Pluto is approximately 2.7 miles from the Sun. Venus is approximately 6.7 miles from the Sun.
Approximately how many times greater is the distance of Pluto from the Sun than the distance of Venus from the Sun?

The ordering of the numbers will be 1.25, 1 3/8, ✓2, 1 3/5 and 1.875.

It should be noted that ✓2 = 1.414

It should be noted that 1 3/8 = 1.375

It should be noted that 1 3/5 = 1.6

The other numbers given are 1.25 and 1.875

Therefore, the ordering of the numbers will be 1.25, 1 3/8, ✓2, 1 3/5 and 1.875.

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Answer:

0.05 metrs = 5 cetimeters

Step-by-step explanation:

1 meter = 100 centimeters

0.05 meters = 0.05 * 100 = 5 centimeters

Answer:

30,000

Step-by-step explanation:

Add 6,000 to 48,000, which equals 54,000

You then divide 54,000 by three = 18,000

Multiply 18,000 by 2 = 36,000

Subtract 6,000 frome 36,000 = 30,000

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Answer: f(x)=4

f(x)=√3x−4

f(x)=4x−5

Step-by-step explanation:

Answer:

Rebecca originally had 240 dollars.

Step-by-step explanation:

Let's set B as Rebecca's money and C as Rachel's.

Rebecca has twice as much money as Rachel

B = 2C

If Rebecca gives Rachel $60, then the two of them will have the same amount of money

B - $60 = C + $60

let's combine the 2 by subtracting the second from the first

B - (B - $60) = 2C - (C + $60)

$60 = C - $60

$120 = C

so Rachel had 120 dollars.

Rebecca had twice as much, so 240 dollars.

If Rebecca gives $60 to Rachel, they have $180 each. Everything checks out.

Answer: 1/3-5(n)

Step-by-step explanation:

Answer:

15.5

Step-by-step explanation:

We are trying to find out:

38.7% of what number is 6?

38.7% as a decimal is .387

.387x = 6  Divide both sides by .387

x = 15.503875969

Round 15.5

Answer:

Step-by-step explanation:

90 degree

The product of ∛3 and 5√3 is 15√3⁸ (Option C).

This question can be easily solved by using the concept of roots. The two terms mentioned in the question are ∛3 ( cubic root of 3 ) and  5√3 (5th root of 3 ). This question can be solved in 4 easy steps

Step 1 : Identify the power of the root and take LCM of those numbers.

In this case, the powers of root for ∛3 and 5√3 are 3 and 5, respectively. Take LCM of 3 and 5.

LCM = 3 x 5 = 15

=> We get the LCM of 3 and 5 as 15.

Step 2 : Write the given numbers in the form of fractional powers

∛3 = 3¹ˡ³  => The power of 3 = 1/3

5√3 = 3¹ˡ⁵  => The power of 5 = 1/5

Step 3 : Multiply and divide the powers of the base number ( in this case 3 ) with a number such that you get the denominator as the LCM ( in this case 15 )

1/3  can be multiplied and divided by 5 to get the denominator as 15

=> 1 * 5 / 3 * 5 = 5 /15

1/5  can be multiplied and divided by 3 to get the denominator as 15

=> 1 * 3 / 5 * 3 = 3 /15

Step 4 : Find the product of the two terms

15√3⁵ x 15√3³ = 15√3³⁺⁵ = 15√3⁸

Therefore, using the concept of roots and fractions, we get the product of ∛3 and 5√3 as 15√3⁸.

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Answer:

true,true,false,false

Step-by-step explanation:

true it's the amount of decimal places

true: same with this true

false: if it was 10^5 then yes but it's not

false: there is one too many 10s

The simplified form of the expression [tex]\frac{(2x^{2} +3x^{3} -3x^{2} -3x-4x-3)}{(x-2)}[/tex] is [tex]\frac{3x^{3}-x^{2} -7x-3 }{(x-2)}[/tex]

As per the question statement, we are provided with an expression  [tex]\frac{(2x^{2} +3x^{3} -3x^{2} -3x-4x-3)}{(x-2)}[/tex].

We are supposed to simplify the above mentioned expression.

To solve this question, let us simplify the expression, part by part, i.e., first, let us consider the numerator part which is

[2x² + 3x³ - 3x² -3x -4x - 3].

Here, it is clearly visible that the numerator expression consists of terms having same same variable but with different coefficients, such as

[2x², -(3x²)] and [-(3x), -(4x)]. Therefore, we can perform the mentioned operations on the like terms and thus simplify our numerator.

[tex][2x^{2} +(-3x^{2} )]=(2x^{2} -3x^{2} )=-(x^{2})\\[/tex]

And, [tex][(-3x) + (-4x)]=-(3x+4x)=-x(3+4)=-(7x)[/tex].

Hence, [tex](2x^{2} +3x^{3} -3x^{2} -3x-4x-3)=[+3x^{3}+(2x^{2} -3x^{2})-(3x+4x)-3]\\or, (2x^{2} +3x^{3} -3x^{2} -3x-4x-3)=[+3x^{3}+(-x^{2} )-7x-3]\\or, (2x^{2} +3x^{3} -3x^{2} -3x-4x-3)=(+3x^{3}-x^{2}-7x-3)\\[/tex]

And our denominator is (x - 2). Since, [2x² + 3x³ - 3x² -3x -4x - 3] does not equate to Zero for (x = 2), there (x - 2) is not a factor of the numerator, i.e., the numerator cannot be exactly divided by the denominator.

Therefore, the simplest form of our expression  [tex]\frac{(2x^{2} +3x^{3} -3x^{2} -3x-4x-3)}{(x-2)}[/tex] is [tex]\frac{3x^{3}-x^{2} -7x-3 }{(x-2)}[/tex].

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Answer:

Step-by-step explanation:

56.6 tons.

Based on the slope of the demand curve and the new price of iron ore, the new quantity demanded at the new price of $211 is 49.60 tons

The equation given will allow us to find the new quantity demanded:

y = Mx + c

y = new quantity demanded

m = slope of the demand curve

x = change in price of iron ore

c = y intercept

Solving for the new quantity demanded at the new price gives:

= -3.2 x (211 - 104) + 392

= -342.40 + 392

= 49.60 tons

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The simplest form of the quotient √72x⁵y³z⁸/√3xy²z² is (B) 2x²z³√6y.

So,

Then,

Therefore, the simplest form of the quotient √72x⁵y³z⁸/√3xy²z² is (B) 2x²z³√6y.

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Answer:

1300

Step-by-step explanation:

455 divided by 35%

= 455 x 100/35

= 455 x 20/7

= 65 x 20

= 1300

The total number of people attending the game is 2100.

Given that, at a baseball game, 35% of people attending were supporting the home team, while 65% were supporting the visiting team.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Let the total number of people attending the game be x.

Given, 735 people attending the game supported the home team.

Now, 35% of x=735

⇒ 35/100 × x=735

⇒ 35x=73500

⇒ x=73500/35

⇒ x=2100

Therefore, the total number of people attending the game is 2100.

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We know that 6, 8, 10 and 5, 12, 13 are Pythagorean triples.

The formula to see if a set of three numbers is a pythagorean triple is:

[tex]a^{2} +b^{2} =c^{2}[/tex]

For the first one, we can do

6^2 + 8^2 = 10^2 and see if it is true.

36 + 64 = 100, so this works.

The next one, we can do

5^2 + 12^2 = 13^2

25 + 144 = 169

This also works.

So in conclusion, using the formula, we can prove that they are both Pythagorean triples.

I hope this is clear to you, have a great day! :)

a = y² - x²

b = 2xy

c = x² + y²

where x and y are positive integers y > x

→ In Pythagorean triple number set 6,8,10

→ In Pythagorean triple number set 5,12,13

Answer: 53.2 meters

Step-by-step explanation:

Since 15 seconds is 1/4 of 1 minute, multiply 13.3 by 4 to get 53.2.

The correct interpretation for the given expression is the sum of x and y raised to the power of half n

The expression is given as

(x + y)^n/2

To interpret the expression, we start by evaluating the expression in the bracket and the exponent

So, we have

Hence, the correct interpretation for the given expression is the sum of x and y raised to the power of half n

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Answer:

inductive

Step-by-step explanation:

vbkugu stottlxd5xlhlhclxylyyldydpdyxyo

Answer:

Choice 3 (2/3)

Step-by-step explanation:

Slope is equal to the change in y over the change in x.

If we look at the two coordinates, we'll see that to get from (1, 5) to (7, 9), you need to move up 4 and to the right 6.

4/6 = 2/3, which matches the 3rd choice

Hope this helps

The expression log₃4 + log₃y + log₃8x can be written as [tex]log_{3}32xy[/tex] in  a single logarithm form.

Given that the expression is log₃4 + log₃y + log₃8 x.

We are told to write the expression as a single logarithm.

Change of base theorem is basically used when we have to find the log values having different bases from 10 as we have tables which tell the log values with base 10. We know that [tex]log_{a}b[/tex]=[tex]log_{x}b/log_{x}a[/tex] and

log mn=log m+log n.

The expression is log₃4 + log₃y + log₃8 x.

log₃4 + log₃y + log₃8x=[tex]log_{3}[/tex] (4*y)+  [tex]log_{3}[/tex] 8x

=[tex]log_{3}[/tex] (4*y*8x)

=[tex]log_{3}[/tex] 32xy

Hence the expression log₃4 + log₃y + log₃8x can be written as [tex]log_{3}32xy[/tex] in  a single logarithm form.

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After expanding logarithm equation is : [tex]\frac{3log_{10}(m)p^2}{n^4}[/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} m^3}{n^4 \\ p^-2} \\[/tex]

apply formula log a^x = x log a

[tex]= > \frac{3 log_{10} (m)}{\frac{n^4}{p^2} }\\ \\= > \frac{3 log_{10} (m) p^2}{{n^4} }[/tex]

Thus, after expanding the logarithm equation is :  [tex]\frac{3log_{10}(m)p^2}{n^4}[/tex]

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If something is priced at 30$,then 70% off would make it 9.00$!

Answer:

B

Step-by-step explanation:

35 [tex]\frac{3}{4}[/tex] ≈ 36 ( to the nearest whole number

17 [tex]\frac{5}{6}[/tex] ≈ 18 ( to the nearest whole number )

then 36 in × 18 in

Answer:

The answer to the given question is 6

Logarithmic scale: A measurement scale in which the position is marked using the logarithm of a value rather than the actual value.

A logarithmic equation includes a logarithm in the variable x.

An exponential equation is one in which the variable is represented by an exponent. A logarithmic equation is one in which the logarithm of a variable-containing expression is used.

For logarithmic equations, log b (x) = y is equivalent to b^y = x such that x > 0, b > 0 and b is not equal to 1.

In the given problem, b = 6, x = 6 and y = 1

b = 6

x = 6

y = 1

Substituting the values of b, x and y into the equation b^y = x;

6^(1) = 6

therefore, the value of the given equation log₆6=1 is 6

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the value of the given equation 5x +3=12 Round to the nearest ten-thousandth =   1.8000

In a given base, a round number is a number that ends with one or more "0s." So, 590 is more round than 592, but less round than 600. A round number is frequently interpreted in both technical and casual language to stand for a value or values close to the nominal value represented.

given:- 5x +3=12

simplifying:

5x +3=12

5x = 12 - 3

5x  = 9

x = 9/5

x = 1.8000

the value of the given equation 5x +3=12 Round to the nearest ten-thousandth =   1.8000

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Step-by-step explanation:

3x² - 16x + 2 = 0

ax² + bx + c = 0

a = 3 , b = -16 , c = 2

= p + q.(1 + p)

= p + q + p.q

= -b/a + c/a

= -(-16)/3 + 2/3

= (16 + 2)/3

= 18/3

= 6

Answer:

The exact conversion rates between Liters and Gallons is as follows...

1 Liter = 0.264 Gallons

and

1 Gallon = 3.785 Liters

Yes the students have a party is mrs. Morton reward them 313131 additional times.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most of the time, size comparisons between two numbers on the number line are to be made.  Different types of inequalities are represented by a variety of notations, including: The symbol a b indicates that an is smaller than b. When a > b is used, it indicates that an is bigger than b. A is not equivalent to b in any scenario. Since a is apparently less than or solely greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.

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Answer:

i guess X=5 because 3+5=8?

Step-by-step explanation: