[tex]\sqrt{ 6^{2} +(x-2)^{2} }[/tex]

value of variable x in the circle is 4unit.

A circle is a two-dimensional form that may be described as a collection of points that are equally spaced out from the centre.

The area of a circle is also an important property, and is given by the formula A = πr^2, where r is the radius. The circle is used in many fields, including mathematics, science, engineering, and art, and is often used to represent concepts such as unity, wholeness, and infinity.

Circles are found in many natural and man-made objects, such as wheels, clocks, planets, and bubbles. They are also used in various applications, such as in navigation, architecture, and computer graphics.

AE=8

CE=12

DE=x

BE=6x

As we know that

AE×CE=DE×BE

8×12=x×6x

96=6x²

x²=16

x=4

Hence, value of variable x in the circle is 4unit.

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a. True: We need to know the size of the pizza in order to calculate the unit price per square inch. Pi times the radius squared, or approximately 78.5 square inches, is the area of a 10-inch pizza.

b. False: We need to know the price of the entire pizza as well as the price per slice in order to determine if the restaurant would turn a profit by selling the 16-inch pizza by the slice. The cost is not specified in the problem, so we are unable to determine the profit.

c. False: The circumference of a circle is the distance around the edge, which is not directly related to the size of the pizza. To determine if the tray is big enough to hold the personal-sized pizza, we need to know the diameter or radius of the pizza. The radius of the personal pizza is 5 inches, which means the diameter is 10 inches. Therefore, the tray with a circumference of 32 inches is not big enough to hold the personal-sized pizza.

d. False: The area of the large pizza is pi times the radius squared, which is approximately 254.5 square inches. The area of the small pizza is pi times the radius squared, which is approximately 201 square inches. The difference between the areas is 254.5 - 201, which is approximately 53.5 square inches, not 2. Therefore, the statement is false.

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The exact volume of the cone is 168π cubic feet and the approximated volume is 528 cubic feet

To find the volume of a cone, we can use the formula:

V = (1/3)πr²h

where r is the radius of the base and h is the height of the cone.

Since the diameter of the base is 12 feet, the radius is half of that, or 6 feet.

Using the given height of 14 feet, we can plug in the values into the formula:

V = (1/3)π(6²)(14)

V = (1/3)π(36)(14)

V = (1/3)π(504)

V = 168π

Therefore, the exact volume of the cone is 168π cubic feet.

If we want to approximate the value using 3.14 for π, we can use a calculator to get:

V ≈ 168 * 22/7

V ≈ 528

Therefore, the approximated volume of the cone is 528 cubic feet

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Let's assume that Mr. Paquette has x pencils.

From the problem, we know that for each pencil he has, he also has 3 pens. So the total number of pens he has is 3 times the number of pencils:

Number of pencils = x

Number of pens = 3x

The total number of pencils and pens combined is given as 8, so we can write:

x + 3x = 8

Simplifying, we get:

4x = 8

x = 2

Therefore, Mr. Paquette has 2 pencils and 3x2=6 pens.

The lake activity with a central angle of 46.8° is waterskiing, since it is the lake activity chosen by 13% of the campers.

what is central angle ?

A central angle is an angle formed by two radii of a circle that intersect at its center. The central angle is measured in degrees and is used in circle graphs or pie charts to represent the proportion or percentage of each category in the data.

In the given question,

To find out which lake activity has a central angle of 46.8°, we first need to calculate the total number of campers who participated in the survey:

Total number of campers = 15 + 11 + 7 + 13 + 54 = 100

Next, we need to find the percentage of campers who chose each lake activity:

Percentage of campers who chose kayaking = (15/100) x 100% = 15%

Percentage of campers who chose wakeboarding = (11/100) x 100% = 11%

Percentage of campers who chose windsurfing = (7/100) x 100% = 7%

Percentage of campers who chose waterskiing = (13/100) x 100% = 13%

Percentage of campers who chose paddleboarding = (54/100) x 100% = 54%

Now we can use the formula for calculating the central angle of a circle graph:

Central angle = (Percentage/100) x 360°

For the lake activity with a central angle of 46.8°, we can set up the following equation:

(Percentage/100) x 360° = 46.8°

Solving for Percentage, we get:

Percentage = (46.8°/360°) x 100% = 13%

Therefore, the lake activity with a central angle of 46.8° is waterskiing, since it is the lake activity chosen by 13% of the campers.

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Answer:

6 pieces of the original pizza remain.

Step-by-step explanation:

Initially, the pizza was divided into 16 equal pieces. Violet and Sophie each ate 1/8 of the pizza on Friday, so a total of 1/8 + 1/8 = 1/4 of the pizza was eaten on Friday.

This means that 3/4 of the pizza remained after Friday.

The next day, Sophie ate 1/2 of the remaining pizza. So she ate 1/2 * 3/4 = 3/8 of the original pizza.

Therefore, the amount of pizza that remains is 3/4 - 3/8 = 3/8 of the original pizza.

To convert this fraction to a number of pieces, we need to multiply it by the total number of pieces the pizza was divided into:

3/8 * 16 = 6 pieces

The weight of the compact car, which is approximately 1,354 kilograms, can be converted to 1,354,000 grams.

In the metric system, "kilo" means thousand, so 1 kilogram is equal to 1000 grams. To convert from kilograms to grams, we simply multiply the weight in kilograms by 1000.

In this case, the weight of the compact car is given in kilograms as 1,354. To convert to grams, we multiply by 1000 to get:

1,354 kg x 1000 g/kg = 1,354,000 g

Therefore, the weight of the compact car in grams is approximately 1,354,000 grams.

The weight of an object is a measure of the force with which gravity pulls on the object. The unit of weight in the metric system is the newton (N), but kilograms (kg) are commonly used as a unit of mass and weight in everyday life. The conversion between mass and weight depends on the local acceleration due to gravity, which is approximately 9.81 m/s^2 at the Earth's surface.

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Answer: $4.22

Step-by-step explanation:

bananas: 2kg x [tex]\frac{2.10}{5kg}[/tex] = $0.84

mangoes: 3kg x [tex]\frac{2.48}{4kg}[/tex] = $1.86

pineapples: 2kg x [tex]\frac{2.28}{3kg}[/tex] = $1.52

add together:

$4.22

The number of students enrolled in the Spanish class who are also enrolled in the French class is 0.

Let the number of students enrolled in French class be F

Let the number of students enrolled in Spanish class be S

Let the number of students enrolled in German class be G

From the given information, we have

S + F + G = Total number of students...... (1)

Total number of students = 34S = 34 - F - G...... (2)

Now, we need to find out how many students are enrolled in both Spanish and French classes. So, let us assume that x students are enrolled in both Spanish and French classes.

So, the total number of students in Spanish and French classes will be S + F - x (as x students are enrolled in both the classes).

But we are given that there are 34 students enrolled in the Spanish class. Hence, the above expression will be equal to 34.

Therefore, S + F - x = 34

Now, substituting the value of S from equation (2) we get,

34 - F - G + F - x = 34 or, - G - x = 0 or, x = - G

But x represents the number of students enrolled in both Spanish and French classes, which cannot be negative.

Hence, there are no students enrolled in the Spanish class who are also enrolled in the French class.

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Answer:

120°

Step-by-step explanation:

The sum of the measurement of the interior angles of a parallelogram is 360

t +  2t + t + 2t = 360  Combine like terms

6t = 360  Divide both sides by 6

[tex]\frac{6t}{6}[/tex] = [tex]\frac{360}{6}[/tex]

t = 60

If t = 60, then 2t = 120

Helping in the name of Jesus.

Answer:

1.49m

Step-by-step explanation:

Trigonometry:

cosθ = adjacent/hypotenuse

cos(74) = adjacent/(5.39)

adjacent = 5.39 × cos(74)

adjacent = 2.3125974152

1.49 (to 2 d.p.)

It is equal to (x-4)² - (x- 4) ⁶ = 0 to solve the quadratic equation u² - u - 6 = 0 where u = (x -4).

A numerical assertion known as a situation comprises of two mathematical articulations isolated by equivalent signs (=) on one or the other side.

It demonstrates that the printed statements on the left and right are in equal relationship.

In all formulas, the left side equals the right side. Equations can be solved to determine the values of unknown variables, which represent unknown quantities.

Without the equals sign, a statement is not an equation. A mathematical statement known as an equation will include the symbol "equal to" between two expressions that have the same value.

According to our question-

(x-4)² – (x − 4) − 6 = 0

Let (x - 4) = u

u² - u - 6 = 0

Hence, It is equal to (x-4)² - (x- 4) ⁶ = 0 to solve the quadratic equation u² - u - 6 = 0 where u = (x -4).

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Using the concept of the ratio of similar triangles, we can say that the length of LM is: 12 units

Similar triangles are defined as triangles that have the same shape, but then their sizes may very well vary. This means that we can say that, if two triangles are said to be similar triangles, then it means that their corresponding angles are congruent and corresponding sides are in equal proportion.

Looking at the given image, we can see that:

LM is similar to PN and LM is similar to QP

Thus:

LN/PN = LM/QP

(x + 3)/(x - 1) = 18/12

2(x + 3) = 3(x - 1)

2x + 6 = 3x - 3

3x - 2x = 6 + 3

x = 9

LM = 9 + 3

LM = 12

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The greatest number of wristbands that can be made from a rectangular piece of paper that measures 18 centimeters by 85 centimeters is 36.

To calculate the greatest number of wristbands that can be made from a rectangular piece of paper that measures 18 centimeters by 85 centimeters, we need to divide the width of the paper by the width of each wristband, and then divide the length of the paper by the length of each wristband, and then multiply the two numbers together. The result will be the greatest number of wristbands that can be made from the paper.

Using the dimensions given in the question, and assuming that each wristband measures 1.5 centimeters by 22 centimeters (which is a typical size for a wristband), we can calculate the number of wristbands as follows:

Width of paper = 18 centimeters

Width of each wristband = 1.5 centimeters

Number of wristbands in width = (18 / 1.5) = 12

Length of paper = 85 centimeters

Length of each wristband = 22 centimeters

Number of wristbands in length = (85 / 22) ≈ 3.86 (round down to 3)

Total number of wristbands = (12 x 3) = 36

Therefore, the greatest number of wristbands that can be made from a rectangular piece of paper that measures 18 centimeters by 85 centimeters is 36.

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According to the question the equation has been solved by using Pythagorean. The left-hand side of the identity simplifies to [tex]cos^2(x)[/tex]

The Pythagorean Theorem can be used to find the correct angled triangle's missing length. The triangle contains three sides: the hypotenuse, this same opposite, which will always be the longest, and the adjacent side, which really doesn't touch the hypotenuse. The Pythagorean equation is: [tex]a^2+b^2=c^2.[/tex]

We can start by using the reciprocal identity for cosecant:

[tex]cos(x) = 1/sin(x)[/tex]

Then, we substitute this into the left-hand side of the identity:

[tex]sin(x)(csc(x) - sin(x)) = sin(x)(1/sin(x) - sin(x))\\= sin(x)/sin(x) - sin^2(x)\\= 1 - sin^2(x)[/tex]

Using the Pythagorean identity for sine and cosine, we know that:

[tex]1 - sin^2(x) = cos^2(x)[/tex]

Thus, the left-hand side of the identity simplifies to [tex]cos^2(x)[/tex], which is equal to the right-hand side of the identity.

Therefore, the identity is verified.

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Answer: 30 mil

Step-by-step explanation:

The answer is in the picture below

3600/p is an algebraic expression that represents the Share of each partner.

What is the algebraic expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

Here, we have

Given: Suppose that p partners equally share the profits from a sale of $3,600.

Number of Partners  = p

Total Profit  = $ 3600

Profit of Each Partner  = Total Profit/number of Partners

=> Profit of Each Partner  = 3600 / p

Hence,  3600/p is an algebraic expression that represents the Share of each partner.

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Answer:

Loss = Rs. 198

Step-by-step explanation:

[tex]{ \sf{\%loss = \frac{loss}{cost \: price} \times 100\%}} \\ \\ { \sf{10 = \frac{loss}{1980} \times 100}} \\ \\ { \sf{loss = \frac{10 \times 1980}{100} }} \\ \\ { \sf{loss = 198}}[/tex]

the graph οf y=-2sin(-3x) οver the interval [0, 2π] will lοοk like a wave that οscillates 3 times between y=-2 and y=2, with a periοd οf 2π/3. The graph will start at the x-axis at y=0 and be reflected acrοss the x-axis.

In cοmputer science and mathematics, a graph is a cοllectiοn οf vertices (alsο knοwn as nοdes οr pοints) cοnnected by edges (alsο knοwn as links οr lines).

I can help yοu graph the functiοn y=-2sin(-3x) οver the interval [0, 2π].

Tο start, let's analyze the functiοn. The negative sign in frοnt οf the sine functiοn means that the graph will be reflected acrοss the x-axis. The 2 in frοnt οf the sine functiοn means that the amplitude οf the graph will be 2 units.

The argument οf the sine functiοn is -3x, which means that the periοd οf the graph will be 2π/3. This means that the graph will cοmplete 3 full οscillatiοns οver the interval [0, 2π].

Using this infοrmatiοn, we can sketch the graph as fοllοws:

At x=0, the sine functiοn is 0, sο the graph starts at the x-axis at y=0.

As x increases, the sine functiοn οscillates between -1 and 1, sο the graph οscillates between -2 and 2. Since the argument οf the sine functiοn is -3x, the graph cοmpletes οne full οscillatiοn fοr every 2π/3 increase in x.

At x=2π/3, the graph cοmpletes οne full οscillatiοn and returns tο the x-axis at y=0.

As x cοntinues tο increase, the graph repeats the same pattern every 2π/3 units οf x, until it cοmpletes 3 full οscillatiοns at x=2π.

Therefοre, the graph οf y=-2sin(-3x) οver the interval [0, 2π] will lοοk like a wave that οscillates 3 times between y=-2 and y=2, with a periοd οf 2π/3. The graph will start at the x-axis at y=0 and be reflected acrοss the x-axis.

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The expression [tex]x^4y^4+x^5y^2[/tex] can be factored to [tex](x^4y^2 + x^3y^2)(x + y^2).[/tex]

To factor [tex]x^4y^4+x^5y^2[/tex], we start by taking out the highest common factor, which is [tex]x^4y^2[/tex]. We then divide the expression by [tex]x^4y^2[/tex] to get [tex]x+y^2[/tex].

We can then rewrite the expression as ([tex]x^4y^2 + x^3y^2)(x + y^2).[/tex]

To verify this solution, we can multiply it out to get [tex](x^4y^2 + x^3y^2)(x + y^2) = x^5y^2 + x^4y^4[/tex], which is equal to the original expression. Therefore, the expression [tex]x^4y^4+x^5y^2[/tex] can be factored to [tex](x^4y^2 + x^3y^2)(x + y^2[/tex]).

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Sin(300°) = -√3 / 2 .

Therefore, the length of the x is 24.04.

A triangle is a geometric shape that consists of three sides and three angles. It is a closed shape with three straight sides that connect at three vertices (corners). Triangles can be classified based on the lengths of their sides or the measures of their angles. For example, a triangle with three sides of equal length is called an equilateral triangle, while a triangle with two equal sides is called an isosceles triangle. Triangles can also be classified based on their angles, such as acute, obtuse, or right triangles. Triangles have a variety of properties and applications in mathematics, physics, and engineering.

by the question.

So, in this case, we have:

[tex]21 > x+7[/tex]

Where x is the length of the third side.

Simplifying the expression, we get:

[tex]21 > x+7[/tex]

Therefore, the length of the third side must be less than 28.

We can also use the Pythagorean theorem to determine if this triangle is a right triangle.

If a triangle is a right triangle, then the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).

In this case, we have:

[tex]21^2 - 7^2 = x^2[/tex]

Simplifying, we get:

[tex]441 - 49 = x^2[/tex]

[tex]392 = x^2[/tex]

Taking the square root of both sides, we get:

x ≈ 19.79

Again, If a triangle is a right triangle, then the sum of the squares of the two shorter sides is equal to the square of the longest side.

[tex](x+3)^2 = (19.79)^2-(4)^2\\(x+3)^2= 391.64-16\\(x+3)^2= 225.64\\(x+3)= \sqrt225.64\\(x+3)= 15.021\\x = 15.021-3\\x = 12.021[/tex]

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El ángulo -3π / 4 está en el tercer cuadrante del plano cartesiano.

Answer:

her mistake was in step2.

Step-by-step explanation:

in the parenthesis 4.5^2 would be 20.25 then you would multiply by 2 and get 40.5.

from there you can x by 3.14

The probability that a particular serving contains fewer than 300 calories is 0.71, more than 250 calories is -2.86, between 275 and 310 calories is  0.7186.

To solve this problem, we need to use the normal distribution and the corresponding z-scores. We can find the z-score for a particular value of x (number of calories) using the following formula:

z = (x - μ) / σ

where μ is the mean, σ is the standard deviation, and x is the specific value we are interested in.

Probability of serving containing fewer than 300 calories:

z = (300 - 290) / 14 = 0.71

Using a standard normal distribution table or calculator, we find that the probability of a z-score being less than 0.71 is 0.7611. Therefore, the probability of a serving containing fewer than 300 calories is 0.7611.

Probability of serving containing more than 250 calories:

z = (250 - 290) / 14 = -2.86

Using a standard normal distribution table or calculator, we find that the probability of a z-score being greater than -2.86 is 0.9977. Therefore, the probability of a serving containing more than 250 calories is 0.9977.

For 275 calories:

z = (275 - 290) / 14 = -1.07

For 310 calories:

z = (310 - 290) / 14 = 1.43

Next, we use a standard normal distribution table or calculator to find the probability of z falling between -1.07 and 1.43. For example, using a standard normal distribution table, we can find that the probability of z falling between -1.07 and 1.43 is approximately 0.7186.

Therefore, the probability that a particular serving of McDonald's Egg McMuffin contains between 275 and 310 calories is approximately 0.7186, or 71.86%.

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Glen spends average 1 1/2 times more hours writing the paper than finishing the project, so he spends 9x/(x+y) hours writing the paper and 9y/(x+y) hours finishing the project.

Glen spends a total of 9 hours writing a paper and finishing a project. We can define x as the number of hours he spends writing the paper and y as the number of hours he spends finishing the project. Since Glen spends 1 1/2 times more hours writing the paper than finishing the project, we can set up an equation that states that x = 1.5y. We can then substitute 1.5y for x in the equation for the total number of hours, 9x + 9y, and simplify it to 9(1.5y + y). This simplifies to 13.5y and since y = x/1.5, we can substitute x/1.5 for y and get 13.5(x/1.5). Simplifying this equation, we get 9x, meaning that Glen spends 9x hours writing the paper and 9y/(x+y) hours finishing the project.

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For isosceles triangle we have proved a) ∆AHB = AHC b) AH is the median of ∆ABC c) BC = 2AD

a) To prove that ∆AHB = AHC, we need to show that the two triangles have equal sides and angles. Since ABC is an isosceles triangle at A, we know that AB = AC. Also, since AH is the altitude of the triangle, we know that it is perpendicular to BC. Therefore, angle AHB and angle AHC are both right angles.

Now, to prove that the triangles have equal sides, we need to show that HB = HC. Since AB = AC, we have:

[tex]AB^{2} = AC^2\\AB^2 - AH^2 = AC^2 - AH^2\\BH^2 = CH^2[/tex]

Therefore, HB = HC, and we have proved that ∆AHB = AHC.

From this, we can deduce that angle BHA = angle CHA, as they are opposite angles in congruent triangles. Also, we know that angle ABC = angle ACB, as it is an isosceles triangle. Therefore, angle ABH = angle ACH, and we have proved that ∆ABH = ∆ACH.

b) To prove that A, G, and H are collinear, we need to show that AH is the median of ∆ABC. Since ∆AHB = AHC, we know that HB = HC. Therefore, BG and CG are medians of the triangle, and they intersect at G.

Now, to prove that ∆GBC is equal, we can use the fact that medians of a triangle divide it into six equal triangles. Therefore, we have:

Area(∆GBC) = 2/3 * Area(∆BGC)

Area(∆GBC) = 2/3 * Area(∆ACG)

Area(∆GBC) = 2/3 * Area(∆ABG)

Since ∆ABH = ∆ACH, we know that the altitude from A to BC passes through H, which is the midpoint of BC. Therefore, AH is also the median of ∆ABC.

c) Let E be the midpoint of BC. Since AE is the median of the triangle, we know that it divides BC into two equal parts, so EC = EB. Let X be the midpoint of AD. Since M is the midpoint of HD, so:

HX = (1/2) * HD

HX = (1/2) * (2AD)

HX = AD

AX is parallel to DE so:

AB/AD = AE/AX

2 = AE/AX

Since EC = EB and HX = AD, so:

AE = EC + HX

AE = EB + HX

AE = 2HX

Therefore, substitute, simplify:

2 = 2HX/AX

2AX = 2HX

AX = HX

Since AX = HX, DX is also equal to HX, so:

AD = DX

Also, since AE = 2HX, so:

BC = 2AE

Substitute in HX = AD and AE = 2HX, so:

BC = 2AE

BC = 2(2HX)

BC = 4HX

BC = 4AD

Therefore, we have proved that BC = 2AD.

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The most accurate estimate of the distance on the ground between the wall and the bottom of the ladder is 2 meters.

One approach to tackle this problem is to apply trigonometry to establish the connection between the angle, height, and distance. Specifically, we can utilize the cosine function, which relates the adjacent side and the hypotenuse of a right triangle. In this case, the adjacent side represents the distance between the wall and the ladder, and the hypotenuse corresponds to the ladder's length. The given angle is 72 degrees.

By employing the formula cos(angle) = adjacent/hypotenuse, we can input the known values and determine the unknown distance:

cos(72) = distance/6

distance = 6 * cos(72)

distance is approximately 1.9 m

Thus, the most accurate estimation for the ground distance from the ladder's bottom to the wall is 2 m.

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Answer:2m

Step-by-step explanation:

i took the test