The triangles shown below must be congruent.?

True or false

Answer:

Step-by-step explanation:

\(\mathrm{4\left(x+2\right)+2\left(x+5\right)}\)

Expand:-

\(\mathrm{4x+8+2x+10}\)

Combine like terms:-

\(\mathrm{4x+2x+8+10}\)

\(\mathrm{6x+18}\)

__________________

Hope this helps!

Answer:

\( \sf \: 6x + 18 \)

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ 4(x + 2) + 2(x + 5)

Let's simplify the expression,

→ 4(x + 2) + 2(x + 5)

→ 4(x) + 4(2) + 2(x) + 2(5)

→ 4x + 8 + 2x + 10

→ 4x + 2x + 8 + 10

→ (4x + 2x) + (8 + 10)

→ 6x + 18

Hence, the answer is 6x + 18.

In this case, the exponential term (4^n) grows much faster than the quadratic term (n^2). Therefore, the numerator will grow at a much faster rate than the denominator as n approaches infinity. Consequently, the limit does not exist, and the sequence is divergent.

The given sequence is: f_n = 9/(4^n) + 13.

To determine whether this sequence is convergent or divergent, we can take the limit of f_n as n approaches infinity:

lim (n → ∞) f_n = lim (n → ∞) (9/(4^n) + 13)

As n approaches infinity, (4^n) goes to infinity much faster than 9, so the entire first term of the sequence goes to 0. Therefore:

lim (n → ∞) f_n = lim (n → ∞) (0 + 13) = 13

Since the limit exists and is finite, the sequence converges. Its limit is 13.
To determine whether the given sequence is convergent or divergent, we first need to identify the sequence. Based on your question, it appears the sequence is:

f(n) = (9(4^n) + 13) / (n^2)

Now, let's evaluate the limit as n approaches infinity:

lim (n → ∞) (9(4^n) + 13) / (n^2)

In this case, the exponential term (4^n) grows much faster than the quadratic term (n^2). Therefore, the numerator will grow at a much faster rate than the denominator as n approaches infinity. Consequently, the limit does not exist, and the sequence is divergent.

Your answer: The sequence is divergent.

To learn more about quadratic term, click here:

brainly.com/question/28323845

#SPJ11

To calculate the price of a common stock that pays regular dividends, we could begin with the general formula for the valuation of a dividend-paying stock.

The formula is known as the Dividend Discount Model (DDM) or the Gordon Growth Model. It calculates the present value of all future dividends and the stock's expected growth rate. The general formula is:

Price of Stock = Dividend / (Required Rate of Return - Dividend Growth Rate)

In this formula:

- Dividend refers to the expected dividend payment for a specific period.

- Required Rate of Return is the minimum rate of return an investor expects to receive from the stock. It represents the opportunity cost of investing in that stock.

- Dividend Growth Rate is the estimated rate at which the company's dividends are expected to grow over time.

By plugging in the appropriate values for the dividend, required rate of return, and dividend growth rate, you can calculate the price of a common stock using this formula. It's important to note that this formula assumes a constant growth rate in dividends, which might not be applicable for all stocks.

To know more about Dividend visit-

brainly.com/question/32568431

#SPJ11

The mode is the most common value in a set of data values then the mode of the given set of data is 56.

The mode is the most common value in a set of data values. If X is a discrete random variable, the mode is the x value at which the probability mass function maximizes. In other words, it is the most likely value to be sampled.

The most common number, or the number that appears the most frequently. Example: Since the number 2 occurs three times, more than any other number, it is the mode of the sequence "4, 2, 4, 3, 2, 2."

Let the given data be 39, 41, 44, 50, 54, 56, 56, 56, 61

The mode is the most common value in a set of data values.

Then the mode of the given set of data is 56.

To learn more about mode, refer to:

https://brainly.com/question/14532771

#SPJ4

Answer:

16

Step-by-step explanation:

Answer:

What is statement and reason in geometry?

The order of the statements in the proof is not always fixed, but make sure the order makes logical sense. Reasons will be definitions, postulates, properties and previously proven theorems. “Given” is only used as a reason if the information in the statement column was told in the problem.

Step-by-step explanation:

As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

To know more about Similarity theorem here.

https://brainly.com/question/24167205

#SPJ4

The volume of the pyramid is B) 192ft

The volume of a pyramid can be calculated utilizing the condition:

V = (1/3) * base region * height...........(1)

In the case of a square pyramid, the base area is given by the condition:

base area = (edge length)²

Thus, in this issue, we have:

base area = (6 ft)² = 36 ft²

height = 16 ft (given)

Substituting these values into the condition for the volume of a pyramid ( equation (1) ), we get:

V = (1/3) * 36 ft² * 16 ft

V = 192 cubic feet

In this way, the volume of the pyramid is 192 cubic feet.

To know more about the volume of the pyramid refer to this:

https://brainly.com/question/18994842

#SPJ4

For the function f(x) = ⌊x²/3⌋, the values of f(s) for different sets s are as follows: a) f(s) = {1, 0, 0, 0, 1, 3}, b) f(s) = {0, 0, 1, 3, 5, 8}, c) f(s) = {0, 8, 16, 40}, d) f(s) = {1, 12, 33, 77}

The function f(x) = ⌊x²/3⌋ represents the floor of x²/3. To find f(s) for different sets s, let's evaluate it for each case:

a) For s = {-2, -1, 0, 1, 2, 3}:

  - For -2, (-2)²/3 = 4/3, and ⌊4/3⌋ = 1.

  - For -1, (-1)²/3 = 1/3, and ⌊1/3⌋ = 0.

  - For 0, (0)²/3 = 0/3 = 0.

  - For 1, (1)²/3 = 1/3, and ⌊1/3⌋ = 0.

  - For 2, (2)²/3 = 4/3, and ⌊4/3⌋ = 1.

  - For 3, (3)²/3 = 9/3 = 3.

  Therefore, f(s) = {1, 0, 0, 0, 1, 3}.

b) For s = {0, 1, 2, 3, 4, 5}:

  - For 0, (0)²/3 = 0/3 = 0.

  - For 1, (1)²/3 = 1/3, and ⌊1/3⌋ = 0.

  - For 2, (2)²/3 = 4/3, and ⌊4/3⌋ = 1.

  - For 3, (3)²/3 = 9/3 = 3.

  - For 4, (4)²/3 = 16/3, and ⌊16/3⌋ = 5.

  - For 5, (5)²/3 = 25/3, and ⌊25/3⌋ = 8.

  Therefore, f(s) = {0, 0, 1, 3, 5, 8}.

c) For s = {1, 5, 7, 11}:

  - For 1, (1)²/3 = 1/3, and ⌊1/3⌋ = 0.

  - For 5, (5)²/3 = 25/3, and ⌊25/3⌋ = 8.

  - For 7, (7)²/3 = 49/3, and ⌊49/3⌋ = 16.

  - For 11, (11)²/3 = 121/3, and ⌊121/3⌋ = 40.

  Therefore, f(s) = {0, 8, 16, 40}.

d) For s = {2, 6, 10, 14}:

  - For 2, (2)²/3 = 4/3, and ⌊4/3⌋ = 1.

  - For 6, (6)²/3 = 36/3 = 12.

  - For 10, (10)²/3 = 100/3, and ⌊100/3⌋ = 33.

  - For 14, (14)²/3 = 196

The values of f(s) for the given sets show how the function ⌊x²/3⌋, which represents the floor of x²/3, behaves for different inputs.

Learn more about sets here: https://brainly.com/question/28860949

#SPJ11

The pοssible values οf angle J is 76 degrees.

It is a triangle in which οne οf the angles is 90 degrees and the οther twο are sharp angles. The sides οf a right-angled triangle are knοwn as the hypοtenuse, perpendicular, and base.

Given that,

Triangle = Triangle HIJ

j = 91 inches

i = 90 inches

Angle I = 106 degrees

The pοssible values οf angle J can be calculated using the fοllοwing law οf sines

sin(J)/j = sin(I)/i

By substituiοn, we have

sin(J)/91 = sin(106)/90

Sο, we have

sin(J) = 0.9719

Take the arc sin οf bοth sides

J = 76 and 104 degrees

The measure 104 degrees is nοt pοssible because a triangle cannοt have twο οbtuse angles

Hence, the measure οf J is 76 degrees

To learn more about the right-angle triangle here:

brainly.com/question/3770177

#SPJ1

Answer:

I believe its A, correct me if i'm wrong.

Step-by-step explanation:

A hypothesis test involves a comparison between research results from a sample and a hypothesis about a population.

Thus, option (A) is correct.

In hypothesis testing, a researcher starts with a null hypothesis, which represents the assumption of no difference or no effect in the population.

The researcher collects data from a sample and performs statistical analysis to determine whether the evidence supports or rejects the null hypothesis in favor of an alternative hypothesis.

The research results obtained from the sample are compared to the hypothesis about the population to determine whether there is enough evidence to reject the null hypothesis and accept the alternative hypothesis.

Thus, option (A) is correct

Learn more about Hypothesis here:

https://brainly.com/question/32562440

#SPJ6

Answer:

n-2=10

n=10+2

n=12

please thnx my answer

Answer:

12

Step-by-step explanation:

n - 2 = 10

(add 2 to the other side (Addition property of equality))

10 = n

When a postal worker counts the number of complaint letters received by the united states postal service in a given day, the type of data collected is quantitative.

Quantitative data is data that can be measured and expressed in numbers. In this case, the number of complaint letters received by the United States Postal Service in a given day can be measured and expressed as a number.

Qualitative data, on the other hand, is data that cannot be measured or expressed in numbers. For example, the contents of the complaint letters would be qualitative data.

Learn more about data on

https://brainly.com/question/26711803

#SPJ1

Answer:

50°

Step-by-step explanation:

angle 5 = angle 4 ( Alternative Interior Angles are equal )

But angle 3 & angle 4 are linear pairs. So,

angle 3 + angle 4 = 180°

=> angle 3 + angle 5 = 180° (angle 5 = angle 4)

=> angle 3 + 130° = 180°

=> angle 3 = 180° - 130° = 50°

Answer: 52 1/2

Step-by-step explanation: I just found the average of the numbers.

The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

To know more about marginal utility related question visit:

https://brainly.com/question/30841513

#SPJ11

Answer:

y=5/4x+10

Have a nice day.

Answer:

5/4x + 10

Step-by-step explanation:

If it's parallel, the slope will remain the same.

To find the y-intercept, you have to plug in the coordinates into the equation which is, y = 5/4x + b.

y = 5/4x + b

0 = 5/4 (-8) + b

0 = -10 + b

10 = b

The equation is 5/4x + 10.

Answer:

Step-by-step explanation:

Remark

The moment you put Tan(45) in the choices, non of the other choices can compete.

Tan(45) = 1

Sin(a) or cos(a) are all less then one except when a = 0 or 90. Even then they can only have a value of 1. Since none of the angles = 0 or 90 then the  largest value is Tan(45) = 1.

The specific solution depends on the given matrix A.

To find a basis for each of the subspaces r(AT), N(A), r(A), and N(AT), we first need to understand what each of these terms represents:

1. r(AT) - the row space of the transpose of matrix A
2. N(A) - the null space of matrix A
3. r(A) - the row space of matrix A
4. N(AT) - the null space of the transpose of matrix A

To find a basis for each of these subspaces, follow these general steps:

1. For r(A) and r(AT), row reduce the matrix A and its transpose AT to their row echelon forms. The non-zero rows in the reduced matrices will form a basis for the row spaces.

2. For N(A) and N(AT), set up the homogenous system of linear equations (Ax = 0 and ATx = 0), where x is the vector of variables. Then, solve the systems using Gaussian elimination, and find the general solutions. The general solutions will provide the basis vectors for the null spaces.

Note that specific solutions depend on the given matrix A. The process outlined above will help you find the basis for each of the subspaces r(AT), N(A), r(A), and N(AT) once you have the matrix A.

The correct question should be :

What is the matrix A for which you would like to find the basis for each of the subspaces r(AT), N(A), r(A), and N(AT)?

To learn more about subspaces visit : https://brainly.com/question/13045843

#SPJ11

the answer should be 12 if it isn't it's my bad

The manager of the sport store can afford to pay $80 for each Nike baseball glove in order to have a markup of amount $50 and a 25% markup on the selling price.

$50 / 0.25 = $200

To calculate the cost of the Nike baseball gloves with a markup of 25% and a margin of $50, use the following formula:

Cost = (Price + Markup) / (1 + Markup Percentage)

Cost = ($50 + $50) / (1 + 0.25)

Cost = $100 / 1.25

Cost = $80

Therefore, the manager can afford to pay amount $80 for each baseball glove.

The manager of the sport store can afford to pay $80 for each Nike baseball glove in order to have a markup of $50 and a 25% markup on the selling price.

Learn more about amount here

https://brainly.com/question/8082054

#SPJ4

The proportion of the committee that is left-handed is 4/15, which is equivalent to 0.267 when rounded to three decimal places.

A proportion is a way of expressing the relationship between two quantities. It is often written as a fraction, where the numerator represents the quantity of interest, and the denominator represents the total quantity.

In this case, we are interested in the proportion of left-handed senators, so the numerator will be the number of left-handed senators, which is 4. The denominator will be the total number of senators in the committee, which is 15. Therefore, the proportion of left-handed senators can be written as:

4/15

This fraction can also be expressed as a decimal by dividing the numerator (4) by the denominator (15) using a calculator or long division. When rounded to three decimal places, the decimal equivalent of the fraction is:

0.267

To know more about fraction here.

https://brainly.com/question/10354322

#SPJ4

Using the concepts of mean and standard deviation, and the central limit theorem, it is found that:

a. The mean is of: 3.3

b. The standard deviation is of: 1.23.

c. They would have a mean of 3.3 and a standard deviation of 0.55.

For this problem, the mean is given by:

M = (2 + 3 + 2 + 3 + 3 + 4 + 2 + 4 + 3 + 2 + 2 + 7 + 3 + 4 + 5 + 3 + 3 + 3 + 3 + 5)/20 = 3.3

The standard deviation is:

\(S = \sqrt{\frac{(2 - 3.3)^2 + (3 - 3.3)^2 + \cdots + (3 - 3.3)^2 + (5 - 3.3)^2}{20}} = 1.23\)

It states that for distribution of sample means of size n:

Hence, since 1.23/sqrt(5) = 0.55, the sample means would have a mean of 3.3 and a standard deviation of 0.55.

More can be learned about the standard deviation of a data-set at https://brainly.com/question/24754716

#SPJ1

(a) The equation that estimates the population t years after 2010 is

P(t) = 5655(1.014)^t.

(b) Population of the town in 2022 is 6,681.

We have given that the population of a town was 5655 in 2010.

And the population grow at a rate of 1.4% annually.

(a) We have to find equation that estimates the population t years after 2010.

We know the formula for exponential growth,

P(t) = P₀(1 + r)^t

where P₀ is the initial population,

r is the relative growth rate,

t is the time unit.

Putting the values in above equation we get,

P(t) = 5655(1 + 0.014)^t

P(t) = 5655(1.014)^t

(b) Now we have to find population of the town in 2022.

Here t = 2022 - 2010 = 12

Therefore equation of growth will become,

P(12) = 5655(1.014)^12

P(12) = 6681

Hence the population of the town in 2022 is 6,681.

To know more about population here

https://brainly.com/question/15660998

#SPJ4

The function f(x) = 8sin(x) + cot(x) does not have an inflection point across the interval -1 ≤ x ≥ 1

To find the inflection points of the equation f(x) = 8sin(x) + cot(x) within the assumed interval of -1 ≤ x ≤ 1, we need to calculate the second derivative of the function and then identify the values of x where the second derivative changes sign.

Let's start by finding the first derivative of f(x). Since f(x) = 8sin(x) + cot(x), we have:

f'(x) = 8cos(x) - csc²(x)

Next, let's find the second derivative by taking the derivative of f'(x):

f''(x) = -8sin(x) + 2csc(x)cot(x)

Now, we need to identify the values of x where the second derivative changes sign. These points correspond to the potential inflection points.

Within the given interval -1 ≤ x ≤ 1, we can evaluate the second derivative at the critical points and determine if there is a sign change.

First, let's check x = -1:

f''(-1) = -8sin(-1) + 2csc(-1)cot(-1)

Next, let's check x = 1:

f''(1) = -8sin(1) + 2csc(1)cot(1)

By evaluating the second derivative at these points, we can determine if there is a sign change, which indicates an inflection point.

Note: Since cot(x) and csc(x) are not defined at certain points, we need to be careful in evaluating the second derivative at those points.

However, in this case, we can observe that the function f(x) = 8sin(x) + cot(x) is undefined when x = 0, due to the cot(x) term. Therefore, we can conclude that there are no inflection points within the given interval of -1 ≤ x ≤ 1.

Learn more on inflection points here;

https://brainly.com/question/29249123

#SPJ1

Answer:3048.7804878

Step-by-step explanation:

I took the same test p.s. you may need to round.

Answer:

Not enough information.  See below.

Step-by-step explanation:

Z-M = 2

x= 33.5, then Z = ?

How does x relate to Z or M?  Is the Z-M= 2 equation correct?  Or is it M=33.5?

The simplest form is: