What is the simplified base of the function f(x)=1/4([tex]\sqrt[3]{108} ^{x\\}[/tex])

The function is an exponential function; the initial value is -6.1 and the base is 3

The equation of the function is given as:

y = -6.1 *(3^x)

An exponential function is represented as:

y = ab^x

Where:

Initial value = a

base = b

By comparison, we have

a = -6.1 and b = 3

Hence, the function is an exponential function; the initial value is -6.1 and the base is 3

Read more about exponential function at:

https://brainly.com/question/11487261

#SPJ1

25

The angle sum theory says that the sum of all the interior angles in a triangle is 180 degrees.

Finding X

To solve for y, we must first find x. This way we know 2 of the interior angles. Luckily, angle x is a part of a linear pair.

Angle x and the angle with a measurement of 115 form a linear pair. Thus, we can create an equation to find x.

By subtracting 115 from both sides we know that x = 65.

Solving for Y

Now that we know x, we can find y. We know that one of the interior angles is 65 and that the other is 90 degrees. The square marking the bottom angles in the middle show that they are right angles.

Lastly, we can create a formula to find y with the angle sum theory.

Combine like terms

Subtract 155 from both sides

This means that the angle y is 25 degrees.

Answer:

14x^7-56x^6=9

Step-by-step explanation:

distribute

(7x^2)(2x^3 +6)(x^2 -4 * 9=x)

(2x^3+6)(x^2 -4 * 9=x)=2x^5-8x^4=9

(7x^2)(2x^5-8x^4=9)

14x^7-56x^6=9

If the square pyramid has side length 9 inches and volume of 270 inches cube then by putting the values within the formula of volume height are going to be 10 inches.

Given Length and volume of a square pyramid are 9 inches and 270 inches cube. Square pyramid is the pyramid having square base. It is a right square pyramid.

We know that the amount of square pyramid is 1/3 *[tex]l^{2} *h[/tex]

Put the values in formula to induce the values oh h.

Volume=1/3*[tex]9^{2}*h[/tex]

270=1/3* 81*h

h=(270*3)/81

h=810/81

h=10

Hence the peak of the square pyramid having length 9 inches and volume of 270 inches cube is 10 inches.

Learn more about volume at https://brainly.com/question/1972490

#SPJ10

The original dimensions of the metal sheet are 22 inches by 52 inch

The volume is defined as the space occupied by any object in three dimensions. For a rectangular box, the volume will be calculated by multiplying the length, width, and height of the object.

If the Width of the metal = x

The length is 30 inches longer than its width= x+30

If Squares with sides 6 in long are cut from the four corners and the flaps are folded.

The length of the pre-folded box =x+30-12=(x+18)inch

The width of the pre-folded box = (x-6-6)inch = (x-12) inch

The height of the flap= 6 inch

The volume of the box = 2400-inch cubed

Volume of a Cuboid = LWH

6(x-12)(x+18)=2400

6x²+36x-1296=2400

6x²+36x-1296-2400=0

6x²+36x-3696=0

6(x-22)(28+x)=0

x-22=0 or x+28=0

Therefore the original dimensions of the metal sheet are 22 inches by 52 inch

The complete question with correct data is given below:-

A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 2400 incubated​what were the original dimensions of the piece of​ metal?

To know more about volume follow

https://brainly.com/question/46030

#SPJ1

The interest based on the information given is $2564.

From the information given, the following can be deduced:

Principal = $36900

Time = 178 days

Rate = 14.25%

The simple interest will be:

= (PRT)/100

= (36900 × 14.25 × 178/365)/100

= $2564

Learn more about interest on:

brainly.com/question/26011426

#SPJ1

Answer: 132 million

Exponential growth formula: [tex]P=A e^{rt}[/tex]

[P is final amount, A is initial amount, r is growth rate, x is time intervals]

To find growth rate:

[tex]112 = 107 e^{r(3)}[/tex]

[tex]3r= ln(112/107)[/tex]

[tex]r= ln(112/107)/3 = 0.01522334561[/tex]

Population in 2008:

[tex]P_{2008}=107 e^{(0.01522334561(14))}[/tex]

[tex]P_{2008}=132.4169522[/tex]

[tex]P_{2008}=132\:million \quad (rounded \:to\:nearest\:million)[/tex]

Answer:

52m

Step-by-step explanation:

rhombus

its like a slanted square

all its 4 sides are equal like a square

both pairs of opposite sides are parallel

when the diagonals criss cross they make 4 triangles inside

the sides of the rhombus become the hypotenuse of a triangles inside

if the diagonal is 24 and 10 then

its radius is 12 and 5

the sides of the rhombus become the hypotenuse of a triangle that have the sides 12 and 5

hypotenuse of a triangle that has the sides 12 and 5 is

13

(its a special triangle: its a 5, 12, 13 right triangle)

13 times 4 is 52

Answer:

See below

Step-by-step explanation:

P = 4pir^2 l     divide both sides by  4 pi r^2

l  =  P /(4pir^2)

Answer:

Step-by-step explanation:

The value of a and b are 5.5 and 11.0.

The sides a and b of the triangle can be found as follows:

∠B = 29°

c = 11

∠C = 75°

∠A = 180 - 75 - 29 = 76°

Using sine ratio,

b / sin 29° = 11 / sin 75

b sin 75 = 11 sin 29

b =  11 sin 29 / sin 75

b = 5.33290582271 / 0.96592582628

b = 5.51816958277

b = 5.5

Let's find a,

a / sin 76 = 11 / sin 75

a sin 75 = 11 sin 76

a = 11 sin 76 / sin 75

a = 10.673252989 / 0.96592582628

a = 11.0466922042

a = 11.0

learn more on triangle here: https://brainly.com/question/3649623

#SPJ1

Answer:

  62,400 J

Step-by-step explanation:

As the problem statement tells you, the work done to lift the mass is the product of the force applied and the distance the mass is lifted. Here, the force decreases as the height of the mass increases.

For x meters of exposed cable, the force required to lift it is 3x newtons. The force required to lift the object is 1500 newtons, so the total force required to lift the masses an incremental distance (dx) is (3x +1500) newtons.

The work done lifting the mass that distance is the product of force and distance. The total work done is the integral of the incremental work over the total of distance lifted:

  [tex]\displaystyle W = \int_0^{40}(3x+1500)\,dx[/tex]

The value of the integral is ...

  [tex]\displaystyle W=\left.\left(\dfrac{3}{2}x^2+1500x\right)\right|_{x=0}^{x=40}=40\left(\dfrac{1}{2}(3\cdot40)+1500\right)=62\,400\qquad\text{joules}[/tex]

The work done to lift the cable and weight is 62,400 joules.

__

Additional comment

One reason for writing the integral evaluation this way is to demonstrate that the total of work done is that required to lift the weight (1500 N, 40 m) and that required to lift the center of mass of the cable (120 N, 20 m).

This will generally be the case for "disappearing mass" or "increasing distance" problems. Pumping from a pool is a similar kind of problem with a similar kind of solution.

Effectively, you're doing work on the center of mass of the system, moving it from its initial position to the top of the building.

Answer:

If a numbed substitutes x in f (x), you must substitute that number in the function for x.

Step-by-step explanation:

f(5) = 3(5) + 2

f(5 )= 17

Answer:

[tex]y=-\frac{3}{2}x-3[/tex]

Step-by-step explanation:

The slope-intercept form is written as y= mx +c, where m is the slope and c is the y-intercept.

For the equation to be in the slope-intercept form, first leave the y term on the left-hand side of the equation and bring the rest to the right-hand side.

2y= -3x -6

Ensure that the coefficient of y is 1. In this question, we can divide both sides of the equation by 2 to achieve the slope-intercept form.

[tex]y=\frac{-3x}{2}-\frac{6}{2}[/tex]

Simplify:

[tex]\bf{y=-\frac{3}{2}x-3 }[/tex]

Additional:

For more questions on slope-intercept form, do check out the following!

Answer: 105

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so

[tex]\frac{x}{14}=\frac{97.5}{13}\\\\=\frac{x}{14}=7.5\\\\x=\boxed{105}[/tex]

The numerator for the following rational expression is 13

The rational expression is given as:

6/t + 7/t

Take the LCM of the denominator;

The LCM of t and t is t

So, we have:

6/t + 7/t = (6 + 7)/t

Evaluate the sum

6/t + 7/t = 13/t

13 is the numerator, while t is the denominator

Hence, the numerator for the following rational expression is 13

Read more about rational expression at:

https://brainly.com/question/19585906

#SPJ1

Answer:yes

15x times 2=30x

15x times 3= 45x

3y tines 2 =6y

3y times 3=9y

Step-by-step explanation:

The shaded region shown in the graph of the normal distribution corresponds to P(x < 92.5).

An equation is an expression that shows the relationship between two or more numbers and variables.

The z score shows by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean)/standard deviation

The diagram represents z < 1.5 mean = 100, standard dev = 5 hence:

-1.5 = (x - 100)/5

x = 92.5

The shaded region shown in the graph of the normal distribution corresponds to P(x < 92.5).

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

The speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.

Step-by-step explanation:

Let’s assume the speed of the plane =x miles/hr

And let the speed of wind =y miles/hr

So, the speed of the aeroplane in the direction of wind =(x+y) miles/hr

Speed of the aeroplane in the opposite direction of wind =(x–y) miles/hr

We know that, distance=speed×time

Then according to the given conditions, we have

3300=(x+y)×(3+(18/60))

here convert 18mins to hour by dividing by 60 and add to 3hrs.

⇒x+y= 3300/3.3

⇒x+y=1000 … (i)

And,

3300=(x-y)×(4+(24/60))

here convert 24mins to hour by dividing by 60 and add to 4hrs.

⇒x-y= 3300/4.4

⇒x-y=750 … (ii)

Adding equation (i) and (ii), we get

2x=1750

⇒x= 1750/2

=875

Substituting the value of x in equation (ii), we get

875−y=750

⇒y=875-750

⇒y=125

Therefore, the speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.

The value of the probability P(S or T) is 39%

The probability values are given as:

P(S) = 12% P(T) =27%

For mutually exclusive events,

P(S or T) = P(S) + P(T)

This gives

P(S or T) = 12% + 27%

Evaluate the sum

P(S or T) = 39%

Hence, the value of the probability P(S or T) is 39%

Read more about probability at:

https://brainly.com/question/11234923

#SPJ1

The values of the functions are f(4) = 47, f(k) = 2(k)^2 + 4(k) - 1 and f(x + h) = 2x^2 + 4hx + 2h^2 + 4x + 4h - 4

The function is given as:

f(x) = 2x^2 + 4x - 1

To calculate f(4), we have:

f(4) = 2(4)^2 + 4(4) - 1

Evaluate the expression

f(4) = 47

To calculate f(k), we have:

f(k) = 2(k)^2 + 4(k) - 1

To calculate f(x + h), we have:

f(x + h) = 2(x + h)^2 + 4(x + h) - 1

Expand

f(x + h) = 2(x^2 + 2hx + h^2) + 4x + 4h - 4

Expand

f(x + h) = 2x^2 + 4hx + 2h^2 + 4x + 4h - 4

Read more about functions at:

https://brainly.com/question/4025726

#SPJ1

Answer:

D

Step-by-step explanation:

If you substitute the radius, 10, and the center of the circle, the origin (also known as (0,0) into the equation of a circle, you should get: [tex](x - 0)^{2} + (y - 0)^{2} = 10 ^{2} [/tex]

Multiplying this out should leave you with D as your answer.

Answer:

See below

Step-by-step explanation:

density = mass/volume

   re-arrange to    density * volume = mass

                                 20 * 64 = 1280 gm

Density = mass/volume    

   re-arrange to      volume = mass / density

                                                 560 / 14 = 40 cm^3

The difference of two squares expression is (c) (5x + 3y)(5x - 3y)

The difference of two squares expression is represented as:

a^2 - b^2 = (a + b)(a - b)

Using the above as a guide, we have the following expression in option (c)

(5x + 3y)(5x - 3y)

Hence, the difference of two squares expression is (c) (5x + 3y)(5x - 3y)

Read more about difference of two squares at:

https://brainly.com/question/914765?referrer=searchResults

#SPJ1

The area of the figure is 11. 27 cm²

The figure given is a parallelogram

The formula for the area of a parallelogram is given thus;

Area = base × height

From the figure, we have that

base = 2. 3 cm

height = 4. 9 cm

Substitute into the formula

Area = 2. 3 × 4. 9

Area = 11. 27 cm²

Thus, the area of the figure is 11. 27 cm²

Learn more about a parallelogram here:

https://brainly.com/question/970600

#SPJ1

The largest possible area of the forest is 2500 km^2

The perimeter is given as:

P = 200 km

The shape that will give the largest possible area for the forest is a square, and the area is calculated as:

A = (P/4)^2

This gives

A = (200/4)^2

Evaluate

A = 2500 km^2

Hence, the largest possible area of the forest is 2500 km^2

Read more about areas at:

https://brainly.com/question/24487155

#SPJ1

Answer:

47/14 is a mixed number i think

The value of m and n to show the solution of the equation x² + 6x - 5 = 0 is m = -3 and n = ± √14

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the equation:

x² + 6x - 5 = 0

x² + 6x = 5

x² + 6x + 9 = 5 + 9

(x + 3)² = 14

x + 3 = ±√14

x = -3 ± √14

The value of m and n to show the solution of the equation x² + 6x - 5 = 0 is m = -3 and n = ± √14

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1