Hyperbola Question:

Two neighbors who live one mile apart hear an explosion while they are talking on the telephone. One neighbor hears the explosion two seconds before the other. If sound travels at 1100 feet
per second, determine the equation of the hyperbola on which the explosion was located.

(i know the answer is
[tex] \frac{ {x}^{2} }{1210000} - \frac{y {}^{2} }{5759600} = 1[/tex]
but i don't understand how you get it)​

Answer:

14

Step-by-step explanation:

Let's find (f-g)(x)

[tex]3x^{2} + 1 - (1-x)\\3x^{2} + 1 -1 + x\\3x^{2} + x[/tex]

Now let's plug in x=2, so to find (f-g)(2)

[tex]3(2)^{2} + 2\\12 + 2 = 14[/tex]

Answer:

The building is 13.91 m tall

Step-by-step explanation:

The parameters given are;

Angle of elevation to the top of the building = 71°

Angle of depression to the bottom of the building = 26°

Height of the man = 2  m

Therefore, the sight of the man, the man's height, and the distance of the man from the building forms a triangle where:

The hypotenuse side = The sight of the man to the bottom of the building

Hence;

In ΔABC, A being at the eye level or head level of the man, B at the foot and C at the bottom of the building

∴ ∠A + Angle of depression to the bottom of the building = 90°

∠A = 90° - 26° = 64°

∠B = 90° and ∠C = 26° (Sum of angles in a triangle)

[tex]Tan(C) = \frac{AB}{BC}[/tex]

Distance of the man from the building = BC

[tex]Tan(26) = \frac{2}{BC}[/tex]

[tex]BC= \frac{2}{ Tan(26) } = 4.1 \, m[/tex]

Given that the angle of elevation to the top of the building = 71°, we have;

ΔAET

Where:

A is at the head level of the man,

E is the point on the building directing facing the man and

T is the top of the building

Hence AE = BC and ∡TAE = 71°

TE + AB= The height of the building

[tex]Tan(TAE) = \dfrac{TE}{AE}\\\\Tan(71) = \dfrac{TE}{4.1}[/tex]

∴ TE = tan(71°) × 4.1 = 11.91 m

Hence the height of the building = 11.91 + 2 = 13.91 m.

Answer:

Equation;

(3/4)x = 2/3

Solving;

x = 8/9

she would need 8/9 of her sugar to make a full batch.

Step-by-step explanation:

Let x represent the amount of sugar that would be needed to make the whole batch.

Given that;

Pia used 2/3 of her sugar to make 3/4 of a batch of cookies.

Since 2/3 of her sugar is needed to make 3/4 of a batch of cookies, then;

(3/4)x = 2/3

Solving the equation, dividing both sides by 3/4;

(3/4)x ÷ 3/4 = 2/3 ÷ 3/4

x = 2/3 × 4/3

x = 8/9

Therefore she would need 8/9 of her sugar to make a full batch.

Answer:

Step-by-step explanation:

Let the number be x

Therefore the expression is 2(x-5)

Hope this helps

Plz mark it as brainliest!!!!

Answer:

2(x-5)

Step-by-step explanation:

x = number

then you subtract 5 from that number so that would look like

x-5

Then you double the result so then it would end up being:

2(x-5)

Please mark me brainliest :)

Answer:

Option A shows the image of RST after the rotation

Step-by-step explanation:

Coordinates of S=(1,3)

Coordinates of R = (-2,1)

Coordinates of T = (-1,7)

We are given that after rotation(x,y)→(y,-x)

So, The new coordinates after rotation will be :

Coordinates of S'=(3,-1)

Coordinates of R'= (1,2)

Coordinates of T'= (7,1)

These are the coordinates of triangle of Option A

So, Option A is true .

Hence Option A shows the image of RST after the rotation

A. shows the image of RST after the rotation.

In the geometry, an equilateral triangle is the triangle in which have all 3 sides have same length. an equilateral triangle is also equiangular; that is, all 3 internal angles are also congruent to each other and are each 60 degrees It is also a regular polygon, so it is also referred to as the regular triangle.

Which plane does the triangle RST belong to?

The XY-coordinate plane or triangle RST are equilateral. Points R or In the x y -coordinate plane, triangle R S T is equilateral. Points R and T had coordinates ( 0, 2) and ( 1, 0), respectively.

Coordinates of S=(1,3)

Coordinates of R = (-2,1)

Coordinates of T = (-1,7)

We are given that after rotation(x,y)→(y, -x)

So, The new coordinates after the rotation will be :

Coordinates of S'=(3,-1)

Coordinates of R'= (1,2)

Coordinates of T'= (7,1)

These are the coordinates of the triangle of Option A

So, Option A is true.

Hence Option A shows the image of RST after the rotation.

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Answer:

2

Step-by-step explanation:

You are trying to find (f' o f)(2).  This means that you need to put f(x) into f'(x) and solve for 2.

First, find f'(x).  To do this, take the original function and switch the x and y values.

y = 2x⁵ + 12

x = 2y⁵ + 12

x - 12 = 2y⁵

(x - 12)/(2) = y⁵

y = ⁵√(x - 12)/(2)

Now, you need to put f(x) into the inverse function through the x-value.  Simplify completely.

y = ⁵√((2x⁵ + 12) - 12)/(2)

y = ⁵√((2x⁵)/(2)

y = ⁵√x⁵

y = x

Now plug in the value given to you.

(f⁻¹ o f)(2) = 2

The answer is 2.

Answer:

It'd be $4,700

Step-by-step explanation:$500 + $2,400 + $1,800 = $4,700. Minus that amount from her savings account total and that's how much money she has left.

Answer:

15$

Step-by-step explanation:

cost of 1 cookie = 10/6

cost of 9 cookies = 9* 10/6 = $15

Answer:

15 dollars

Step-by-step explanation:

6 cookies for 10 dollars

3 cookies for 5 dollars.

6+3 cookies for 10+5 dollars

Answer:

Option D is the correct answer

Step-by-step explanation:

Since, dimensions of both the matrices are different. Hence we can't add them.

Answer:

None are equivalent

Step-by-step explanation:

Answer: 1600

Step-by-step explanation:

2(8+2x6)

2(8+12)

2(20)

40

[tex]40^{2}[/tex]

1600

Mark me as the brainiest answer.

you have two walls that are  10 by 7.5 so 75 feet ^2 in area each

you have another two walls that are 14 by 7.5  so 105 feet^ 2 each

so all of that together is 360 feet^2 to cover for one coating, so you have 720 feet^2 to cover for 2 coats on the walls. so take that and divide it by the area that one gallon would cover, then round up giving you how many gallons you would have to buy

for the ceiling you do the same, the area is 140 and you only need one coat

Answer:

36.87°

Step-by-step explanation:

With reference angle C

perpendicular (p) = 27

base(b) = 36

Now

Tan C = p/b

Tan C = 27/36

C = tan ^-1( 27/36)

= 36.87°

Hope it helps

:)

Answer:

36.87

Step-by-step explanation:

Answer:

47.8

_____

1

Step-by-step explanation:

Answer:

she got it by breaking up the problem step by step  for

Step-by-step explanation:

she has done this putting the form like so

10 - 478

I hope this

Answer:

Step-by-step explanation:

4) (-2,3)   ;  (-1,-2)

[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{-2-3}{-1-[-2]}\\\\=\frac{-5}{-1+2}\\\\=\frac{-5}{1}\\\\=-5[/tex]

5) line is parallel to x-axis. So, slope= 0

6) (1,1) ;  (-2, -1)

[tex]Slope=\frac{-1-1}{-2-1}\\\\=\frac{-2}{-3}\\\\=\frac{2}{3}[/tex]

Answer: [tex]y=-\frac{3}{4} x+3.5[/tex] or [tex]y=-\frac{3}{4}x+\frac{7}{2}[/tex]

Step-by-step explanation:

A parallel line has the same slope and different y-intercepts.

Let's change our equation to slope-intercept.

[tex]3x+4y=12[/tex]

[tex]4y=12-3x[/tex]

[tex]y=\frac{12-3x}{4} =3-\frac{3}{4}x[/tex]

[tex]y=3-\frac{3}{4} x[/tex]

Now that we know our slope is -3/4, we know the equation will have -3/4 as the slope. Let's leave b blank so that we can find the y-intercept of the parallel line.

[tex]5=-\frac{3}{4}(-2)+b[/tex]

[tex]5=\frac{3}{2} +b[/tex]

[tex]3.5=b[/tex]

Our parallel equation is [tex]y=-\frac{3}{4}x+3.5[/tex] or [tex]y=-\frac{3}{4} x+\frac{7}{2}[/tex]

Answer:

[tex]42.7\,\,cubic\,\, meters[/tex]

Step-by-step explanation:

Given: Perimeter of base of a pyramid = 12.8 m

Height of the pyramid = 12.5 m

To find: volume of a pyramid

Solution:

Perimeter of base of a pyramid = 12.8 m

As base of the pyramid is a square,

12.8 = [tex]4(side\,\,of\,\,a\,\,square)[/tex]

side of a square = [tex]\frac{12.8}{4}=3.2\,\,m[/tex]

Area of a square (A) = [tex](side\,\,of\,\,a\,\,square)^2=(3.2)^2=10.24\,\,m^2[/tex]

Height of the pyramid (h) = 12.5 m

Volume of the pyramid = [tex]\frac{Ah}{3}=\frac{1}{3}(10.24)(12.5)=42.7\,\,cubic \,\,meters[/tex]

Answer:

3.06

Step-by-step explanation:

[tex]\log_{5}(\dfrac{2}{3}x-2)+2=0\\\\\log_{5}(\dfrac{2}{3}x-2)=-2\\\\[/tex]

This means that 5 to the power of -2 is [tex](\dfrac{2}{3}x-2)[/tex], meaning that:

[tex]\dfrac{2}{3}x-2=5^{-2}=\dfrac{1}{25} \\\\\dfrac{2}{3}x=\dfrac{51}{25} \\\\2x=\dfrac{153}{25} \\\\x=\dfrac{153}{50}=3.06[/tex]

Hope this helps!

Answer:

42 feet.

Step-by-step explanation:

h=-10t² + 40t +2

The vertex of the quadratic function described by the equation is located at

 t = -(40)/(2(-10)) = 2

Next is to find the value of height at t=2 will be

 h = -10(2²) +40(2) +2 = -40 +80 +2 = 42feet

The maximum height is 42 feet.

Answer:

6

Step-by-step explanation:

The measure of the missing side of the given parallelogram with an area of 30 unit² will be 6 units.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram.

There are 4 types of parallelograms, including 3 special types. The four types are parallelograms, squares, rectangles, and rhombuses.

The area of a parallelogram is given as (1/2) × (sum of parallel sides) × (distance between parallel sides).

Area = (1/2) × (5 + 5) × h

30 = 10h/2

5h = 30

h = 6 units.

Hence "The measure of the missing side of the given parallelogram with an area of 30 unit² will be 6 units".

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Given the question missing the figure attached below,

Answer:

A

Step-by-step explanation:

Given

x + yi + 6i = 2 ( subtract 6i from both sides )

x + yi = 2 - 6i → A

Answer:

l=5.12 & w=2.62

Step by step explanation:

A=l×w

13.42=lw

w=13.42/l

[tex]p = 2(l + w) \\ 16.6 = 2(l + \frac{13.42}{l} ) \\ 16.6 = 2( \frac{ {l}^{2} + 13.42}{l}) \\ 16.6 = 2(l + 13.42) \\ 16.6 = 2l + 26.84 \\ 2l = 26.84 - 16.6 \\ 2l = 10.24 \\ l = \frac{10.24}{2} \\ l = 5.12km[/tex]

Since you have found the value of the length you can find the value.of the width.

[tex]w = \frac{13.42}{l} \\ w = \frac{13.42}{5.12} \\ w = 2.62km[/tex]

Given Information:

Volume of candle = V = 75 in³

Height of candle = h = 6 in

Required Information:

Radius of candle = r = ?

Answer:

Radius of candle = r = 2 in

Step-by-step explanation:

Recall that the volume of a cylindrical shape is given by

[tex]V = \pi \times r^{2} \times h[/tex]

Where V is the volume, r is the radius and h is the height

Re-arrange the above equation for radius

[tex]r^{2} = \frac{V}{\pi \times h} \\\\r = \sqrt{\frac{V}{\pi \times h}}[/tex]

Now substitute the given values into the above equation

[tex]r = \sqrt{\frac{75}{\pi \times 6}}\\\\r = 1.99 \: in[/tex]

Rounding to the nearest inch

[tex]r = 2 \: in[/tex]

Therefore, the radius of this candle is 2 inches.

Answer:125.66cm

Step-by-step explanation:

Circumference formula is C=2pi (r)

So C=2(pi or 3.14) (20)

Just plug the 20 (radius for the r) and you have the answer.

Answer:

4 cm and 2cm

Step-by-step explanation:

Volume of the rectangular prism is 10.5 cm³.

Rectangular prism is a three dimensional shape which consist of six faces. The two faces are at the top and bottom and the other faces are lateral faces.

Given three dimensions of a rectangular prism as given below in the image.

Length = 3 cm

Width = 7/4 cm

Height = 2 cm

Volume of a rectangular prism = Length × Width × Height

                                                   = 3 × 7/4 × 2

                                                   = 3 × 7/2

                                                   = 10.5 cm³

Hence the volume of the rectangular prism is 10.5 cm³.

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Answer:

2291

Step-by-step explanation:

Given: Radius of a city's town hall is equal to 5-mile and about 180,000 people live in a city's town hall

To find: population density per square mile

Solution:

Population density refers to the number of people per unit of area.

Let r denotes radius of the town hall = 5 miles

Area of the town hall = [tex]\pi r^2=\pi (5)^2=25\,\pi[/tex] square miles

Population density per square mile = Population of a city's town hall/area of the town hall = 2290.9 [tex]\approx 2291[/tex]

Answer:

-6

Step-by-step explanation:

(2x + 4) – (3x + 6)

Distribute the minus sign

2x +4 -3x -6

-x -2

Let x = 4

-4-2

-6

Answer:

-6

Step-by-step explanation:

(2x + 4) – (3x + 6) =

= 2x + 4 - 3x - 6

= -x - 2

= -(4)  2

= -6

Answer:

1/5 =  0.2

0.3 = 1/3

1/2 = 0.5

Answer:

1/5 =0.2

3/10 = 0.3

1/2 =0.5

Answer:

1,5

Step-by-step explanation:

1,5 is located within the shaded region.