A teacher has 600 counters. He keeps 96 counters at his desk and gives the rest to 3 groups of students. The first group of students gets twice as many counters as the second group of students. The third group of students gets four times as many counters as the second group. How many counters did the second group get?

S1: ∠YLF ≅ ∠FRY (Given)

S2: ∠RFY ≅ ∠LFY (Given)

S3: FY ≅ FY (Transitive property)

S4: ΔFRY ≅ ΔFLY (AAS theorem)

The AAS congruence theorem states that if two triangles have two pairs of corresponding congruent angles, and a pair of corresponding non-included side that are congruent, then both triangles area congruent.

To prove that ΔFRY ≅ ΔFLY, the proof that shows they are congruent by the AAS congruence theorem is:

S1: ∠YLF ≅ ∠FRY (Given)

S2: ∠RFY ≅ ∠LFY (Given)

S3: FY ≅ FY (Transitive property)

S4: ΔFRY ≅ ΔFLY (AAS theorem)

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According to given conditions, the solution for c is (P - 5)/2.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that can be evaluated to produce a numerical value. Expressions can also contain functions, parentheses, brackets, and other symbols that indicate the order of operations.

Starting equation: P = 2c + 5

Add 5 to both sides of the equation:

P + 5 = 2c + 5 + 5

Simplify:

P + 5 = 2c + 10

Subtract 5 from both sides of the equation:

P + 5 - 5 = 2c + 10 - 5

Simplify:

P = 2c + 5

Substitute c with (P - 5)/2:

P = 2((P - 5)/2) + 5

Simplify:

P = P - 5 + 5

Simplify further:

P = P

Therefore, according to given conditions, the solution for c is (P - 5)/2.

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The figure's circumference, as seen in the diagram, is 60.84 m.

What are some instances of perimeters?

The perimeter of an object is the space surrounding it. For instance, your house has a fenced-in yard. The perimeter is the length of the fence. If the yard is 50 feet by 50 feet, your fence is 200 feet long.

The formula below is used to determine the figure's perimeter.

Formula:

Equation 1: P = 2L + W + W / Equation 1:

P = The figure's perimeter

L is the figure's length.

W is the figure's width.

Considering the query,

Given:

L = 15 m\sW = 12 m\sπ = 3.14

Replace the values in equation 1 with these ones.

P = (15×2)+12+(12×3.14/2)

P = 30+12+18.84

P = 60.84 m

As a result, the figure's perimeter is 60.84 meters.

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Answer:

The distance between the two is 5.099 or rounded to 5.1 units.

Step-by-step explanation:

Answer:

2

1

Step-by-step explanation:

I will assume you want to find the slope [ y2-y1/x2-x1 ]

11-7/3-1

4/2

2

Hald the distance.

2/1 = 1

Best of Luck!

We want to imagine where the shading should be, and with that determine which point is a solution for both inequalities. We will see that the solution is the point (7, -8)

In this case, the inqualities are:

You can see that in both cases, y is smaller than the line, thus, for both inequalities, we must shade the part that is below the lines.

With that in mind, the region of solution will be the region that is below both lines at the same time, and that region will be the "triangle" that you can see at the middle below the horizontal axis.

Now that we know the region of solutions, we only need to see which point belongs there, from the given options the only that belongs to that region is the point (7, -8), which means that this point is a solution for both inequalities.

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Answer:

inspector" (and any subsequent words) was ignored because we limit queries to 32 words.

Step-by-step explanation:

hope this is correct!

When two tables have a one-to-many relationship, you typically need to add a foreign key to the table on the "many" side to link the records to the corresponding record in the "one" table.

In a one-to-many relationship, the table on the "one" side is usually the primary key table, and the table on the "many" side is usually the foreign key table. The foreign key is used to link the records in the "many" table to the corresponding record in the "one" table. This is done by adding a column to the "many" table that contains the primary key value from the "one" table.

When designing a database, it is important to establish relationships between tables to ensure data integrity and avoid redundant data. In a one-to-many relationship, one record in the primary key table can be associated with many records in the foreign key table. To establish a one-to-many relationship, you need to create a primary key in the "one" table and a foreign key in the "many" table. The foreign key is a column that contains the primary key value from the "one" table. For example, if you have a "customers" table and an "orders" table, the "customers" table would be the primary key table and the "orders" table would be the foreign key table. Each record in the "orders" table would have a foreign key column that contains the customer ID from the "customers" table.

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Let,

Perform the operation (1)+(2),

Substitute the value of x=-2/5 in the expression (1).

Thus, the value of x is -2/5 and value of y is -96/25.

Answer: 232

Step-by-step explanation:

Surface area = everything multiplied x 2

Answer:

166

Step-by-step explanation:

30+30+12+12+41+41

=166

When two tangents intersects with another tangent, the both are equal in length I think.

If we take a simple random sample of size n=500 from a population of size 5,000,000, the variability of our estimate will be  (c) about the same as the variability for a sample  size n=500 from a population of size 50,000,000.

The variability of an estimate primarily depends on the sample size (n) rather than the population size. Since both scenarios have a sample size of 500, the variability will be approximately the same.

The correct answer is (d) slightly greater than the variability for a sample size n = 500 from a population of size 50,000,000. This is because the larger the population size, the smaller the sampling variability. In other words, if we take a sample of the same size from a larger population, there will be more variability due to the increased number of potential outcomes. However, the difference in variability between a population size of 5,000,000 and 50,000,000 is not significant enough to make a substantial impact on the estimate.

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Answer:

B. (1, 4)

Step-by-step explanation:

2x + 3y = 14

5x - 4y = -11

Multiply the first equation by -5 and the second by 2:

-10x - 15y = -70

10x - 8y = -22       Add these 2 equations:

0   - 23y = -92

y = -92/-23 = 4

Now substitute y = 4 in the first equation:

2x + 3*4 = 14

2x = 14 - 12

2x = 2

x = 1.

The average number of viewers over the two weeks written in scientific notation is 3.85 × 10^8. option C

Average number of viewers over the two weeks = (First week + Second week) / 2

= {(3.6 x 10⁴) + (4.1 x 10⁴)} / 2

= {3.6 + 4.1 × 10^(4×4) } / 2

= (7.7 × 10^16) / 2

= 3.85 × 10^8

Therefore, the average number of viewers over the two weeks written in scientific notation is 3.85 × 10^8.

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Answer:

4x+5y=87

Step-by-step explanation:

thanks for the points

Answer:

(9,-2)

Step-by-step explanation:

Answer:

7 degrees colder

Step-by-step explanation:

15 degrees - 8 degrees = 7 degrees

Answer:

64 is the answer glad to help

Answer:

Step-by-step explanation:

4/(8/9)-(1/2)=4

Answer:

19

Step-by-step explanation:

If a=17, then:

2 + 17 = 19

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Have a great summer :)

Answer:

4y - x = 20

Step-by-step explanation:

y-y1 = m (x-x1)

y - 6 = 1/4 (x - 4)

4y - 24 = x - 4

4y - x = 20

The three angles above the bottom line are supplementary, so they add up to 180° in measure:

2x° + 90° + x° = 180°

3x° + 90° = 180°

3x° = 90°

x = 30

The angles with measure x° and 2y° are congruent, since they form a pair of interior angles that alternate with respect to the transversal (in this case, this is the ray that starts from the bottom line and point up and to the right, and passes through the parallel upper line). So

2y° = x°

2y° = 30°

y = 15

Below the upper line, the two angles 2y° and z° are supplementary, so

2y° + z° = 180°

30° + z° = 180°

z = 150

The value of y will be more as the number is repetitive, and both x and y initial three digits after the decimal are the same.

A rational number is one that has the form p/q, where p and q are integers and q is greater than zero. Some rational number examples are 1/3, 2/4, 1/5, 9/3, and so on.

The complete question is, Let x = 0.147 and let y = \(0.\overline{147}\).  Is x a rational number? Is ya rational number? Which is larger, x or y?

Given the value of x is 0.147. As it can be written in the form of a fraction,

\(0.147 = \dfrac{147}{1000}\), we can conclude that x is a rational number.

The value of y = \(0.\overline{147}\) can also be written in the form of a fraction,

\(0.\overline{147} = \dfrac{147}{999}\), therefore, we can conclude that y is also a rational number.

The value of y will be more as the number is repetitive, and both x and y initial three digits after the decimal are the same.

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Answer:

standard deviation

Step-by-step explanation:

The standard deviation is defined as the measure of how spread out the numbers are in a given population. In other words, statistics refers to the amount of the dispersion or variation of a set of given values.

It is denoted by the Greek letter sigma, σ.

Thus the standard deviation is the measure of how dispersed the data are in the population which can be used to provide context to a larger data sets.

You should invest $22,627.84 if you want to receive payments of $3,000 at the end of each year for 10 years, with the first payment 3 years from now, if the money is compounded at 5% annually.

To solve this problem, we can use the present value formula for an ordinary annuity: PV = PMT * [1 - (1 + r)^-n] / r

Where:

PV = present value

PMT = periodic payment

r = interest rate

n = number of payments

In this case, we have:

PV = unknown

PMT = $3,000

r = 5%

n = 10 years (first payment in 3 years, so there are 10 payments after that)

Plugging these values into the formula,

we get:

PV = $3,000 * [1 - (1 + 0.05)^-10] / 0.05

PV = $22,627.84

Therefore, you should invest $22,627.84 if you want to receive payments of $3,000 at the end of each year for 10 years, with the first payment 3 years from now, if the money is compounded at 5% annually.

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The answer is :

The volume of the replacement cone holds 4·π cubic inches more than the volume of the original cone.

The given measurements of the cones are;

The volume of cone, V = (\(\frac{1}{3}\))·π·r²·h

The volume of an original cone, V₁ = (\(\frac{1}{3}\))·π·r₁²·h₁

∴ V₁ = (\(\frac{1}{3}\)) × π × (3)² × 4 ≈ 37.7 in.³

The replacement cone's volume is, V₂ = (\(\frac{1}{3}\))·π·r₂²·h₂

∴ V₂ = (\(\frac{1}{3}\)) × π × (4)² × 3  ≈ 50.27 in.³

The volume ratio of the cone  = V₁/V₂

∴ Volume ratio = (\(\frac{1}{3}\)) × π × (3)² × 4 in. /((\(\frac{1}{3}\)) × π × (4 )² × 3) = 3/4

The difference in volume of two cone, ΔV = V₂ - V₁ = (\(\frac{1}{3}\)) × π × ((4)² × 3- (3 )² × 4  = 4·π in.³

Therefore, the volume of the replacement cone is 4·π cubic inches more than the volume of the original cone.

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It would be

\( \sqrt{ \frac{x - 2}{ 2} } \)

I hope this is what you're looking for!

Answer:

Let's start by rearranging this polynomial.

x^3 - 2x^2 + x - 2

x^3 + x - 2x^2 - 2

Now, factor out the common terms in the first two terms, and the second t wo terms. So we have: x(x^2 + 1) - 2(x^2 +1)

Apply the distributive property, and you have: (x-2)(x^2+1), which can't be factored further.

There's definitely something wrong with the answer choices here, or the problem itself.

Hopefully this helps!

The complete factorization of the polynomial is,

⇒ (x + i) (x - i) (x - 2)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The polynomial is,

⇒ x³ - 2x² + x - 2

Now, We can factor the polynomials as;

The polynomial is,

⇒ x³ - 2x² + x - 2

⇒ x² (x - 2) + 1 (x - 2)

⇒ (x² + 1) (x - 2)

⇒ (x + i) (x - i) (x - 2)

Therefore, The complete factorization of the polynomial is,

⇒ (x + i) (x - i) (x - 2)

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A linear equation in slope intercept form is: \(y = mx+ c\).

The slope intercept form of \(3x + 3y = 24\) is \(y = -x + 8\)

Given

\(3x + 3y = 24\)

Subtract 3x from both sides

\(3x - 3x + 3y = -3x + 24\)

\(3y = -3x + 24\)

Divide both sides by 3

\(\frac{3y}3 = \frac{-3x}3 + \frac{24}3\)

\(y = -x + 8\)

By comparing \(y = -x + 8\) and \(y =mx + c\);

We can conclude that: \(y = -x + 8\) is the slope intercept form of \(3x + 3y = 24\)

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