How do you prove that two angles are congruent in two triangles?

Answer:

Hope this helps!

23 is a prime number, so therefore the factors of it is just 1 and itself (23)

The angle ∠2 is a vertically opposite angle to the angle 145°, so they are congruent:

∠2 = 145°

The angles 1 and 3 are supplementary angles to the angle 145°, so they are equal to:

180° - 145° = 35°

∠1 = 35°

∠3 = 35°

The angle 8 is a corresponding angle to the angle 145°, so they are congruent:

∠8 = 145°

The angle ∠6 is a vertically opposite angle to the angle ∠8 so they are congruent:

∠6 = 145°

The angles 5 and 7 are supplementary angles to the angle ∠8, so they are equal to:

180° - 145° = 35°

∠5 = 35°

∠7 = 35°

Answer:

40, leg

Step-by-step explanation:

The triangle has side lengths of 9, 40, and 41.

41 is the hypotenuse, so 40 is a leg.

To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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Answer:

Multiply the numbers inside the parenthesis with the number outside. In the case of the negative, use -1

Step-by-step explanation:

5(x-4)+3x-9x=6-(2x+5)+8x

5(x)- 5(4) +3x-9x=6 -(2x)-(5)+8x

5x-20+3x-9x=6-2x-5+8x

-x-20=6x+1

-x-6x=20+1

-7x=21

-7x/-7=21/-7

x=-3

Answer:

Step-by-step explanation:

The surface area of solid cylinder = 231 cm²

and curved surface area = 2/3 * 231 cm² = 154 cm²

Now, 2πrh = 154 ...........(i)

2πrh+2πr² = 231

Subtracting, 2πr² =  231 - 154 = 77

⇒2 * 22/7 * r² = 77

⇒r² = 77*7/2*22 ⇒ 49/4 ⇒ (7/2)²

so, r = 7/2 cm

Now, from (i),

2 * 22/7 * 7*h/2 = 154

⇒22h = 154 ⇒ 154/22 = 7

and volume = πr²h = 22/7 * 7/2 * 7/2 * 7cm³ ⇒ 539/2 = 269.5 cm²

Answer:

-1

Step-by-step explanation:

write it in the following manner:

-3x + 7  - 5x = 15

-8x + 7 = 15

-8x = 8

x = -1

Thus, the number has to be smaller than -1.

The smallest integer that makes the given inequality true is 0.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given inequality,

-3x + 7 - 5x < 15

We have to find the value of x.

(-3x - 5x) + 7 < 15

-8x < 8

Dividing whole sides by -1, the inequality sign changes.

x > -1

Smallest possible value is 0.

Hence the smallest posible value is 0.

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Answer:

5.5

Hope it helps!

Answer:

they are in order cross x with the y across from it

Step-by-step explanation:

Answer:

C;27t15 units3

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Georgia experienced the GREATEST economic growth due to industrial development during World War II. Georgia experienced the greatest economic growth during World War II.

Option D is the correct answer

This was due to an increase in the number of jobs available to people due to the high demand for supplies for the war. Many of the soldiers who were fighting in the war were from Georgia, and Georgia was able to benefit from the extra money and supplies that were being produced during this time.Growth in the economic sector was largely a result of several different factors. One of the most important of these was the fact that Georgia was home to several different military installations that were used to house and train soldiers.

These installations required a large number of supplies, which in turn created a high demand for workers. As a result, Georgia experienced a significant influx of people from other parts of the country who were looking for work in these areas.Another factor that contributed to the growth of Georgia's economy during this time period was the fact that the state was home to a number of factories and other manufacturing facilities. Many of these facilities were used to produce goods that were needed for the war effort, and the high demand for these goods led to an increase in the number of jobs available to people. As a result, the state's population grew rapidly, and many people who had previously been unemployed were able to find work in these industries.

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Answer:

  symmetric property

Step-by-step explanation:

The symmetric property is the one that tells you A=B means also B=A.

The obfuscating factor in this question is the renaming of angle SZW to angle WZS. Both names refer to the same angle.

Answer:

Phoebe: 180

Andy: 60

Polly: 30

Step-by-step explanation:

Let Polly's money be P  

Then Andy's money = P * 2 = 2P  

Then Pheobe's money = 2P * 3 = 6P  

There are 9 P's (P + 2P + 6P)

270 / 9 P's = 30

Therefore P = 30

Polly gets $30

Andy gets 30 * 2 = $60

Phoebe gets 60 * 3 = $180

Checking:    

180 + 60 + 30 = 270

Please mark as Brainliest.

1. \(-4, |3-7|, 5, |2*(-3)-(-1)|\)

2. a) -33

b) 34

c) -26

Explanation:

For #1: since absolute values cannot be negative, \(|3-7|\) = 4, and

\(|2*(-3)-(1)|\) = 7

For #2: Just work through the equations using P.E.M.D.A.S

Answer: x=26

Step-by-step explanation:

Simplifying

2x + 3x + 50 = 180

Reorder the terms:

50 + 2x + 3x = 180

Combine like terms: 2x + 3x = 5x

50 + 5x = 180

Solving

50 + 5x = 180

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-50' to each side of the equation.

50 + -50 + 5x = 180 + -50

Combine like terms: 50 + -50 = 0

0 + 5x = 180 + -50

5x = 180 + -50

Combine like terms: 180 + -50 = 130

5x = 130

Divide each side by '5'.

x = 26

Simplifying

x = 26

Your going to keep the first fraction then change the sign to multiplatation and flip the last fraction. -77/9 (mixed number into fraction) x -7/11

539/99 and then you can simplify that into 5 4/9

Answer:

ik you have a answer already I just really needed points so please don't repeat the answer

The regression formula estimated when performing a test for the stationarity of a time series variable y is y(t) = α + β*t + ε(t).

a. The null hypothesis of this test is that the time series variable y is non-stationary, meaning it has a unit root.

b. To determine whether two variables are cointegrated, the following steps are typically involved:

1) Identify the two variables: Select two time series variables, denoted as X(t) and Y(t), that are suspected to be related in a long-run equilibrium.

2) Test for unit roots: Conduct unit root tests on both X(t) and Y(t) to determine if they are stationary.

3) Estimate the cointegration regression: If both variables are non-stationary, estimate the cointegration regression model, typically using methods like the Engle-Granger two-step procedure or the Johansen test. This regression model takes the form Y(t) = α + β*X(t) + ε(t).

4) Test for the presence of a cointegrating relationship: Perform hypothesis tests on the estimated coefficients to check if the β coefficient is significantly different from zero, indicating the presence of a cointegrating relationship.

5) Interpret the results: If the null hypothesis of no cointegration is rejected, it suggests that X(t) and Y(t) are cointegrated, meaning they have a long-run relationship.

Cointegration analysis is used to determine whether two variables move together over time, despite being non-stationary individually. It helps in understanding the long-run equilibrium relationship between variables and can be valuable in modeling and forecasting.

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Answer: B

Step-by-step explanation:

The value of P(B|A) is 0.4, which is option C.

If two events A and B are independent, then the probability of one event occurring does not affect the probability of the other event occurring. In other words, P(B|A) = P(B) and P(A|B) = P(A).

Independent events are those events whose occurrence is not dependent on any other event.

For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.

Given that P(A) = 0.3 and P(B) = 0.4, we can use the formula for independent events to find the value of P(B|A):

P(B|A) = P(B) = 0.4

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Answer:

its -1

Step-by-step explanation:

cuz

Answer: it’s -1

Step-by-step explanation:

I just did the test

Answer:

48units

Step-by-step explanation:

Find the diagram of the rhombus attached

From the diagram, LM = MN

Hence;

3x - 3 = x + 7

Find x

Add 3 to both sides

3x - 3 + 3 = x + 7 + 3

3x = x + 10

3x - x = 10

2x = 10

x = 10/2

x = 5

LM= 3x - 3

LM = 3(5) - 3

LM = 12

Since LM = MN, then MN = 12

Since all the sides of the rhombus are equal then;

Perimeter of the rhombus = LM + MN + NO + OL

Perimeter of the rhombus = 12 + 12 +1 2 + 12

Perimeter of the rhombus = 48units

Answer:

48 Units is the answer

Step-by-step explanation:

EDGE2021

Answer:

18: x<32/5 19: c>-202

Step-by-step explanation:

\(x < \frac{32}{5}\\\)

\(c > -202\)

Solving \(x +\frac35 < 7\\\):

\(x +\frac35 < 7 \\ x +\frac35 -\frac35 < 7 -\frac35 \\ x < \frac{35}{5} -\frac35 \\ x < \frac{32}{5}\)

Solving for \(4 < 206 +c\):

\(4 < 206 +c \\ 206 +c > 4 \\ 206 +c -206 > 4 -206 \\ c > -202\)

Answer:

1.5 hours

Step-by-step explanation:

Carlos = x

Maria = y

55x + 47y = 197

x + y = 3.8

x = 3.8 - y

55(3.8 - y) + 47y = 197

209 - 55y + 47y = 197

-8y = -12

y = 3/2 = 1.5

Answer:

20: 2 years

Step-by-step explanation:

The value of  x of chord = 5

By definition of circle,

The chord of a circle is defined as the line segment connecting any two locations on the circle's perimeter; nevertheless, the diameter is the longest chord of a circle that goes through the centre of the circle.

The chord is one of the several line segments that may be made in a circle, and its endpoints are on the circumference.

⇒ 6 (6 + x) = 7 (7 + 11)

Solve for x;

⇒ 36 + 6x = 7 × 18

⇒ 36 + 6x = 126

⇒ 6x = 126 - 36

⇒ 6x = 90

⇒ x = 15

Thus, The value of x = 5

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Answer:

200.96

Step-by-step explanation:

So, we have to find the area of both.

The area for the mat is

(pi)12^2=3.14x144. However, since it is HALF a circle, we divide it by two.

So, 226.08

Next, the water bowl.

(3.14)4^2=50.24.

226.08-25.12=200.96

I may be wrong!

Answer: she drove 3 miles per gallon

Step-by-step explanation:

21 / 7 = 3 i hope this helps

Patrick's goal will reached by 30.7 hours

The inequality is 163 + (10x) > 470

Let's use x to represent the number of hours it will take to reach Patrick's goal.

First step: The total number of chandeliers made must be greater than 470.

163 + (10x) > 470

Second step: Solve for x by isolating it on one side of the inequality.

10x > 307

x > 30.7

Therefore, it will take more than 30.7 hours to reach Patrick's goal of making greater than 470 chandeliers.

The inequality can be written as: 163 + (10x) > 470

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The researcher is assessing item equivalence, If a study is in parallel forms of the measurement instrument to the same person. The correct option is C).

When a study introduces parallel forms, the researcher is assessing item equivalence. Item equivalence refers to the extent to which the different forms of the measurement instrument produce similar results for the same individual.

This assessment is crucial in research because it allows researchers to evaluate the consistency and reliability of the measurement instrument across different versions. By administering parallel forms to the same person, any differences in responses can be attributed to individual factors rather than variations in the instrument.

This helps ensure that the instrument is measuring the intended construct consistently and accurately. The correct option is C).

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