Find the volume of this prism

The value of logarithm expression 2log₅(5x³) + (1/3)log₅(x² + 6) is simplified as log₅[{25x⁶}{∛(x² + 6)}].

Logarithms are another way of writing exponent. A logarithm with a number base is equal to the other number. It is just the opposite of the exponent function.

The logarithmic expression is given as

[tex]2\log _55x^3 + \dfrac{1}{3} \log _5(x^2 +6)[/tex]

We know that formulas

[tex]a \log b = \log b^a\\\\\log a + \log b = \log ab[/tex]

Then we have

[tex]\rightarrow \log _5(5x^3)^2 + \log _5(x^2 +6)^{1/3}\\\\\rightarrow \log _525x^6 + \log _5\sqrt[3]{(x^2 +6)}\\\\\rightarrow \log _5 25x^6 (\sqrt[3]{(x^2 +6)})[/tex]

More about the logarithm link is given below.

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Answer:

B

Step-by-step explanation:

Edge 2022

Answer:

14 - hope this helped :)

Step-by-step explanation:

42 divided by 3

= 13

therefore

42/3 is simplified to 14

Answer:

2

Step-by-step explanation:

To find the x-intercept of the equation we have to substitute y = 0 in it.

=> 0 = 3x - 6

=> 3x = 6

=> x = 2

Therefore the line will meet x-axis at (2,0) which means it'll have x - intercept of 2 units.

Answer:

50 degrees

Step-by-step explanation:

All of the angles in the picture need to add up to 180 degrees.

<TVU = 30 degrees, so the 3 remaining angles need to add up to 150 degrees.

<QVR is = to <RVS  and <RVS is = to <SVT, so all 3 angles are = to each other

<QVR = <RVS = <SVT

We have 150 degrees remaining & all 3 angles have to be the same, so each angle is 50 degrees

Answer:

4

Step-by-step explanation:

20-8 = 12

12/3 = 4

Answer:

EH = 16

Perimeter = 46

Step-by-step explanation:

We see that the ratio between the big shape and small shape is 3:2. 3x=24, so x=8. EH=2x=16.

For the second problem, the perimeter is 46.

This is because it also follows the same rule as 3:2. If you do this for every side, you find out that the sides are 10, 10, 6, 12, and 8. Add them together to get 46.

I hope this helped!

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Answer:

the awnswer is 112 just so you know thats right

Answer: II and III only (2 and 3 only)

Step-by-step explanation: took test and got it right

10^4 micrometres

Step-by-step explanation:

the answer is in the image above

Answer:

n = 2

Step-by-step explanation:

Given equation:

[tex]\left(\dfrac35\right)^2 \times 25=3^n[/tex]

[tex]\textsf{Apply exponent rule }\left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c} :[/tex]

[tex]\implies \left(\dfrac{3^2}{5^2}\right) \times 25=3^n[/tex]

[tex]\textsf{Apply}\: \left(\dfrac{a}{b}\right) \times c=\dfrac{ac}{b} :[/tex]

[tex]\implies \dfrac{3^2\cdot 25}{5^2}=3^n[/tex]

[tex]\textsf{Apply}\:5^2=5 \times 5=25:[/tex]

[tex]\implies \dfrac{3^2\cdot 25}{25}=3^n[/tex]

Cancel the common factor 25:

[tex]\implies 3^2=3^n[/tex]

[tex]\textsf{If}\:a^{f(x)}=a^{g(x)},\:\textsf{then}\:f(x)=g(x) :[/tex]

[tex]\implies 2=n[/tex]

Answer:

n = 2

Step-by-step explanation:

Hello!

We can use the exponent rule to square 3/5.

Now, we can multiply

Now, we need to find how many times 3 is multiplied to get 9 ,and that would be 2

Answer:

2) 2^8

3)7^9

4)  1/3^6

5)x^10

6) y^8

7) x^10

Step-by-step explanation:

The order in which the numbers are drawn is not important will be 1287.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.

When order of selecting things does not matter, then the combination odd n things taking r at a time is given by :-

[tex]nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Given : The total numbers in lottery = 13

The total numbers to choose to win the lottery =- 5

Then the combination of 13 numbers taken 5 at a time is given by

[tex]13C_r=\dfrac{13!}{5!(13-5)!}=1287[/tex]

Hence the order in which the numbers are drawn is not important will be 1287.

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                                        Add the values together

                                                     8 + 9 + 4

                                                          21

Answer:

B) y = x+1

Step-by-step explanation:

the point is (2,3), so x = 2, y = 3

A. y = 3x.  
3 ≠ 3*2

B. y = x + 1.
3 = 2+1

C. y = -3x
3 ≠ -3*2

D. y = x-1
3 ≠ 2-1

An equation is formed of two equal expressions. The equation that demonstrates the additive identity property is (7+4i)+0 = (7+4i).

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The additive identity property states that any number when added to 0, the result is the number itself. Therefore, the equation that demonstrates the additive identity property is (7+4i)+0 = (7+4i).

Learn more about Equation:

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Answer: B on edge

Step-by-step explanation:

Mr. Murphy's calculation of the taxes they are to pay this year is wrong because He has calculated only federal taxes.

State income tax is a direct tax levied by a state on income earned in or from the state.

There are several taxes that an employed person must pay including:

Mr. Murphy only calculated the federal taxes and did not include the state ones which are usually higher than the federal tax. Once he includes the state tax, his calculation will be correct.

In conclusion, state taxes need to be paid as well.

To know more about state taxes at;

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Answer:

a. he has calculated only federal taxes

Step-by-step explanation:

Answer:

D. -1

Step-by-step explanation:

[tex]\text{slope}= -6 =\frac{q-\left( -7\right) }{\left( -1\right) -0} =\frac{q+7}{-1} = -(q+7) = -q - 7\\\Longrightarrow -6=-q-7\Longrightarrow q=6-7=-1[/tex]

Answer:

X = 81

Missing angle measurement = 73 Degrees

Step-by-step explanation:

Sense the angle presented is a strait angle, meaning it has an exact mesurment of 180°

You can take the known portion of 107° and subtract that from 180°, giving you 73°

To find X you take the missing angle's value and add 8, leaving you with 81

Step-by-step explanation:

Unfortunately, you haven't given the coordinates of RST so I can't tell you exactly what the new points will be, but I can tell you what process to follow.

To find a new point rotated 90 degrees counterclockwise around the origin, simply apply the rule:

(x,y) ----> (-y,x)

You would apply this rule of switching the x and y coordinates and y becomes the opposite(so if it was a positive coordinate, it becomes negative and if it was negative, it becomes positive), to get your new coordinates.

Hope this helps :)

Lucy caught 0 ants and 4 beetles on tuesday which he added to his collection.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the number of ants and y represent the number of beetles. Hence:

x + 2y = 8   (1)

also:

x - y = -4   (2)

x = 0, y = 4

Lucy caught 0 ants and 4 beetles on tuesday which he added to his collection.

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Answer:Lucy caught 0 ants and 4 beetles on tuesday which he added to his collection.

Step-by-step explanation:

Answer:

180 degrees

Step-by-step explanation:

A full circle is 360 degrees

Parallel is half of a circle, so, 360/2=180

Hope it Helps

Answer:

c, I believe.

Step-by-step explanation:

Answer:

60000

Step-by-step explanation:

Answer:

Other than your answer...

Step-by-step explanation:

5^6 x 5^5

48,828,125

5^2 x 5^9

hope this helps :)

Answer:

12% :)

Step-by-step explanation:

0.12 x 100 = 12%

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

Angle 3 = 86.8

Angle 6 = 96.4

Angle 7 = 93.2

Step-by-step explanation:

Given :

angle 6 = 4x + 10

angle 7 = 2x + 40

=> angle 6 + angle 7 = 180° { linear pair }

=> 4x+10 +2x+40 = 180

=> 6x+50 = 180

=> 6x = 180-50

=> 6x = 130

=> x = 130/6

=> x = 21.6

so ,the measure of angle 6 = 4x + 10 = 4(21.6) +10 = 86.4+10 = 96.4

the measure of angle 7 = 2x + 40 = 2(21.6) +40 = 43.2+50 = 93.2

now angle 7 = angle 4 + angle 5

and angle 3 + angle 4 + angle 5 = 180°

so, angle 7 + angle 3 = 180

=> 93.2 + angle 3 = 180

=> angle 3 = 180 - 93.2

=> angle 3 = 86.8

Answer:

Step-by-step explanation:

To find the unknown angle in this geometry, you must make use of several facts.

__

The long arc intercepted by the inscribed 130° angle will measure 2×130° = 260°. The sum of arcs of a circle is 360°, so the short arc intercepted by the 130° angle (and by x°) is ...

  x° = 360° -260° = 100°

The measure of angle x is 100°.

Answer:

239

Step-by-step explanation:

239 because do the answers in the parenthesis first then do the rest.

Answer:

[tex]3 \times 3 \times 3 = 27[/tex]

This is a correct answer

Step-by-step explanation:

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Answer:

Step-by-step explanation: