Express the length a, b, c, and d in the figure in terms of the trigonometric ratios of θ.
a = b = c = d =

In two-dimensional space, only two coordinates are required to specify the location and orientation of a rigid body.

In two-dimensional space, a rigid body can only move in two directions (up/down and left/right) and rotate around a single axis. As a result, only two coordinates are needed to specify the location and orientation of a rigid body in two-dimensional space. The two coordinates needed to specify the rigid body's position are the x-coordinate and y-coordinate, which define the position of the body in the plane. The orientation of the rigid body can be determined by determining the angle between the x-axis and the body's orientation, which is referred to as the angle of rotation. The combination of these two coordinates (position and rotation) specify the full state of the rigid body in two-dimensional space.

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For triangle ACE, if BD ∥AE , then BA/CB = DE/CD is proved.

For given triangle ACE,

BD || AE                             ...............(Given)

∠4 ≅ ∠1 and ∠3 ≅ ∠2      ..............(Corresponding Angles Postulates)

ΔACE ~ ΔBCD                  .............(Angle-Angle Similarity Postulate)

CA/CB = CE/CD                ............(Definition of similar triangles)

CA = CB + BA, CE = CD + DE           ..........(Segment Addition Postulate)

(CB + BA)/CB = (CD + DE)/CD   ..........(Substitution Property of Equality)

CB/CB + BA/CB = CD/CD + DE/CD  .........(Addition of Fractions)

1 + BA/CB = 1 + DE/CD                  .............(Siplification of fractions)

BA/CB = DE/CD                   ...............(Subtraction Property of equality)

Hence proved.

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Answer:

-8g+16-12t is the answer

Step-by-step explanation:

multiply everything by 4

In the parallelogram PQRS, x = 2 and  y=7

Parallelogram:

A parallelogram is a quadrilateral with two pairs of parallel sides. A parallelogram has opposite sides of equal length and opposite angles of equal length. Also, the interior angles on the same side of the horizontal line are supplementary angles. The sum of all interior angles is 360 degrees. A three-dimensional shape whose faces are parallelograms is called a parallelepiped. The area of ​​a parallelogram depends on its base (one of its parallel sides) and its height (height drawn from top to bottom). The perimeter of a parallelogram depends on the length of its four sides.

Given that

PT=​y, TR=3x+​1, QT=3​y, TS=5x+11

The diagonals of a parallelogram bisect each other

PT = TR    and  QT = TS

y = 3x+1     and 3y = 5x+11

Now,

We have a system of equations

Multiply the first equation by 3

3y = 9x+3  and 3y = 5x+11

Set them equal

   9x + 3 = 5x + 11

⇒ 9x - 5x = 11 -3

⇒ 4x = 8

⇒ x =2

Now,

Putting the value of x =2 in equation :

y = 3x+1

  =3(2)+1

  =7

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9 hours will it take to clean the 15 pools.

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:

Dave can clean pools at a constant rate of 3/5 pools per hour.

This also means that he cleans 3 pools in 5 hours

So, the time taken to clean 15 pools is

= 15×3/5

= 9 hours.

Hence, the time taken is 9 hours.

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On solving the provided question we cans ay that - the value of the following exponent is

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where

here,

= [tex]10^2 X 10^-3[/tex] X 32

= 100 X 1/1000 X 32

=1/10 X 32

=3.2

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Natha can chew between 9 to 10 chewing gum each day so that it could last for 6 days.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Nathan had 58 pieces of gum that he wants to make last six days.

Therefore, The number of chewing gums he can chew is the total number of chewing gums he has divided by the total number of days which is,

= (58/6).

= 9.66 chewing gums but it should be a whole number.

So, Nathan can chew between 9 to 10 chewing gums each day.

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As all the exponents of x are whole numbers, the expression 4x² – 3x + 7 is a polynomial in one variable.

The exponent of a number shows how many times the original value of the number has been multiplied. For example, the number 34 indicates that we have multiplied three by four. 3 × 3 × 3 × 3 × 3 is its expanded form. Exponent is another term for a number's power. It might be a decimal, a fraction, a negative number, or a whole number.

Exponents are important because without them, writing the product when a number was repeated many times on its own would be very difficult. For example, it is much easier to write 57 than it is to write 5 × 5 × 5 × 5 × 5.

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Answer: B

Step-by-step explanation:

Correlation tells us the relationship of 2 variables. Looking at the graph, the data appears to going down, as we read graphs from left to right. We can automatically eliminate C and D, since we have determined going down. We know it's also not A because if the correlation is constant, then all the dots would be lined up, and not scattered around. Since the dots are going down, this tells us that it is a negative correlation. Hence, B is the answer.

Answer:

B. negative correlation

Step-by-step explanation:

The sprinkler should be set to rotate through  the angle 6.42 degrees.

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

r =  50 yards

Area, A = 140 square yards

Θ = angle

A= (Θ /360) πr²

140 = (Θ /360) * 3.14 * 50*50

Θ = (140*360)/(3.14*25*100) = 6.42 degrees

The sprinkler should be set to rotate through  the angle 6.42 degrees.

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Answer: I'm sorry bro i don't know

Step-by-step explanation:

Answer: Constructions A, B, and D can be accomplished with paper folding.

Construction A involves constructing a line segment of length 2 and then finding the midpoint, which can be done by folding the paper in half.

Construction B involves drawing a perpendicular line segment through a given point on a given segment, which can also be done by folding the paper.

Construction D involves drawing a perpendicular line segment from a given point to a given segment, which can also be done by folding the paper.

Construction C, drawing a line through a given point parallel to a given line, cannot be accomplished with paper folding. To do this construction, you would need a straightedge, such as a ruler.

Step-by-step explanation:

The following constructions can be accomplished with paper folding -

Constructions are accurate drawings of shapes, angles and lines in geometry. Some basic constructions -

Given is to find which of the following constructions can be accomplished with paper folding.

The following constructions can be accomplished with paper folding -

Therefore, the following constructions can be accomplished with paper folding -

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Calculating the LCM of all these, one gets  2^2. 3^2 . 5^4 .7^5. Using the factor counting formula, the answer is 3.3.5.6 = {270}

Step-by-step explanation:            

Note that for all n, 149^n-2^n  is divisible by 149-2=147  by difference of nth powers. That is 3.7^2, so now we can clearly see that the smallest n to make the expression divisible by 3^3  is just 3^2 Similarly, we can reason that the smallest n to make the expression divisible by 7^7 is just 7^5.
       

Finally, for 5^5, take (mod {5}) and ( mod {25} )of each quantity (They happen to both be -1 and 2 respectively, so you only need to compute once). One knows from Fermat's theorem that the maximum possible minimum n for divisibility by 5 is 4, and other values are factors of 4. Testing all of them(just 1,2,4 using mods-not too bad), 4 is indeed the smallest value to make the expression divisible by 5, and this clearly is NOT divisible by 25. Therefore, the smallest (n) to make this expression divisible by 5^5 is $2^2 .5^4.    

Using the factor counting formula, 2^2. 3^2 . 5^4 .7^5 = 3.3.5.6 = {270}

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Answer:

C And D

Step-by-step explanation:

94 Inches Is 7.8 Feet Tall & 79 Inches is 6.5 Feet Tall

Answer:

C and D

Step-by-step explanation:

You should start by changing the inches to feet

(there are 12 inches in foot [ 12 inch = 1 foot ])

A. 9 foot

B. 9.5

C. about 7 feet

D. about 6 feet

C and D are correct. Hope this helps!

Answer:

[tex]x=7[/tex]

Step-by-step explanation:

Angles opposite congruent sides in a triangle are congruent.

[tex]6=2x-8 \\ \\ 2x=14 \\ \\ x=7[/tex]

Answer: O x<12

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

5x+25<85

Step 2: Subtract 25 from both sides.

5x+25−25<85−25

5x<60

Step 3: Divide both sides by 5.

5x/5 < 60/5

x<12

When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm,  [tex]\sqrt{21}[/tex]     is the measurement of the other leg.

Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The Pythagorean Theorem demonstrates how to calculate the side lengths of a right triangle by adding the areas of three intersecting squares. As the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite, this theorem is a very helpful tool. Given a triangle ABC with sides measuring a, b, and c, and the equation a2 + b2 = c2, Make another triangle with sides of lengths a and b and a right angle.

given

by Pythagoras theorem

[tex]c^{2} = a^{2} + b^{2} \\5^{2} = 2^{2} + b^{2} \\5^{2} - 2^{2} = b^{2} \\25 - 4 = b^{2} \\21 = b^{2} \\b =\sqrt{21}[/tex]

When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm,  [tex]\sqrt{21}[/tex]     is the measurement of the other leg.

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Answer:

Some key features quadratic functions have are:

Step-by-step explanation:

Answer: You could say something like this ''I think the opposite function of a quadratic function would have an inverted parabolic curve that always opens upwards, since a quadratic function can open upwards or downwards. It would also have a single maximum or minimum point, depending on the coefficient of the quadratic term, since a quadratic function has a single vertex. Finally, the opposite function would have either no real roots or two real roots with opposite signs, depending on the discriminant, since a quadratic function can have either two distinct real roots or two complex roots.''

A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.

Perfect squares result from squaring an integer. One such example is the number 81, which is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since it can be generated by squaring the number 12, which results in 12. 169 is a perfect square since it can be squared to produce the number 13. mathematics-specific language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the result is referred to as a square number, a perfect square, or simply "a square". Accordingly, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.

given

A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.

If a binomial is found to be a difference of squares, it is factored into two binomials. the first being the first term's square root less the second term's square root.

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The equivalent ratio that represents Cameron's run is 1 : 8

Equivalent Ration:

In mathematics, the definition of equivalence ratio says: The equality of two ratios is also called a ratio. Front and follow have different values, but reducing them to their simplest form gives the same value.

For example, to find out if 2:3 and 16:24 are equivalent ratios, we need to reduce both ratios to their simplest form. The HCF of 2 and 3 is 1, so 2:3 is already in the simplest form. The HCF for 16 and 24 is 8. Divide these two numbers by 8 to get the reduced form. This means (16÷8):(24÷8) = 2:3. It's clear that 2:3 and 16:24 are the same value, equivalent ratios.

Based on the question :

Cameron ran 3 miles in 24 minutes.

Now,

Therefore we can say that :

Cameron ran 1 miles in 8 minutes;

Therefore, the equivalent ration is 1 : 8.

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The beads in each bucket will weigh 1 pound

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.

From the graph, we have weights of 0, 1/2, 1 1/2 and 2 pounds.

In order for Clare to distributes all of the beads equally among the buckets, she need to add up weight of the beads and divide by 5.

weight in each bucket = (0 + 1/2 + 1 1/2 + 2)/5 = 5/5 = 1 pound

Thus, each bucket weighs 1 pound

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Answer:

[tex]x=7[/tex]

Step-by-step explanation:

Angles opposite congruent sides in a triangle are congruent.

[tex]6=2x-8 \\ \\ 2x=14 \\ \\ x=7[/tex]

Triangle is always 180 degrees because the sum of all angles in a triangle is 180 degrees. This is known as the "Triangle Angle Sum Theorem." The theorem states that the sum of all angles in a triangle is equal to 180 degrees.

1. A triangle is a three-sided polygon with three angles.

2. The sum of the three angles in any triangle must be 180 degrees.

3. This is known as the Triangle Angle Sum Theorem.

4. The Triangle Angle Sum Theorem states that the sum of the angles in a triangle must equal 180 degrees.

5. It does not matter which angles the triangle has, the sum will always equal 180 degrees.

6. This theorem is based on the fact that the sum of the angles in any triangle is equal to two right angles or 180 degrees.

7. The Triangle Angle Sum Theorem can be proven by drawing a triangle, and then measuring and adding the three angles.

8. The sum of the three angles will always equal 180 degrees.

9. Therefore, triangle is always 180 degrees.

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Answer:

Step-by-step explanation:

Answer:

? ≈ 20°

Step-by-step explanation:

using the cosine ratio in the right triangle

cos ? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{16}{17}[/tex] , then

? = [tex]cos^{-1}[/tex] ( [tex]\frac{16}{17}[/tex] ) ≈ 20° ( to the nearest degree )

a) The flowchart for the congruency of triangles is given below.

b) The triangles are congruent as DQ ≅ XZ, PQ ≅ XY, and ∠PQD ≅ ∠ZXY.

What is congruency?

The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.

In the given diagram, it can be seen that -

Line segment DQ = Line segment XZ.

Similarly, Line segment PQ = Line segment XY.

Since, the two sides of the triangle are equal, hence the third side must also be equal.

Line segment PD = Line segment ZY.

Also, in the diagram it can be seen that ∠PQD ≅ ∠ZXY.

Therefore, the triangles PDQ and ZXY are equal and congruent.

The flowchart for the same is given below.

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The perimeter of each semicircular shape disc created by Amrita by dividing a circular disc of radius 7 cm into two equal parts is 44 cm. This is calculated by multiplying the circumference of the circle (2πr = 2 × 22/7 × 7 = 44 cm) by half.

Amrita divided a circular disc of radius 7 cm into two equal parts. This created two semicircular shape discs

Step 1: Calculate the circumference of the original circle.

Circumference of a circle = 2πr

Circumference of the circle with a radius of

7 cm = 2πr = 2 × 22/7 × 7 = 44 cm

Step 2: Calculate the perimeter of each semicircular shape disc.

The semicircular shape discs are created by dividing the original disc into two equal parts. Therefore, the perimeter of each semicircular shape disc is half of the circumference of the original circle.

Perimeter of each semicircular shape disc

= 44 cm/2

= 22 cm

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Therefore ,we can conclude from answering the offered question that the region of the circle, triangle, and square is where the darkest area is. A=210-123 = 87 square units

A triangle is a polygon since it has three sides plus three vertices. It is one of the basic geometric forms. An illustration of a triangle with the sides A, B, and C is Triangle ABC. A distinct plane or triangle in Geometrical are discovered when the three aspects are not collinear. Three sides & three corners define a triangle as a polygon. The triangle's corners are defined as the locations where three sides converge. 180 degrees is the result of multiplying three triangle angles.

Here,

The total of the circle, triangle, and square's surface areas.

The region of the darkish area is comprised of the areas of the Circle, Triangle, and Square.

=>A = 210 – 123 = 87 square units

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Answer:

x = $25,400 [the original price of the Junko car]

Step-by-step explanation:

The price Ben paid, $23,622, is after the 7% discount.  Let x be the original price of the Jinko car.   Ben's prices reflect a 7% discount:

 x*(1-0.07) = $23,622  [The expression (1-0.07) means the original price, 1, is reduced by 7%, -0.07, to give the final price]

(0.93)x = $23,622

x = $25,400