Wesley covered this figure with the unit square shown to find the area. A rectangle and square are shown. The square is labeled 1 square unit. The length of the rectangle is approximately 6 times as long as a side of the square, and the width of the rectangle is approximately 3 times as long as a side of the square. Which figure shows how he covered the square and the correct area?

Answer:

abeni suq ae

Step-by-step explanation:

8 pairs of socks are there.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Sixteen socks are put into pairs.

As, the pair consist two objects.

So, the number of pairs are

= 16/2

= 8 pair

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On solving the provided question, we can say that , in the triangle  x = 2x + x + 40 + 59 = 180 => x = 81/4

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here, in the triangle

m∠D=121°

m∠A=​(2x)°

m∠B=(x+40)°

x = 2x + x + 40 + 59 = 180

4x = 81

x = 81/4

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x = 2

Like-terms are terms within an expression or equation with the same variable and degree (aka exponent). Like-terms can be combined through addition or subtraction.

Properties of Equality

To solve the equation above, we have to use properties of equality, which is often shortened to PoE. There are different types of PoE, but for this question, there is one part we need to understand. The properties of equality state, that you can do anything to the equation if you do it to both sides.

For example, we can add 3 to the left side as long as you also add 3 to the right side.

Solving For X

In any equation, to solve for a variable, you have to isolate it. The first step is combining like terms. 9x and 3x are like terms, so we should combine them on the same side of the equation.

Subtract 9x from both sides.

Then, divide both sides by -6.

For the given equation, x = 2.

The time taken is 5.3 years.

Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.

Compound interest is when you receive interest on both your interest income and your savings.

Given:

P = 50, 000

W= 5000

r= 1.8%= 0.018

n= 2

Using, P = W (1- [tex](1+ r/n)^{-nt}[/tex]) / (r/n)

Putting all the values we get

P = W (1- [tex](1+ r/n)^{-nt}[/tex]) / (r/n)

50000 = 5000 (1- [tex](1+0.018/2)^{-2t}[/tex]) / (0.018/2)

10 = (1- [tex](1+0.009)^{-2t}[/tex]) / (0.009)

0.09 = 1 - [tex](1.009)^{-2t[/tex]

[tex](1.009)^{-2t[/tex] = 0.91

Taking log on both side

-2t log 1.009 = log 0.91

t= log 0.91/ (log 0.091) / (-20

t= 5.3

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I'll go ahead and help you with what I can.  :)

ADEG: Rectangle
What we know: all sides are 90 degree angles, opposite sides are parallel (two pairs of opposite parallel sides)  by definition of a rectangle.  This also means that AG is congruent/parallel to DE, and GE is congruent/parallel to AD.

Segment GE bisects (splits in half) both segments BC and AB (given).  

The transitive property: GE bisects segment BC and AB, which means that the resulting two segments from AB, BG and GA, are congruent to each other.  Not only this, but BE is congruent to EC.  So, if we already know that BG is congruent to GA, and GA is congruent to DE, then, by transitive property of congruence, BG is congruent to DE.

So, one side (hypotenuse, longest side) done.  BE is congruent to EC.

Next -- BG is congruent to DE, as we found.  Two sides done.

Last but not least, you can see that BEG and DEC are vertical angles.  Now you know that these angles are congruent.  

Of course, by construction, you can extend AD from point D to the right and find that its exterior angle, EDC, is congruent to GAD by the corresponding angles theorem.  You could also use construction again and extend AG by G upwards and find that BGE is congruent to GAD by, again, corresponding angles theorem.  

What we know:

Angle BGE is congruent to EDC, both 90 degrees.

BEG and DEC are vertical angles, both congruent.
BG is congruent to DE.  
BE is congruent to EC.
GBE is congruent to DEC by corresponding angles theorem.
So you can use ASA (angle B, side BG, and angle G) and (angle E, side ED and angle D) for the rest.  Then make sure to use CPCTC (congruent parts of congruent triangles are congruent).  :)

Good luck!

The key features of the graph of the function would be

1) Domain - (1, infinity).

2) The range of the function is (2, infinity).

3) The graph of the function is a monotonically increasing function.

4) The graph of the function is asymptotic to the x-axis as it approaches x = 1.

5) The graph is a straight line, that is passing through the point (1,2) and has a slope of 1.

6) The graph is a shifted version of the function log2(x) by 2 units upward.

What is the graph of the function?

The graph of a function is a visual representation of the relationship between the inputs and outputs of the function. It is a diagram that shows the set of all possible points (x,y) that satisfy the equation of the function y = f(x) or in the case of a multivariable function y = f(x,z).

The graph of the function g(x) = log2(x-1) + 2 has several key features. Some of these features include:

1) The domain of the function is (1, infinity) since the logarithm is defined for x>0 and x-1 >0.

2) The range of the function is (2, infinity) since the minimum value of log2(x-1) + 2 is 2.

3) The graph of the function is a monotonically increasing function, meaning that as the input x gets larger, the output g(x) also increases.

4) The graph of the function is asymptotic to the x-axis as it approaches x = 1. This means that as x gets closer to 1, the graph of the function gets closer to the x-axis but never touches it.

5) The graph is a straight line, that is passing through the point (1,2) and has a slope of 1.

6) The graph is a shifted version of the function log2(x) by 2 units upward.

Hence, the key features of the graph of the function would be

1) Domain - (1, infinity).

2) The range of the function is (2, infinity).

3) The graph of the function is a monotonically increasing function.

4) The graph of the function is asymptotic to the x-axis as it approaches x = 1.

5) The graph is a straight line, that is passing through the point (1,2) and has a slope of 1.

6) The graph is a shifted version of the function log2(x) by 2 units upward.

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The instructions telling Robot Rob how to move and turn are as listed from 1 to 8

To make Robot Rob's path a parallelogram with a 10-foot side, a 20-foot side, and a 70-degree angle, you can use the following instructions:

1. Have Robot Rob move forward 10 feet.

2. Have Robot Rob turn left by 70 degrees.

3. Have Robot Rob move forward 20 feet.

4. Have Robot Rob turn left by 110 degrees (the angle that completes the parallelogram).

5. Have Robot Rob move forward 10 feet.

6. Have Robot Rob turn left by 110 degrees.

7. Have Robot Rob move forward 20 feet.

8. Have Robot Rob turn left by 70 degrees.

You can determine these instructions by using basic geometry and trigonometry. A parallelogram has opposite sides that are parallel and equal in length, so the 10-foot and 20-foot sides are opposite sides.

An angle of 70 degrees is used because the opposite angles of a parallelogram are supplementary. The total of the opposite angles of a parallelogram is 180 degree, which means the other angle is 180 - 70 = 110 degree.

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An equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since the line passes through the points (-6, 3) and (-6, 6), we can see that the x-coordinate is the same for both points. This means that the line is a vertical line, and has an undefined slope (division by zero).

The equation of a vertical line is x = constant, where the constant is the x-coordinate of the line. In this case, the constant is -6, so the equation of the line is:

x = -6

Dilation is the process of enlarging or contracting a figure. Dilations are transformations that result in an enlargement or a decrease.

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The side lengths of trigonometry a, b, and c are determined by the traveled distances, and the internal angles of the triangle are A, B, and C.

Trigonometry, a branch of mathematics, studies how triangle side lengths and angles relate to one another. Around the third century BC, the use of geometry in astronomical study led to the first appearance of the area. The study of specific trigonometric functions and how they could be applied to calculations is a topic covered in the branch of mathematics known as precise techniques. Trigonometry includes six well-known trigonometric operations. The names and acronyms for each are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle properties, specifically of right triangle properties. But geometry is the study of geometric figures and their features.

Here,

Given :

The sine rule or cosine rule, c2=a2+b2-2ab. cos(C), may be used to solve the issue if bearings between three sites result in the formation of a non-right-angled triangle between them.

The side lengths a, b, and c are determined by the traveled distances, and the internal angles of the triangle are A, B, and C.

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The complete question is " For what reason the cosine rule is used  in trigonometry  ?"

Answer:

y = 4/5x + 1

Step-by-step explanation:

Let P(x) represent the profit function. Let R(x) represent the revenue function. Let C(x) represent the cost function. Then P(x) = R(x) - C(x).

By deducting the cost function from the revenue function, the profit function can be calculated. Let the profit be denoted by P(x), the revenue by R(x), the cost by C(x), and x be the quantity of goods sold.

The profit function is therefore expressed as P(x) = R(x0 - C) (x). The function that depicts the profit produced by deducting the cost of revenue is known as a profit function.

The break even point of the profit function is at its x-intercept. It illustrates the point at which the sum of the costs incurred in creating a good and the sum of the proceeds from its sale are equal. A domain for the set exists in a profit function.

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A polynomial, which is a mathematical expression. Numerous monomials, which are mathematical expressions, are gathered together in it.

When a variable in an equation like the quadratic equation, cubic equation, etc. has only non-negative integer powers or only positive integer exponents, the function is said to be polynomial.

When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).

An expression in mathematics known as a polynomial. It is a collection of several monomials, which are mathematical expressions. That is, a quantity, a variable, or the result of a quantity and multiple variables.

Polynomial equations are equations that contain variables, exponents, and coefficients.

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The given equation is slope - intercept form, is y = -3x + 41.

What is slope - intercept form?

When the slope of the line being studied is known, and the given point is also the y intercept, the slope intercept formula, y = mx + b, is used (0, b). The y value of the y intercept point is represented by b in the equation.

Writing an equation for a line in the form y = mx + b is known as slope intercept form in mathematics. The m indicates the line's slope, and the b indicates the y-intercept.

Consider, the given equation  3x + y - 27 = 14

We have to write this equation is slope - intercept form of the line.

Let

3x + y - 27 = 14

Add 27 on both sides,

3x + y - 27 + 27 = 14 + 27

3x + y = 41

Subtract 3x from both sides,

3x + y - 3x = 41 - 3x

              y = 41 - 3x

              y = -3x + 41

Hence, the given equation is slope - intercept form, is y = -3x + 41.

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The value of y, found using the vertical angles theorem is 101°

Vertical angles are the angles formed on opposite sides of the point where two lines intersect.

The angles in the question are vertical angles.

The expression representing the angles are;

(y - 212)°

(-y - 10)°

The vertical angles theorem indicates that the vertical angles formed by two lines are congruent, therefore, according to the vertical angles theorem, we get;

The angle with measure (y - 212)° is congruent to the angle with measure (-y - 10)°

The measure of two angles that are congruent are equal, therefore, by the definition of congruency, we get;

(y - 212)° = (-y - 10)° (definition of congruency)

y - 212 = -y - 10

y + y = 212 - 10 = 202

2·y = 202

y = 202 ÷ 2 = 101

The measure of angle y is 101°

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The value of y in the vertically opposite angle is 101.

When lines intersect each other, angles relationships are formed such as vertically opposite angles, linear angles etc.

Vertically opposite angles are angles that share the same vertex. In other words, vertical angles are angles that are opposite of each other when two lines cross.

Vertically opposite angles are congruent to each other.

Therefore,

y - 212 = - y - 10

y + y = -10 + 212

2y = 202

divide both sides by 2

2y / 2 = 202 / 2

y = 101

Therefore,

y = 101

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The factorisation of  x² - x -12 is (x-4)(x+3) and the factors are 4, -3.

A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, often smaller or simpler things of the same sort. For instance, factorizing the number 15 as 3*5

A number is swiftly factorized into smaller numbers or factors of the number using the factorization formula. A factor is a number that evenly divides the inputted number.

The subsequent stages aid in the polynomial factoring process. The steps to factorizing a polynomial are listed below.

The expression is x² - x -12

⇒ x² - x -12 = 0

⇒x² - 4x + 3x - 12 = 0

⇒x(x-4) + 3(x-4) = 0

⇒(x-4)(x+3) = 0

or, x-4 = 0 ⇒ x = 4     and,

x+3 = 0 ⇒ x= -3

The factorisation of  x² - x -12 is (x-4)(x+3) and the factors are 4, -3

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Answer:

IK = 24

Step-by-step explanation:

Since is says that O is the point of intersection of the three medians (also known as centroid) the segment JN which passes through a vertex of the triangle, would have to be a median to segment IK.

Medians divide a segment into two congruent parts, so IN = NK = 12 as we are given IN = 12.

IK is the sum of the measure of IN and NK, so in other words:

IK = IN + NK = 12 + 12 = 24

Total there are 3600 people working in that company.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, in a​ company, ​65% of the workers are women.

1,260 people work for the company who​ aren't ​women

So, here 35% of people work for the company who​ aren't ​women.

Let x be the total number of people.

Now, 35% of x=1260

35/100 ×x=1260

0.35x=1260

x=1260/0.35

x=3600

Therefore, total there are 3600 people working in that company.

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Answer: 1 is that 10 is an exponent

Step-by-step explanation: 1 times anything is 1

Answer:

V = 38π/3 cubic units

Step-by-step explanation:

The formula for the shell method is given by:

V = 2π ∫(y)(x)dx

where x and y are the equations of the upper and lower bounds of the region being rotated. In this case, we have:

y = x

x = 2

So, the volume is given by:

V = 2π ∫(x)(x)dx from x=2 to x=3

V = 2π (x^3/3) from x=2 to x=3

V = 2π ((3^3/3) - (2^3/3))

V = 2π (27/3 - 8/3)

V = 2π (19/3)

V = 38π/3 cubic units

The length of the arc is equivalent to 5.024 miles.

The formula to calculate the arc length is -

L{arc} = (θ/360°) x 2πr

Given is that an arc that subtends a central angle of 12° in a circle of radius 24 miles.

We can write the length as -

L{arc} = (θ/360°) x 2πr

L{arc} = (12/360°) x 2 x 3.14 x 24

L{arc} = 1/30 x 2 x 3.14 x 24

L{arc} = 5.024 miles.

Therefore, the length of the arc is equivalent to 5.024 miles.

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The appropriate unit for measurement for momentum p is kgm/s ( option C)

momentum is defined as the product of mass of a body and it's velocity. momentum is a vector quantity. It is represented by p

From the definition of momentum, momentum can be expressed as :

p = m× v

where m is the mass of the body and v is the velocity of the body.

For example if a body of mass 5kg is moving with a velocity of 10 m/s, it momentum will be 5×10 = 50kgm/s

The change in momentum of a body is referred to as the impulse of the body.

from the formula;

v has a unit of meter per second (m/s)

m has a unit if kilogram (kg)

therefore the unit of measurement of p will be:

p = kg × m/s

p = kgm/s

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Answer:

Step-by-step explanation:

[tex]x = \frac{11 - 13(15)}{13} [/tex]

[tex]x = \frac{11 - 195}{13} [/tex]

[tex]x = \frac{ - 184}{13} [/tex]

When written as an exponential expression, the radical expression is represented by: 15 1/2

When all of a radical expression's perfect squares, cubes, etc. are eliminated from the radical, the radical is in its simplest form.Radical: The sign used to represent the square root or nth root.Square-root-containing expressions are known as radical expressions.

Radicand: A number or statement contained within the radical symbol.

When written as an exponential expression, the radical expression is represented by: 15 1/2

The square root of a number is equal to the number increased to a power of 1/2 in accordance with the rule of indices.

On that point, the exponential expression given for the radical expression 15 can be represented as follows:

15^1/2.

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Answer: 3145728

Step-by-step explanation: 6 times 2, 20 times is 3145728 the equation is 6 times 2x or 6(2x)

x representing the square the king is on

The following expression can be expressed as 3/4x + y/2 (4x) + y/2 using the distributive property (7).

Floating point, also called to as "b raised to that same nth power," is a mathematical operation that requires two numbers: a ground number, b, and an exponent, or force, n. It is represented by the sign bn. A number's exponent reveals how many times that number has been multiplied by itself. For instance, the number 2-3 (read as 23) means 2 × 2 x 2 = 8. 2 + 3 = 6 does not equal 23. Remember that an integer multiplied by one equals itself. Exponents are a method for expressing large numbers as powers. The amount that illustrates how many times a number has been doubled by itself is called an exponent. As an example, multiplying 6 by 4 results in 6 x 6 x 6.

given

A power of a power is sped up by multiplying the exponents while maintaining the base constant.

As an illustration, (23)5 = 215 (xa)b= xa b for any positive number x and integers a and b.

Rephrase this as:

3/4x + y/2 (4x + 7).

The following expression can be expressed as 3/4x + y/2 (4x) + y/2 using the distributive property (7).

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The complete question is :-

Simplify the expression property of exponents of  3/4x + y/2 (4x + 7).