PLEASE HELP WILL GIVE BRAINLISET AND 60 PTS !

[tex]$$16[(x_2 - x_1)^2 + (y_2 - y_1)^2]x^2 - 32(x_2 - x_1)x^3 + 16(x_2 - x_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]x + 16[(y_2 - y_1)^2 + (x_2 - x_1)^2]y^2 - 32(y_2 - y_1)y^3 + 16(y_2 - y_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]y + [(x_2 - x_1)^2 + (y_2 - y_1)^2 - 180^2]^2 = 0$$[/tex]

this is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola.

What is hyperbola ?

A hyperbola is a type of conic section that has two separate parts, called branches, which are mirror images of each other. It is defined as the set of all points in a plane, such that the difference between the distances from two fixed points, called foci, is a constant. Hyperbolas have many applications in science, engineering, and mathematics.

Given two LORAN transmitters located at the coordinates [tex]$(x_1, y_1)$[/tex] and [tex](x_2, y_2)$[/tex], where unit distance on the coordinate plane is measured in miles.

Let the coordinates of the receiver be [tex](x,y)$.[/tex]

The distance from the receiver to the first transmitter is given by [tex]$\sqrt{(x - x_1)^2 + (y - y_1)^2}$[/tex], and the distance from the receiver to the second transmitter is given by [tex]\sqrt{(x - x_2)^2 + (y - y_2)^2}$.[/tex]

Since the difference in the distances from the receiver to these transmitters is 180 miles, we have:

[tex]$$\sqrt{(x - x_1)^2 + (y - y_1)^2} - \sqrt{(x - x_2)^2 + (y - y_2)^2} = 180$$[/tex]

Squaring both sides, we get:

[tex]$$(x - x_1)^2 + (y - y_1)^2 - 2\sqrt{(x - x_1)^2 + (y - y_1)^2} \sqrt{(x - x_2)^2 + (y - y_2)^2} + (x - x_2)^2 + (y - y_2)^2 = 180^2$$[/tex]

Rearranging, we get:

[tex]$$(x - x_1)^2 + (y - y_1)^2 - (x - x_2)^2 - (y - y_2)^2 = 4\sqrt{(x - x_1)^2 + (y - y_1)^2} \sqrt{(x - x_2)^2 + (y - y_2)^2} - 180^2$$[/tex]

Using the identity $a^2 - b^2 = (a + b)(a - b)$, we can simplify the left-hand side as:

[tex]$$4x(x_2 - x_1) + 4y(y_2 - y_1) = 4\sqrt{(x - x_1)^2 + (y - y_1)^2} \sqrt{(x - x_2)^2 + (y - y_2)^2} - 180^2$$[/tex]

Squaring both sides again and simplifying, we get:

[tex]$$16[(x_2 - x_1)^2 + (y_2 - y_1)^2]x^2 - 32(x_2 - x_1)x^3 + 16(x_2 - x_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]x + 16[(y_2 - y_1)^2 + (x_2 - x_1)^2]y^2 - 32(y_2 - y_1)y^3 + 16(y_2 - y_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]y + [(x_2 - x_1)^2 + (y_2 - y_1)^2 - 180^2]^2 = 0$$[/tex]

this is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola.

Therefore, [tex]$$16[(x_2 - x_1)^2 + (y_2 - y_1)^2]x^2 - 32(x_2 - x_1)x^3 + 16(x_2 - x_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]x + 16[(y_2 - y_1)^2 + (x_2 - x_1)^2]y^2 - 32(y_2 - y_1)y^3 + 16(y_2 - y_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]y + [(x_2 - x_1)^2 + (y_2 - y_1)^2 - 180^2]^2 = 0$$[/tex]

this is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola.

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Answer:

10 cm

Step-by-step explanation:

Given:

A circular piece of paper of a radius of 20 cm is cut in half and each half is made into a hollow cone by joining the straight edges.

To find:

Find the slant height and base radius of each cone.

Solution:

The radius of the circular piece of paper = 20 cm

Finding the slant height of each cone:

Since the straight edges of the semi-circular part is joined together to form a cone

∴ Slant height of the cone so formed = Radius of the circular piece = 20 cm

Thus, the slant height of the cone is → 20 cm.

Finding the base radius of each cone:

Let "r" cm be the base radius of each cone.

We have,

[Length of the base of each cone] = [Length of each semi-circular part of the original circular piece of paper]

⇒

2

�

�

=

2

�

×

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

2

2πr=

2

2π × radius of original circle

⇒

2

�

=

2

×

20

2

2r=

2

2×20

⇒

2

�

=

20

2r=20

⇒

�

=

10

�

�

r=10cm

Thus, the base radius of each cone is → 10 cm.

The surface area of the box shown is 186 square inches (186 in²).

Surface area is the measure of the area on a two-dimensional surface. It is the sum of the areas of all the shapes that make up a two-dimensional object. It can be used to calculate the area of a sphere, a cylinder, a rectangular prism, and more.

The box shown is a three-dimensional rectangular prism. The surface area (S.A.) of a rectangular prism is calculated by adding the area of each of its six faces. The area of each face is calculated by multiplying the length of the face by its width.

For the box shown, the length is 3 inches (3 in), the width is 12 inches (12 in), and the height is 10 inches (10 in). To find the surface area, we need to calculate the area of each face and add them together. The surface area of this box is calculated as follows:

Front and back faces: 3 in x 10 in = 30 in²

Left and right faces: 12 in x 10 in = 120 in²

Top and bottom faces: 3 in x 12 in = 36 in²

Total surface area: 30 in² + 120 in² + 36 in² = 186 in²

Therefore, the surface area of the box shown is 186 square inches (186 in²).

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The circumference of the circle is 144.44 yards

The circumference of a circle is the total distance around the edge of the circle. It's computed using the following formula:

Circumference = 2πr.

where r is the circle's radius and represents the ratio of a circle's circumference to its diameter by a mathematical constant π that roughly equals 3.14159.

We can also use the formula below whenever we have the diameter of the circle given

c = πd

where d is the diameter of the circle (the distance across the circle passing through the center).

From the image given, the circumference of the circle is given as;

c = 2πr

r = 23yd

c = 2 * 3.14 * 23

c = 144.44

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Answer:

cm³ and ml

m³ and litre

This is the all you will need to know

If the car travels 160 miles, it will take approximately 2.7 hours to cover that distance.

An inverse function is a function that "undoes" the effect of another function. More specifically, if we have a function f(x), its inverse function g(x) will undo the effect of f(x), such that if we apply f(x) and then g(x) to an input x, we get back the original input.

To find the inverse function of d(t) = 60t, we need to solve for t in terms of d. We start by setting d equal to the original function and solving for t:

d = 60t

Dividing both sides by 60, we get:

t = d/60

So the inverse function is t(d) = d/60.

To find t(160), we substitute 160 for d in the equation t(d) = d/60:

t(160) = 160/60

t(160) = 2.67 (rounded to 1 decimal place)

Therefore, if the car travels 160 miles, it will take approximately 2.7 hours to cover that distance.

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Hence, in answering the stated question, we may say that As a result, the  function mass of the 30 cm long PVC pipe is roughly 733.48 grammes, rounded to the nearest tenth.

Mathematicians investigate numbers and their variants, equations and associated structures, forms and their locations, and prospective locations for these things. The term "function" refers to the relationship between a group of inputs, each with its own output. A function is a connection of inputs and outputs in which each input results in a single, distinct outcome. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four basic types of accessible functions.

The volume of the PVC pipe can be estimated by subtracting the volumes of the outer and inner cylinders:

V = π/4 × (D² - d²) × L

where V denotes volume, is the mathematical constant pi (roughly equivalent to 3.14159), D denotes outer diameter, d denotes inner diameter, and L denotes pipe length.

V = π/4 × (6.5² - 5²) × 30\sV = 531.13 cm³

PVC pipe mass can be estimated by multiplying its volume by its density:

m = V × ρ

With the provided density, we get:

1.38 g/cm3 m = 733.48 g m = 531.13 cm3

As a result, the mass of the 30 cm long PVC pipe is roughly 733.48 grammes, rounded to the nearest tenth.

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The area of the rectangle is 35.1 cm²

To find the area of a rectangle, you need to multiply its length by its width.

Given that the dimensions of the rectangle are 5.85 cm and 6 cm, respectively, the area of the rectangle is:

Area = Length x Width

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

Area = 5.85 cm x 6 cm

Evaluate the product

Area  = 35.1 cm²

Hence, the area of the rectangle to the nearest tenth is 35.1 cm²

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Complete question

The dimension of a rectangle is 5.85 cm by 6 cm. Find its area to the nearest tenth.

Answer:

Approxiamaltely 91.95 feet

Step-by-step explanation:

Option D : Based on the given data, the best prediction for the number of students who prefer ice cream at the college, which is approximately 1,440 students.

To make prediction of the number of students who prefer ice cream, we need to use the proportion of students who prefer ice cream from the sample to the entire population of 4,000 students.

Based on the given data, 81 out of 225 students prefer ice cream. To estimate the number of students who prefer ice cream in the entire college, we can use the ratio of students who prefer ice cream in the sample to the total number of students in the college.

The total number of students in the college is 4,000, so we can set up a proportion:

81/225 = x/4000

Solving for x, we get:

x = (81/225) * 4000 = 1,440

Therefore, the best prediction for the number of students who prefer ice cream in the entire college is 1,440.

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A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.

Ice Cream Candy Cake Pie Cookies

81 9 72 36 27

Which statement is the best prediction about the scoops of ice cream the college will need?

A. The college will have about 480 students who prefer ice cream.

B. The college will have about 640 students who prefer ice cream.

C. The college will have about 1,280 students who prefer ice cream.

D. The college will have about 1,440 students who prefer ice cream.

Answer:

Z = 2.91

Step-by-step explanation:

Mean:  123

Sample Size:  26

Standard Deviation:  7

x = 127

z = (x - μ) / (σ / [tex]\sqrt{n}[/tex] )

[tex]z=\frac{127-123}{\frac{7}{\sqrt{26} } } \\z= 2.91[/tex]

**If this is a z-table question, then P (x = 127) = P (z = 2.91) = 0.9982.**

Answer:

x = 13.44 (2 d.p.)

y = 13.44 (2 d.p.)

Step-by-step explanation:

The interior angles of a triangle sum to 180°. Therefore, the missing angle of the given triangle is 45°. This means the triangle is a 45-45-90 triangle.

A 45-45-90 triangle is a special right triangle in that the measures of its sides are in the proportion x : x : x√2 where:

As the given triangle is a 45-45-90 triangle, sides x and y are the same length.

As the hypotenuse (side opposite the right angle) is 19 units in length, then x√2 = 19.  To find the length of x (and y), solve for x:

[tex]\implies x\sqrt{2} = 19[/tex]

[tex]\implies \dfrac{x\sqrt{2}}{\sqrt{2}} = \dfrac{19}{\sqrt{2}}[/tex]

[tex]\implies x= \dfrac{19\sqrt{2}}{2}[/tex]

[tex]\implies x=13.44\; \sf units\;(2\;d.p.)[/tex]

Answer: 13/25

Step-by-step explanation:

The calculated volume of the prism with the dimension 6 1/2 cm by 2 1/2 cm by 2 1/2 cm is 325/8 cm³

To find the volume of a rectangular prism, we need to multiply its length, width, and height.

In this case, the length is 6 1/2 cm, the width is 2 1/2 cm, and the height is also 2 1/2 cm.

First, we need to convert the mixed numbers to improper fractions.

6 1/2 = 13/2

2 1/2 = 5/2

Now, we can multiply the three values together to find the volume:

Volume = length x width x height

Volume = (13/2) x (5/2) x (5/2)

Volume = (13 x 5 x 5) / (2 x 2 x 2)

Volume = 325/8

Therefore, the volume of the rectangular prism is 325/8 cm³

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Answer: -1280

Step-by-step explanation:

in a geometric sequence it either multiplies or divides negatively or positively, in this case -5 to -20 is multiplied 4 positively and so is -20 to -80

then -80x4= -320

-320x4= -1280

After answering the provided question, we can conclude that As a result, expression the likelihood that the sample mean book cost of 36 UCF students exceeds $1,278.6 is approximately 0.0427, or 4.27%.

In mathematics, an expression is a collection of symbols, digits, and companies that portray a statistical correlation or formula. An expression can be a single number, a mutable, or a combination of both of them. Addition, subtraction, proliferation, division, and exponentiation are examples of mathematical operators.  Expressions are used extensively in mathematics, including arithmetic, calculus, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification. \

[tex]P(x > 1278.6) = P(z > (1278.6-1245)/(102/36)) P(z > 1.72) = 0.0427 P(z > 1.72) = 0.0427[/tex]

As a result, the likelihood that the sample mean book cost of 36 UCF students exceeds $1,278.6 is approximately 0.0427, or 4.27%.

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Answer:

x-intercept(s):  

(

6

,

0

)

y-intercept(s):

(

0

,

−

9

)

Step-by-step explanation:

The probability that the sum of the numbers when two dice are rolled is an odd number is given as follows:

0.5.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Each dice has six possible outcomes, hence the total number of outcomes when two dice are rolled is given as follows:

6² = 36.

When we look at the pattern of the sum of two dice, from (1,1), (1,2), ..., to (6,6) we see that they alternate between even numbers and odd numbers, hence:

Hence the probability is given as follows:

p = 18/36 = 0.5.

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Answer:

$18 were given to each class

Step-by-step explanation:

90÷5=18

a) After one second in the air, the cannonball's height is:

[tex]h = -16(1)^2 + 128(1) + 6 = 118 feet[/tex]

b) 8 seconds pass while the cannonball is in the air (from when it is fired until it hits the ground).

The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction. Its SI equivalent is the meter per second (ms-1). A body is considered to be accelerating if its velocity changes, either in magnitude or direction.

from the question:

a) We can enter values of t into the equation[tex]h = -16t^2 + 128t + 6[/tex] and evaluate to obtain the height of the cannonball each second after it is shot.

The height of the cannonball at time t = 0 is as follows:

[tex]h = -16(0)^2 + 128(0) + 6 = 6 feet[/tex]

When t = 1, the cannonball has been in the air for 1 second, so its height is:

[tex]h = -16(1)^2 + 128(1) + 6 = 118 feet[/tex]

b) The graph of the function [tex]h = -16t^2 + 128t + 6[/tex] can be used to calculate how long the projectile has been in the air. When the cannonball is six feet above the ground, it is said to be in the air. The values of t must be determined when h is larger than or equal to 6.

Finding the values of t where the graph crosses the line y = 6 is one technique to do this. Another is to graph the function. Another method is to solve for t while setting h = 6:

[tex]-16t^2 + 128t + 6 = 6[/tex]

[tex]-16t^2 + 128t = 0[/tex]

-16t(t - 8) = 0

t = 0 or t = 8

Hence, the cannonball flies for 8 seconds (from when it is fired until it hits the ground).

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Answer:

Step-by-step explanation:

70/33.8=2.07100592

The length οf the diagοnal is 20 feet.

A rectangle is a type οf quadrilateral with parallel sides that are equal tο οne anοther and fοur vertices that are all 90 degrees apart. It is alsο knοwn as an equiangular quadrilateral fοr this reasοn. The term "parallelοgram" can alsο be used tο describe a rectangle because the οppοsing sides are equal and parallel.

Given that 16 feet and 12 feet make up a rectangle.

The diagοnal and twο cοnsecutive sides οf a rectangle make a right-angled triangle.

Tο find the diagοnal apply Pythagοrean theοrem.

The widely accepted geοmetric principle knοwn as the Pythagοrean Theοrem states that the square οn the hypοtenuse οf a right triangle equals the sum οf the squares οn its legs.

Draw a rectangle:

Cοnsider △ABC:

AB² + BC² = AC²

12² + 16² =AC²

AC² = 144+ 256

AC² = 400

Take square rοοt οn bοth sides:

AC = 20

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Width of the table = 3.5 feet , Length of the table = 5.5 feet and Perimeter of the table = 18 feet

What is Rectangle ?

A rectangle is a 2-dimensional shape with four straight sides, where opposite sides are parallel and equal in length. It has four right angles and its diagonals bisect each other. It is a type of quadrilateral, and its area is calculated by multiplying the length and width of the rectangle. It is commonly found in many geometric shapes and everyday objects such as doors, windows, and computer screens.

Let's convert all measurements to the same unit for easier calculation. Since the table width is given in inches, we can convert it to feet by dividing by 12 (since 1 foot = 12 inches).

Table width: 42 inches = 42÷12 = 3.5 feet

Let's denote the length of the table as 'l' feet. The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (Length + Width)

Given that the perimeter is 18 feet, we can substitute the values into the formula:

18 = 2 * (l + 3.5)

Now, we can solve for 'l':

18 = 2l + 7 (distributing 2 to both terms in the parentheses)

2l = 18 - 7 (subtracting 7 from both sides)

2l = 11 (simplifying)

l = 11÷2 (dividing both sides by 2)

Therefore, Width of the table = 3.5 feet , Length of the table = 5.5 feet

and Perimeter of the table = 18 feet

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A written history ​means the writing of history, such as the writing of history based on the critical examination of sources which is also known as historiography.

Also known as recorded history describes the historical events that have been recorded in a written form or other documented communication which are subsequently evaluated by historians using the historical method.

Historiography also includes the theory and history of historical writing. Modern historians strive to reconstruct a record of human activities and gain a deeper understanding of them.

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The expression will give 36 after evaluating.

What is an Expression?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated or simplified. An expression may contain one or more terms, which are separated by operators such as addition (+), subtraction (-), multiplication (*), division (/), and exponentiation (^).

Expressions can represent various mathematical concepts, such as equations, inequalities, functions, and polynomials.

Given:  m = -7 and n = 2,

We know that, the mode function converts the function into positive value.

So, |m - n| = |-7 - 2| = 9

Now,

4 |m - n| = 4 * 9 = 36

So the expression 4 |m - n| evaluates to 36 when m = -7 and n = 2.

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Answer:

2x+15

Step-by-step explanation:

Answer:

2x + 15

Step-by-step explanation:

First, we are doubling x.

We know that doubling is the same thing as multiplying by 2:

2x

Next, we are adding fifteen:

2x + 15

Answer:

The area of the shaded region is 160.2 in² (to the nearest tenth).

Step-by-step explanation:

The area of the shaded region can be calculated by subtracting the area of the inner circle from the area of the outer circle.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a circle}\\\\$A=\pi r^2 $\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]

If the circles have the same center, and the inner circle has a radius of 7 in, then the outer circle has a radius of:

[tex]\implies r = 7 + 3 = 10\; \sf in[/tex]

Therefore, the area of the shaded region is:

[tex]\begin{aligned}\sf Area_{shaded\;region}&=\sf Area_{outer\;circle}-Area_{inner\;circle}\\&=\pi \cdot 10^2 - \pi \cdot 7^2\\&=100\pi - 49 \pi\\&=51 \pi\\& = 160.221225...\\&=160.2\; \sf in^2\;(nearest\;tenth)\end{aligned}[/tex]

The number of smaller card that could be cut from the larger rectangular card is 64.

Yuri has a large rectangular card measuring 1.2 meters by 0.8 meters, he wants to cut it up to make small rectangular cards each measuring 13 cm by 11.5 cm.

Let's convert the units.

1.2 m = 120 cm

0.8 = 80 cm

Therefore, let's find the area of the rectangular card.

area of the large rectangular card = lw

where

area of the large rectangular card = 120 × 80

area of the large rectangular card = 9600 cm²

area of each small rectangular card = 11.5 × 13.5

area of each small rectangular card = 149.5 cm²

Therefore,

largest number of card that can be cut out from the larger card = 9600 / 149.5 = 64.2140468227

largest number of card that can be cut out from the larger card ≈ 64

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The only pair of quadrilaterals that have congruent diagonals is a rectangle and a square, and the answer is C.

These attributes are:

C) A rectangle and a square: A rectangle's diagonals are congruent, and a square's diagonals are also congruent. The solution is C because a square is a particular case of a rectangle in which all sides are congruent.

Hence, a rectangle and a square are the only pair of quadrilaterals with congruent diagonals, and the answer is C.

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The area of the composite figure is the sum of the area of the sector and the triangle . Therefore, the area of the composite figure is 95.52 cm².

This composite figure is created by placing a sector of a circle on a triangle. The area of the composite figure can be found as follows:

The composite figure is a combination of a sector and a right triangle. Therefore, the area of the composite figure is the sum of the area of the sector and the area of the right triangle.

area of the composite figure = area of the triangle + area of the sector

Hence,

area of the composite figure =  1 / 2 bh + ∅ / 360 × πr²

area of the composite figure = 1 / 2 × 6 × 8 + 82 / 360 × 3.14 × 10²

area of the composite figure = 48 / 2 + 25748 / 360

area of the composite figure = 24 + 71.5222222222

area of the composite figure = 95.5222222222

Therefore,

area of the composite figure = 95.52 cm²

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