Sixteen and eight hundred fifty-two thousandths written in standard form

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

Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse 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:

80+40x

Step-by-step explanation:

-5x2(2x2-4x-12)

-10(2x2-4x-12)

-20-20+40x+120

-40+120+40x

80+40x

Answer:

x = 16

Step-by-step explanation:

3√x = x - 4

Raise the equation to the second power.

(3√x)² = (x - 4)²

9x = x² - 8x + 16

Rewrite the equation with the values on the left.

-x² + 17x - 16 = 0

x² - 17x + 16 = 0

Factor.

(x - 16)(x - 1) = 0

Set each part equal to 0.

x - 16 = 0

x = 16

x - 1 = 0

x = 1

Your solutions are 16 and 1, but it doesn't end there. Both of these may not satisfy the original equation, so plug them back in.

3√x = x - 4

3√16 = 16 - 4

3(4) = 12

12 = 2

16 is a solution.

3√x = x - 4

3√1 = 1 - 4

3(1) = -3

3 ≠ -3

1 is NOT a solution.

Answer:

32.24

Step-by-step explanation:

To get the height, use Pythagoras theorem on the smaller triangle

8^2=2^2+x^2

x^2=64-4

x=√60=2√15.

then for the base use P.T for the bigger triangle

10^2=y^2+√60^2

y^2=100-60

y=√40=2√10

1/2×(2√10+2)×2√15

=32.24

Then the maximum value of both the quadratic functions is the same. Then the correct option is A.

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

The quadratic functions f(x) and g(x) are described as follows:

f(x) = −4x² + 5

x     g(x)

0       0

1         1

2       5

3        1

4       0

The value of x for which f(x) will be maximum

[tex]\begin{aligned} \dfrac{d}{dx} \ f(x) = 0\\\\\dfrac{d}{dx} \ (-4x^2 + 5) = 0\\\\-8x =0\\\\x = 0 \end{aligned}[/tex]

Then the maximum value of f(x) will be

f(x) = −4(0)² + 5

f(x) = 5

Then the maximum value of both the functions is the same.

More about the quadratic equation link is given below.

https://brainly.com/question/2263981

Answer:

The maximum values is the same for both functions.

Step-by-step explanation:

I took the test on flvs and got it right. And it should be correct too on other places like flvs. Hope this helps.

(please don't report me for advertisement of other websites. I believe how I have put it doesn't break that rule.)

Answer:

The answer is that they both payed $9.00.

Step-by-step explanation:

The both payed $60.00, and 30% of that is $18.00.

( $60.00*.03=$18.00)

$18.00 divided by two (two people, James and Sarah) is $9.00.

So they both payed $9.00 individually.

Answer:

a₄ = 75

Step-by-step explanation:

using the recursive formula and a₁ = 5 , then

a₂ = 2a₁ + 5 = 2(5) + 5 = 10 + 5 = 15

a₃ = 2a₂ + 5 = 2(15) + 5 = 30 + 5 = 35

a₄ = 2a₃ + 5 = 2(35) + 5 = 70 + 5 = 75

Answer:

[tex]a_4=75[/tex]

Step-by-step explanation:

Given:

[tex]\implies a_2=2(a_1)+5=2(5)+5=15[/tex]

[tex]\implies a_3=2(a_2)+5=2(15)+5=35[/tex]

[tex]\implies a_4=2(a_3)+5=2(35)+5=75[/tex]

Answer:

i think its between 2-5

Step-by-step explanation:

Answer:

Step-by-step explanation:

A cube has 6 faces. Area of one face is 4x². To find the total suface area of cube, multiply 4x² by 6

Area of cube = 6 * 4x²

                      = 24x²

Answer:

4 sets

Step-by-step explanation:

16 + 17 + 18 = 51

17 + 18 + 19 = 54

18 + 19 + 20 = 57

19 + 20 +21 = 60

Answer:

A because a prism is the only solid they can be used in that way

We are given the function to differentiate:

[tex]{\quad \qquad \sf \rightarrow y=x^{e^x}}[/tex]

Do take natural log on both sides, then we will be having

[tex]{:\implies \quad \sf ln(y)=ln(x^{e^{x}})}[/tex]

[tex]{:\implies \quad \sf ln(y)=e^{x}ln(x)\quad \qquad \{\because ln(a^b)=bln(a)\}}[/tex]

Now, differentiate both sides by using so called chain rule and the product rule

[tex]{:\implies \quad \sf \dfrac{1}{y}\dfrac{dy}{dx}=e^{x}ln(x)+\dfrac{e^x}{x}}[/tex]

[tex]{:\implies \quad \boxed{\bf{\dfrac{dy}{dx}=x^{e^x}\bigg\{\dfrac{e^x}{x}+ln(x)e^{x}\bigg\}}}}[/tex]

Hence, Option B) is correct

Product rule of differentiation:

Where, u and v are functions of x

The length of the segment AB is the number of units on AB, and the length of segment AB is 14.4 units

The points are given as:

A = (-1,7)

B = (11,-1)

The length of the segment is then calculated using:

AB = √(x₁ - x₂)² + (y₁ - y₂)²

So, we have:

AB = √(-1 - 11)² + (7 + 1)²

Evaluate the exponent

AB = √144 + 64

Evaluate the sum

AB = √208

Evaluate the exponent

AB = 14.4

Hence, the length of segment AB is 14.4 units

Read more about length at:

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Answer:

the first one

Step-by-step explanation:

absolute value is a number's distance from zero, so distance from zero can not possibly be negative. Therefore, |4x-2|=-6 has no solution.

Answer:

It would be the first one because there is no value of x that makes the equation be true since an absolute value can never be negative.

Step-by-step explanation:

Hope this helps:)....if don't help then sorry for wasting your time and may God bless you:)

Answer:

The thickness of the paper doubles each fold: it's an exponential growth.

Step-by-step explanation:

The volume of the post = volume of rectangular prism - volume of cylindrical hole = 3,223.0 cm³.

Volume = (l)(w)(h)

Volume = πr²h

Volume of the post = volume of rectangular prism - volume of cylindrical hole

= (l)(w)(h) - πr²h

= (10)(12)(30) - π(2²)(30)

Volume of the post = 3,223.0 cm³

Learn more about volume of rectangular prism on:

https://brainly.com/question/12917973

Answer:

x < 16

Step-by-step explanation:

∣x−7∣ < 9

x < 9 + 7

x < 16

Answer:

7x < 9

Step-by-step explanation:

because the absolute value of -7 is 7 and 7 + x = 7x.

Answer:

Volume of prism = Area of base× height

= l×b×h

=4.8×23×0.9

= 99.36 m³

All options are incorrect : )

Answer:

The answer is B

Step-by-step explanation:

Im 3 weeks late lol sorry. I took the quiz.

Answer:

- 43

Step-by-step explanation:

f ( x ) = - 2x² + 2x - 3

To find : f ( 5 )

f ( 5 ) = f ( x )

Here,

x = 5

f ( 5 ) = - 2x² + 2x - 3

        = - 2 ( 5 )² + 2 ( 5 ) - 3

        = - 2 ( 25 ) + 10 - 3

        = - 50 + 7

f ( 5 ) = - 43

Answer:

-43

Step-by-step explanation:

oon edge

mark me brain

Answer:

[tex]\bf Area= 90\;in[/tex]

Step-by-step explanation:

Area of ABCD = L * W

[tex]\bf 6\times 12[/tex]

[tex]\bf 72 \;in^2[/tex]

Area of EFGC:- L * W

[tex]\bf 6 \times 3[/tex]

[tex]\bf 18\; in^2[/tex]

Now, the area of the combind rectangles:-

ABCD + EFGC

[tex]\bf 72+18[/tex]

[tex]\boxed{\bf 90\; in}[/tex]

Answer:

21sqrt(6)

Step-by-step explanation:

Hope it helps......

The only true statement that compares the two functions is:

B: The solution to f(x)=g(x) is 1

Here we have the functions:

f(x) = |x - 3| + 1

g(x) = 2x + 1

First, let's find the solution for:

f(x) = g(x)

|x - 3| + 1 = 2x + 1

|x - 3| = 2x

Notice that we have two options, x = 3:

|3 - 3| = 2*3

0 = 6  (x = 3 is not a solution)

And x = 1:

|1 - 3| = 2*1

2 = 2  (x = 1 is a solution).

Now to get the y-value where the graphs intersect, we just evaluate one of the functions in the solution we found above;

f(1) = |1 - 3| + 1  = 2 + 1 = 3

The graphs intersect when y = 3.

Then we conclude that the only true statement is:

B: The solution to f(x)=g(x) is 1

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

Answer:

Step-by-step explanation:

Answer:

X.

10, 20, 30, 40, 50, 60

Add them:

10 + 20 + 30 + 40 + 50 + 60

= 210

Then divide that sum by the many numbers there are, and there are 6 numbers in which we added.

210 ÷ 6

= 35, the mean for this is 35.

F.

4, 5, 6, 2, 3, 5

Add them:

4 + 5 + 6 + 2 + 3 + 5

= 25

Then divide that sum by the many numbers there are, and there are 6 numbers in which we added.

25 ÷ 6

= 4.1666..., the mean for this is 4.17.

I belive the correct answer would be A because if M and N are the signatures it would make sense to add them. Multiply the signatures by the days, and you have your self an equation. So because we added the first two... Nikkis's petition is still the same so we would have to add hers to M again leaving you with the equation of A.

Hope this helps :)

The statement must be true according to the box plot if the data is skewed, and the lowest number of crackers in a package was 7. Option C is correct.

A number line is drawn with numbers equally spaced or sections running the length of it.

A number line should be drawn horizontally and can be extended in any direction indefinitely.

The number line shows the number of crackers lies between 7 and 13. Which is numerically as 7,8,9,10,11,12,13.The number of the digit on the number line skewed is 7.

Hence statement must be true according to the box plot if the data is skewed, and the lowest number of crackers in a package was 7. Option C is correct.

To learn more about the number line refer to the link;

https://brainly.com/question/13189025

Answer:

the answer is C

Step-by-step explanation:

Because im js swag

Answer:

a= 1/b-c

Step-by-step explanation:

Answer:

2/2 = 1

Step-by-step explanation:

Slope intercept equation:

y2 - y1 / x2 - x1 = slope