What type of triangle has 3 sides that are the same length?

What logarithmic equation has the same solution as x-4=2^3

Solution:

x-4=2³

x-4=2*2*2

x-4=8

TO solve for x, Let us add 4 on both sides

x-4+4=8+4

x+0=12

So, x=12

But, x=12 is not a logarithmic equation and there are no options

So, an equation like, x=㏒

As log has base 10,

So, x=㏒ =12

So, logarithmic equation like x=log has same solution as x-4=2³

Answer:

is required lograthmic equation.

Step-by-step explanation:

Given: Given equation, x - 4 = 2³

To find: Logarithmic function whose solution is same as given equation.

First we find the solution of given Equation.

consider,

x - 4 = 2³

x - 4 = 8        ( ∵ 2³ = 2×2×2 = 8 )

x = 8 + 4       ( Transposing 4 to RHS )

x = 12

Now we find the logarithmic equation whose solution is also x = 12.

( There exist many such equations )

Lets say one of them is,

Now we find its solution to check if it is same or not.

  (using lograthmic rule,)

⇒ 2 × ( x + 2 ) = 28  (using lograthmic rule, )

⇒ 2x + 4 = 28

⇒ 2x = 28 - 4     (transposing 4 to RHS)

⇒ 2x = 24          (transposing 2 to RHS)

⇒

⇒ x = 12

Therefore, is required lograthmic equation.

The solution for the given system of equations are (6, 20).

What is a linear system of equations?

A system of linear equations is a set of two or more equations involving two or more variables. All of the equations must be considered at once in order to find the solution, which is any pair of values that makes each equation true independently.

The given system of linear equations are y=x+14 -----(i) and y=3x+2 -----(ii).

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

x+14=3x+2

3x-x=14-2

2x=12

x=6

Substitute x=6 equation (i), we get

y=20

Therefore, the solution for the given system of equations are (6, 20).

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Answer:

(6, 20), because both lines pass through this point

Step-by-step explanation:

We see that both equations are equal to y.  This means we can set the two equations equal to each other:

x+14 = 3x+2

Subtract x from each side:

x+14-x = 3x+2-x

14 = 2x+2

Subtract 2 from each side:

14-2 = 2x+2-2

12 = 2x

Divide both sides by 2:

12/2 = 2x/2

6 = x

Substitute this into the first equation:

y = x+14

y = 6+14

y = 20

This makes the solution (6, 20).

The area of the circular DVD is given by A = 111.33 cm²

What is a Circle?

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the area of the circular DVD be A

Let the diameter of the DVD = 12 cm

So , the radius of the DVD = 6 cm

Now , the diameter of the hole = 1.5 cm

So , the radius of the hole = 0.75 cm

And , area of the circular DVD be A = π [ ( 6 )² - ( 0.75 )² ]

On simplifying , we get

The area of circular DVD is A = π ( 36 - 0.5625 )

The area of circular DVD is A = π ( 35.4375 )

The area of circular DVD is A = 111.33 cm²

Hence , the area of the circular DVD is 111.33 cm²

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