help with the question

Answer:

[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{100})[/tex]

Step-by-step explanation:

Given

[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right)[/tex]

Required

The sum

Using the laws of logarithm, we have:

[tex]\log(a) + \log(b) = \log(ab)[/tex]

Take the first two terms of the series

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{2} * \frac{2}{3})[/tex]

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{3})[/tex]

Include the third term

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{3} * \frac{3}{4})[/tex]

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{4})[/tex]

Include the fourth term

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{4} *\frac{4}{5})[/tex]

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{5})[/tex]

Notice the following pattern

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{3})[/tex] ---------------- n =2

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{4})[/tex] -------------- n = 3

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{5})[/tex] ----------- n = 4

So the sum of n series is:

[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ ............ + \log(\frac{n}{n+1}) = \log(\frac{1}{n+1})[/tex]

So, the sum of the series is:

[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right)[/tex]

[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{99+1})[/tex]

[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{100})[/tex]

Step-by-step explanation:

To find the equation of a parabola we need to have 3 points. The intercept of the X axis is the X intercept. The definition of an intercept is when the other value is equal to zero. (3,0) and (9,0)

There appears to not be enough points to answer your question. we also need a vertex

Answer:

[tex]\frac{-4x+7}{2(x-2)}[/tex]

Step-by-step explanation:

[tex]For x \neq 1 \\\frac{\frac{3}{x-1}-4}{2-\frac{2}{x-1}}=\frac{\frac{3}{x-1}-\frac{4x-4}{x-1}}{\frac{2x-2}{x-1}-\frac{2}{x-1}}=\frac{\frac{-4x+7}{x-1}}{\frac{2x-4}{x-1}}=\frac{-4x+7}{2(x-2)}[/tex]

The equivalent expression is 2(x - 2) / (-4x + 7).

Option A is the correct answer.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To simplify the given expression:

[3/(x - 1) - 4] / [2 - 2/(x - 1)]

We need to find a common denominator for the two fractions in the numerator and denominator of the main fraction.

The common denominator for the numerator is (x - 1) and for the denominator is 2(x - 1).

We can then rewrite the expression as:

[3 - 4(x - 1)/(x - 1)] / [2(x - 1) - 2/(x - 1)]

Simplifying the numerator by distributing the -4:

(3 - 4x + 4) / (x - 1)

(-4x + 7) / (x - 1)

Now, simplifying the denominator by finding a common denominator:

2(x - 1) - 2/(x - 1)

= (2x - 2 - 2)/(x - 1)

= 2(x - 2)/(x - 1)

Substituting back into the original expression, we get:

(-4x + 7)/(x - 1) / [2(x - 2)/(x - 1)]

Multiplying by the reciprocal of the denominator:

(-4x + 7)/(x - 1) x (x - 1)/[2(x - 2)]

(-4x + 7)/[2(x - 2)]

Therefore,

The equivalent expression is 2(x - 2) / (-4x + 7).

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ5

Answer:

The length of AC is 12.08 cm.

Step-by-step explanation:

Given:

In triangle ABC, AB = 8.2 cm, C = 13.5 cm and angle A = 81 degrees.

Solution:

https://brainly.com/question/21977218

This is erinna's answer, no need to thank me, thank her instead

Using Law of Sines, we get

Using angle sum property, we get

Now,

Therefore, the length of AC is 12.08 cm.

The length of the side AC of the triangle ABC whose side AB is of 8.2 cm and side BC is of 13.5 cm length with angle A of 81° is 12.1 cm approx.

Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

[tex]a^2 + b^2 -2ab\cos(\theta) = c^2[/tex]

(c is opposite side to angle A)

When one angle and two sides of a triangle are known, and we want to know the length of the remaining third side, then we can use the law of cosines.

We're specified that:

Let the third side's length = |AC| = b cm (don't mix this notation with the notation of the formula said above. We just used notation such that its the smaller case version of the vertex opposite to that side, for example, opposite to AC lies b).

For using formula, we just need to take care that the angle θ is the angle opposite to the side which is going to be on one side (the notation c^2 in the formula given and here since we know the angle A, so the side opposite to A which is BC will be used in one side of the cosine rule, as shown below).

The side opposite to the angle A is BC, thus, we get:

[tex]|BC|^2 = |AB|^2 + |AC|^2 -2|AB||AC| \cos(m\angle A)\\\\13.5^2 = 8.2^2 + b^2 -2(8.2)b \cos(81^\circ)\\\\b^2 - 2.566 b - 115.01 \approx 0\\\\b \approx \dfrac{2.566 \pm \sqrt{2.566^2 - 4(-115.01)}}{2}\\\\b= 12.0835, -9.5175[/tex]

b represents side length, therefore positive. Thus, we obtained the length of the side |AC| approximately 12.1 cm

Thus, the length of the side AC of the triangle ABC whose side AB is of 8.2 cm and side BC is of 13.5 cm length with angle A of 81° is 12.1 cm approx.

Learn more about law of cosines here:

https://brainly.com/question/17289163

Answer:

(a) -1

(b) -2

Step-by-step explanation:

(a) Replace the a's with 1 and the b's with 3 to get 1*3 = 1-3+1 = -1

(b) We already figured out that (1*3) equals -1 so we just need to find -1*2. Using same strategy as part a, replace a and b with -1 and two, respectively. -1*2 = -1-2+1= -2. Hope this helps and sorry if I made a mistake. :)

Answer:

question one:

x = 6.018150231520483

adjacent angle = 7.986355100472928

Step-by-step explanation:

i have no links, but try to search triginometry calculator and pick carbide calculator for fast trigonometry calculations

it automaticly does sin, cos, and tan for you.

Answer:

Step-by-step explanation:

3rd one

Answer:

GIRL NO WAY IM LITTERALY TAKING THAT TEST RN AND IM TRYING TO FIGURE OUT THAT SAME QUESTION LOL

Step-by-step explanation:

BUT I THINK ITS -0.5 DONT TAKE MY WORD FOR IT IM JUST ASSUMING ITS THE ANSWER BC ITS THE ONLY ONE THAT MAKES SENSE

Answer:

∠ RST = 68°

Step-by-step explanation:

Since RT = ST then the triangle is isosceles with 2 base angles congruent

∠ RST = [tex]\frac{180-44}{2}[/tex] = [tex]\frac{136}{2}[/tex] = 68°

Answer:19

Step-by-step explanation: draw the tanks put 6 fish in each tank until you get all 115 in each tank

Answer:

[tex]P(Win) = 0.30[/tex]

Step-by-step explanation:

Given

[tex]P(Win) = 0.30[/tex]

[tex]P(Lose) = 0.55[/tex]

Required

[tex]P(Win)[/tex]

This is already stated in the question as:

[tex]P(Win) = 0.30[/tex]

Answer:

The answer is (-2/3)x + 4.. I have added a picture with the solution

Answer:

Step-by-step explanation:

constant of proportionality : 60/4 = 15

Number : 2

Cost : 15 * 2 = $30

Number 6

Cost = 15 * 6 = $90

Number 8

Cost = 15 * 8 = $120

Step-by-step explanation:

answer is in photo above

Answer:

0.25

Step-by-step explanation:

f(1)=(1/4)^1

0.25

Given:

Consider the dimensions of the rectangle are [tex](x^2+7x-9)[/tex] and [tex](3x^2-2x)[/tex].

To find:

The perimeter in terms of x, of the rectangle.

Solution:

Let the length of the rectangle be [tex](x^2+7x-9)[/tex] and the width of the rectangle is [tex](3x^2-2x)[/tex] units.

The perimeter of a rectangle is:

[tex]P=2(l+w)[/tex]

Where, l is the length and w is the width of the rectangle.

Substituting [tex]l=(x^2+7x-9)[/tex] and [tex]w=(3x^2-2x)[/tex] in the above formula, we get

[tex]P=2((x^2+7x-9)+(3x^2-2x))[/tex]

[tex]P=2(4x^2+5x-9)[/tex]

[tex]P=2(4x^2)+2(5x)+2(-9)[/tex]

[tex]P=8x^2+10x-18[/tex]

Therefore, the perimeter of the rectangle is [tex]8x^2+10x-18[/tex] units.

√(x + 1) + 3 = 0   ==>   √(x + 1) = -3

has no real solutions, since the square root cannot be a negative number. But if we were to ignore that for the moment, one might try taking the square of both sides, which gives

(√(x + 1))² = (-3)²   ==>   x + 1 = 9   ==>   x = 8

But this is not a valid solution, since

√(8 + 1) = √9 = 3 ≠ -3

While -3 is a square root of 9, we had started off with the *positive* square root of x + 1.

Answer:

[tex]\frac{-7}{12} , \frac{-6}{12} , \frac{-5}{12},\frac{-4}{12} ,\frac{-3}{12} ,\frac{-2}{12} ,\frac{-1}{12},\frac{1}{12} ,\frac{2}{12}[/tex]

Step-by-step explanation:

Given :

To find rational number between -2/3 and 1/2

Firstly need to equate their denominator

[tex]\frac{-2(4)}{3(4)} =\frac{-8}{12} \\\frac{1(3)}{4(3)} =\frac{3}{12}[/tex]

Now,

Rational number between these two numbers will be :

[tex]\frac{-7}{12} , \frac{-6}{12} , \frac{-5}{12},\frac{-4}{12} ,\frac{-3}{12} ,\frac{-2}{12} ,\frac{-1}{12},\frac{1}{12} ,\frac{2}{12}[/tex]

Answer:

B. [tex]\frac{x + 6}{10x}[/tex]

Answer:

4/27

Step-by-step explanation:

F(x) = 4(1/3)^x

Let x =3

F(3) = 4(1/3)^3

Exponents first

F(3) = 4 * 1/27

Then multiply

f(3) = 4/27

Answer:

4/27

Step-by-step explanation:

f(x) = 4(1/3)^x

f(3) = 4(1/3)^3

f(3) = 4(1/27)

f(3) = 4/27

hope that helps

Answer:

Original Price = $72.

Step-by-step explanation:

You first need to know that $3.60 is 5% of the original price.

Then you need to multiply by 20, because 100/5 is 20, meaning that the price multiplied is $72.

The answer is $72.

Answer:

662.44 total paid

Step-by-step explanation:

907.07X.33(33% off)=299.33 discount

907.07-299.33=607.74 sales price

607.74+.09=54.70 sales tax

607.74+54.70=662.44 sales price including sales tax

Answer: [tex]100\ cm^3[/tex]

Step-by-step explanation:

Given

The ratio of mixture of sand and cement is 5:3

If the total volume of mixture is [tex]160\ cm^3[/tex]

Suppose there is 5x and 3x cubic centimeter of sand and cement respectively i.e.

[tex]\Rightarrow 5x+3x=160\\\Rightarrow 8x=160\\\Rightarrow x=20\ cm^3[/tex]

Sand [tex]5x=5\times 20=100\ cm^3[/tex]

So, there is [tex]100\ cm^3[/tex] of sand in the mixture

Answer:

In a cube, the length and width are the same, so both sides will be 7 cm, yielding an area of 49 square centimeters. The surface area of a 7 cm cube will be 294 cm2 . Hope this helps!

Answer:

There are no graphs

Step-by-step explanation:

"what graph below best represents the range for a tip "

Brian

120 * .2 = 24

24 < d

Hayden

120 * .25 = 30

d ≤ 30

24 < d ≤ 30

Answer:

20 km

Step-by-step explanation:

Circumference is given by

C = pi*d

20 pi = pi *d

Divide  each side by pi

20 =d

I dkabouthtisoneiuisrhihurg

Answer:

Option A is correct answer

hear is explaination

[tex]\longrightarrow{\blue{a.\:90}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] - 3xy[/tex]

Plugging in the values "[tex]x = 5[/tex]" and "[tex] y = -6[/tex]", we have

[tex] = - 3(5)( - 6)[/tex]

[tex] = - 3( - 30)[/tex]

[tex] = 90[/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]