What is the equation of a hyperbola with a = 1 and c = 9? Assume that the transverse axis is horizontal.

Answer:

[tex]\frac{11^{4} }{11^{11} } ,\frac{1}{11^{-4} }, 11^{5}*11^{2}, (11^{-3})^{-3}[/tex]

Step-by-step explanation:

For this, you need to know the rules of exponents:

If the coefficient is the same, you can do things to it (which I will get into)

In this case, all the coefficients are 11, so we don't have to worry about the coefficients being different.

For the first one, you can subtract the denominator exponent by the numerator exponent like so:

[tex]11^{4} * 11^{-11} = 11^{-7}\\[/tex]

(When you multiply, you add the exponents)

Also, the rule is: [tex]x^{-y} = \frac{1}{x^{y} }[/tex] or [tex]\frac{1}{x^{-y} } = x^{y}[/tex]

For the second one, you can use the rule mentioned before:

[tex]\frac{1}{11^{-4} } = 11^{4}[/tex]

For the third one, you want to multiply the exponents (in these kinds of cases, you can multiply the exponent by the exponent)

So:

[tex](11^{-3} )^{-3} = 11^{9}[/tex]

Finally, the fourth one, you can simply just add the exponents:

[tex]11^{5} * 11^{2} = 11^{7}[/tex]

Then, just order them from least to greatest by their exponents value :)

Answer:

[tex]x=2; y=1[/tex]

Step-by-step explanation:

Let's remember that if we replace one equation in a system with a linear combination of the equations (ie adding or subtracting them together, after multiplying them with some nice numbers) we are left with an equivalent system. So let's add and subtract them together, and use the new equations to work with.

[tex]I+II: 2x+2y=6\\I-II:200x-200y=200[/tex]

Better, now let's simplify the expression and let's use the new system

[tex]x+y=3\\x-y=1[/tex]

Done. At this point you can use whatever method you like to solve the system to get to the final solution. Adding and subtracting works great, and you get [tex]x=2, y=1[/tex] which, if you check by replacing in the original, is indeed a valid solution.

Answer:

24 cubic inches

Step-by-step explanation:

Volume is side x side x side. You already have done side x side so it is just side x area.

Answer:

Step-by-step explanation:

when  3(2x^2+4x+7)−(x^2−8x+11) is solved you get

5x^2 + 20x + 10.

the x term is

−

2

+

√

2

,

0

)

,

(

−

2

−

√

2

,

0

)

[tex]3(2x^2+4x+7)-(x^2-8x+11)\\\\=6x^2 +12x + 21 -x^2+8x -11\\\\=5x^2+20x +10\\\\\text{The coefficient of the x term is 20}[/tex]

g(f(x)) = x

What is inverse function?

An inverse function is defined as a function, which can reverse into another function.

[tex]f(x)= \frac{(x + 5)}{(2x + 1)}[/tex]

[tex]g(x)= \frac{(5 - x)}{(2x - 1)}[/tex]

 [tex]g(f(x))=g( \frac{(x+5)}{(2x +1)})[/tex]

Substitute the value of f(x),

[tex]g(f(x))= \frac{(5 - \frac{(x + 5)}{(2x + 1)})}{(2 \frac{(x + 5)}{(2x + 1)} - 1)}[/tex]

[tex]g(f(x))= \frac{\frac{10x+5-x-5}{2x+1} }{ \frac{2x+10-2x-1}{2x+1}}[/tex]

[tex]g(f(x)) = \frac{9x}{9}[/tex]

g(f(x)) = x

Hence, g(f(x)) = x

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Step-by-step explanation:

the area of a rectangle is length × width.

in our case

37 × 18 = 666 ft²

so, we need 666 ft² of tiles.

Answer:

666 square feet

Step-by-step explanation:

To find the number of square feet of tile, we need to find the area:

A = L × W

A = 18 × 37

A = 666 ft²

Answer:

Her average speed would be 62 mph.

Step-by-step explanation:

Step 1. Do 186 divided by 3
Step 2. The answer you would get is 62
Step 3. Label to get 62 miles per hour (mph)
I hope that this helps! :)

Step-by-step explanation:

Displacement = 186 miles

Time taken = 3hours

Average speed = ?

Now,

[tex]average \: speed = \frac{total \: distnce}{total \: time \: } \\ = \frac{186}{3} \\ [/tex]

= 62 miles per hour

The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.

Area is the amount of space occupied by a two dimensional shape or object.

The area of a circle is given by:

Area = π * diameter²/4

The rug has an area of 40 square feet. Hence:

40 = π * diameter²/4

Diameter = 7.14 feet

The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.

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Answer:

5 startrood 3 endroot units .

The length of YA from the figure is 10√3 units

According to the pythagoras theorem;

YZ² = AZ² + YA²

Given that YZ = 2AZ, hence;

20²  = 10² + YA²

YA²  = 400 - 100
YA²  = 300

YA = √300

YA = 10√3 units

Hence the length of YA from the figure is 10√3 units

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Answer:

Step-by-step explanation:

The value of x in the triangle is 205.24 calculated by using tan function.

By using tan function we find the value of x.

Let us divide x to two parts which includes two right triangles.

We know than tan function is a ratio of opposite side and adjacent side.

tan 55 = 106/adj

adj= 106/1.428

adj=74.22

Now let us find the adjacent side length of larger triangle similarly.

tan 39  = 106/ adj

0.809 = 106/adj

adj=106/0.809

adj=131.025

So the value of x is 74.22+131.025

=205.245

Hence, the value of x in the triangle is 205.24.

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✰ Given Information :-

⠀

⠀

✰ To Find :-

⠀

⠀

✰ Formula Used :-

⠀

[tex] \qquad \star \: \red{ \underline{ \boxed{ \sf Time = \dfrac {Distance} {Speed} }}} \: \star[/tex]

⠀

✰ Solution :-

⠀

Putting the values in the formula, we get,

⠀

[tex] \sf \longrightarrow Time = \dfrac{80 }{32} \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = \cancel{\frac{80}{32} } \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = \dfrac{10}{4} \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = 2.5 \: hrs \\ \\ [/tex]

Thus, the time taken to travel 80 km with that speed is 2.5 hours.

⠀

[tex] \underline{ \rule{227pt}{2pt}}[/tex]

⠀

Answer: 5/2

Step-by-step explanation:

Answer: 19

Step-by-step explanation:

As per the model created by Jack; f(x) determines the area and x represents length so f(3) = 9+9+1

Therefore, f(3) = 19

Answer:

x = 35°

Step-by-step explanation:

sin x = cos (90° - x)

sin 55° = cos (90° - 55°)

sin 55° = cos 35°

x = 35°

Answer:

2

Step-by-step explanation:

[tex] \frac{8x}{4x - 7} - \frac{14}{4x - 7} \\ \\ = \frac{8x - 14}{4x - 7} \\ \\ = \frac{2 \cancel{(4x - 7)}}{\cancel{(4x - 7)}} \\ \\ = 2[/tex]

Set up:-

Solution:-

Here it's a cuboid

Volume:-

[tex]\\ \rm\rightarrowtail V=LBH[/tex]

[tex]\\ \rm\rightarrowtail V=6.5(4)(12.5)[/tex]

[tex]\\ \rm\rightarrowtail V=325ft^3[/tex]

For cubes

Volume:-

[tex]\\ \rm\rightarrowtail V=side^3[/tex]

[tex]\\ \rm\rightarrowtail V=(0.25)^3[/tex]

[tex]\\ \rm\rightarrowtail V=0.015625ft^3[/tex]

Now

Total cubes:-

[tex]\\ \rm\rightarrowtail \dfrac{325}{0.015625}[/tex]

[tex]\\ \rm\rightarrowtail 20800cubes[/tex]

Answer: 8.

Step-by-step explanation: There are 4 sizes, so let's say that the sizes are small, medium, large, and extra large.  There are 2 flavors, so let's say that the flavors are chocolate and vanilla.  The possible combinations are below:

As you can see, there are 8 possible combinations that she can choose from as far as 4 sizes and 2 flavors go.

Have a great day! :)

Hey there!

Here's what happens to the coordinates of a point when it's reflected around the x-axis:

(x, y) --> (x, -y) or (x, -y) --> (x, y)

So the point's x-coordinate hasn't changed.

Here's what happens to the coordinates of a point when it's reflected around the y-axis:

(x, y)--> (-x, y) or (-x, y) --> (x, y)

So the point's y-coordinate hasn't changed.

Hope everything is clear.

Let me know if you have any questions!

Always remember: Knowledge is power!

Answer:

B

Step-by-step explanation:

62x4=248

4x2=8

6x4=24 and carry the 0 and get 240

240+8=248 and you get B

B for question 12

B for question 13

Step-by-step explanation:

U = Union

n= intercestion

B'= not b

A"= not a

so AnB'

should be B

if 2.50 = 1

2.50x8=

20

1×8 =

8

should be $8

Answer: sqrt(285)

Step-by-step explanation:

Answer:

y = -3

Step-by-step explanation:

y = | x | - 4

y = | -1 | - 4

y = 1 - 4

y = -3

Comment any questions!

Let's see

[tex]\\ \rm\rightarrowtail 1-sinx\neq 0[/tex]

[tex]\\ \rm\rightarrowtail sinx\neq 1[/tex]

[tex]\\ \rm\rightarrowtail x\neq \dfrac{n\pi}{2}[/tex]

So

[tex]\\ \rm\rightarrowtail Domain\in R-\left\{\dfrac{n\pi}{2}\right\}[/tex]

Step-by-step explanation:

the volume of this object is the sum of the volume of the 2 blocks.

the large block is a cube of 4×4×4 = 64 ft³

the small block is 1×1×2 = 2 ft³

so, in total, he can fit 64+2 = 66 ft³ of plaster into the mold.

$7,015.11

Depth meanings:

[tex]\sf P = \dfrac{A} { (1 + \dfrac{r}{n})^{nt}}[/tex]

[tex]\rightarrow \sf P = \dfrac{12,158.10} { (1 + \dfrac{3.7\%}{2})^{(2)(15)}}[/tex]

[tex]\rightarrow \sf P = \dfrac{12,158.10} { (1 + \dfrac{0.037}{2})^{(2)(15)}}[/tex]

[tex]\rightarrow \sf P = 7015.113646[/tex]

Answer:

C

Step-by-step explanation:

Okay, the catch of this question is that they do a very good job of explaining Maria's age in terms of George's age, but they leave George's age in terms of Maria's all up to you.

First start off by doing an expression of what they explicitly give you. Maria's age in terms of George's age.

Let's use variables g, representing George's age and m representing Maria's age

m = 2g + 3

Okay, this is all dandy and all, but they ask us for George's age in terms of Maria's, so we need to isolate for g.

subtract the 3 from both sides, like so:

m - 3 = 2g

then divide 2 from both sides: (remember we're dividing the whole thing)

(m-3)/2 = g

Now we have an expression for George's age in terms of Maria's.

g = (m-3)/2 or [tex]g = \frac{m-3}{2}[/tex]

The answer that gives us this, is C.

Answer:

MQ = 16.4

By the Parallelogram Diagonals Theorem , MP = PQ

So MQ = 2 · MP

Step-by-step explanation:

Parallelogram Diagonals Theorem

The diagonals of a parallelogram bisect each other, i.e. they divide each other into two equal parts.

P is the point of intersection of the diagonals.

Therefore, MP = PQ and LP = PN

If MP = 8.2, then PQ = 8.2

⇒ MQ = 8.2 + 8.2 = 16.4

The value of x in the special right triangle is 39.60 ft.

Right angle triangle has one of its angles as 90 degrees. The side and angles can be found using trigonometric ratios.

Therefore, let's find the base of the triangle with 30 degrees.

sin 30° = opposite / hypotenuse

1 / 2 = 7 / b

b = 14 ft

Let's use the value(14 ft) to find the height of the biggest triangle.

sin 30 = opposite / hypotenuse

sin 30 = 14 / h

0.5h = 14

h = 14 / 0.5

h = 28 ft

Therefore, let's find the value of x .

sin 45° = 28 / x

x = 28 / 0.70710678118

x = 39.5979797464

x = 39.60 ft

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The area of the rectangular base is the amount of space on the rectangular base

The area of the rectangular base is 60 square inches

The question is incomplete; as the diagram is not given.

So, I will apply the concept of similar shapes to determine the area of the rectangular base

To determine the area of the rectangular base, we make use of the following equivalent ratio:

Ratio = Height : Area

This gives

3 : 36 = 5 : Area

Express as fraction

36/3 = Area/5

Evaluate the quotient

12 = Area/5

Multiply both sides by 5

Area = 60

Hence, the area of the rectangular base is 60 square inches

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