Which expression is equivalent to (x^-6/x^2)^3
1/x
1/x^5
1/x^9
1/x^24

Answer:

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Step-by-step explanation:

Answer:

[tex]for~x=3[/tex]

[tex]f(x)=-5[/tex]

[tex]So,f(3)=-5[/tex]

Answer:

Step-by-step explanation:

[tex]\frac{9a^{2}-5}{b^{2}+2}+\frac{-2a^{2}+4}{b^{2}+2}=\frac{9a^{2}-5-2a^{2}+4}{b^{2}+2}\\\\=\frac{9a^{2}-2a^{2}-5+2}{b^{2}+2}\\\\=\frac{7a^{2}-3}{b^{2}+2}[/tex]

Given:

Consider the given function is:

[tex]P(t)=4000(1.2)^t[/tex]

To find:

a. The type of exponential function (growth or decay).

b. Percentage change in population.

c. Population after 5 years.

Solution:

a. The general exponential function is:

[tex]P(t)=P_0(1+r)^t[/tex]          ...(i)

Where, [tex]P_0[/tex] is the initial population and r is the rate of change in decimal.

If r<0, then the function represents exponential decay and if r>0, then the function represents exponential growth.

We have,

[tex]P(t)=4000(1.2)^t[/tex]

It can be written as:

[tex]P(t)=4000(1+0.2)^t[/tex]          ...(ii)

On comparing (i) and (ii), we get

[tex]P_0=4000[/tex]

[tex]r=0.2[/tex]

Since r>0, therefore the given function represents exponential growth.

b. From part (a), we have

[tex]r=0.2[/tex]

So, the rate of change in the population is 0.2. Multiply is by 100 to get the percentage change in population.

[tex]r\%=0.2\times 100[/tex]

[tex]r\%=20\%[/tex]

Therefore, the yearly percentage change in population is 20%.

c. We have,

[tex]P(t)=4000(1.2)^t[/tex]

Substitute [tex]t=5[/tex] in the given function to find the population living on the island after 5 years.

[tex]P(5)=4000(1.2)^5[/tex]

[tex]P(5)=4000(2.48832)[/tex]

[tex]P(5)=9953.28[/tex]

[tex]P(5)\approx 9953[/tex]

Therefore, the estimated population living on the island after 5 years is 9953.

Answer:

can can travel 280 miles

Step-by-step explanation:

Answer:

should be 359.18876

Step-by-step explanation:

if you round it to the nearest hundredth it will give you your answer in units

Answer:

5 ÷ 1/3

5 × 3/1

5 × 3

=15

Step-by-step explanation:

the answer is 15

Answer:

Step-by-step explanation:

Answer:

for No1 answer is 0. for no 2 answer is 9.

Step-by-step explanation:

for no 3 answer is 14. no 4 =5,no 5 = 0 ,no 6= -16/3 ,no 7 =-3 ,no 8=180 and no 9 = 3

Answer: g(f)= 2f - The input is f

h(g)=-4+g - The input is g

f(h)=h-7 - The input is h

Step-by-step explanation:

The matches are:

h(g) = -4 + 9 corresponds to input g.

f(h) = h - 7 corresponds to input h.

g(t) = 21 corresponds to input t.

We have to given that,

To Match each function with its input.

h(g) = -4+9

The input is f.

f(h) = h - 7

The input is h.

g(t) = 21

The input is g.

Now, We get;

h(g) = -4 + 9 corresponds to input g.

f(h) = h - 7 corresponds to input h.

g(t) = 21 corresponds to input t.

So the matches are:

h(g) = -4 + 9 corresponds to input g.

f(h) = h - 7 corresponds to input h.

g(t) = 21 corresponds to input t.

Learn more about the function visit:

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Answer:

D

Step-by-step explanation:

YD and TH

TH is in HOT and YD is in DAY

They go from end to the front in the same way

Making a straight line from left to right that are on the same place

the bottom one... i think

Answer:

∠ 1 = 53°, ∠ 2 = 37°

Step-by-step explanation:

let ∠ 2 be x then ∠ 1 = x + 16

Complementary angles sum to 90° , then

x + 16 + x = 90

2x + 16 = 90 ( subtract 16 from both sides )

2x = 74 ( divide both sides by 2 )

x = 37

Then

∠ 2 = 37° and ∠ 1 = 37 + 16 = 53°

Answer:

24-12

Step-by-step explanation:

Answer:

[tex]P=1259.26N/m^2[/tex]

Step-by-step explanation:

From the question we are told that:

Force [tex]F=68N[/tex]

Area [tex]A=540cm^2=0.054m^2[/tex]

Generally the equation for Pressure is mathematically given by

 [tex]P=\frac{F}{A}[/tex]

 [tex]P=\frac{68}{0.054}[/tex]

 [tex]P=1259.26N/m^2[/tex]

5√2

Step-by-step explanation:

By the Pythagorean theorem,

A² + B² = C²

5² + 5² = C²

25 + 25 = C²

C² = 50

C = √50

C = √(2 • 25)

C = √2 x √25

C = √2 • 5

C = 5√2

Answer:

5[tex]\sqrt{2\\}[/tex]

Step-by-step expla

chọn  tam giác ==> cạnh huyền là đường chéo của hình vuông  ảg

sin(∝)= đối / huyền

⇒huyền= đối /sin(45°)

⇒huyền=  5/ sin(45°)

⇒huyền=  5[tex]\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

(-1, 3)

y=3

Answer:

(x + 1, y - 3)

Step-by-step explanation:

The translation is 1 unit right and 3 units down.

Answer:

x+1 y-3

Step-by-step explanation:

Because with any of the points it goes to the right 1 and down 3

Answer:

A = 2π in2

Step-by-step explanation:

See the image I have shared

===================================================

Explanation:

Focusing on triangle ACD, we see that AC = 20 is the hypotenuse and AD =  20/2 = 10 is the short leg. The short leg is half that of the hypotenuse when working with 30-60-90 triangles.

Also, for these types of triangles, the long leg is sqrt(3) times that of the short leg. That makes CD = AD*sqrt(3) = 10*sqrt(3)

The opposite sides are the same length, meaning BC = AD and AB = CD.

-----------

The perimeter of rectangle ABCD is

P = AB+BC+CD+AD

P = 10*sqrt(3) + 10 + 10*sqrt(3) + 10

P = 20 + 20*sqrt(3)

P = 54.6410161513776

P = 54.6 cm is the approximate perimeter

Answer:

54.64 cm

Step-by-step explanation:

The perimeter of a rectangle is the total length of all the sides of the rectangle. Hence, we can find the perimeter by adding all four sides of a rectangle. Perimeter of the given rectangle is a + b + a + b.

Length of CD = 17.32 cm from :

[tex] \sin(60) = \frac{cd}{20} \\ then \: x = 17.32 \: cm[/tex]

now CD = BA

Now we must determine length of AD :

[tex] \sin(30) = \frac{ad}{20} \: then \: ad \: = 10 \: cm[/tex]

Now :

perimeter = 17.32 + 17.32 +10+10 = 54.64 cm

Answer:

8 feet, 256 ft^2

Step-by-step explanation:

The function of the area can be graphically rapresented with a parabola that opens downwards

in this specific case the vertex is the maximum point of the parabola.

(X) Vertex = -64/-8 = 8 feet

(Y) Vertex = -4(64) + 512 = -256 + 512 = 256 ft^2

Answer:

Maximum Width = 8 feet.

Maximum area = 256 ft^2.

Step-by-step explanation:

Part A.

A = -4w^2 + 64w

Finding the derivative:

dA/dw = -8w + 64 = 0  for maxm/minm, so

-8w  = -64

w = 8

The second derivative is -8 so w = 8 gives a maximum.

Part B.

The maximum area = -4(8)^2 + 64*8

= -256 + 512

= 256 ft^2.

Answer:

(D) $1 050

Step-by-step explanation:

Simple interest = 7000 × 3 × 5/100 =

70 x 15 = 1 050

Answer:

C = 32π

Step-by-step explanation:

The circumference (C) of a circle is calculated as

C = 2πr ( r is the radius ) , then

C = 2π × 16 = 32π units

2y + 5 = 3y + 2

=> 5 - 2 = 3y - 2y

= 3 = y

Answer:

y = 3

Step-by-step explanation:

2y + 5 = 3y + 2

2y - 3y + 5 = 3y - 3 y + 2                  [ subtract both sides by 3y ]

- y + 5 = 0 + 2                                  [ 3y - 3y = 0 ]

- y + 5 - 5 = 2 - 5                              [ subtract by 5 on  both sides ]

- y + 0 = - 3                                      [ -5 + 5 = 0 ]

  - y = - 3                      

     y = 3                                          [ divide by - 1 on both sides ]            

Answer:

134.04 cubic units

Step-by-step explanation:

Step 1

Find the Volume of the Sphere

Formula = 4/3πr³

r= radius = 4

Hence,

Volume = 4/3 × π × 4³

= 268.08 cubic units

Step 2

Find the Volume of the cylinder

Formula = πr²h

r = radius = 4

h = Height = Diameter of the sphere

Radius of a sphere = 4

Diameter = Height of cylinder = 2 × r = 2 × 4 = 8

Hence: π × 4² × 8

= 402.12 cubic units

Step 3

The expression that describes the volume of the cylinder that is not occupied by the sphere = Volume of Cylinder - Volume of sphere

= 402.12 cubic units - 268.08 cubic units

= 134.04 cubic units

The expression that describes the volume of the cylinder that is not occupied by the sphere is 134.04 cubic units

We have given radius of sphere is 4

[tex]V= 4/3\pi r^3[/tex]

r= radius

We have given that r=4

[tex]Volume = 4/3 \times \pi \times 4^3[/tex]

V= 268.08 cubic units

[tex]Formula = \pi r^2h[/tex]

r = radius = 4

h = Height = Diameter of the sphere

Radius of a sphere = 4

Diameter = Height of cylinder

= 2 × r

= 2 × 4

= 8

Therefore we get

[tex]V=\pi \times 4^2 \times 8[/tex]

V= 402.12 cubic units

The expression that describes the volume of the cylinder that is not occupied by the sphere = Volume of Cylinder - Volume of sphere

= 402.12 cubic units - 268.08 cubic units

= 134.04 cubic units

Therefore the expression that describes the volume of the cylinder that is not occupied by the sphere is

(402.12  - 268.08) cubic units.

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Answer:

[tex]\displaystyle m = 2[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify points from graph

Point (0, -1)

Point (1, 1)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

Step-by-step explanation:

Answer:

100-89/100=11/100

=0.11

Answer:

Step-by-step explanation:

1- Order in descending order the following polynomial with respect to the

variable n. Then identify the independent term:

[tex]6n^3 + 7n^4 - 2n^2 - 5 + 9n^5[/tex]

The independent term is - 5.  

3- Look at the following polynomial and identify what the terms are

similar:

[tex]- 8 + 3m^3 n - 4m^2n + 7mn^2 - 11nm^3 + 6 m^2 n[/tex]

The similar terms are + 3m^3 n and - 11 nm^3 and

- 4 m^2 n and 6 m^2 n