ≈ 34.06

(14 - 12.11)^2 ≈ 3.56

(10 - 12.11)^2 ≈ 4.48

Step 3: Calculate the mean of the squared differences

Mean = (4.48 + 0.01 + 4.48 + 37.02 + 34.06 + 1.23 + 34.06 + 3.56 + 4.48) / 9 ≈ 12.95 (rounded to two decimal places)

Step 4: Take the square root of the mean

Standard Deviation = √12.95 ≈ 3.60 (rounded to two decimal places)

Therefore, the standard deviation of the given data set is approximately 3.60.

Learn more about standard deviation from the given link

https://brainly.com/question/475676

#SPJ11

The automorphism group Aut(S) of a subfield S of Q[i, z] can be determined by examining the properties of the subfield and the elements it contains.

To list each Aut(S) (Q[i, z]), we need to consider the structure of the subfield S and its elements. Aut(S) refers to the automorphisms of the field S that are also automorphisms of the larger field Q[i, z]. The specific automorphisms will depend on the characteristics of the subfield.

Learn more about automorphism visit:

https://brainly.in/question/55541637

#SPJ11

To find the battery life of the latest model 10 months from now, we need to calculate the cumulative increase in battery life over the 10-month period.

The battery life of each model increases by 4% compared to the previous model. Therefore, the battery life of the second model is [tex]\displaystyle 100\% + \dfrac{4}{100} = 104\%[/tex] of the first model's battery life. Similarly, the battery life of the third model is [tex]\displaystyle 104\% + \dfrac{4}{100} = 108.16\%[/tex] of the second model's battery life, and so on.

Using this pattern, the battery life of the latest model 10 months from now can be calculated as follows:

[tex]\displaystyle 632.0 \, \text{minutes} \times \left(1 + \dfrac{4}{100}\right)^{10}[/tex]

Simplifying this expression, we get:

[tex]\displaystyle 632.0 \times \left(1.04\right)^{10}[/tex]

Calculating this expression, we find that the latest model's battery life 10 months from now is approximately 1057.1 minutes.

Therefore, the correct answer is A) 1057.1.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

The roots of the equation x³ + 4x² + x - 6 = 0 are x = 1, x = -2, and x = -3.

To find the roots of the equation x³ + 4x² + x - 6 = 0 without using a calculator, we can use factoring or synthetic division. By trying out different values for x, we can find that x = 1 is a root of the equation. Dividing the equation by (x - 1) using synthetic division, we obtain:

1 |   1    4    1   -6

   |        1    5    6

   |........................

      1    5    6    0

The result after dividing is the quadratic expression x² + 5x + 6. To find the remaining roots, we can factor this quadratic expression:

x² + 5x + 6

= (x + 2)(x + 3)

Setting each factor equal to zero, we have:

x + 2 = 0 or x + 3 = 0

Solving these equations, we find that x = -2 and x = -3.

To learn more about roots, refer here:

https://brainly.com/question/16932611

#SPJ11

- Eigenvalues: λ₁ = (1 + √5)/2 and λ₂ = (1 - √5)/2.

- Eigenspaces: Eigenspace corresponding to λ₁ is span{(1 + √5)/2, 0, 0, 0}. Eigenspace corresponding to λ₂ is span{(1 - √5)/2, 0, 0, 0}.

- Diagonalizability: The matrix B is not diagonalizable.

To find the eigenvalues, eigenspaces, and determine diagonalizability for matrix B, let's proceed with the following steps:

Step 1: Find the eigenvalues λ by solving the characteristic equation det(B - λI) = 0, where I is the identity matrix of the same size as B.

B = [0 0 0 -1; 1 0 0 0; 0 1 0 -2; 0 0 1 0]

|B - λI| = 0

|0-λ 0 0 -1; 1 0-λ 0; 0 1 0-2; 0 0 1 0-λ| = 0

Expanding the determinant, we get:

(-λ)((-λ)(0-2) - (1)(1)) - (0)((-λ)(0-2) - (0)(1)) + (0)((1)(1) - (0)(0-λ)) - (-1)((1)(0-2) - (0)(0-λ)) = 0

-λ(2λ - 1) + λ + 2 = 0

-2λ² + λ + λ + 2 = 0

-2λ² + 2λ + 2 = 0

Dividing the equation by -2:

λ² - λ - 1 = 0

Applying the quadratic formula, we get:

λ = (1 ± √5)/2

So, the eigenvalues for matrix B are λ₁ = (1 + √5)/2 and λ₂ = (1 - √5)/2.

Step 2: Find the eigenspaces corresponding to each eigenvalue.

For λ₁ = (1 + √5)/2:

Solving the equation (B - λ₁I)v = 0 will give the eigenspace for λ₁.

For λ₁ = (1 + √5)/2, we have:

(B - λ₁I)v = 0

[0 -1 0 -1; 1 -λ₁ 0 0; 0 1 -λ₁ -2; 0 0 1 -λ₁]v = 0

Converting the augmented matrix to reduced row-echelon form, we get:

[1 0 0 (1 + √5)/2; 0 1 0 0; 0 0 1 0; 0 0 0 0]

The resulting row shows that v₁ = (1 + √5)/2, v₂ = 0, v₃ = 0, and v₄ = 0. Therefore, the eigenspace corresponding to λ₁ is span{(1 + √5)/2, 0, 0, 0}.

Similarly, for λ₂ = (1 - √5)/2:

Solving the equation (B - λ₂I)v = 0 will give the eigenspace for λ₂.

For λ₂ = (1 - √5)/2, we have:

(B - λ₂I)v = 0

[0 -1 0 -1; 1 -λ₂ 0 0; 0 1 -λ₂ -2; 0 0 1 -λ₂]v = 0

Converting the augmented matrix to reduced row-echelon form, we get:

[1 0 0 (1 - √5)/2; 0 1 0 0; 0 0 1 0; 0 0

0 0]

The resulting row shows that v₁ = (1 - √5)/2, v₂ = 0, v₃ = 0, and v₄ = 0. Therefore, the eigenspace corresponding to λ₂ is span{(1 - √5)/2, 0, 0, 0}.

Step 3: Determine diagonalizability.

To determine if the matrix B is diagonalizable, we need to check if the matrix has n linearly independent eigenvectors, where n is the size of the matrix.

In this case, the matrix B is a 4x4 matrix. However, we only found one linearly independent eigenvector, which is (1 + √5)/2, 0, 0, 0. The eigenspace for λ₂ is the same as the eigenspace for λ₁, indicating that they are not linearly independent.

Since we do not have a set of n linearly independent eigenvectors, the matrix B is not diagonalizable.

Learn more about Eigenspaces here :-

https://brainly.com/question/28564799

#SPJ11

Explanation cannot be summarized in one row as it requires multiple factors and considerations to determine the asymptotes of different functions.

In order to find the horizontal and vertical asymptotes of a function, we need to analyze its behavior as x approaches infinity or negative infinity.

In the given question, we are provided with multiple functions (a) to (h) and asked to find their asymptotes, if any exist.

To find the horizontal asymptote, we look at the highest degree term in the numerator and denominator.

If the degrees are equal, the horizontal asymptote is the ratio of their coefficients.

If the degree of the numerator is greater, there is no horizontal asymptote.

For vertical asymptotes, we examine the values of x that make the denominator zero.

These values represent vertical lines that the graph approaches but never crosses.

By analyzing the given functions based on these criteria, we can determine whether they have horizontal or vertical asymptotes, if any.

Learn more about considerations to determine

brainly.com/question/30513848

#SPJ11

Answer: stated down below

Step-by-step explanation:

To calculate profitability ratios, specific financial data is required, such as net income, revenue, and assets. Since I don't have access to specific financial information for the years 2024 and 2025, I'm unable to provide the exact profitability ratios for those years.

However, I can provide you with a list of common profitability ratios that you can calculate using the relevant financial data for a company. Here are a few commonly used profitability ratios:

Gross Profit Margin = (Gross Profit / Revenue) * 100

This ratio measures the percentage of revenue that remains after deducting the cost of goods sold.

Net Profit Margin = (Net Income / Revenue) * 100

This ratio shows the percentage of revenue that represents the company's net income.

Return on Assets (ROA) = (Net Income / Total Assets) * 100

ROA measures the efficiency of a company's utilization of its assets to generate profits.

Return on Equity (ROE) = (Net Income / Shareholders' Equity) * 100

ROE calculates the return earned on the shareholders' investment in the company.

Operating Profit Margin = (Operating Income / Revenue) * 100

This ratio assesses the profitability of a company's core operations before considering interest and taxes.

Remember, to calculate these ratios, you need specific financial information for the years 2024 and 2025. Once you have the relevant data, you can plug it into the formulas provided above to obtain the respective profitability ratios.

The solution to the equation is x = -5.

To solve the equation (0.8 + 0.7x) / x = 0.86, we can begin by multiplying both sides of the equation by x to eliminate the denominator:

0.8 + 0.7x = 0.86x

Next, we can simplify the equation by combining like terms:

0.7x - 0.86x = 0.8

-0.16x = 0.8

To isolate x, we divide both sides of the equation by -0.16:

x = 0.8 / -0.16

Simplifying the division:

x = -5

Learn more about equation here :-

https://brainly.com/question/29538993

#SPJ11

Answer:

B

Step-by-step explanation:

the 'dot' between 11 and x represents multiplication.

two numbers being multiplied are referred to as a product.

11 • x ← is the product of 11 and x

The radius of curvature (r) is -100 cm and Magnification (m) is 11.26. The mirror is a concave mirror.

Given Data: Object distance, u = -1.03 cm; Image distance, v = 11.6 cm

To find: The radius of curvature (r) and Magnification (m).

Formula used:

1/f = 1/v - 1/u;

Magnification, m = -v/u

Calculation:

Using the formula,

1/f = 1/v - 1/u

1/f = 1/11.6 - 1/-1.03 = -0.02

f = -50 cm

The radius of curvature,

r = 2f

r = 2 × (-50) = -100 cm

Since the radius of curvature is negative, the mirror is a concave mirror.

Magnification, m = -v/u= -11.6/-1.03= 11.26

Hence, the radius of curvature (r) is -100 cm and Magnification (m) is 11.26.

Learn more about magnification visit:

brainly.com/question/21370207

#SPJ11

a) AD can be expressed as AD = 6a - 4b.

b) ABCD is a parallelogram.

a) To express AD in terms of 'a' and/or 'b', we can observe that AD is the difference between AB and BC. Using the given values, we have:

AD = AB - BC

= (8a + 12b) - (2a + 16b)

= 8a + 12b - 2a - 16b

= 6a - 4b

Therefore, AD can be expressed as 6a - 4b.

b) Based on the given information, the shape ABCD is a parallelogram. This is because a parallelogram has opposite sides that are parallel and equal in length, which is satisfied by the given sides AB and DC.

for such more question on parallelogram

https://brainly.com/question/3050890

#SPJ8

The last digit in the product of the given expression is 3.

Here, we have,

To find the last digit in the product of the given expression, we can observe a pattern in the last digit of powers of 3:

3¹ = 3 (last digit is 3)

3² = 9 (last digit is 9)

3³ = 27 (last digit is 7)

3⁴ = 81 (last digit is 1)

3⁵ = 243 (last digit is 3)

3⁶ = 729 (last digit is 9)

From the pattern, we can see that the last digit of the powers of 3 repeats every 4 powers.

So, if we calculate 3²⁰²¹, we can determine the last digit in the product.

3²⁰²¹ can be written as

(3⁴)⁵⁰⁵ × 3

= 1⁵⁰⁵ × 3

= 3.

Therefore, the last digit in the product of the given expression is 3.

To learn more on multiplication click:

brainly.com/question/5992872

#SPJ4

A=[−10,5)∪{7,8} is a closed set.

A closed set is a set that contains all its limit points. In the given set A=[−10,5)∪{7,8}, the interval [−10,5) is a closed interval because it includes its endpoints and all the points in between. The set {7,8} consists of two isolated points, which are also considered closed. Therefore, the union of a closed interval and isolated points results in a closed set.

Learn more about set

brainly.com/question/8053622

#SPJ11

Answer:

Your answer is here 1.56666666667

Step-by-step explanation:

first make 2.35 in form of p/q then multiply by 2/3 then divide the answer

you cannot also write in fractions

please mark as brainliest

YOU CAN ALWAYS ASK FOR HELP WE ARE ALWAYS HERE

The expressions that have a product with three decimal places are 0.271 times 5, 4.2 times 0.08, and 56.8 times 1.34. Option A,B,D.

To determine which expressions will have a product with three decimal places, we need to calculate the products and see if they have three digits after the decimal point. Let's evaluate each expression:

0.271 times 5:

The product is 0.271 * 5 = 1.355

The product has three decimal places.

4.2 times 0.08:

The product is 4.2 * 0.08 = 0.336

The product has three decimal places.

1.975 times 0.1:

The product is 1.975 * 0.1 = 0.1975

The product has four decimal places, not three.

56.8 times 1.34:

The product is 56.8 * 1.34 = 76.112

The product has three decimal places. Option A,B,D are correct.

For more such question on three decimal places . visit :

https://brainly.com/question/28393353

#SPJ8

The correct regular expressions to describe the language L = {w | na(w) is odd} are b* ab* (b* ab* ab*)* and b*a(b* ab*a)*b*.

The language L consists of strings in which the number of 'a's is odd. To construct a regular expression that describes this language, we need to consider the possible combinations of 'a's and 'b's.

The first correct expression, b* ab* (b* ab* ab*)*, breaks down as follows:

- b* matches zero or more occurrences of 'b'.

- ab* matches 'a' followed by zero or more occurrences of 'b'.

- (b* ab* ab*)* matches zero or more occurrences of 'b' followed by zero or more occurrences of 'a' followed by zero or more occurrences of 'b' followed by one or more occurrences of 'a'.

The second correct expression, b*a(b* ab*a)*b*, can be explained as:

- b* matches zero or more occurrences of 'b'.

- a matches a single occurrence of 'a'.

- (b* ab*a)* matches zero or more occurrences of 'b' followed by zero or more occurrences of 'a' followed by zero or more occurrences of 'b' followed by one or more occurrences of 'a'.

- b* matches zero or more occurrences of 'b'.

These regular expressions accurately capture the language L, as they allow for any combination of 'a's and 'b's where the number of 'a's is odd. The expressions account for the possibility of leading and trailing 'b's, as well as the presence of multiple groups of 'a's and 'b's.

Learn more about: regular expressions

brainly.com/question/32344816

#SPJ11

It will take approximately 35 days before 1000 people are infected.

Initially, 100 people were diagnosed with the virus.

A virus is spreading at a rate of 4% each day.

Let us calculate how many days it will take for 1000 people to be infected.

Let us assume that x represents the number of days it will take for 1000 people to be infected.

Since the number of people infected increases by 4% each day, after one day, the number of people infected will be 100 × (1 + 0.04) = 104 people.

After two days, the number of people infected will be 104 × (1 + 0.04) = 108.16 people

.After three days, the number of people infected will be 108.16 × (1 + 0.04) = 112.4864 people.

Thus, we can say that the number of people infected after x days is given by 100 × (1 + 0.04)ⁿ.

So, we can write 1000 = 100 × (1 + 0.04)ⁿ.

In order to solve for n, we need to isolate it.

Let us divide both sides by 100.

So, we have:10 = (1 + 0.04)ⁿ

We can then take the logarithm of both sides and solve for n.

Thus, we have:

log 10 = n log (1 + 0.04)

Let us divide both sides by log (1 + 0.04).

Therefore:

n = log 10 / log (1 + 0.04)

Using a calculator, we get:

n = 35.33 days

Rounding this off, we get that it will take about 35 days for 1000 people to be infected.

To learn more on logarithm:

https://brainly.com/question/30340014

#SPJ11

Answer:

It would be H.

Explanation:
I'm good at math

(a) Without knowing the effect size, it is not possible to calculate the type II error for the given hypothesis test. (b) To detect a true mean diameter of 1.55 inches with a power of at least 0.9, approximately 65 bearings would be needed.

(a) If the true mean diameter is 1.55 inches, the probability of not rejecting the null hypothesis when it is false (i.e., the type II error) depends on the chosen significance level, sample size, and effect size. Without knowing the effect size, it is not possible to calculate the type II error.

(b) To calculate the required sample size to detect a true mean diameter of 1.55 inches with a power of at least 0.9, we need to know the chosen significance level, the standard deviation of the population, and the effect size.

Using a statistical power calculator or a sample size formula, we can determine that a sample size of approximately 65 bearings is needed.

to know more about  hypothesis test, visit:
brainly.com/question/32874475
#SPJ11

The argument is valid, and the possible truth value of the conclusion is true (T).

(i) Let's define the propositional variables as follows:

P: It is going to snow.

Q: The school is closed.

The premises and conclusion can be represented as:

Premise 1: P → Q (If it is going to snow, then the school is closed.)

Premise 2: Q (The school is closed.)

Conclusion: P (Therefore, it is going to snow.)

(ii) To determine the validity of the argument, we can construct a truth table for the premises and the conclusion. The truth table will consider all possible combinations of truth values for P and Q.

(truth table is attached)

In the truth table, we can see that there are two rows where both premises are true (the first and third rows). In these cases, the conclusion is also true.

Since the argument is valid (the conclusion is true whenever both premises are true), the possible truth values of the conclusion are true (T).

To know more about propositional logic, refer here:

https://brainly.com/question/33632547#

#SPJ11

In order to determine if the trapezoids in the design are isosceles, you can measure the lengths of their bases and legs. If the trapezoids have congruent bases and congruent non-parallel sides, then they are isosceles trapezoids.

1. Identify the trapezoids in the design. Look for shapes that have one pair of parallel sides and two pairs of non-parallel sides.

2. Measure the length of each base of the trapezoid. The bases are the parallel sides of the trapezoid.

3. Compare the lengths of the bases. If the bases of a trapezoid are equal in length, then it has congruent bases.

4. Measure the length of each non-parallel side of the trapezoid. These are the legs of the trapezoid.

5. Compare the lengths of the legs. If the legs of a trapezoid are equal in length, then it has congruent non-parallel sides.

6. If both the bases and non-parallel sides of a trapezoid are congruent, then it is an isosceles trapezoid.

To know more about trapezoids and their properties, refer here:

https://brainly.com/question/31380175#

#SPJ11

Answer:

B

Step-by-step explanation:

The domain is asking for all the values of x and according to the graph, the only values of x are in between 0 and 4, therefore B

We have found a line segment joining two lattice points whose midpoint is also a lattice point. So, among any five lattice points, there must be a pair, the midpoint of which is also a lattice point.

Let’s assume that there are five lattice points on a plane and they are represented as follows:

(x1, y1), (x2, y2), (x3, y3), (x4, y4), (x5, y5)

To prove that among any five lattice points, there must be a pair, the midpoint of which is also a lattice point, we can follow the following steps.

Step 1: Let's consider any two points from the five lattice points, and let's call them P and Q.

Their coordinates are represented as (x1, y1) and (x2, y2), respectively.

Step 2: Let's apply the midpoint formula to find the midpoint of the line segment PQ. The midpoint formula is given by,

Midpoint of PQ = ( (x1+x2)/2, (y1+y2)/2 )

We know that the sum of two integers is always an integer, and the product of two integers is always an integer. Therefore, (x1+x2) and (y1+y2) are integers, and thus the midpoint of PQ is also a lattice point.

Step 3: Let's repeat step 2 with other pairs of points. There are a total of 10 pairs of points in five lattice points, and we can apply the midpoint formula to each pair. Therefore, we have 10 midpoints.

Step 4: Let’s observe that if one of these midpoints coincides with any of the five lattice points, then we are done. If not, then each midpoint must be a new point that is not among the five lattice points. And because the coordinates of each midpoint are the average of two integer coordinates, we know that each midpoint must be a point with integer coordinates (as mentioned in step 2).

Step 5: Let’s consider two midpoints, M1 and M2, that we calculated in step 3. Since M1 and M2 are each midpoints of a line segment joining two lattice points, we know that M1M2 is also a line segment. And because the coordinates of M1 and M2 are both integers, we know that the coordinates of the endpoints of M1M2 are integers too.

Hence Proved.

To learn more on  lattice points:

https://brainly.com/question/19476124

#SPJ11

The area of the regular octogon is 196.15 square inches.

For a regular octogon with apothem A and side length L, the area is given by:

area =(2*A*L) * (1 + √2)

Here we know that:

A = 7in

L = 5.8 in

Replacing these values in the area for the formula, we will get the area:

area = (2*7in*5.8in) * (1 + √2)

area = 196.15 in²

Learn more about area at:

https://brainly.com/question/24487155

#SPJ1

Here is a diagram of the points described:

(2,3)      (2, -3)

  |             |

  |             |

  c----------d

Based on the given points, let's consider the following:

Point A: A (2, 3)

Point B: B (2, -3)

Points A and B have the same x-coordinate, indicating that they lie on a vertical line. The y-coordinate of A is greater than the y-coordinate of B, suggesting that A is located above B on the y-axis.

Now, you mentioned that points C and D are collinear. Collinear points lie on the same line. Assuming that points C and D lie on the same vertical line as A and B, but at different positions.

The points A (2,3) and B (2, -3) are collinear, but the points A, B, C, D, and F are not. This is because the points A and B have the same x-coordinate, so they lie on the same vertical line. The points C and D also have the same x-coordinate, so they lie on the same vertical line. However, the point F does not have the same x-coordinate as any of the other points, so it does not lie on the same vertical line as any of them.

Learn more about points here:

brainly.com/question/18481071

#SPJ11

The rational roots of the polynomial equation are -3/2, 1/2, -1, and 5/2.

To find the rational roots of the polynomial equation P(x) = 6x⁴ - 13x³ + 13x² - 39x - 15, we can use the Rational Root Theorem.

The Rational Root Theorem states that if a rational number p/q is a root of the polynomial, then p is a factor of the constant term (-15 in this case) and q is a factor of the leading coefficient (6 in this case).

To find the factors of -15, we can list all possible combinations of positive and negative factors of 15: ±1, ±3, ±5, ±15.

To find the factors of 6, we list all possible combinations of positive and negative factors of 6: ±1, ±2, ±3, ±6.

Now, we can test each combination of p and q to see if it satisfies the equation P(p/q) = 0.

By trying all the possible combinations, we find that the rational roots of P(x) = 6x⁴ - 13x³ + 13x² - 39x - 15 are:

x = -3/2, x = 1/2, x = -1, x = 5/2.

Learn more about rational roots from the given link!

https://brainly.com/question/29629482

#SPJ11