Express the area A of a circle as a function of its circumference C. (A = πr² and C = 2πr)

Answer:

See below

Step-by-step explanation:

2 ^(5+x) = 2^8            (because 256 = 2^8)

 equate the exponents    5+x = 8     then x = 3

1/3 ^(2+x) = 1 / 3^ 6        (because 729 = 3^6 )

  equate the exponents  2+ x = 6    then x = 4

Answer:

a) x = 3

b) x = 4

Step-by-step explanation:

Use the Exponential Power Rule.

[tex]a^x \times a^y = a^{x+y}[/tex]

Also covert the term on the right to the same base as on the left.

If you are allowed to have calculator do [tex]\log_{\text{base}} (\text{number})[/tex] to get the exponent. For example [tex]\log_{2} (256) = 8[/tex], that means [tex]256 = 2^8.[/tex]

Without calculator you can divide with base untill you have it fully factored, then count. For example:

256/2 = 128
128/2 = 64
64/2 = 32
32/2 = 16
16/2 = 8
8/2 = 4
4/2 = 2
2/2 = 1

We had to divide with base two 8 times so 256 = 2⁸.

a)

[tex]2^5 \cdot 2^x = 256\\2^{5+x} = 2^8[/tex]

Now that we have same base we can equate the exponents!

[tex]5 + x = 8\\x = 8 - 5\\x = 3[/tex]

b)

[tex](\frac{1}{3})^2 \cdot (\frac{1}{3})^x = \frac{1}{729}\\\\(\frac{1}{3})^{2+x} = \frac{1}{3^6}\\\\(\frac{1}{3})^{2+x} = (\frac{1}{3})^6[/tex]

[tex]2 + x = 6\\x = 6 - 2\\x = 4[/tex]

Answer: 4) 24

Step-by-step explanation:

Answer:

(5^6)/(5^3) = 5^3 or 125

Step-by-step explanation:

^ = raised power

(5^6)/(5^3)

because base (5) is same:

law of indices: n^a ÷ n^d = n^(a-d)

therefore

5^6 ÷ 5^3 = 5^(6-3)

= 5^3 which is 125

Answer:

x = 5

Step-by-step explanation:

make them equal to each other

3x = 4x-5

x = 5

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The quotient of  (x⁴ - 3x² + 4x - 3) and (x² + x - 3)  is x² - x + 1

The quotient expression is given as:

(x⁴ - 3x² + 4x - 3) ÷ (x² + x - 3)

Factor the dividend of the quotient expression

(x² + x - 3)(x² - x + 1)  ÷ (x² + x - 3)

Cancel out the common factors

x² - x + 1

The above means that:

The quotient of  (x⁴ - 3x² + 4x - 3) and (x² + x - 3)  is x² - x + 1

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Answer:

a triangle with two equal sides

Step-by-step explanation:

Answer:

you did it wrong you have to subtract X from 8900.

First you want to subtract 390 from 8900 and that equals

Answer:

Step-by-step explanation:

from the figure and the values ​​we understand that it is an isosceles right triangle, therefore with the two sides and the 2 angles are congruent,

so x = 25

Answer:

A). X = -3

Step-by-step explanation:

Step 1: Add 20 to both sides.

Step 2: Divide both sides by 7.

Step 3: Check if solution is correct.

Answer:

160in³

Step-by-step explanation:

V = lwh

V = 5(4)(8)

V = 40(4)

V = 160in³

Natural numbers are those that can be counted and ordered. The two consecutive whole numbers between which √37 lies are 6 and 7.

Natural numbers are those that can be counted and ordered. Cardinal numbers are those used for counting, while ordinal numbers are those used for ranking.

The value of √37 is equal to 6.0827 units. Therefore, the two consecutive whole numbers between which √37 lies are 6 and 7.

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Answer:

-16 -14 -12

Step-by-step explanation:

This is the answer because if you subtract -18 from 2, you would get -16 and so on and so on.

Answer:

you have to make a fraction into a whole number.

Step-by-step explanation:

Answer:

  f(3) = 84

Step-by-step explanation:

To evaluate a function for a specific value of the variable, put the value in the function's expression where the variable is, and do the arithmetic.

__

Sometimes it works well to simplify the expression a bit.

  f(x) = 16x^2 -20x = 4x(4x -5)

  f(3) = 4(3)(4(3) -5)) = (12)(7)

  f(3) = 84

The tables that can be used to show that the functions that made them are inverses of each other are the tables attached.

When functions are inverses of each other, they will give inverted x and y values.

This means that the value of x for one function, will be the value of y for the other function.

The tables that have inverse functions will therefore have a table where x values of:

627, 227, 27, 2, and 27 which will be y values in the other table.

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To produce a 75% solution, it is required to add a total of 3.85 ounces of pure salt to the initial solution.

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Answer:

some people an fly high until good bye

Step-by-step explanation:

Answer:

The final balance would be $1,528.84

Step-by-step explanation:

The final balance would be $1,528.84 and the total compound interest would be $993.84

By applying the central angle property, the measure of angle HLK is equal to 29°.

The central angle property states that an inscribed angle is equal to half the measure of a central angle that is subtended by the same arc.

This ultimately implies that, a central angle is double (twice) the measure of an inscribed angle that is subtended by the same arc.

By applying the central angle property, we have:

HK = 2m∠HLK

58 = 2m∠HLK

m∠HLK = 58/2

m∠HLK = 29°.

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Answer:

7

Step-by-step explanation:

Substitute 2 into x

g(2)= 3(2)+1

     = (3x2)+1

     = 6+1

     = 7

Answer:

the answer is c 4 hours because it's 75 per hour

Answer:

2 190km

Step-by-step explanation:

365×3= 1 095

1 095×2km= 2 190km

Answer:

Its a linear function as there is a common difference of -9.

Step-by-step explanation:

x  y      Difference

1   4    

2  -5      -9

3 -14      -9

4 -23     -9

5 -32     -9

For a difference in x of we have a difference in y  of -9.

Answer:

Pick up point  is 1.43 km from the school and drop point is 3.57 km from the school  ( to the nearest hundredth).

Step-by-step explanation:

School <----------- 5 km ---------------> Home

_______ P _______ D _______        

      x  km          y km        5-x-y km

                     _______

                           y      

                     _________________

                                  5-x km

D is the point where Peter drops off N and P is the pick point x km from the school  where  Peter picks up R. He travels back y km to pick up R.

We work in times:

Time = distance / speed

The time that  R walks from the school to point P is the same  as Peter travels the distance  (x + 2y) km, so we have

x/5 =  (x + 2y)/20

20x = 5x + 10y

15x - 10y = 0     A

The time that N walks home equals the time that Peter travels y + 5 - x km.

So (y + 5 - x)/20 = (5 - x - y)/5

5y + 25 - 5x = 100 - 20x - 20y

15x  + 25y = 75

3x + 5y = 15   B

Solving equation A and B

15x - 10y = 0

3x + 5y = 15

Multiply the second equation by 2:

6x + 10y = 30

Adding this to the first equation

21x = 30

x = 30/21 = 1.4285

So  3(1.4285) + 5y = 15

y = 2.1428

Pick up x  = 1.43 km

and the drop is 1.43 + 2.14 = 3,57 km from the school

Answer:

9.73  cm to 2 DP

Step-by-step explanation:

Total of the  lengths involved = 7*9.4 +  5*10.2

= 116.8 cm

So the mean of the 12 fingers

= 116.8/12

= 9.73  cm to 2 DP.

Answer:

This is correct because linear equations have to be in slope-int form

Step-by-step explanation:

Step-by-step explanation:

to add 8% the simplest operation is to multiply the basic amount by 1.08.

so,

£9.45 = original price × 1.08

original price = £9.45/1.08 = £8.75

the price before the increase was £8.75.

Answer:

A

Step-by-step explanation:

The formula for a rectangular prism is length*width*height. Thus, the equation would be 6*4*16, which equals 384 cm^3.

Answer:

hello!!!!

im pretty sure the answer is (x, y) --> (-3x, -3y)

please read the explanation it always helps!!!

Step-by-step explanation:

reduction most likely means that you are dealing with dilations in geometry....

and that means you will need to multiply both x and y by a negative number.

i hope this helps!!!