Mathematics High School

Write (3n)^3 without exponents

Answers

Answer 1
(3n)³
= (3n)×(3n)×(3n)
= 27 × n × n × n
Answer 2

Answer:

Without exponents, we can write the term as:  [tex]27(n)(n)(n)[/tex]

Step-by-step explanation:

The given term is :

[tex](3n)^{3}[/tex]

This can be written as:

[tex](3n)(3n)(3n)[/tex]

= [tex]27n^{3}[/tex]

= [tex]27(n)(n)(n)[/tex]

Hence, without exponents, we can write the term as:  [tex]27(n)(n)(n)[/tex]

Related Questions

If the ratio of the radii of two spheres is 8:9, what is the ratio of the volumes of the two speheres

Answers

let 
A------------> smaller sphere
B----------> larger sphere
radius of sphere A-------> rA
radius of sphere B----> rB

we know that
rA/rB=8/9
the scale factor is equal to 8/9
volume smaller sphere A=[scale factor]³*volume larger sphere B
volume smaller sphere A/volume larger sphere B=[scale factor]³
volume smaller sphere A/volume larger sphere B=[8/9]³----> 512/729

the answer is
512/729

Troy has a box of 600 tiny blocks. Each block is a cube with dimensions of 1 cm x 1cm x 1cm. The blocks are arranged in the box in rows and layers so that there are no gaps. Which could be the dimensions of the box?
a. 5 cm x 10 cm x 12 cm
b. 5 cm x 10 cm x 10 cm
c. 10 cm x 10 cm x 12 cm
d. 200 cm x 200 cm x 200 cm

Answers

you need help or not lol

Blue marbles, green marbles and red marbles are in a ratio of 5 to 7 to 8 in a box. if the total number of marbles is 240, how many green marbles are in the box?

Answers

The fraction of marbles in the box that is green = ⁷/₍₅₊₇₊₈₎
                                                                               
                                                                                =  ⁷/₂₀

If there are 240 marbles in the box, then the number of green marbles = (240 × ⁷/₂₀) = 84 marbles

∴ 84 of the marbles in the bag are green.
                          

Help with algebra 2 please!!!!!!!

Answers

On your graph, you're looking for the little tick between 0 and pi/2. It's at 1. This is your answer, the last option. 

i really need help. please help


Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4^−x and y = 8^(−x−1) intersect are the solutions of the equation 4^−x = 8^(−x−1). (4 points)



Part B: Make tables to find the solution to 4^−x = 8^(−x−1). Take the integer values of x between −3 and 3. (4 points)



Part C: How can you solve the equation 4^−x = 8^(−x−1) graphically? (2 points)

Answers

I'm pretty sure the answer to A would be this: the common point that satisfies both equations (where they intersect) can be shown AS 4^(-x) = 8^(-x-1). 

The answer to B is forming a table. This is quite easier than you think :D.

Start with x on one side (3) and go all the way down to -3 like this:

(x)    4^-x    8^-x-1
-3      64       (Do the same with this)
-2      16
-1       4
0        1
1       1/4
2     .0625 
3   .015625  

So basically you just fill in the x variable with every number between 3 and -3. After that, it's just a bit of math and you've done it!

C is a bit misguided. I think it would be quite simple to just use a graphing calculator, but you would have to actually input all the x and y values from the table. After that, you will have a graph.

I hope I helped! Good luck and good day!

What is the best estimate of the mean price of all the sunglasses on the rack?

Answers

$17 is the answer to this problem
.
The mean of the sample is
  (12 +12 +14 +15 +18 +20 +20 +25)/8 = 136/8 = 17

The best estimate of the mean of the population is
  $17

find the greatest common factor 9x^2a + 9xa^2

Answers

To get the GCF we proceed as follow:
9x^2a+9xa^2
factor out 9 we get:
9(x^2a+xa^2)
=factoring out x we get
9x(xa+a^2)
factoring out a we get
9ax(x+a)
therefore the GCF is 9ax

A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds:f(t) = −16t2 + 48t + 100The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____feet per second.

Answers

For this case we have the following function:
 f (t) = -16t2 + 48t + 100
 The average rate of change is:
 (f (t2) - f (t1)) / (t2 - t1)
 We have then:
 For t1 = 3:
 f (3) = -16 * (3) ^ 2 + 48 * (3) + 100
 f (3) = 100
 For t2 = 5:
 f (5) = -16 * (5) ^ 2 + 48 * (5) + 100
 f (5) = -60
 Substituting values:
 AVR = (-60 - 100) / (5 - 3)
 AVR = -80
 Answer:
 The average rate of change of f (t) from t = 3 seconds to t = 5 seconds is -80 feet per second.

SOLVE FOR X one question 20 points

Answers

We simply need to use the Pythagorean theorem:
a^2 + b^2 = c^2 (c^2 is the hypertenuse)
The equation will look like this:
14^2 + 14^2 = x^2
196 + 196 = x^2
x^2 = 392
So the answer is the square root of 392:
14[tex] \sqrt{2} [/tex]
If you want a decimal form:
14 * 1.414 = 19.796

Answer:

ANSWER IS

Step-by-step explanation:

Find the area of the shaded region.

Answers

1)
Area of bigger rectangle
A = (x+1)(x+1) = x^2 + 2x + 1

2)
Area of smaller rectangle
A = 5(x - 7) = 5x - 35

3)
The difference:
(x^2 + 2x + 1) - (5x - 35)
= x^2 + 2x + 1 - 5x +35
= x^2 - 3x + 36

area of the shaded region = x^2 - 3x + 36
Hello!

You first have to find the area of the bigger rectangle

You find this by multiplying the sides

(x + 1)(x + 1) = x^2 + 2x + 1

Next you have to find the area of the smaller rectangle

(x - 7) * 5 = 5x - 35

Subtract the two polynomials

(x^2 + 2x + 1) - (5x - 35) = x^2 - 3x + 36

The answer is [tex] x^{2} -3x + 36[/tex]

Hope this helps!

Use the given graph to determine the limit, if it exists.
Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x.

Answers

We can see from the graph, as the value of x approaches 2 from the left hand side i.e. the negative side, the value of the function approaches 4.

As the value of x approaches 2 from the positive side i.e. the right hand side, the value of function approaches -4

Since the Right hand limit and the Left hand limit as x approaches 2 are not the same, the limit does not exist at x = 2

Factor this trinomial completely.

–6x2 + 26x + 20

A. –6x2 + 26x + 20
–2(3x2 – 13x – 10)
–2(3x + 2)(x – 5)
B. –6x2 + 26x + 20
–2(3x2 + 11x + 10)
–2(3x + 5)(x + 2)
C. –6x2 + 26x + 20
–2(3x2 – 13x – 10)
–2(3x – 10)(x + 1)
D. –6x2 + 26x + 20
–2(3x2 – 13x + 10)
–2(3x – 5)(x – 2)

Answers

I cannot see the options clearly so I will just do the work and the answer will be at the end.

6x² + 26x + 20
6x² + 6x + 20x + 20
6x(x + 1) + 20(x + 1)
(6x + 20)(x + 1)
2(3x + 10)(x + 1)

2(3x + 10)(x + 1) is your answer.

First, factor out -2 from the trinomial, and then factor the resulting quadratic expression by grouping. The correct factored form is -2(3x + 2)(x - 5).

To factor the trinomial “6x² + 26x + 20 completely, follow these steps:

First, factor out the greatest common factor, which is -2:

“6x² + 26x + 20 = –2(3x² – 13x – 10).Next, factor the quadratic expression inside the parentheses:

3x² – 13x – 10.
We need to find two numbers that multiply to (3 × -10 = -30) and add up to -13. Those numbers are -15 and 2.Rewrite the quadratic equation using these numbers:

3x² – 15x + 2x – 10.Now, factor by grouping:

3x(x – 5) + 2(x – 5) = (3x + 2)(x – 5).Combining everything, we get:

–2(3x + 2)(x – 5).

Therefore, the correct factored form is (Option A) “2(3x + 2)(x – 5).

Write an algebraic expression for the verbal description. the distance a car travels in t hours at a rate of 50 miles per hour

Answers

The correct answer is
d=50t
Where; d is the distance covered in miles
t is the time taken in hours

The algebraic expression is D = 50t where D is the distance covered in miles and t is the time taken in hours.

What is the distance?

Distance is defined as the product of speed and time.

What are Arithmetic operations?

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operations is called arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

Given that the distance a car travels in t hours at a rate of 50 miles per hour

Let the distance covered in miles = D

And t is the time taken in hours

Since distance is defined as the multiplication of speed and time.

So an algebraic expression for the verbal description as

⇒ D = 50t

Hence, the algebraic expression is D = 50t where D is the distance covered in miles and t is the time taken in hours.

Learn more about Arithmetic operations here:

brainly.com/question/25834626

#SPJ2

How many degrees is w?

Answers

See the attached picture:

w = 180 - (180 -142) - 49
w = 180 -38 - 49
w = 93

Answer
w = 93°

does anyone know the surface area for this problem. if so i will mark brainliest.

Answers


From the given volume, we know that the ratio is:
[tex]\text {Ratio of yellow eraser to white eraser = } \sqrt[3]{ \dfrac{16}{2} } [/tex]

From the given area, we know that the ratio is:
[tex]\text {Ratio of yellow eraser to white eraser = } \sqrt{ \dfrac{52}{x} } [/tex]

Equate the two ratio and solve for x:
[tex]\sqrt[3]{ \dfrac{16}{2} } = \sqrt{ \dfrac{52}{x} } [/tex]

Cube both sides:
[tex]\dfrac{16}{2} = \bigg(\sqrt{ \dfrac{52}{x} }\bigg)^3[/tex]

Square both sides:
[tex]\bigg(\dfrac{16}{2} \bigg)^2 = \bigg( \dfrac{52}{x} }\bigg)^3[/tex]

Simplify each term:
[tex]\dfrac{16^2}{2^2} = \dfrac{52^3}{x^3} [/tex]

Cross multiply:
[tex]256x^3 = 562432[/tex]

Divide both sides by 256:
[tex] x^3 = 2197[/tex]

Cube root both sides:
[tex] x = 13[/tex]

Rewrite with only sin x and cos x. Sin2x-cos2x

Answers

From trig identities, we know that sin2x = 2sinxcosx and cos2x = [tex]cos^{2} x - sin^{2} x[/tex]

So sin2x-cos2x = 2sinxcosx - ([tex]cos^{2} x - sin^{2} x[/tex]) in terms of sinx and cosx

On a​ map, 1 inch equals 9.2 miles. two houses are 3.5 inches apart on the map. what is the actual distance between the​ houses? use pencil and paper. show how you can represent the scale with two different ratios. what ratio is more helpful for solving the​ problem? explain.

Answers

The actual distance between the houses is 18.9 miles.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

Given that On a​ map, 1 inch equals 9.2 miles. Two houses are 3.5 inches apart on the map.

To find the actual distance between the​ houses.

Given that,

1 inch = 9.2 miles

Therefore,

∴ we get

3.5 inches = 3.5 × 9.2 miles

                = 13.8 miles

The actual distance is 13.8 miles.

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ5

Final answer:

To find the actual distance between the houses, we can set up a proportion using the given map scale. The actual distance between the houses is 32.2 miles. Using the ratio 1 inch/9.2 miles = 3.5 inches/x is more helpful in solving the problem.

Explanation:

To find the actual distance between the houses, we need to use the scale of 1 inch equals 9.2 miles. We are given that the two houses are 3.5 inches apart on the map.

First, we can set up a proportion to find the actual distance:

1 inch / 9.2 miles = 3.5 inches / x

Cross-multiplying, we have:

1x = 3.5 * 9.2 miles

Simplifying, we get:

x = 32.2 miles

The actual distance between the houses is 32.2 miles.

To represent the scale with two different ratios, we can use the proportion:

1 inch / 9.2 miles = 3.5 inches / x

This ratio is more helpful for solving the problem as it allows us to directly calculate the actual distance using the given map distance and the scale ratio.

if (x+1) is a factor of x^3+2x^2-x-2, find the remaining factors.

Answers

Using synthetic division to divide x³ + 2x² - x - 2.  Since (x + 1) is the factor, we can divide by -1.  See the attached file for the synthetic division.  After that, we are left with x² + x - 2.  This can easily be factored into (x + 2)(x - 1).  The remaining factors are (x + 2) and (x - 1).

Answer:

The other factors are (x-1) and (x+2).

look at the image then answer the question that goes with it

Answers

[tex]\sin(\theta) = \dfrac{\text{opp}}{\text{hyp}}[/tex]

[tex]\sin(60) = \dfrac{x}{8} [/tex]

[tex]x = 8\sin(60) [/tex]

[tex]x = \dfrac{8 \sqrt{3} }{2} [/tex]

[tex]x = 4 \sqrt{3} [/tex]
x =  8 x sin(60)
x = 4sqrt3

Given that the two triangles shown are congruent, explain one way to verify that the corresponding angles of the two triangles are congruent.

A) reflect triangle 1 across the y-axis

B) reflect triangle 2 across the y-axis

C) rotate triangle 2 counter-clockwise 90° about the origin

D) reflect triangle 2 across the y axis and rotate 90° about the origin at

Answers

The two triangles shown are congruent because triangle 1 has been formed from triangle 2 by rotating triangle 2 through and angle of 90°. Thus the correct answer will be:

C) rotate triangle 2 counter-clockwise 90° about the origin 

Answer:

The correct option is C.

Step-by-step explanation:

From the given graph it is noticed that the vertices of triangle 1 are P'(-2,2), Q'(-4,4) and R'(-2,4). The vertices of triangle 2 are P(2,2), Q(4,4) and R(4,2).

If a figure rotated counter-clockwise 90° about the origin, then

[tex](x,y)\rightarrow (-y,x)[/tex]

If we rotate triangle 2 counter-clockwise 90° about the origin, then[

[tex]P(2,2)\rightarrow P'(-2,2)[/tex]

[tex]Q(4,4)\rightarrow Q'(-4,4)[/tex]

[tex]R(4,2)\rightarrow R'(-2,4)[/tex]

If we rotate triangle 2 counterclockwise, then we get the triangle 1.

Therefore the correct option is C.

What is the value of x?

a. 6
b. 6√3
c. 12
d. 12√3

Answers

The answer should be 6(square root of)3 because in a 30 60 90 triangle the small leg is equal to half the length of the hypotenuse and the long leg is equal to the small leg times the square root of 3

Given y = 4x + 3, what effect does changing the equation to y = 2x + 3 have on the slope? 

Answers

the answer is C
Hope this helps!
can I get a brainleist pls!
Final answer:

Changing the slope of the equation from 4 to 2 reduces the steepness of the line in the graph, with the y-intercept remaining constant at 3.

Explanation:

The student asked about the effect on the slope of the linear equation when changing from y = 4x + 3 to y = 2x + 3. The slope of the first equation is 4, which can be seen from the coefficient of x, indicating a rise of 4 on the vertical axis for every increase of 1 on the horizontal axis. When the equation changes to y = 2x + 3, the slope is reduced to 2, which means there is a rise of 2 on the vertical axis for every increase of 1 on the horizontal axis. This change in the slope would cause the line to rotate clockwise when graphed on a coordinate plane. The y-intercept remains the same at 3 since it is unchanged in both equations. Therefore, changing the equation has the effect of decreasing the steepness of the line, but the location where the line crosses the y-axis does not change.

A field goal post in football is 3.33 yards above the ground. If a football player kicks the ball at a 10 degree square angle in a straight line toward the goal post what is the distance away in yards where the ball barely goes over the goal post

Answers

  The distance is 19 yards or 18.9 yards:
because tan(10)=opposite/adjacent=3.33/x and x is distance
x=3.33/tan(10)=18.9 yd
If u multiply 3.33•10 your answer will be 33.3

Write the inverse function for the function, ƒ(x) = x + 4. Then, find the value of ƒ -1(4). Type your answers in the box.

ƒ -1(x) = _________ x ___________ ______

ƒ -1(4) = _____________

Answers

hope you'll understand the workings :)

Answer:  The required values are

[tex]f^{-1}(x)=x-4~~~~~~~~\textup{and}~~~~~~~~~f^{-1}(4)=0.[/tex]

Step-by-step explanation:  We are given the following function f(x) :

[tex]f(x)=x+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We are to find the values of [tex]f^{-1}(x)[/tex] and [tex]f^{-1}(4).[/tex]

Let us consider that

[tex]y=f(x)~~~~~~~~\Rightarrow x=f^{-1}(y).[/tex]

So, from equation (i), we get

[tex]f(x)=x+4\\\\\Rightarrow y=f^{-1}(y)+4\\\\\Rightarrow f^{-1}(y)=y-4\\\\\Rightarrow f^{-1}(x)=x-4.[/tex]

Substituting x = 4 in the above equation, we get

[tex]f^{-1}(4)=4-4=0\\\\\Rightarrow f^{-1}(4)=0.[/tex]

Thus, the required values are

[tex]f^{-1}(x)=x-4~~~~~~~~\textup{and}~~~~~~~~~f^{-1}(4)=0.[/tex]

Which of these is an example of continuous random variable

A. Number of flights leaving an airport
B. Distance of a javelin throw
C. Pieces of mail in your mailbox
D. Attendance at a sporting event

Answers

The correct answer would be Choice B. Distance of a javelin throw.

A continuous random variable is a variable that can be any number between the integers not just the integers themselves.

For example, the distance for a javelin throw could be 6.70819203 feet.
However, you would not say that you have 6.70819203 flights, pieces of mail or people at a sporting event.
Final answer:

The B. distance of a javelin throw is an example of a continuous random variable.

Explanation:

A continuous random variable is a variable that can take any value within a specified range, often associated with measurements and quantities. Unlike discrete variables, it can assume an infinite number of values, typically represented by intervals on the real number line.

Out of the given options, the distance of a javelin throw is an example of a continuous random variable. A continuous random variable is one that can take on any value within a given range. In the case of a javelin throw, the distance can be any real number value within a certain range, such as 0 to infinity. This is in contrast to the other options, which are discrete random variables that can only take on specific whole number values.

Solve system by elimination
y=x^2
y=x+2
SHOW YOUR WORK

Answers

we have that
y=x²----> equation 1
y=x+2-----> equation 2

multiply equation 1 by -1
-y=-x²

add equation 1 and equation 2
-y=-x²
 y=x+2
------------
0=-x²+x+2-------------> -x²+x+2=0-----> x²-x-2=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(x²-x)=2
Complete the square. Remember to balance the equation by adding the same constants to each side
(x²-x+0.5²)=2+0.5²

Rewrite as perfect squares

(x-0.5)²=2+0.5²
(x-0.5)²=2.25-----> (x-0.5)=(+/-)√2.25-----> (x-0.5)=(+/-)1.5
x1=1.5+0.5-----> x1=2
x2=-1.5+0.5---- > x2=-1

for x=2
y=x²----> y=2²----> y=4
the point is (2,4)

for x=-1
y=x²----> y=(-1)²---> y=1
the point is (-1,1)

the answer is
the solution of the system are the points
(2,4) and (-1,1)


describe the steps you would use to solve the following inequality

Answers


[tex] \frac{x + 1}{2x - 3} > 2 \\ x + 1 > 2(2x - 3) \\ x + 1 > 4x - 6 \\ - 3x + 1 > - 6 \\ - 3x > - 7x \\ x < \frac{7}{3} [/tex]

Answer:

Rewrite the inequality so there is a single rational expression on one side, and 0 on the other.

Combine under a common denominator.

Test points in the critical regions.

Construct the solution.

Step-by-step explanation:

Answer Above

On a scatter plot what does it mean when both variables are increasing

Answers

both are getting bigger or increasing you need to rephrase the question 
it means that we have a linear relationship

divide r+5/ r^2+5r-14 by r^2+4-21/r-2

Answers

So we want to divide [tex] \frac{r+5}{r^2+5r-14} [/tex] by [tex] \frac{r^2+4r-21}{r-2} [/tex].
The first thing we are going to do is factor the denominator of the first fraction and the denominator of the second one:
- For our first fraction:
[tex]r^2+5r-14=(r+7)(r-2)[/tex]
Now we can rewrite our first fraction: 
[tex]\frac{r+5}{r^2+5r-14} = \frac{r+5}{(r+7)(r-2)} [/tex]
- For our second fraction: 
[tex]r^2+4r-21=(r+7)(r-3)[/tex]
Now we can rewrite our second fraction:
[tex] \frac{r^2+4r-21}{r-2} = \frac{(r+7)(r-3)}{r-2} [/tex]

Last but not least, we can express our division as a fraction and simplify: 
[tex] \frac{\frac{r+5}{(r+7)(r-2)}}{ \frac{(r+7)(r-3)}{r-2}} = \frac{(r+5)(r-2)}{(r+7)(r-2)(r+7)(r-3)} = \frac{r+5}{(r+7)^2(r-3)} [/tex]

We can conclude that the result of dividing r+5/ r^2+5r-14 by r^2+4r-21/r-2 is: [tex] \frac{r+5}{(r+7)^2(r-3)} [/tex]

The shorter leg of a right triangle is 7 inches shorter than the longer leg. The hypotenuse is 17 inches longer than the longer leg. Find the side lengths of the triangle.

Answers


Or round them all up.

a² + b² = c²

c² - a² = b²

17² - 7² = x²   ↓

289 - 49 = √240

√240 = 15.49193338482967 (rounded 15.49 or 15.5)

Hope this helps,

♥A.W.E.S.W.A.N.♥

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