What is each logarithm expanded?
b. log₃9x⁵

Answer:

Step-by-step explanation:

What is the value of m in the equation 1/2m - 3/4n when n = 8?

1/2m - 3/4*8 =

1/2m = 6

m = 12

--------------------

The density of iodine is about 6.281 times the density of acetone. The density of acetone is about 785 kilograms per cubic meter. What is the density of iodine as a repeating decimal?

The density of iodine as a repeating decimal is 4930.585 kilogram.

Given the density of iodine is about 6.281 times the density of acetone.

We can write as x=6.281y      (take x=6.281y as equation(1))

Here, x is the density of iodine and y is the density of acetone

Now take the density of acetone is about 785 kilograms per cubic meter.

We can write as y=785 kg.

Now substitute y=785 kg in equation (1)

We get x=6.281[tex]\times\\[/tex]785 kg

x=4930.585 kg

Therefore, The density of iodine as a repeating decimal is 4930.585 kilogram.

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The density of iodine as a repeating decimal is 4930.585 kilogram. when the density of iodine is about 6.281 times the density of acetone, the density of acetone being 785 kilograms per cubic meter.

As given in the question the density of iodine is about 6.281 times the density of acetone.

It can be written as x=6.281y      (take x=6.281y as equation(1))

Here, x is the density of iodine and y is the density of acetone

Now the density of acetone is about 785 kilograms per cubic meter as given in question

So, y=785 kg.

Now substituting y=785 kg in equation (1)

it is calculated as x=6.281 x 785 kg

x=4930.585 kg

Therefore, The density of iodine as a repeating decimal is 4930.585 kilogram.

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The graphical representation in the sample that would be best for her data is a bar graph.

It should be noted that based on the information, the doctor gathered data from a random sample of 10 pediatricians in the state and wanted to create an appropriate graphical representation for the data.

It should be noted that the bar graph will be applicable. This is because it will display the categories of data with a bar to represent the blood pressure of the children.

This can then be used to analyze the needed information.

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The required expression or inequality for possible widths of the rectangle is -4 < x < 3.

Given:

A rectangle has a length 6 meters more than six times the  width.

The area of the rectangle is less than 72 meters  squared.

We have to find,

The expression or inequality that represents all possible  widths of the rectangle.

Let x be the width of the rectangle.

Length of the rectangle is 6 meters more than six times the  width.

length = 6x + 6

Area of rectangle is:

Area = length × width

Area = (6x + 6) × x

Area = 6x² + 6x

The area of the rectangle is less than 72 meters  squared.

6x² + 6x < 72

6x² + 6x -72 < 0

Divide both sides by 6.

x² + x - 12 < 0

x² + 4x - 3x - 12 < 0

x(x + 4) - 3(x + 4) < 0

(x + 4) (x - 3) < 0

It is true if one factor is negative and other is positive. So,

x - 3 < 0 ⇒ x < 3  ...(i)

x + 4 > 0 ⇒ x > -4  ...(ii)

Using (i) and (ii), we get

-4 < x < 3

Therefore, the required expression or inequality for possible widths of the rectangle is -4 < x < 3.

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Answer:

AD

Step-by-step explanation:

It is the only segment that meets a side of triangle ABC at a right angle.

Rearrange the Fraction in the order of least to largest:

A fraction is a portion of a larger total. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complicated fraction contains a fraction in either the numerator or the denominator.

Fractions are significant because they indicate what percentage of a whole you require, have, or desire. In baking, fractions are used to indicate how much of an ingredient to use.

Fractions are a vital basis for studying more advanced math's. As a student's first introduction to abstraction in mathematics, fractions give the greatest foundation for algebra.

Rearrange the items in the order of least to largest.: 1/8 > 1/9

Rearrange the items in the order of least to largest.: 1/3 > 1/9

Rearrange the items in the order of least to largest.: 1/10 < 1/9

Rearrange the items in the order of least to largest : 5/9 > 1/9

Rearrange the items in the order of least to largest.:1/90​ < 1/9

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Answer:

74

Step-by-step explanation:

All the angles of a triangle add up to 180

66+40 = 106

To find the missing angle...

180-106 = 74

Answer:

ANGLE A=74

Step-by-step explanation:

LET ANGLE A BE X

ANGLE B=40°

ANGLE C=66°

SUM OF ADJACENT ANGLE IS 180°

SO, WHEN:

40+66+X=180

X=180-106

ANGLE A=74°

HAVE A NICE DAY!!

Answer:

*A = 60 sq units

Step-by-step explanation:

Area(*A) = Length(*l)×breath (*b)

Answer:

Area = 60

Step-by-step explanation:

First make the rectangle 12 and 4 and a square 6 and 2.

12*4=48

6*2=12

48+12=60

Step-by-step explanation:

t - 5 = 12 | add 5 to both sides

t = 17

and that is it. that's all we needed to do.

The quotient of 3 and 1 over 5 divided by 1 over 3 is 9.6

We we would start first by having the definition for the term quotient. This is defined as the value that is gotten when we divide on quantity by another quantity.

From the definition that we have gotten here, we would have to divide the values by themselves and get the final solution.

We have  3 and 1 over 5 divided by 1 over 3 to be represented as

[tex]3\frac{1}{5} / \frac{1}{3}[/tex]

This would be rewritten as

(16 /5) / (1/3)

= 16 / 5 x 3/1

= 48 / 5

= 9.6

Hence the quotient of 3 and 1 over 5 divided by 1 over 3 is 9.6

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The simplest ratio of squares to total shapes will be 2:7.

A ratio in mathematics shows how many times one number is contained in another. When two objects are related using numbers or amounts, the relationship is known as a ratio. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

A ratio can have any number of quantities, such as counts of people or things or measurements of length, weight, time, etc. Both numbers must be positive in most situations. From the information, there are 4 squares as 10 triangles.

Therefore, the simplest ratio of squares to total shapes will be:

Number of squares = 4

Total shapes = 4 + 10 = 14

Ratio = 4 / 14

Ratio = 2/7

Therefore, the simplest ratio of squares to total shapes will be 2:7.

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There are4 squares and 10 triangles. What is the simplest ratio of squares to total shapes?

After direct variation y = -4 when x = -3.

So,

The initial statement is y = kx

Then to find y when x = -3.

When x = -3:

Therefore, y = -4 when x = -3.

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Answer:

  a. P = 190t -373,930 . . . . . t=actual year number

  b. P = 6640

Step-by-step explanation:

Given the two points (1991, 4360) and (1999, 5880) on a linear relation between years and moose population, you want a formula for the population (P) and an estimate of the population in 2003.

We can use the point-slope form of the equation for a line to write the formula for moose population. To do that, we need to know the slope of the line.

The slope is given by the formula ...

  m = (y2 -y1)/(x2 -x1) . . . . . . . . line through points (x1, y1) and (x2, y2)

Using the given point values, we have ...

  m = (5880 -4360)/(1999 -1991) = 1520/8 = 190

The point-slope equation for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

Using the first ordered pair, we can write the equation as ...

  y -4360 = 190(x -1991)

  y = 190x -373,930 . . . . . . . where x is the actual year number

Using P and t for the variables, the formula is ...

  P = 190t -373,930

Using t=2003, the above formula evaluates to ...

  P = 190(2003) -373,930 = 380,570 -373,930

  P = 6,640

The linear model predicts the 2003 population to be 6640 moose.

__

Additional comment

The formula above uses actual year number. The year value can be translated any way you might want. For example, using t = years after 1991, the formula would be ...

  P = 190(t +1991) -373,930

  P = 190t +4360

Then t=12 for year 2003.

The greatest integer that is less than the value of the logarithm log17.52 is 1.

We are required to check the value of greatest integer that is less than log17.52

As no base is mentioned, let us consider the base to be 10

Thus, we are required to find the value of log₁₀17.52

log₁₀17.52=log₁₀10+log₁₀7.52

log₁₀10=1

log₁₀7.52=log₁₀752/log₁₀100

                =log₁₀752-2log₁₀10

                = 2.876-2=0.876

Thus, log₁₀17.52=1+0.876 =1.876

Thus , log₁₀17.52 is 1.876

Therefore, The greatest integer that is less than the value of the logarithm log17.52 is 1

Disclaimer:

Since no base has been provided for the logarithm, 10 has been considered to be the base.

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Answer:

D)21

Step-by-step explanation:

I hope I can help. You won't make a mistake there

Answer:

Answer is D) 21

[tex]{ \tt{ {x}^{2} - 7x + 3 = 0}}[/tex]

Sum of roots [L + M]: -(-7) = 7

Product of roots [ LM ]: 3

[tex]{ \rm{L {}^{2} M +LM {}^{2} = LM(L + M )}} \\ \\ = { \rm{3(7)}} \\ \\ = 21[/tex]

Answer:

3,308

Step-by-step explanation:

the internet said that 3,308 was the answer.

[tex]827 \times 4 \approx820 \times 4[/tex]

[tex]820 \times 4 = 800 \times 4 + 20 \times 4 \\ 820 \times 4 = 3200 + 80 \\ 820 \times 4 = 3280[/tex]

[tex]827 \times 4 \approx3280[/tex]

In reality it's just that additional 4 sevens,so

[tex]827 \times 4 = 820 \times 4 + 4 \times 7 \\ 827 \times 4 = 3280 + 28 \\ 827 \times 4 = 3308[/tex]

Using logarithmic quotient and power rule, we expand each logarithm function log (2√x/5)³ as  3. log (2√x) - log (5).

According to the question, we need to expand  we expand logarithm function log (2√x/5)³.In Logarithms, the power is raised to some numbers (usually, base number) to get some other number. It is an inverse function of exponential function.

Power rule for logarithm: log (a)ˣ = x log (a)

Quotient rule for logarithm: log (a/b) = log (a) - log(b).

⇒log (2√x/5)³

Applying power rule to the above logarithm function, we get

log (2√x/5)³ = 3. log (2√x/5)    →(1)

Applying quotient rule to the equation (1), we get

3. log (2√x/5)  = 3. log (2√x) - log (5)

Hence, using logarithmic quotient and power rule, we expand each logarithm function log (2√x/5)³ as  3. log (2√x) - log (5).

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Answer:

(10+t)*25

Step-by-step explanation:

25 students so the cost for 1 student needs to be multiplied by 25 for all the students

If lunch costs $10 by itself not including the ticket, we don't know how much the ticket costs so lets say ticket cost = t

$10+t = the cost for ONE student

but there are 25 students so, ($10+t)*25 could work

Expressions don't have equal signs so the total is  (10+t)*25

Answer:

x = 61

Step-by-step explanation:

2x + 6 + x - 9 = 180

3x - 3 = 180 add 3 to the side

3x = 183 Divide the sides by 3 And you get 61 for x

Answer:

The correct answer is D) 3.

Step-by-step explanation:

Since the number 63 is a composite number, 63 has more than two factors. Thus, the factors of 63 are 1, 3, 7, 9, 21 and 63.

After expanding logarithm equation is : [tex]\frac{\sqrt{2} \log_{10}(x) }{2y^2}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

            x define expression

Mathematically, if   [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as   [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression can be written as,

[tex]\frac{log_{10}(\sqrt{x})(\sqrt{2} )}{y^2}[/tex]

as, log (√x) = 1/2 log (x)

[tex]= > \frac{\sqrt{2} \frac{1}{2} log_{10}x }{y^2} \\\\= > \frac{\frac{log_{10}x}{\sqrt{2} } }{y^2}\\ \\= > \frac{log_{10}(x)}{\sqrt{2} y^2} \\\\= > \frac{\sqrt{2}log_{10}x }{2y^2}[/tex]

Thus, Simplification of given expression is : [tex]\frac{\sqrt{2} \log_{10}(x) }{2y^2}[/tex]

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Step-by-step explanation:

so first just think about the question 7(x + 5)

Based on the formulas given for PR and QR, the length of PR is 19.8 units.

The shape that is given is an equilateral triangle. What this means is that all the sides of the triangle are equal.

This means that PR and QR are therefore equal:

PR = QR

This can help us to find the value of n by equating both formulas:

2n + 9 = 7n - 18

The value of n can then be found as:

7n - 2n = 18 + 9

5n = 27

n = 5.4

The length of PR can then be solved by substituting n into the formula:

= 2n + 9

= 2 (5.4) + 9

= 19.8 units

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The consecutive integers are 12 , 13 ,14, and 15 .

Of the four consecutive integers let us consider the smallest integer be x.

Therefore the other 3 integers are x+1 , x+2 and x+3 .

Therefore the sum of the integers are:

x +(x+1)+(x+2)+(x+3)=4x+6

The sum of the integers is given 54.

∴4x + 6 = 54

or, 4x = 54 - 6

or, 4x = 48

or, x = 48 ÷ 4

or, x = 12

Therefore the three other integers are 13,14 and 15.

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Answer:

0.0373

Step-by-step explanation:

move the decimal over 2 spots to the left

when the power is negative, move left

when the power is positive, move right

The three digit number is 727 while the one digit number is 4

Given data

The sum of a three-digit number and a one-digit number is 731.

The product of the numbers is 2,908

let three digit number be x, y, and z

let the one digit be w

The sum

xyz + w =731

xyz * w = 2,908

making xyz the subject of formula

xyz = 731 - w

plugging in xyz into xyz * w = 2,908

( 731 - w ) * w = 2908

731w - w^2 = 2908

w^2 - 731w + 2908 = 0

solving the quadratic equation gives

w = 727 or 4

since w is a one digit number then w = 4

plugging in w = 4 into xyz + w =731 we have

xyz + w =731

xyz + 4 =731

xyz =731 - 4

xyz  = 727

Hence the three digit number is 727 while the one digit number is 4

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Converting the given radicals into their exponential forms, √x³ / ³√x² = ⁶√x⁵

When work with radical numbers, sometimes it is easier to express them in exponential form first.

[tex]\sqrt[n]{a^{b}}=a^{\frac{b}{n}[/tex]

Recall the rules of exponent operations:

Note that the first 3 rules use the same base. If there are more than 1 base number, then group the exponent that have the same base first.

Example:

[tex](2^{3}.3^{-2}) : (2^{-3}.3^{2})=( 2^{3}:2^{-3}).(3^{-2}:.3^{2})[/tex]

Tips: To simplify exponent numbers, sometimes it is useful to modify the base whenever possible.

Example:

8².2⁻⁵ = (2³)². 2⁻⁵ = 2⁶. 2⁻⁵ = 2⁶⁻⁵ = 2¹ = 2

The given problem:

Simplify   √x³ / ³√x²

[tex]\sqrt{x^{3}}=x^{\frac{3}{2}}[/tex]

[tex]\sqrt[3]{x^{2}} =x^{\frac{2}{3}[/tex]

Using quotient rule of exponent:

[tex]x^{\frac{3}{2}}:x^{\frac{2}{3}}=x^{(\frac{3}{2}-\frac{2}{3}) }=x^{\frac{5}{6} }=\sqrt[6]{x^{5}}[/tex]

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Answer:

6

Step-by-step explanation:

(f / g)(x)

= [tex]\frac{f(x)}{g(x)}[/tex]

= [tex]\frac{10x}{2x-1}[/tex] ← substitute x = 3

= [tex]\frac{10(3)}{2(3)-1}[/tex]

= [tex]\frac{30}{6-1}[/tex]

= [tex]\frac{30}{5}[/tex]

= 6