Which supplementary angles can prove
that lines L and M are parallel?

A. 5 and 6
B. 3 and 8
C. 2 and 4

The surface area of the juice box is 24 square inches, which is calculated by multiplying the height, length, and width.

The surface area of the juice box is 24 square inches, which is calculated by multiplying the four sides together. The juice box measures 4 inches high, 3 inches long, and 2 inches wide, so to find the surface area, one must multiply each of these measurements. 4 multiplied by 3 multiplied by 2 equals 24, and this is the surface area of the juice box. Each side of the juice box has a different area, but when all of the sides are combined, they equal to the total surface area. This measurement is useful when determining the size of the juice box and the amount of material needed to create it. Knowing the surface area of the juice box can also help when determining the cost of materials and the overall price of the product. Having the surface area of the juice box allows for an accurate calculation of the amount of material needed, as well as the cost of the materials and the overall price of the product.

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Answer:

\( (gof)x= 4(x - 5) ^{2} + 2 \\ = 4( {x}^{2} - 10x + 25) + 2 \\ = 4x^{2} - 40x + 100 + 2 \\ = 4x ^{2} - 40x + 102\)

Answer:

A = 6.4

Step-by-step explanation:

A - 5.36 = 1.04

    +5.36   +5.36

A = 6.4

Hello !

Answer:

\(\boxed{\sf V{cone} \approx 2408.55 m^3}\)

Step-by-step explanation:

To find the volume of a cone with the radius of its base and its height, we will apply the following formula:

\( \sf V{cone} = \dfrac{\pi \times r^2 \times h}{3} \)

Where r is the radius of its base and h is its height.

Given:

Let's substitute our values into the formula:

\(\sf V{cone} = \dfrac{\pi (10)^2(23)}{3} = \dfrac{2300\pi}{3} \ \ \\\boxed{\sf V{cone} \approx 2408.55 m^3}\)

Have a nice day ;)

Answer:

0

Step-by-step explanation:

63 * 0 is 0. 0 * (-7) is also 0.

Anything multiplied by 0 is 0, no matter how big the number is, or how many numbers there are.

Hope this helps :)

Answer:

y = 8

Step-by-step explanation:

for the triangles to be congruent, 2y + 20 must equal 36.

2y + 20 = 36

subtract 20 from each side of the equation:

2y = 16

divide both sides by 2:

y = 8

Answer:

  ∆QRS / ∆XZY = 1/2

Step-by-step explanation:

You want the similarity ratio of ∆QRS to ∆XZY. Side lengths are marked in the diagram.

The similarity ratio will be the ratio of two corresponding side lengths.

You can find corresponding sides several ways:

The ratios of corresponding sides are 1:2, 2:4, and 2:4. The 2:4 ratios reduce to 1:2, which is the answer you're looking for. Written as a fraction, the ratio is ...

  1/2 . . . . ratio of ∆QRS to ∆XZY

Answer:

Domain: {-2,-9,8}

Range: {4,-2}

Step-by-step explanation:

For the domain, any values dealing with x is the domain. For range, any values dealing with y is the range. So we can see that all the x values is -2, -9, 8. For the y values, we can see that we have 4, and -2. Therefore your domain is {-2,-9,8} and you range is {4,-2}

Answer:

Domain = {-2, -9, 8}

Range = {4, -2,}

Step-by-step explanation:

The domain is the x-values

The range is the y-values

set notation doesn't have a particular order so I'll list them in the order they appear. {}

Domain = {-2, -9, 8}

Range = {4, -2,}

I hope this helps!

Answer:

Step-by-step explanation:

As per picture we have:

Since GI = GJ + JI, substitute:

Then the lengths are:

As point J divides the segment IG in the ratio of 2:1 we can state it is the centroid of ΔFHI

Answer:

see explanation

Step-by-step explanation:

From the diagram

GI = GJ + JI , substitute values

9x - 9 = 2x + 3 + 5x

9x - 9 = 7x + 3 ( subtract 7x from both sides )

2x - 9 = 3 ( add 9 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

Thus

GJ = 2x + 3 = 2(6) + 3 = 12 + 3 = 15

JI = 5x = 5(6) = 30

GI = 9x - 9 = 9(6) - 9 = 54 - 9 = 45

The centroid is where the 3 medians of a triangle intersect.

On each median, the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint.

Here JI = 30 and twice as long as GJ, thus J is the centroid of the triangle.

Answer: 1.2 miles

You can find the answer by using the pythagorean theorem.

a^2 + b^2 = c^2.

(5000)^2 + (4000)^2 = c^2

25 million +16 million = c^2

41 million = c^2

Take the square root of both sides in order to get the value of C.

C = about 6,403 feet.

1 mile = 5280 feet

6403/5280 = 1.2

Buddy would walk about 1.2 miles

The fourth term in the geometric sequence is -81.

What is a geometric sequence?

In mathematics, a geometric progression, also known as a geometric sequence, is a set of non-zero numbers where each term after the first is derived by multiplying the previous one by a fixed, non-zero amount called the common ratio.

We are given a sequence as 3, –9, 27, ...

We can observe that each term is being multiplied by -3.

So, the common ratio i.e. r = -3

Here x = 4 and a₁ = 3.

Now, using aₓ = a₁ r⁽ˣ⁻¹⁾ , we get

⇒a₄ = a₁ r⁽⁴⁻¹⁾

⇒a₄ = a₁ r³

⇒a₄ = 3 (-3)³

⇒a₄ = 3 * -27

⇒a₄ = -81

Hence, the fourth term in the geometric sequence is -81.

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Answer:

79507

Step-by-step explanation:

because 64000(1+15/200)^3= 79507

Answer:

Im unaware what you are asking?

Step-by-step explanation:

hmmmm

Answer:

Step-by-step explanation:

d=2q, q=d/2

10d+25q=630, using q=d/2

10d+25d/2=630

20d+25d=1260

45d=1260

d=28

So he has 28 dimes.

The terminal side of a 180° angle in standard position is negative x-axis

Shape of an object can drawn is two dimension. Also, object can be located on two dimensional graph. Two dimension consists of x and y axis.

According to standard positioning,

positive x-axis is from 0° to 90°

positive y-axis is from 90° to 180°

negative x-axis is from 180° to 270°

negative y-axis is from 270° to 360°

Therefore, the terminal side of a 180° angle in standard position is negative x-axis

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In a case whereby Kouroche is organising an overnight camping trip. the cost of renting a cabin is $20. (flat rate)  if cost of food is $9 per person .  the amount it will the trip cost if 5 people go is $65.

Based on the given information that cost of food for each person = $9

And the  cost of renting a cabin= $20

Then we can calculate the amount it will the trip cost if 5 people go which can be expressed as ;

[ 20 + (9*5)]

=(20 + 45)

=$65

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Check the complete question:

Kouroche is organising an overnight camping trip. the cost of renting a cabin is $20. (flat rate) The cost of food is $9 per person .  how much will the trip cost if 5 people go?

We are given two rational expressions: one with (y² - 13y + 36) in the numerator and (y² + 2y – 3) in the denominator, and the other with (y² - y – 12) in the numerator and (y² - 2y + 1) in the denominator. We need to simplify these rational expressions.

Simplifying the first rational expression:
The numerator of the first expression, y² - 13y + 36, can be factored as (y – 4)(y – 9).
The denominator, y² + 2y – 3, can be factored as (y + 3)(y – 1).
Therefore, the first rational expression simplifies to (y – 4)(y – 9) / (y + 3)(y – 1).

Simplifying the second rational expression:
The numerator of the second expression, y² - y – 12, can be factored as (y – 4)(y + 3).
The denominator, y² - 2y + 1, can be factored as (y – 1)(y – 1) or (y – 1)².
Therefore, the second rational expression simplifies to (y – 4)(y + 3) / (y – 1)².

By factoring the numerator and denominator of each rational expression, we obtain the simplified forms:

First rational expression: (y – 4)(y – 9) / (y + 3)(y – 1)
Second rational expression: (y – 4)(y + 3) / (y – 1)²

These simplified expressions are in their simplest form, with no common factors in the numerator and denominator that can be further canceled.


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The value for x is 30 cm.

equivalent triangles

According to  the following equation is valid:

x/75 = 12/30

30x = 900 is obtained by dividing by 12 * 75.

Divide both sides of 30x/30 to get 900/30x = 30.

As a result, the value of x is 30 cm.

Two rectangles are said to be comparable if the ratio of one triangle's two sides to the two sides of that other triangle is the same, and the angles that the two sides of both triangles inscribe are equal. This means that if A = X and Acceptor = AC/XZ, then ABC XYZ.

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I understand the question looking for is :

What is the value of x?

X= 4.8 cm

X= 30 cm

X= 93 cm

X= 187.5 cm

The value for x is 30 cm.

equivalent triangles

x/75 = 12/30

30x = 900 is obtained by dividing by 12 * 75.Divide both sides of 30x/30 to get 900/30x = 30.

As a result, the value of x is 30 cm.

What are some similar triangles?

Two rectangles are said to be comparable if the ratio of one triangle's two sides to the two sides of that other triangle is the same, and the angles that the two sides of both triangles inscribe are equal. This means that if A = X and Acceptor = AC/XZ, then ABC XYZ.

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I understand the question looking for is :

What is the value of x?

X= 4.8 cm

X= 30 cm

X= 93 cm

X= 187.5 cm

The scale that Desmond used in the drawing is 11 inches : 4 feet

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

Actual length of shopping center is 64 feet long

Scale length of shopping center is 176 inches long

using the above as a guide, we have the following:

Scale = Scale length : Actual length

substitute the known values in the above equation, so, we have the following representation

Scale = 176 inches : 64 feet

Simplify the ration

Scale = 11 inches : 4 feet

Hence, the scale that Desmond used in the drawing is 11 inches : 4 feet

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Answer:

7.14 in^2

Explanation

Find the area of the rhombus and the trapezoid, then add them together and you get 7.139 (about 7.14)

The probability that the insurance representative will sell a policy to three out of four prospective clients is 0.0256.

The probability that the insurance representative sells to more than two prospective clients is 0.0272.

To calculate the probability that the insurance representative will sell a policy to a specific number of prospective clients out of four, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = \((n C k) * p^k * (1 - p)^(n - k)\)

Where:

P(X = k) is the probability of exactly k successes (selling a policy) out of n trials (appointments).

(n C k) represents the combination or "n choose k" which calculates the number of ways to choose k successes out of n trials.

p is the probability of success on a single trial (probability of making a sale).

(1 - p) is the probability of failure on a single trial (probability of not making a sale).

Using this formula, we can calculate the probability of selling a policy to three out of four prospective clients.

Probability of selling a policy to three clients:

P(X = 3) = (4 C 3) * (0.20)^3 * (1 - 0.20)^(4 - 3)

Calculating:

P(X = 3) = 4 * 0.008 * 0.80

P(X = 3) = 0.0256

To calculate the probability that she sells to more than two clients, we need to sum the probabilities of selling to three clients and selling to all four clients.

Probability of selling to more than two clients:

P(X > 2) = P(X = 3) + P(X = 4)

Substituting the values:

P(X > 2) = \(0.0256 + (4 C 4) * (0.20)^4 * (1 - 0.20)^(4 - 4)\)

Calculating:

P(X > 2) = 0.0256 + 1 × 0.0016 × 1

P(X > 2) = 0.0272

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Answer:

Step-by-step explanation:

\(\sqrt{x-3} +5=x\\\sqrt{x-3} =x-5\\squaring ~both~sides\\x-3=x^2-10x+25\\x^2-10x-x+25+3=0\\x^2-11x+28=0\\x^2-7x-4x+28=0\\x(x-7)-4(x-7)=0\\(x-7)(x-4)=0\\x=7,4\)

put x=7 in the given equation

\(\sqrt{7-3} +5=7\\\sqrt{4} +5=7\\2+5=7\\7=7\)

which is true .

∴ x=7 is a solution of the given eq.

now put x=4 in the given eq.

\(\sqrt{4-3} +5=7\\1+5=7\\6=7\\\)

which is not true.

∴x=4 is an extraneous solution.

-Q->P is proved from the contrapositive of 1.-P->Q.

What is Contrapostive ?

In logic, the contrapositive of a conditional statement of the form "if A, then B" is a statement of the form "if not B, then not A".

Here is a possible formal proof of the contrapositive of 1.-P->Q, which is -Q->P:

-P->Q Premise

Assume -Q Assume for sub proof

Assume -P Assume for subproof

From 2 and 1, we have P Modus tollens (MT)

From 4, we have P and -P Conjunction (CONJ)

From 3 and 5, we have # Contradiction (CONTR)

From 3-6, we have -Q-># Conditional proof (CP)

From 2 and 7, we have P Proof by contradiction (PC)

From 2-8, we have -Q->P Conditional proof (CP)

Therefore, -Q->P is proved from the contrapositive of 1.-P->Q.

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The radius of the cone is 783.84/√h

A cone is the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex).

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of a cone is expressed as;

V = 1/3πr²h

643072 × 3 = 3.14 × r²h

r²h = 614400

r² = 614400/h

r = 783.84/√h

therefore the radius of the cone is 783.84/√h

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The code efficiently identifies prime numbers using the ancient Greek algorithm. It initializes an array, marks the multiples of each prime number as non-prime, and then prints the prime numbers.

This algorithm demonstrates a straightforward and efficient method for finding prime numbers within a given range.The ancient Greek algorithm for finding prime numbers less than or equal to a given number is implemented in the provided Python code. The algorithm follows a simple approach of marking numbers as prime or non-prime.

It starts by assuming all numbers as prime and then proceeds to mark the multiples of each prime number as non-prime. The code initializes an array where each element represents a number and marks them all as prime initially. Then, it iterates over each number from 2 to the given number, checking if it is marked as prime. If it is, the algorithm crosses out all its multiples as non-prime. Finally, it prints the numbers that remain marked as prime.

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The x- and y-coordinates of the center of mass are; (20, 0)

The center of mass is the location where the sum of the relative position of the masses in a mass distribution is zero. It is the point where force can be applied on the distributed mass without causing a rotation of the system.

The mas of the steel plate = 800 g = 0.8 kg

The base length of the isosceles triangular plate = 20 cm = 0.2 m

The height of the isosceles triangular plate = 30 cm = 0.3 m

Considering a small strip of height, dx and width, I, we get

Area of small strip, dA = I·dx

Density of the plate for a unit thickness, ρ = M/A

Density of the small strip of mass dm = dm/dA

Considering the density of the plate as uniform, we get;

\(\displaystyle {\frac{dm}{dA} =\frac{M}{A}\)

Therefore;

\(\displaystyle {dm=\frac{M}{A}\times dA}\)

The area of the triangular plate, A = (1/2) × 0.2 m × 0.3 m = 0.03 m²

Mass of the plate, M = 0.8 kg

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx}\)

The width of the small strip, I, located at a distance x from the vertex of the triangular plate, using similar triangles, indicates;

\(\dfrac{I}{20} = \dfrac{x}{30}\)

\(I=20\times \dfrac{x}{30} = \dfrac{2}{3} \cdot x\)

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx} = \frac{0.8}{0.03}\times \dfrac{2}{3} \cdot x\cdot dx}\)

The center of mass, \(x_{cm}\), can be obtained with the formula; \(\displaystyle {x_{cm} = \dfrac{1}{M} \cdot \int\limits {x} \, dm }\)

Therefore; \(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx }\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx } = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0\)

\(\displaystyle {x_{cm} = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0=\frac{200}{9} \times \frac{0.027}{3} =0.2\)

The location of the x-coordinate center of mass, \(x_{cm}\) = 0.2 m = 20 cm from the vertex, which is the same location as the x-coordinate of the centroid of the plate of uniform density.

The plate is symmetrical about the x-axis, therefore, the y-coordinate of the center of mass is along the x-axis, which is \(y_{cm}\) = 0

The coordinate of the center of mass = (0.2, 0)

Part of the question requires the location of the coordinate of the center of mass of the triangular plate

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To find the limit of cos(x)/(1-sin(x)) as x approaches (π/2)+, we can use l'Hospital's Rule.

First, we can take the derivative of both the numerator and denominator with respect to x: lim cos(x)/(1 − sin(x)) x → (π/2)+ = lim [-sin(x)/(cos(x))] / [-cos(x)] x → (π/2)+ = lim sin(x) / [cos(x) * cos(x)] x → (π/2)+

Now, plugging in (π/2)+ for x, we get: lim sin(π/2) / [cos(π/2) * cos(π/2)] x → (π/2)+ = 1 / (0 * 0) = undefined

Since the denominator approaches 0 as x approaches (π/2)+, and the numerator is bounded between -1 and 1, the limit does not exist.

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Answer:

12 minutes

Step-by-step explanation:

my guts are always right

Therefore, the distance between Greensville and Bluesburg is 412.5 miles.

Caitlin drove from Greensville to Bluesburg at a speed of 50 miles per hour. On the way back, she drove at 75 miles per hour. The total trip took 7 and 1/2 hours of driving time. We are to find the distance between the two cities.Solution:

Let the distance between the two cities be d.Caitlin drove from Greensville to Bluesburg at a speed of 50 miles per hour. Let the time taken for this journey be t.

Using the formula, distance = speed x time, we get

;d = 50t (1)

On the way back, Caitlin drove at 75 miles per hour.

Let the time taken for this journey be t1.Using the formula, distance = speed x time, we get;d = 75t1 (2)We know that the total trip took 7 and 1/2 hours of driving time.Using equations (1) and (2),

we get

;\(50t + 75t1 = d + d = 2dd = 25(2t + 3t1) (3)\)

Also, we know that the total trip took 7 and 1/2 hours of driving time.Using equations (1) and (2),

we get;

t + t1 = 7.5 (4

)From equation (4), we can say;

t1 = 7.5 - t (5)

Substituting equation (5) into equation (3),

we get;

\(d = 25[2t + 3(7.5 - t)]\)

\(d = 25(15/2 + t/2)\)

\(d = 187.5 + 12.5td/25 = 15 + t/2d = 375 + 25td/2\)

Putting t = 3 in the above equation, we get

;\(d = 375 + 25(3)/2d = 375 + 37.5d = 412.5\)\(miles\)

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