(A+B)xC = (AxC)+(BxC) prove this please​

Answer:

Answer: 2

Step-by-step explanation:

\( \frac{2}{3} (4 \frac{1}{6} - \frac{7}{6} ) \\ \)

express the mixed fraction into proper fraction:

\( { \boxed{4 \frac{1}{6} = \frac{(6 \times 4) + 1}{6} = \frac{25}{6} }}\)

then solve simplify:

\( = \frac{2}{3} ( \frac{25}{6} - \frac{7}{6} ) \\ \)

solve the bracket:

\( = \frac{2}{3} ( \frac{25 - 7}{6} ) \\ \\ = \frac{2}{3} ( 3)\)

then simplify:

\( = \frac{2 \times 3}{3} \\ \\ = 2\)

The calculated values of x and y in the figure are x = 2 and y = 4

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

The figure

Where, we have

equal side lengths

This means that

2y - 1 = 3y - 5

Evaluate

y = 4

Next, we have

x + 3 = 3/2x + 2

So, we have

1/2x = 1

This gives

x = 2

Hence, the values of x and y in the figure are x = 2 and y = 4

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The expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

Pascal's Triangle is a triangular array of numbers in which the value in each cell is the sum of the two numbers directly above it.

To expand the given expression (x²-3y)⁴ as per Pascal's triangle:

First, write down the fourth row of Pascal's Triangle as:

1 4 6 4 1

The above numbers represent the coefficients of the terms in the expansion of (a+b)⁴, where a is x² and b is -3y. Therefore, it can be written as,

1×(x²)⁴ + 4×(x²)³×(-3y) + 6×(x²)²×(-3y)² + 4×(x²)(-3y)³ + 1(-3y)⁴

Simplify each term,

x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸

Therefore, the expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

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Answer:

3572 m^3

Step-by-step explanation:

volume of prism = Ah

where A = area of the base, and

h = height of the prism

The base is a regular hexagon. We are given the side length, 8.1 m, and the apothem, 7 m.

A = nsa/2,

where n = number of sides,

s = length of one side

a = apothem

volume = Ah

volume = nsa/2 * h

volume = 6(8.1 m)(7 m)/2 * 21 m

volume = 3572.1 m^3

Answer: 3572 m^3

The implications of Constructivist approach in teaching mathematics is that it helps the students to develop a better way to comprehend the content of what they are being taught.

A constructive approach of teaching mathematics believes that students construct knowledge rather than just passively take in information.

A constructive approach of teaching also believes that students integrate new knowledge with existing knowledge to create a deeper understanding of the mathematics being taught to them.

Therefore, constructive approach of teaching can help the students to comprehend the content of what they are being taught.

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Answer:

c

Step-by-step explanation:

Where is it located?

Answer:

D

Step-by-step explanation:

\(\tt{Hey~there!\)

\(\tt{3\div320\)

\(\tt{Divide~the~two~numbers:\)

\(\tt{3\div320=0.009375\)

\(\boxed{\tt{0.009375}}\)

\(\tt{Hope~this~helps!\)

\(\boxed{\tt{-TestedHyperr}}\)

Answer:

3

Step-by-step explanation:

If I’m wrong sorry

But can I get brainlist

Hey  There!

Answer:

Step-by-step explanation:

HCF

If HCF is  ''9'' that means that ''9'' is the divisible of two numbers.

So 18 and 19 can be divided by 9 and that's the highest divisible for both factors.

And always remeber the answer is a ''Prime factor.''

LCM

If LCM is ''3'' that means ''3'' is the lowest common multiple out of  two numbers.

Hope this helps!

Have a nice Day!:)

Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.

We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.

Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.

Therefore,  y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.

Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.

Simplifying, we have :3x = $90000 + 75 = $90075.

Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.

Therefore, Jane received $30025 and Lydia received $60000.

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Answer:

$460

Step-by-step explanation:

Because if you put 23% over 100 and multiply it by 20,000 you should get that

Objects commonly found in a locality include residential buildings, commercial establishments, public facilities, transportation infrastructure, landmarks, natural features, utilities, street furniture, and vehicles.

The type of objects that can be found in a locality can vary greatly depending on the specific location and its surroundings. Here are some common types of objects that can be found in a locality:

Residential Buildings: Houses, apartments, condominiums, and other types of residential structures are commonly found in localities where people live.

Commercial Establishments: Localities often have various types of commercial establishments such as stores, shops, restaurants, cafes, banks, offices, and shopping centers.

Public Facilities: Localities typically have public facilities such as schools, libraries, hospitals, community centers, parks, playgrounds, and sports facilities.

Transportation Infrastructure: Localities usually have roads, sidewalks, bridges, and public transportation systems like bus stops or train stations.

Landmarks and Monuments: Some localities may have landmarks, historical sites, monuments, or cultural attractions that represent the area's heritage or significance.

Natural Features: Depending on the locality's geographical characteristics, natural features like parks, lakes, rivers, mountains, forests, or beaches can be present.

Utilities: Localities have infrastructure for utilities such as water supply systems, electrical grids, sewage systems, and telecommunications networks.

Street Furniture: Localities often have street furniture like benches, streetlights, waste bins, traffic signs, and public art installations.

Vehicles: Various types of vehicles can be found in a locality, including cars, bicycles, motorcycles, buses, trucks, and possibly other modes of transportation.

It's important to note that the objects present in a locality can significantly differ based on factors such as urban or rural setting, cultural context, economic development, and geographical location.

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Given that x is equal to 1 and S is the centroid of the triangle NLQ, NS will have a length of 4 units.

The centroid of a flat figure or solid figure, also known as the geometric center or center of figure, in mathematics and physics, is the arithmetic mean position of all the points on the figure's surface. Any n-dimensional Euclidean object is included by the same definition. The centroid of a triangle is the location where the triangle's three medians connect. It may alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.

Here,

We may infer from the centroid's features that it divides each median in a ratio of 2:1.

NS=2SR

7x-3=2(5x-3)

7x-3=10x-6

3x=3

x=1

NS=7x-3

=7*1-3

=4 units

The length of NS will be 4 units as the value of x is 1 and S is the centroid of triangle NLQ.

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Check the picture below.

Answer:

I want brainliest!!! u promisteed

Step-by-step explanation:

1) 180-114 = 66

angle three = 66

360 = 70 + 70 + angle two + angle two

220 = angle two + angle two

angle two = 110

The initial temperature of the soda is 22 degrees Celsius, and its temperature after 20 minutes is approximately 10 degrees Celsius.

To find the initial temperature of the soda, we need to evaluate the temperature function T(x) at x = 0.

T(x) = -5 + 27e^(-0.03x)

T(0) = -5 + 27e^(-0.03(0))

T(0) = -5 + 27e^0

Since any number raised to the power of 0 is 1, we have:

T(0) = -5 + 27(1)

T(0) = -5 + 27

T(0) = 22

Therefore, the initial temperature of the soda is 22 degrees Celsius.

To find the temperature of the soda after 20 minutes, we evaluate the temperature function at x = 20.

T(x) = -5 + 27e^(-0.03x)

T(20) = -5 + 27e^(-0.03(20))

T(20) = -5 + 27e^(-0.6)

Using a calculator, we can compute e^(-0.6) ≈ 0.5488.

T(20) = -5 + 27(0.5488)

T(20) = -5 + 14.8152

T(20) ≈ 9.8152

Therefore, the temperature of the soda after 20 minutes is approximately 10 degrees Celsius (rounded to the nearest degree).

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Answer:

Step-by-step explanation:

\(\frac{2}{5} : \frac{1}{15}\\\)

LCM of the denominator = LCM ( 5 , 15 ) = 15

∴ Now we have to multiply LCM by both the fractions , we get ,

\(\frac{2}{5}.15 : \frac{1}{15}.15\\ 6 : 1\)

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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The coordinates of polygon A'B'C'D' after the rotation of 180º are given as follows:

A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).

The five more known rotation rules are given as follows:

The original coordinates for this problem are given as follows:

A(0,0), B(5,2), C(5,-5), D(0,-3).

Exchanging the sign of each of the coordinates, the coordinates after the rotation are given as follows:

A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).

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Parameterize the square (call it S) by

\(\mathbf s(u,v)=2u\,\mathbf x+2v\,\mathbf z\)

with both \(u\in[0,1]\) and \(v\in[0,1]\).

Take the normal vector pointing in the positive y direction to be

\(\dfrac{\partial\mathbf s}{\partial v}\times\dfrac{\partial\mathbf s}{\partial u}=4\,\mathbf y\)

Then the current is

\(\displaystyle\iint_S(y^2+5)\,\mathbf y\cdot4\,\mathbf y\,\mathrm dA=20\int_0^1\int_0^1\mathrm dA=\boxed{20\,\mathrm A}\)

where \(y^2+5\) reduces to just 5 because \(y=0\) for all points in S.

There are 12 lowercase words of length 8 in which each distinct letter appears exactly twice.

To form a lowercase word of length 8 in which each distinct letter appears exactly twice, we can choose 4 distinct letters from the English alphabet and then arrange them in pairs in the word. The number of ways to choose 4 distinct letters from 26 is:

C(26, 4) = 26! / (4! * 22!) = 14,950

Once we have chosen 4 distinct letters, we can arrange them in pairs in the word in the following way:

Therefore, the total number of such words is:

4 * 3 * 1 = 12

Thus, there are 12 lowercase words of length 8 in which each distinct letter appears exactly twice. Here are all the possible words:

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Hello!

We will go tu use the pythagorean theorem!

So:

BA² = BC² + AC²

AC² = BA² - BC²

AC² = 52² - 20²

AC² = 2304

AC = √2304

AC = 48

The count of the denominations of the bills of $1, $5, and $10, are 15, 10, and 5, respectively.

In the question, we are given that there are 3 denominations of bills in a wallet: $1, $5, and $10. There are 5 fewer $5-bills than $1-bills. There are half as many $10-bills as $5-bills.

We are asked to find the count of each denomination, given there was altogether $115 in the bag.

We assume the number of $1-bills in the bag to be x.

Total amount in x bills of $1 =  x * $1 = $x.

Given that there are 5 fewer $5-bills than $1-bills in the bag, number of $5-bills in the bag = x - 5.

Total amount in (x - 5) bills of $5 = (x - 5) * $5 = $5(x - 5).

Given that there are half as many $10-bills as $5-bills in the bag, number of $10-bills in the bag = (x - 5)/2.

Total amount in (x - 5)/2 bills of $10 = (x - 5)/2 * $10 = $5(x - 5).

Thus, the total amount in the bag = $x + $5(x - 5) + $5(x - 5).

But, the total amount in the bag = $115.

Thus, we get an equation:

$x + $5(x - 5) + $5(x - 5) = $115,

or, x + 5x - 25 + 5x - 25 = 115,

or, 11x = 115 + 50,

or, 11x = 165,

or, x = 165/11,

or, x = 15.

Thus, number of $1-bills = x = 15.

The number of $5-bills = x - 5 = 15 - 5 = 10.

The number of $10-bills = (x - 5)/2 = (15 - 5)/2 = 10/2 = 5.

Thus, the count of the denominations of the bills of $1, $5, and $10, are 15, 10, and 5, respectively.

The provided question is incomplete. The complete question is:

There are 3 denominations of bills in a wallet: $1, $5, and $10. There are 5 fewer $5-bills than $1-bills. There are half as many $10-bills as $5-bills. If there is $115 altogether, find the number of each type of bill in the wallet."

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Answer:

6

Step-by-step explanation:

Step 1: equal any two of the three equations together

2x + 3 = 3x - 9

Step 2: isolate the variable

3 = x - 9

6 = x