I need help with the definitions anyone please

The total length of fencing needed for the yard is 46√2 meters.

To find the total length of fencing needed for the yard, we need to add up the length of all four sides of the fence.

The long side of the yard is 12√2 meters, but we need to add the √2-meter section that runs up to the house to get the total length of the fence for that side:

12√2 + √2 = 13√2

The two shorter sides are each 5√2 meters, so the total length of the fence for both of these sides is:

2(5√2) = 10√2

To find the total length of fencing needed, we add up the lengths of all four sides:

f = 13√2 + 10√2 + 13√2 + 10√2

Simplifying the expression, we can combine like terms:

f = (13 + 10 + 13 + 10)√2

f = 46√2 meters

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To prove this identity, we start with Fermat's Little Theorem, which states that if p is a prime number and a is any integer coprime to p, then a^(p-1) ≡ 1 (mod p).

Using this theorem, we can rewrite the given identity as a^(p-1) * a(p-2) ≡ 1 (mod p^2).

Next, we can multiply both sides by a to get a^(p-1) * a(p-1) ≡ a (mod p^2).

Since a and p are coprime, we can use Euler's Totient Theorem, which states that a^φ(p) ≡ 1 (mod p) where φ(p) is the Euler totient function. Since p is prime, φ(p) = p-1, so a^(p-1) ≡ 1 (mod p).

Using this result, we can rewrite our identity as a^(p-1) * a(p-1) * a^-1 ≡ a^(p-1) ≡ 1 (mod p), which implies that a^(p-1) ≡ 1 (mod p^2).

Therefore, we have proven the identity a p(p−1) ≡ 1 (mod p 2 ), where a is coprime to p, and p is prime.

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Answer: JTL, LTK, JTK

Step-by-step explanation:

3,638 more votes were cast by people in the 56 and up age group than by people in the 18 to 35 and 36 to 55 age groups combined.

From the table, the amount of votes for each age range is given as follows:

The combined amount of votes of people in the 18 to 35 and 36 to 55 age groups is given as follows:

10673 + 21372 = 32,045 votes.

Then the difference in the number of votes of people in the 56 and up age range is given as follows:

35683 - 32045 = 3,638.

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Answer:

3,638 votes more than 18 to 35 and 36 to 55.

Step-by-step explanation:

you subtract and you add

Answer:

12cm aka B.

Step-by-step explanation:

In a 30-60-90 triangle, the hypotenuse is always twice as long as the shorter leg, and the longer leg is √3 times as long as the shorter leg.

Since the length of the shorter leg is 6 cm, the hypotenuse is:

2 times the length of the shorter leg = 2 × 6 cm = 12 cm

Therefore, the length of the hypotenuse of the triangle is 12 cm.

Your welcome

The required roots of the equation f(x)=x³+2x²-11x-12  are  -1, -4, and 3 and the value of the largest root is 3.

The given polynomial is f(x)=x³+2x²-11x-12

We have to find the roots of the given polynomial f(x), we can use a method called "factoring by grouping"

The equation can be written as x³+2x²-11x-12

x(x²+2x-11)-12=0

x(x²+2x+1-1-11)-12=0

x((x+1)²-12)-12=0

x(x+1)² - 12x - 12 =0

(x+1)(x²+x-12)=0

(x+1)(x+4)(x-3)=0

x+1 = 0 ---->x=-1

x+4 = 0---->x=-4

x-3=0---->x=3

Hence, the required roots of the equation f(x)=x³+2x²-11x-12  are  -1, -4, and 3 and the value of the largest root is 3.

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Answer:

Total cost = Total volume x Cost per cubic meter = 0.6144 cubic meters x S$10/cubic meter = S$6.14

Therefore, the total cost of the pile of paper is S$6.14.

Step-by-step explanation:

Length = 40 cm = 0.4 m

Width = 32 cm = 0.32 m

Thickness = 0.8 mm = 0.0008 m

The total cost of a pile of paper with a height of 4.8 meters is she.0.0049152.

Length of paper: 40 cm = 0.4 m

Width of paper: 32 cm = 0.32 m

Thickness of paper: 0.8 mm = 0.0008 m

Volume of a single sheet of paper = Length × Width × Thickness

= 0.4 m × 0.32 m × 0.0008 m

= 0.0001024 m³

Total volume of the pile = Volume of a single sheet of paper × Height of the pile

= 0.0001024 m³ × 4.8 m

= 0.00049152 m³

Total cost = Total volume of the pile × Cost per cubic meter

= 0.00049152 m³ × she.10/m³

= she.0.0049152

Therefore, the total cost of a pile of paper with a height of 4.8 meters is she.0.0049152.

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Answer:

SSS, SAS, ASA, AAS, and HL are valid and sufficient criteria to prove that two triangles are congruent.

Answer:

1/3

Step-by-step explanation:

Answer: y = 3x

Step-by-step explanation:

In order to solve this particular question, we're first just going to look at the differences between the x and y values.

2 x 3 = 6

3 x 3 = 9

4 x 3 = 12

5 x 3 = 15

Therefore y = 3x

Answer:

Podemos usar una regla de tres para resolver este problema.

Si 4 máquinas llenan 12 000 botellas en 2,5 horas, entonces en una hora pueden llenar:

12 000 botellas / 2,5 horas / 4 máquinas = 1 200 botellas por hora por máquina

Para llenar 25 200 botellas en 3,5 horas, se necesitaría llenar:

25 200 botellas / 3,5 horas = 7 200 botellas por hora

Para llenar 7 200 botellas por hora, se necesitarían:

7 200 botellas por hora / 1 200 botellas por hora por máquina = 6 máquinas

Por lo tanto, se necesitarían 6 máquinas embotelladoras para llenar el pedido en 3,5 horas.

Step-by-step explanation:

Regarding resolving the given issue, we have Therefore, the system has one solution: (x,y) = (13/6, -21/2)

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

a)

To solve the system, we can multiply the first equation by -2, then add the two equations:

[tex]-6x + 2y = -34\\6x + 2y = -8\\0x + 4y = -42\\y = -42/4\\y = -21/2\\3x - (-21/2) = 17\\3x + 21/2 = 17\\3x = 17 - 21/2\\3x = 13/2\\x = 13/2 * 1/3\\x = 13/6\\[/tex]

Therefore, the system has one solution: (x,y) = (13/6, -21/2)

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After comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.

A transformation known as a rotation involves turning the figure either clockwise or counterclockwise. The centre of rotation is the fixed location where the rotation occurs. The term "angle of rotation" refers to the amount of rotation. A figure can be rotated 90 degrees, or a quarter turn, in either a clockwise or counterclockwise direction.

You have rotated the figure 180 degrees when you have spun it exactly halfway. The figurine may be rotated 360° by turning it all the way around. A counterclockwise turn has a positive magnitude because a clockwise rotation indicates a negative magnitude. Rotational symmetry exists in every regular polygon. When an object is rotated around its centre, it retains its original appearance. The object is then referred regarded as having rotational symmetry.

Let's write the coordinates of the original figure,

A = (1, -5)

B = (6, -2)

C = (6, -5)

D = (1, -8)

Now, if we rotate it 90 degrees counterclockwise, the coordinates are:

A' = ( 5, 1)

B' = (2, 6)

C' = (5, 6)

D' = (8, 1)

Now if we rotate it again 90 degrees counterclockwise, the coordinates are:

A'' = ( -1, 5)

B'' = (-6, 2)

C'' = (-6, 5)

D'' = (-1, 8)

Now from the figure, let's write the coordinates.

A' = ( -1, 5)

B' =  (-6, 2)

C' = (-6, 5)

D' =  (-1, 8)

This is the same as the coordinates of the second 90 degrees counterclockwise rotation.

Since we did two 90 degrees rotations, we can say we did a total of 180° counterclockwise rotation.

Therefore after comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.

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Answer:

Step-by-step explanation:

To calculate the amount Fred paid for Social Security and Medicare taxes in 2020, we first need to calculate the amount of income subject to Social Security tax.

Since Fred earned $125,000, which is less than $157,700, all of his income is subject to Social Security tax.

Therefore, the amount of Social Security tax Fred paid in 2020 is:

$125,000 x 8.25% = $10,312.50

To calculate the amount of Medicare tax Fred paid in 2020, we simply multiply his income by the Medicare tax rate:

$125,000 x 1.5% = $1,875

Therefore, Fred paid a total of $10,312.50 + $1,875 = $12,187.50 for Social Security and Medicare taxes in 2020.

The combined area of the mirror and the frame is equal to  π(r+2)² square inches.

Width of circular frame surrounds the mirror = 2 inches

Let us denote the radius of the circular mirror by r.

Then, the radius of the circular frame that surrounds the mirror is 'r + 2'.

The combined area of the mirror and the frame is the sum of the areas of the mirror and the frame.

The area of the mirror is πr²,

And the area of the frame

= Area of the larger circle with radius r+2  - Area of the smaller circle with radius r

⇒ Area of frame = π(r+2)² - πr²

Simplifying this expression, we get,

⇒ Area of frame = π(r² + 4r + 4) - πr²

⇒ Area of frame = πr² + 4πr + 4π - πr²

⇒ Area of frame = 4πr + 4π

The combined area of the mirror and the frame is,

πr² + 4πr + 4π

There is no specific value for r.

So we cannot calculate the exact area.

Simplify the expression by factoring out π,

=πr² + 4πr + 4π

= π(r² + 4r + 4)

= π(r+2)² square inches.

Therefore, the combined area of the mirror and the frame is π times the square of the sum of the radii of the mirror and the frame, which is (r+2)².

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[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log(49)=y\implies \log_{10}(49)=y\implies 1.690196\approx y \\\\\\ \log_{10}(49)\approx 1.690196\implies \stackrel{\textit{then we can say}}{10^{1.690196}\approx 49}[/tex]

Answer:

Step-by-step explanation:

Answer: A. Graph A

this is the answer because yes

The graph A shows the positive white line, this is because the line cuts across both the x- axis and that of the y- axis

Answer:

1.555,12.099,3.46

Step-by-step explanation:

When rounding 5 and above goes up and 4 and below goes down.

Hope this helps!!! :)

The discount on the game console is 15.89% of the selling price.

To find the discount as a percentage of the selling price, we first need to calculate the discount amount. This can be found by subtracting the selling price from the original price:

Discount = Original Price - Selling Price

Discount = $428 - $360

Discount = $68

Next, we can calculate the discount as a percentage of the selling price by dividing the discount amount by the selling price and multiplying by 100:

Discount % = (Discount / Selling Price) * 100

Discount % = ($68 / $428) * 100

Discount % = 0.1589 * 100

Discount % = 15.89%

Therefore, the discount on the game console is 15.89% of the selling price.

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Applying the inscribed angle theorem and the triangle sum theorem, the measure of angle EGA is: 70°.

The inscribed angle theorem states the following:

Measure of intercepted arc = 2(measure of inscribed angle)

The triangle sum theorem posits that, all three interior angles of a triangle will have a sum of 180 degrees.

m<AEB = 1/2(measure of arc AB) [based on the inscribed angle theorem]

Substitute:

m<AEB = 1/2(64)

m<AEB = 32°

m<DAE= 1/2(measure of arc DE) [based on the inscribed angle theorem]

Substitute:

m<DAE= 1/2(72)

m<DAE= 36°

m<EGA = 180 - m<AEG - m<DAE [based on the triangle sum theorem]

Substitute:

m<EGA = 180 - (42 + 32) - 36

m<EGA = 70°

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The height of the rectangular prism is 1.148 centimeters.

Let the height of the rectangular prism be y centimeters. The surface area of the composite figure is the sum of the surface areas of the rectangular prism and the rectangular pyramid.

Surface area of rectangular prism = 2lw + 2lh + 2wh

= 2(18)(10) + 2(18)(y) + 2(10)(y)

= 360 + 36y + 20y

= 360 + 56y

Surface area of rectangular pyramid = lw + (l/2)[tex]\sqrt{w/2^{2} +h^{2} }[/tex]+ (w/2)[tex]\sqrt{l/2^{2} +h^{2} }[/tex] + l*[tex]\sqrt{w/2^{2} +l/2^{2} +h^{2} }[/tex]

= (1810)/2 + (18/2)*[tex]\sqrt{5^{2} +12^{2} }[/tex]+ (10/2)[tex]\sqrt{9^{2} +12^{2} }[/tex] + 18[tex]\sqrt{5^{2} +9^{2} +12^{2} }[/tex]

= 90 +( 54 + 45 + 324)[tex]\sqrt{29}[/tex]

= 414[tex]\sqrt{29}[/tex] + 90

Therefore, the surface area of the composite figure = Surface area of the rectangular prism + Surface area of the rectangular pyramid

844 = 360 + 56y + 414[tex]\sqrt{29}[/tex] + 90

Subtracting 450 from both sides and then dividing by 56, we get:

y + 15[tex]\sqrt{\frac{29}{2} }[/tex] = 7

y = 1.148

Therefore, the height of the rectangular prism is approximately 1.148 centimeters when rounded to three decimal places.

Hence, the height of the rectangular prism is 1.148 centimeters.

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Answer:

Step-by-step explanation:

The height of the rectangular prism is 1.148 centimeters.

Let the height of the rectangular prism be y centimeters. The surface area of the composite figure is the sum of the surface areas of the rectangular prism and the rectangular pyramid.

Surface area of rectangular prism = 2lw + 2lh + 2wh

= 2(18)(10) + 2(18)(y) + 2(10)(y)

= 360 + 36y + 20y

= 360 + 56y

Surface area of rectangular pyramid = lw + (l/2)+ (w/2) + l*

= (1810)/2 + (18/2)*+ (10/2) + 18

= 90 +( 54 + 45 + 324)

= 414 + 90

Therefore, the surface area of the composite figure = Surface area of the rectangular prism + Surface area of the rectangular pyramid

844 = 360 + 56y + 414 + 90

Subtracting 450 from both sides and then dividing by 56, we get:

y + 15 = 7

y = 1.148

Therefore, the height of the rectangular prism is approximately 1.148 centimeters when rounded to three decimal places.

Hence, the height of the rectangular prism is 1.148 centimeters.

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The change in thermal energy is 75.06 kJ.

To calculate the change in thermal energy, we need to use the specific heat capacity of water, which is 4.184 J/(g°C).

First, we need to calculate the change in temperature:

ΔT = 90°C - 12°C

ΔT = 78°C

Next, we can calculate the change in thermal energy:

ΔQ = m × c × ΔT

where m is the mass of water and c is the specific heat capacity of water.

ΔQ = 230 g × 4.184 J/(g°C) × 78°C

ΔQ = 75060.96 J or 75.06 kJ (rounded to two decimal places).

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Is this a function: No, this is not a function because the input values are not uniquely mapped to the output values.

In Mathematics and Geometry, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable to an output variable.

Based on the table shown above, we can reasonably infer and logically deduce that it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values).

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Option B is correct, the inequality which represents the  length of segment AB is greater than  length of segment AD is 9x-16>1.5x+42

The given rectangle is ABCD.

The length of segment AB is 9x-16 units

The length of segment AD is 1.5x+42 units

We have to find the inequality which represents the  length of segment AB is greater than  length of segment AD

> is the symbol used to represent greater than

AB>AD

9x-16>1.5x+42

Hence, option B is correct, the inequality which represents the  length of segment AB is greater than  length of segment AD is 9x-16>1.5x+42

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The modification to the system of sampling procedure will affect amount of dissolved oxygen in the water, leading to many consequences and finally resulting in rejection of collected data .



In short, the time of day when a sample is collected is regarded as crucial phase which can adversely  affect the results of a water quality test. The temperature of the water plays a important role which can change throughout the day, and also put lots of stress on  the amount of dissolved oxygen in the water.

Dissolved oxygen is an imperative measure for checking the water quality because it is a survival need for aquatic life. The total amount of sunlight that penetrates  the water seriously affects the amount of dissolved oxygen in the water. In the event  if a sample is acquired at a different time than usual, it may not be accurate to other samples that were taken at different times.

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The complete question is

A local citizen science group is monitoring the water quality of a nearby lake. They gather water samples once a week on Wednesday between the hours of 7 A.M. and 9 A.M. from the same location. One day in August they were unable to sample within that time frame and collected the sample at 3 P.M. How might this modification to the sampling procedure affect the results?                                                          

The solution is: a) 1,2,6,24,120 are the first five terms of the sequence in which the nth term is a_n=(n+1)!/n+1.

Here, we have,

The formula for the nth term of the sequence is expressed as

n=(n+1)!/n+1

For the first term, n = 1.

Therefore,

(1+1)!/(1+1)

= 2!/2

= (2×1)/2

= 1

For the second tern, n = 2.

Therefore,

(2+1)!/2+1

= 3! /3

= (3×2×1)/3

= 6/3

= 2

For the third term, n = 3,

therefore

(3+1)!/3+1

= 4!/4

=(4×3×2×1)/4

= 6

For the fourth term, n = 4.

Therefore

(4+1)!/4+1

= 5!/5

= (5×4×3×2×1)/5

= 24

For the fifth term, n = 5.

Therefore

(5+1)!/5+1

= 6!/6

= 6× 5×4×3×2×1)/6

= 120

Hence, The solution is: a) 1,2,6,24,120 are the first five terms of the sequence in which the nth term is a_n=(n+1)!/n+1.

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complete question:

Write the first five terms of the sequence in which the nth term is a_n=(n+1)!/n+1.

a) 1,2,6,24,120

b) 1,2,3,4,5

c) 1,1,3,12,60

d) 1,1,1,1,1