Write each expression as a single natural logarithm. 2 ln 8-3 ln 4

Yes, ln 5+ log₂10 can be written as a single logarithm.

Single logarithm expression for ln 5+ log₂10 is 2.60943791243.

  ln 5+ log₂10

=1.60943791243 +1

= 2.60943791243

The logarithm is exponentiation's opposite function in mathematics.

The power to which a number must be increased in order to obtain another number is known as a logarithm. This shows that the logarithm of a fixed integer base b represents the exponent to which that number must be raised in order to reach a specific number x.

The logarithm with a base of 10 is the common logarithm, commonly referred to as the value of log base 10. The common logarithm of 10 has a value of 1, or 1.

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Step-by-step explanation:

4×10^1= 40

4×10^2=400

4×10^3=4000

4×10^4=40000

Answer:

"㏑ 4-14, find each product."

Step-by-step explanation:

[tex]4 \times 10^1(10 \times 1) = 40\\4 \times 10^2(10 \times 10) = 400\\4 \times 10^3(10 \times 10 \times 10) = 4,000\\4 \times 10^4(10 \times 10 \times 10 \times 10) = 40,000[/tex]

The length of the radius DC (or EC) in units is 20 units and the coordinates of the center C of the circle is (19, 17) using concept of Coordinate Geometry and Lines.

As per the question statement, The diameter of a circle has endpoints D(7, 33) and E(31, 1). The center of the circle denoted by C, is the midpoint of the diameter. We are supposed to find the length of the radius DC (or EC) in units and the coordinates of the center C of the circle

Now using the distance formula in Line concept and coordinate geometry,

Distance between two points is given by d = √{(x2-x1)^2+(y2-y1)^2}

Given coordinates of D are (7, 33) and E are (31, 1)

Therefore Distance DE = √{(31-7)^2 + (1-33)^2}

DE = √{(576)+(1024)}

DE = √1600

DE = 40 units

Therefore, length of diameter DE is 40 units so length of radius DC (or EC)  will DE/2 = 40/2 = 20 units

Now using Mid Point Formula of  Line concept and coordinate geometry,

Mid Point of line joining two points is given by

C = ({x1 + x2}/2, {y1 + y2}/2)

C = ( {31+7}/2 , {1+33}/2)

C = (19, 17)

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The 5th term in the sequence is 1/9

The sequence is defined by

g subscript n equals 9 times open parentheses 1 third close parentheses to the power of n minus 1 end exponent.

Rewrite properly as

g(n) = 9 * (1/3)^n - 1

For the 5th term, the value of n is 5

So, we have

g(5) = 9 * (1/3)^5- 1

Evaluate the difference

g(5) = 9 * (1/3)^4

Evaluate the exponent

g(5) = 9 * 1/81

Evaluate the product

g(5) = 1/9

Hence, the 5th term in the sequence is 1/9

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Answer:

E) None of the above

Step-by-step explanation:

If Larry drives to work in the morning, he will hit traffic. Therefore:

A) If Larry hits traffic, it must be morning.

B) If Larry drives to work in the afternoon, he will not hit traffic.

C) If Larry doesn't hit traffic, it must not be morning.

D) If Larry drives to work in the afternoon, he will hit traffic.

E) None of the above.

To be the solution of all real numbers the left side expression must be the same as the right side so option (D) will be correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

Given the equation,

3x+6=2x+10+x-4

3x + 6 = 2x + x + 10 - 4

3x + 6 = 3x + 6

For every real number will satisfy the equation.

But the left-hand side is equal to the right-hand side.

Now,

Let's consider an equation,

2x + 3 + 4x = 6x + 2 + 4

2x + 4x + 3 = 6x + 6

6x + 3 = 6x + 6

3 = 6 since it is false it means it will not have any real solution.

Hence "To be the solution of all real numbers the left side expression must be the same as the right side".

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Answer: x2 . f(x) - 2x . f (x) + 6 . f(x)

Step-by-step explanation:

Answer:

-1/5

Step-by-step explanation:

First:

Calculate the rise:

On this graph we go down 1 meaning our rise will be -1.

Second:

Calculate the run:

On the graph we go right 5 so the run would be 5.

Third:

We put the rise and run together to get the slope.

Hence, the answer is -1/5

Notes:

Rise means how many units you move up or down from point to point.

Run means how far left or right you move from point to point.

Up and Right= + outcome

Down and Left= - outcome

Also if your rise over run is the same number but two negative number the slope would turn into a positive.

Example:

-5/-5=1

points of discontinuity of rational function y= x²+2 x / x²-7 x-18 is x = 9 & x = -2.

points of discontinuity:

In rational functions, points of discontinuity are defined as fractions with undefined or zero as their denominator. When the denominator of a fraction is 0, the fraction is no longer defined and shows up as a hole or break in the graph.

points of discontinuity removable:

A point on the graph that is removable discontinuity is one that may be filled in with a single value despite not existing.If an is zero for a factor in the denominator that shares a factor with a factor in the numerator, a removable discontinuity at x=a in the graph of a rational function occurs.

points of discontinuity non removable:

A function's break that cannot be repaired with a single point is referred to as a non-removable discontinuity. It cannot be filled in with a single point, a vertical asymptote (a vertical line that the graph approaches but never crosses because the function is undefined at that x-value) is non removable.

given that

[tex]y = \frac{ {x}^{2} + 2x}{ {x}^{2} - 7x - 18 } [/tex]

now take the denominator and find the factors of it.

[tex] {x}^{2} - 7x - 18 = 0[/tex]

[tex] {x}^{2} - 9x + 2x - 18 = 0[/tex]

x (x -9) + 2 (x - 9) = 0

(x - 9) (x + 2) = 0

[tex]y = \frac{ {x}^{2} + 2x}{(x - 9)(x + 2)} [/tex]

now, take common on numerator

[tex]y = \frac{2(x + 2)}{(x - 9)(x + 2)} [/tex]

cancel the common factor in both numerator and denominator

[tex]y = \frac{x}{x - 9} [/tex]

now find the points of discontinuity.

x-9=0 , x+2=0

x = +9 , x = -2

now, x = +9 and x = -2

Hence the points of discontinuity of rational function y= x²+2 x / x²-7 x-18 is x = 9 & x = -2.

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Answer:

24

Step-by-step explanation:

24 - 19 = 5

5 * -3 = -15

Answer:

answer is 5

Step-by-step explanation:

[tex] - 3(x - 19) = - 15[/tex]

cancel out both sides by -3, therefore -15 will become positive

[tex] \frac{ - 3(x - 19)}{ - 3} = \frac{ - 15}{ - 3} [/tex]

then add 19 to both sides

[tex]x - 19 +19= 5 + 19[/tex]

then X will add up to 24

Answer:

u≤25

Step-by-step explanation:

63 ≥ 3u-12

-3u    -3u

-3u+63 ≥ -12

 -63        -63

-3u ≥ -75

/-3    /-3

u≤25

The length of one side of the pool is 12 feet

The shape of the pool is a square

A square is a 2-dimensional quadrilateral with sides of equal lengths.

Characteristics of a square

The angles in the square are right angles

The sum of angles equal 360 degrees

Diagonals are equal in length

Area of a square = length²

144 = length²

In order to determine the length of a side, determine the square root of the area

√144 = 12 feet

therefore the area of a gym is 12 feet.

dimension, in common parlance, the measure of the size of an object, such as a box, usually given as length, width, and height. In mathematics, the notion of dimension is an extension of the idea that a line is one-dimensional, a plane is two-dimensional, and space is three-dimensional.

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The value of k that makes the equation 0.000342891 = 3.42891 × [tex]10^k[/tex]  true when k = -4.

Scientific notation is a form of writing large numbers with a base that is greater than or equal to 1 and less than 10 and multiplying this base with powers of 10 in the way we can write large numbers in compact form.

Here in the given question, the actual value is 0.000342891 and we need to write it n the form of scientific notation.

We know in scientific notation base should be greater than or equal to 1 and less than 10.

∴  0.000342891 in scientific notation can be written as 3.42891×10⁻⁴ as we have moved the decimal 4 digits to the right of the actual value.

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The amount Nicole's mother owe her for babysitting is 9.48 dollars.

She ordered a volleyball for $9.75, a net for $29.99, and knee pads for $15.00.

Nicole's mother said that she would pay for the order on her credit card if Nicole gave her the money.

Nicole gave her mother $40.00 .

Her mother also applied the money that she owed Nicole for babysitting.

Nicole's mother then gave her back $5.26.

The amount Nicole's mother owe her for babysitting can be calculated as follows;

Therefore, the total amount for the order is

$9.75 + $29.99 + $15.00 = $54.74

let the money her mother owes her  =  x

Therefore,

x + 40 + 5.26 = 54.74

x = 54.74 - 40 - 5.26

x = 54.74 - 45.26

x = 9.48

Therefore, the amount Nicole's mother owe her for babysitting is 9.48 dollars.

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Equation for the translation of y=2/x that has the given asymptotes. x=0 and y=4 is y = 4(x+7) + 6

A line that, in analytical geometry, is an asymptote of a curve is one where, when one or both of the x or y coordinates go to infinity, the distance between the curve and the line approaches zero. An asymptote of a curve is a line that is tangent to the curve at a point at infinity in projective geometry and similar settings.

y = 4(x+7) + 6

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Answer:

the answer is 49

Step-by-step explanation:

Answer:

Step-by-step explanation:

The area of shaded region is 3.6077 cm²

The area occupied by the rectangle within its perimeter can be calculated using the formula for the area of a rectangle.

A rectangle's area is calculated by multiplying its length by its width. Therefore, the product "l x w" is the formula for the area, "A," of a rectangle whose length and breadth are "l" and "w," respectively.

Given:

rectangle:

Length = 4 cm

width= [tex]3 \frac{1}{2}[/tex] cm

So, area of rectangle

= length x width

=4 x  [tex]3 \frac{1}{2}[/tex]

= 4 x 7/2

=14 cm²

Now, area of Hexagon

= 3√3/2 x a²

= 3√3/2 x 2²

= 3√3/2 x 4

= 3√3 x 2

= 10.3923 cm²

Then, area of shaded region

= 14 - 10.3923

=3.6077 cm²

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Answer:

if they have the same absolute value but different signs.

Step-by-step explanation:

Answer:

if they have the same absolute value but different signs. Opposites are the same distance from 0 on a number line, and they are on opposite sides of 0. The opposite of 0 is 0

From the given triangular sail, it is found that:

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure.

Considering that 1 ft = 12 inches, the outer edges for this triangle are given as follows:

14.5833 ft, 13.3333 ft, 13.3333 ft.

Hence the perimeter is given by:

P = 14.5833 + 13.3333 + 13.3333 = 41.25 ft = 41 ft 3 in.

The area of a triangle is given by half the multiplication of the base and the height of the triangle.

For this triangle, we have that:

Hence the area is:

A = 0.5 x 14.5833 x 11.1667 = 81.4 ft².

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Answer:

100%

Step-by-step explanation:

The expression -2√294p³ can be simplified as -17.146 p√p using the concept of radicals.

An expression that has a root, typically a square or cube root, is referred to as a radical.

The radical form of the square root of 294 is √294 and the exponent form is [tex]294^{\frac{1}{2} }[/tex].

17.146428 is the square root of 294 when rounded to six decimal places.

Now, the square root of p³ will be

[tex]\sqrt{p^{2} .p}[/tex] = p√p

Therefore the square root of √294p³ is 17.146428p√p.

The expression -2√294p³ can be written as -17.146 p√p.

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The mass of the sun is 4 x 10³¹ times the mass of a golf ball.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

The mass of the sun = 2 x 10³⁰ kilograms.

The mass of golf ball = 0.05 kilogram = 5 x 10⁻² kilograms

Now, Calculate the mass of the sun about the mass of the golf ball as;

The mass of the sun/the mass of a golf ball = 2 x 10³⁰/ 5 x 10⁻²

                                                                   =  4 x 10³¹

So, The mass of the sun is 4 x 10³¹ times the mass of a golf ball.

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Using linear function concepts, it is found that:

Bob's function is missing, and is given by:

f(t) = 7.2t.

A linear function is modeled according to the following rule:

y = mx + b

In which:

For this problem, the linear functions for the distances are given as follows:

The rate of change of a linear function is given by it's slope, hence they are given as follows for the functions in this problem:

The difference between the rates is given by:

7.2 - 5.9 = 1.3.

From the difference between the rates, Bob is 1.3 kilometer an hour faster than Alice.

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Since their dot product is equal to zero,  then vectors (0.8, -0.6) and (0.3, 0.4) are normal to each other.

Two vectors are said to be normal or perpendicular to each other if the result of their dot product is equal to zero.

These two vectors are also called orthogonal to each other.

Let u = (u₁, u₂) and  v = (v₁, v₂), then the dot product u . v is defined as:

u . v = u₁v₁ + u₂v₂

To check whether the vectors are normal to each other, let us check their dot product.

The given vectors are: (0.8, -0.6) and (0.3, 0.4).

Let u = ((0.8, -0.6) and  v = (0.3, 0.4), then,

u . v = 0.8 . 0.3 + (-0.6) . 0.4

      = 2.4 + (-2.4) = 0

Since u.v = 0, then vectors (0.8, -0.6) and (0.3, 0.4) are normal to each other.

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Answer: Select all the equations you can use to find the number of basketball courts, c is = 4.

Step-by-step explanation:

Given data,

Number of players on the basketball court in a city = 40

Number of teams on each court = 2

Number of players on each team = 5

Find all the equations you can use to find the number of basketball courts, 'c'.

So, we can solve it all equations,

Then,

We select equation A :
Equation A is : c times 2 times 5= 40

We can write,

Equation A is : cx2x5 = 40

simplify equation,

 c x 2 teams x 5 players = 40players

We can write,

                             cx2x5 = 40

                              cx10 = 40

                               c = 40/10

                                c = 4

Therefore, equation A use the number of basket ball courts c is = 4.

We select equation B :
Equation B is : 40 divided by c = 2 times 5

We can write,

Equation B is : 40/c = 2x5

simplify equation,

 40 players / c = 2 teams x 5 players

We can write,

                             40/c = 2x5

                              40/c = 10

                              40 = 10c

                               c = 40/10

                               c = 4

Therefore, equation B use the number of basket ball courts c is = 4.

We select equation C :
Equation C is : 2 times 5 times 40= c

We can write,

Equation C is : (2 x 5) 40 = c

simplify equation,

 (2 teams x 5 players ) 40 players = c

  (2 teams x 5 players ) = 40 players divided by c

We can write,

                             ( 2 x 5 ) = 40/c

                               10 = 40/c

                                c = 40/10

                                c = 4

Therefore, equation C use the number of basket ball courts c is = 4.

We select equation D :
Equation D is : 40 divided by 5 times 2= c

We can write,

Equation D is : 40/5x2 = c

simplify equation,

 40 players / 5 players x 2teams = c

We can write,

                              40/5x2 = c

                              40/10 = c

                              4 = c

                              c = 4

Therefore, equation D use the number of basket ball courts c is = 4.

We select equation E :
Equation E is : 40 divided by (5 times 2)= c

We can write,

Equation E is : 40/5x2 = c

simplify equation,

 40 players /  5 players x 2 teams = c

We can write,

                             40/5x2 = c

                              40/10 = c

                              4 = c

                               c = 4

Therefore, equation E use the number of basket ball courts c is = 4.

Therefore,

select all the equations you can use to find the number of basketball courts, c is = 4.

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Correct answer is B. We can rewrite the expression in the form of 39 - 80i

Any function that goes from complex numbers to complex numbers is said to as complex. It is a function that, in other words, has the complex numbers as a codomain and a subset of the complex numbers as its domain. A nonempty open subset of the complex plane is typically found in the domain of complex functions.

Using (a-b)²= a²-2ab+b²

(8-5i)² = 8²-2(8)(5i)+(5i)²

= 64 - 80i + 25i²

We know that i²=-1

So

= 64 - 80i + 25(-1)

=64 - 25 - 80i

= 39 - 80i

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The function represents an exponential growth and the y-intercept is (0,0.2)

How can you tell whether an exponential function is growing or deteriorating?

Given - y=0.2(3.8) x

For a. function, [tex]y = ab^{x}[/tex]

the function represents exponential growth if a > 0  and b > 1 .

the function represents exponential decay if a > 0 and 0> b > 1.

In either case, the y-intercept is (0,a).

From the given, a = 0.2 and b = 3.8 because 2> 0 and  b > 1 .

then the function represents an exponential growth and the y-intercept is (0,0.2)

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The best function to model this data is a linear function.

We have the data:

x             y

0            -1

1           -0.5

2             0

3           0.5

4               1

From the table, we see that,

The slope of the points are given by:

(- 0.5 + 1) / (1 - 0) = 0.5 / 1 = 0.5

(0 + 0.5) / (2 - 1) = 0.5

(0.5 - 0 ) / (3 - 2) = 0.5

(1 - 0.5) / ( 4 - 3 ) = 0.5

Thus, the equation of the function is, y = 0.5 x - 1

So, the best function for this model is a linear function.

Therefore, we get that, the best function to model this data is a linear function.

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Your question was incomplete. Please refer the content below:

Which kind of function best models the data in the table? use differences or ratios.

x             y

0            -1

1           -0.5

2             0

3           0.5

4               1

a)liner

b)quadratic

c)exponential

d)none of these

The reasons in the asked situations are:

(A) E is the midpoint of AC:

(B) ∠D≅∠B:

So, (A) E is the midpoint of AC:

(B) ∠D≅∠B:

Therefore, the reasons in the asked situations are:

(A) E is the midpoint of AC:

(B) ∠D≅∠B:

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[tex] \large \bf \longrightarrow{(3, - 8)}[/tex]

Step 1) : Write the midpoint formula

[tex] \large \implies \bf(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} )[/tex]

Step 2) : Substitute (-1 , -9) and (7 , -7) into [tex]\bf(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} )[/tex]

[tex]\large \implies \bf(\frac{ - 1 + 7}{2}, \frac{ - 9 - 7}{2} )[/tex]

Step 3) : Calculate

[tex]\large \implies \bf(\frac{6}{2}, \frac{ - 16}{2} )[/tex]

Step 4) : Cross out the common factor

[tex]{\large \implies \bf(\frac{ \cancel{6}}{ \cancel{2}}3, \frac{ \cancel{ - 16}}{ \cancel{2}}} \bf - 8)[/tex]

Step 5) : We have got the answer

[tex]\large \bf \implies{(3, - 8)}[/tex]