MATHEMATICS HIGH SCHOOL

What value of n makes the equation true?(2x^9y^n) (4x2 y 10) = 8x^11y^20
0 1
02
O 10
O 30

Answers

Answer 1
Answer:

The value of n which makes the exponential value equation true is n = 10

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be A

Now , the value of A is

A = ( 2x⁹yⁿ ) ( 4x²y¹⁰ ) = 8x¹¹y²⁰

So , from the laws of exponents , we get

mᵃ×mᵇ = mᵃ⁺ᵇ

( 2x⁹yⁿ ) ( 4x²y¹⁰ ) = 8x⁹⁺²yⁿ⁺¹⁰

( 2x⁹yⁿ ) ( 4x²y¹⁰ ) = 8x¹¹yⁿ⁺¹⁰

And , the value of A is = 8x¹¹y²⁰

So , on simplifying , we get

8x¹¹y²⁰ = 8x¹¹yⁿ⁺¹⁰

y²⁰ = yⁿ⁺¹⁰

Since the bases are same , the powers are also same

20 = n + 10

Subtracting 10 on both sides , we get

n = 10

Hence , the exponential equation is solved and n = 10

To learn more about exponents click :

brainly.com/question/28966438

#SPJ7
Answer 2
Answer:

Answer:

02

Step-by-step explanation:

30is the beginning answer

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Solve [4x +2] =6
Select one:
O a. 1
b. 2
O c. 1 or -2
O d. -1 or 2​

Answers

Answer:

x=1

Step-by-step explanation:

Steps:

1: Step 1: Subtract 2 from both sides.

4x+2−2=6−2

4x=4

2: Step 2: Divide both sides by 4.

4x4=44x=1

Answer: x=1

Hope this helps.

Answer:

1

Step-by-step explanation:

Given expression:

4x+2=6

Bringing 2 to the other side, it becomes negative..

4x=6-2 = 4

4x=4

again 4 brought to rhs n divided..

x=4/4

x= 1

So the correct option is (a)

What is the constant of proportionality in the equation StartFraction x over y EndFraction = StartFraction 2 over 9 EndFraction?StartFraction 2 over 9 EndFraction
2
StartFraction 9 over 2 EndFraction
9

I NEED HELP QUICK!

Answers

We have been given an equation (x)/(y)=(2)/(9). We are asked to find constant of proportionality from our given equation.

We know that two directly proportional equations are in form y=kx,where y is directly proportional to x and k is constant of proportionality.

Let us rewrite our given equation by cross multiplying as:

2y=9x

Now we will divide both sides of equation by 2.

(2y)/(2)=(9x)/(2)

y=(9)/(2)x

We can see that our equation is in form y=kx and constant of proportionality is (9)/(2).

Answer:

9

----

2

Picture:

A normal window is constructed by adjoining a semicircle to the top of an ordinary rectangular window, (see figure ) The perimeter of the window is 12 feet. what dimensions will produce a window of maximum area? (Round you answers to two decimal places ) what is the width x= what is the length y.?(Question2) write the function in the form f(×) = ×^3- 6×^2- 15×+9, k = -2.
f (×)=?

Answers

Let's find the perimeter of the window.

The bottom side is x. The left and right sides make 2y.
The perimeter of a circle is 2\pi r, so the perimeter of a semicircle must be \pi r, The radius is \frac{1}2x, so that gives \frac{1}2\pi x for the curve. All of that is equal to 12.

x+2y+\frac{1}2\pi x=12

We only want to use one variable to create the area formula, so let's solve for y.

2y=12-x-\frac{1}2\pi x

y=6-\frac{1}2x-\frac{1}4\pi x

Now that we have a value for y in terms of x, we can find the area in terms of x.

The area of the rectangle is going to be xy, which then becomes

A_r=x(6-\frac{1}2x-\frac{1}4\pi x

A_r=6x-\frac{1}2x^2-\frac{1}4\pi x^2

The area of the semicircle is going to be \frac{1}2\pi r^2.

Since r=\frac{1}2x, A_(sc)=\frac{1}2\pi (\frac{1}2x)^2.

A_(sc)=\frac{1}2\pi \frac{1}4x^2

A_(sc)=\frac{1}8\pi x^2

Now let's add the areas of the rectangle and semicircle.

A=A_r+A_(sc)

A=6x-\frac{1}2x^2-\frac{1}4\pi x^2+\frac{1}8\pi x^2

A=6x-\frac{1}2x^2-\frac{1}8\pi x^2

If you wanted to factor out \frac{1}8 like you did, this would become

\boxed{A(x)=\frac{1}8(48x=4x^2-\pi x^2)}

Now what we want to do is find what x is when A is at its highest point, Once we have the value for x we can also find the value for y, of course.

Let's put our equation in the general form of a quadratic.

A(x)=(-\frac{1}2-\frac{1}8\pi )x^2+6x

Now we can use the vertex formula x=(-b)/(2a).
(a and b refer to ax^2+bx+c.)

x=\frac{-6}{2(-\frac{1}2-\frac{1}8\pi)}

x=\frac{-6}{-\frac{1}4\pi -1}

x=(-24)/(-\pi -4)

\boxed{x=(24)/(\pi +4)}

Now let's plug that in for y=6-\frac{1}2x-\frac{1}4\pi x.

Since our final answers are in decimal form and not exact form, we can make our lives a little easier here and just use x\approx3.36059492.

y\approx6-\frac{1}2(3.36059492)-\frac{1}4\pi(3.36059492)

y\approx6-(1.68029746+2.63940507809)

\boxed{y\approx1.68029746191}

Let's take our answers for x and y and round to 2 decimal places.

\boxed{x\approx 3.36\ ft}

\boxed{y\approx 1.68\ ft}

sand is falling at the rate 27 cubic feet per minute onto a conical pile whose radius is always equal to its height. how fast is the height of the pile growing when the height is exactly (a) 3 feet (b) 6 feet (c) 9 feet.

Answers

Answer:

Step-by-step explanation:

The formula for the volume of a cone is V = (1/3)(area of base)(height).  If the radius is always equal to the height of the cone, then V = (1/3)(πh²)(h), where we have eliminated r.  Shortened, this comes out to V = (1/3)(π)(h³).  

We want to know how fast h is increasing when h = 3 ft.

Taking the derivative dV/dt, we get dV/dt = (1/3)π(3h²)(dh/dt), or, in simpler terms, dV/dt = πh²(dh/dt).  Set this derivative = to 27 ft³/min and set h = 3 ft.

Then 27 ft³/min = π(3 ft)²(dh/dt) and solve for dh/dt:  (3/π) ft/min = dh/dt when h = 3 ft.

1.5 in.1.5 in.
8 inches tall
The tube of toothpaste shown costs $3.45. Estimate the price per cubic inch of toothpaste.

Answers

Answer:

per inch 0.90 cents hhhhhhjjkolllll
Answer:

Per inch 0.90 cents this is not long enough so i take it as a long word

In the fraction 5/8 what is the term used to designate the5?

Answers


5  = numerator
--
8  = denominator 

you can remember this by remembering that denominator is going to be down
both with a d lol
The number on the top, which in this example is 5
Is called the Numerator

(x)/(y)
x is the numerator
y is the denominator
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