Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.) ln x^2-1/x^7 , x>1

Answer:

10.7

Step-by-step explanation:

The only thing I can think of is 10.7. Because when you do this problem you get 10.6666666667. So I'm assuming you're to round it. There is no other way to solve the problem that wouldn't get you either 10.6666666667 or 10.7.

Answer:

10.66

Step-by-step explanation:

[tex]\frac{24}{9}[/tex] + [tex]\frac{8}{1}[/tex]

[tex]\frac{24}{9}[/tex] + [tex]\frac{72}{9}[/tex]

[tex]\frac{96}{9}[/tex]

10.666...

Answer:

[tex]\sf n=\cfrac{1}{2}[/tex]

Step-by-step explanation:

[tex]\sf -12=10n-40n+3[/tex]

[tex]\sf 10n-40n+3=-12[/tex]

Combine like terms:-

[tex]\sf \:(10n-40n)=-30n[/tex]

[tex]\sf -30n+3=-12[/tex]

Subtract 3 from both sides:-

[tex]\sf -30n+3-3=-12-3[/tex]

Simplify:-

[tex]\sf -30n=-15[/tex]

Divide both sides by -30:-

[tex]\sf \cfrac{-30n}{-30}=\cfrac{-15}{-30}[/tex]

Simplify:-

[tex]\sf n=\cfrac{1}{2}[/tex]

_________________

Hope this helps!

Have a great day! :)

Step-by-step explanation:

120 ft relate to 24 inches.

120/80 must be the same ratio as 24/model width.

120/80 = 3/2

so,

24/width = 3/2

48/width = 3

48 = 3width

width = 48/3 = 16 inches

Answer:

2(2x+9)

Step-by-step explanation:

Just break each number up

2 X 2 = 4

2 X 9 = 18

2(2x+9)

Answer:

-4.5

......

......

The slope of the line is -1/2, the coordinates of midpoint is (1,3) and the equation of perpendicular bisector is y = 2x + 1

The slope of a line is a measure of its steepness.

Given that, a line segment has end points = A(-1,4) and B(3,2)

(i) Slope = (y2 - y1)/(x2 - x1) = -1/2

(ii) Coordinates of the midpoint of a line = (Xm, Ym) = (x₁ + x₂)/2, (y₁ + y₂)/2

(Xm, Ym) = (-1+3)/2, (4+2)/2 = (1,3)

(iii) The slope of the two lines perpendicular to each other are negative reciprocal of each other, so, slope of the line perpendicular to the given line is = 2

Standard equation of a line = y = mx + c

Since the line is the perpendicular bisector of AB, it will pass through (1,3)

Solving for c,

3 = 2*1 + c

c = 1

Therefore, the equation of the of line perpendicular to AB is

y = 2x + 1

Hence, the slope of the line is -1/2, the coordinates of midpoint is (1,3) and the equation of perpendicular bisector is y = 2x + 1

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The coordinates of the image of reflecting (3, -2) across the line y = 5 are (3, 12)

When we reflect a point (x, y) across a horizontal line of the form:

y = a

The coordinates of the image after the reflection are:

(x, 2a - y)

In this case we have the point (3, -2), and we reflect this across the line y = 5, then the new coordinates are:

(3, 2*5 - (-2))

(3, 10 + 2)

(3, 12)

The coordinates after the image are (3, 12)

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Answer:

1.5 minutes (or 1 minute and 30 seconds)

Step-by-step explanation:

5 : 40 = x : 12

x = (5 * 12)/40

x = 12/8

x = 1.5 minutes

Answer: 1 min and 50 seconds

Step-by-step explanation:

first, you have to find the unit rate of how many papers the printer can make in a min which is 40 divided by 5 which gets you a unit rate of 8 for every minute then you take your 12 paper and divide it by your unit rate of 8 per minute which gets you how long it would take to print 12 papers which equal 1.5

Answer:

0.83 repeating 3

Step-by-step explanation:

5 goes in the box and 6 goes outside. you can't put 6 into 5 so you would put a 0 on the top and a decimal point. now you would write a 0 next to the 5 and you would do 6×8=48 and so put 8 next to the 0 and the decimal point. then subtract 50-48 which will be 2. Put another 0 next to the 50 and bring it down. you will have 20 which you do 6×3=18. and so put a 3 next to 0.8 and you will subtract 20-18=2. It will be repeating so put a line at the top of 3 to show that it's repeating.

The polynomial function p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 value at x = -2 is -1

given that

polynomial function p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 at x=-2

To find the value of a function at x = -2, put in all the places of  in the function.

Polynomial is made up of two words, poly, and nomial. "Poly" means many, and "nomial" means the term, and hence when they are combined, we can say that polynomials are "algebraic expressions with many terms".

Polynomial functions are expressions that may contain variables of varying degrees, coefficients, positive exponents, and constants.

Here,

p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 put x =-2

p(-2) = 5[tex](-2)^{3}[/tex]+8[tex](-2)^{2}[/tex] - 3(-2)+1

p(-2) = 5(-8) + 8(4) + 6+1

p(-2) = -40+32+6+1

p(-2) = -40+39

p(-2)  =-1

At So, the value of the function at x= -2 is -1

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Answer: Give me brainliest or your mean.

Step-by-step explanation: 1/3 jersey 1/2 short. 1/3 x 1/2 = 1/6 possibility.

Answer:answer is 20

Step-by-step explanation:9/3=3 then add that to 2 times 6 which is 12+3=15 then 15+5+20

Answer:

y = - [tex]\frac{3}{4}[/tex] x - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 12, 4 ) and (x₂, y₂ ) = (0, - 5 ) ← coordinates of 2 end stars

m = [tex]\frac{-5-4}{0-(-12)}[/tex] = [tex]\frac{-9}{0+12}[/tex] = [tex]\frac{-9}{12}[/tex] = - [tex]\frac{3}{4}[/tex]

the lowest star is on the y- axis at (0, - 5 ) ⇒ c = - 5

y = - [tex]\frac{3}{4}[/tex] x - 5

The solution of the given integral [tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]

Given;

To evaluate the value of a given integral;

[tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex]

Let;

[tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]2\cdot \int \left(x^2+4\right)^3xdx[/tex]

Now, assume u = x² + 4

→ [tex]2\cdot \int \left(x^2+4\right)^3xdx[/tex] = [tex]2\cdot \int \frac{u^3}{2}du[/tex]

→ [tex]2\cdot \frac{1}{2}\cdot \frac{u^4}{4}[/tex]

→ [tex]2\cdot \frac{1}{2}\cdot \frac{u^4}{4}[/tex]

→  [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]

By adding constant C;

[tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]+ C

Hence, the solution of the given integral [tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]

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In the given circle the length of the chord marked x is

We know that the length of the chord is bisected by the perpendicular from the center of the circle.

Therefore the length of the chord is 7 × 2 = 14 units.

Again from the chord properties of a circle we know that, chords that are equidistant from the center are equal.

Since both the chords are at a distance of 9 units hence both chord lengths

Hence the length of the other chord = 14 units.

∴ x = 14

The segment of a line that joins any two points on a circle's circumference is known as the chord. It must be emphasized that its longest chord is its diameter, which runs through the center of the circle.

The circle and its chord are depicted in the diagram below. In the center of the circle, equal-length chords subtend equal angles.

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Answer:

49

Step-by-step explanation:

18/42=21/ED

18 ED=882

ED=49

If the team buys 18 jerseys for a total of (18x-36) dollars then we can conclude that the discount the team has received is $36.

According to the question,

We have the following information:

A soccer team receives a discount on each jersey purchased. The original price of each jersey is x dollars. The team buys 18 jerseys for a total of (18x-36) dollars.

Now, the original price of 18 jerseys will be 18x.

Now, when 36 is subtracted from 18x to find the total cost then it means that this is the discount from the original price.

Hence, if the team buys 18 jerseys for a total of (18x-36) dollars then we can conclude that the discount the team has received is $36.

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The slope of the line as shown in the diagram is 4/3.

The slope of a line is the ratio of the amount that y increases as x increases some amount.

To calculate the slope from the diagram, we use the formula below.

Formula:

Where:

From the graph,

At  x = 30, y = 20

And at x = 60, y = 60

Therefore,

Substitute these values into equation 1

Hence, the slope of the is 4/3.

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Answer:

x=8

No it’s not an equilateral

Step-by-step explanation:

Since side AB is about the same length as BC we can set them equal to each other

x-1=7

 +1 +1

x=8

This is not an equilateral because if you fill in X for the third side you will get 5

8-3=5

Answer:

here you go....

Step-by-step explanation:

Proved that ΔABC ≅ ΔDEC

SAS rule of congruent states that if two sides and one angle of the triangle is equal to the two sides and one angle of the another triangle, then the both triangles are congruent

The line BE and AD intersect at point C

The measure of the angle BCA = The measure of the angle ECD

The length of the side BC = The length of the side EC

The length of the side AC = The length of the side DC

Consider the triangle ABC and triangle DEC

Two sides and one angle of the triangle ABC is equal to the two sides and one angle of the triangle DEC, according to SAS rule of congruent the triangle ABC and triangle DEC are congruent

Hence, proved that ΔABC ≅ ΔDEC

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The simplified terms are 12.504 and 17.76 when the terms are in decimal.

Given that,

The numbers are 13.4-0.896 and 8.6 + 9.16

We have to simplify the terms.

We know that,

When a full number and a fraction are combined, decimals are used. The "." symbol, often known as a decimal point, will be used to demarcate the entire number from the fraction in this instance.

Take the numbers,

13.4-0.896

Subtracting the terms

12.504

Take the numbers,

8.6 + 9.16

Adding the terms

17.76

Therefore, The simplified terms are 12.504 and 17.76 when the terms are in decimal.

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Answer:

-0.16

Step-by-step explanation:

Divide the answer :)

The graph of this quadratic function (x² + 3x - 108) is shown in the image attached below. Also, the two roots of this quadratic equation (x² + 3x - 108) are -12 and 9, while the axis of symmetry (vertex) is equal to -1.5.

In Mathematics, a quadratic function is a mathematical expression which defines and represent the relationship that exists between two or more variable on a graph.

Mathematically, the graph of every quadratic functions is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic function would always form a parabolic curve. For this quadratic function, the graph is a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero.

Next, we would determine the axis of symmetry (vertex) of this quadratic function:

Axis of symmetry (vertex), Xmax = -b/2a

Axis of symmetry (vertex), Xmax = -3/2(1)

Axis of symmetry (vertex), Xmax = -1.5.

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The value of x is 15 and the value of y is 4 for the given triangle.

According to the question,

We have the following information:

We have a figure of triangle and a line parallel to the base is drawn. Some measurements of the sides are given.

Now, to find the values of x and y, we will use Basic Proportionality theorem which states that the ratio of the corresponding sides are equal.

For the larger triangle, we have:

12/y = 18/6

Using the cross multiplication method:

y = 12*6/18

y = 4

Now, using the same theorem for the smaller triangle:

12/y = x/5

12/4 = x/5

Using the cross multiplication method:

x = 15

Hence, the value of x is 15 and the value of y is 4 for the given triangle.

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Answer:

Rema receives 90 sweets

Step-by-step explanation:

See attached image

The co-ordinates of J'K'L'M'N' are (0,5), (-2,3), (-3,4), (-4,1), (-1,2)

What is Co-ordinate Geometry?

Coordinate geometry is a field of mathematics that assists in displaying geometric forms on a two-dimensional plane and learning the attributes of these figures.

Solution:

The co-ordinates of J'K'L'M'N' are (0,5), (-2,3), (-3,4), (-4,1), (-1,2)

From the figure it can be clearly observed that

a) L' is located at (-3,4) - True

b) M' is located 4 units left of the y - axis - True

c) The y - co ordinate of zN' is the opposite of the y - co ordinate of N - False

d) J'K' = JK - False

e) M' is located at (-4,1) - True

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The number of hours that helena need to work to generate 165 dollars is

33 hours.

Helena has to work hours to earn $165. 33

Algebraic equations are equations with

unknown variables. The alphabet letters are used to represent algebraic equations.

Total $33.00 in her 6 hours she worked.

This question should find out how long it takes her to earn her $165.00 in that job.

let x hours be required work hours to earn $165.00 ..

This can be expressed in algebraic equations as:

x= 6× 165/33

x= 990/33

x= 30

Hence, helna have to work thirty hours to earn $165.00 ..

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Estimate product of (-25.31) (9.61) using compatible numbers is equal to -250.

As given in the question,

Given expression is equal to :

( -25.31 ) ( 9.61 )

Compatible numbers to calculate the estimate product we have,

Compatible number for ( -25.31 ) is equal to ( -25 ) .

-25 > -25.31 > -26

-25.31 is more nearer to -25 .

Now, 9 < 9.61 < 10

Compatible number for 9.61 is equal to 10 as 9.61 is more close to 10.

( -25.31 ) × ( 9.61 )

= ( -25 ) × (10)

= 250

Therefore, estimate product of (-25.31) (9.61) using compatible numbers is equal to -250.

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The statement that describes the account growth is D. The account is growing exponentially at an annual interest rate of 2.00%.

From the information, the table shows the balance of an investment account at the beginning of each year the account was held.

The percentage change for the second year will be:

= (510 - 500) / 500 × 100

= 10/500 × 100

= 2%

The percentage change for the third year will be:

= (520.20 - 510) / 510 × 100

= 10.20/510 × 100

= 2%

Therefore, there's. 2% growth.

The correct option is D.

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Answer:

D

Step-by-step explanation: