Mathematics College

Simplify 3a • 3b ÷ 3c ÷ 3d. The exponent on 3 is _____.

Answers

Answer 1
abcd is your exponent
Answer 2

The correct answer is  2.

To simplify the expression 3a • 3b ÷ 3c ÷ 3d, we need to apply the laws of exponents and combine the coefficients and variables.

Given expression: [tex]3a \cdot 3b \div 3c \div 3d[/tex]

[tex]\text{Step 1: Rewrite the expression using exponents}[/tex]

[tex](3^1 \cdot a) \cdot (3^1 \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]

[tex]\text{Step 2: Apply the laws of exponents for multiplication and division}[/tex]

[tex](3^1 \cdot 3^1 \cdot a \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]

[tex]= (3^{1 + 1} \cdot a \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]

[tex]= (3^2 \cdot a \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]

[tex]\text{Step 3: Simplify the expression by combining the exponents and coefficients}[/tex]

[tex](3^2 \cdot a \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]

[tex]= (3^2 \cdot a \cdot b) \div (3^{1 + 1} \cdot c \cdot d)[/tex]

[tex]= (3^2 \cdot a \cdot b) \div (3^2 \cdot c \cdot d)[/tex]

[tex]= \frac{a \cdot b}{c \cdot d}[/tex]

Therefore, the simplified expression is [tex]\frac{a \cdot b}{c \cdot d}[/tex], and the exponent on 3 is 2.

Related Questions

Solve. 3x2 − 6x = 24 A) x = 2, x = 4 B) x = 3, x = 4 C) x = −2, x = 4 D) x = −4, x = 3

Answers

 3x^2 − 6x = 24
3x^2 − 6x - 24 = 0
3(x^2 - 2x - 8) = 0
3(x - 4)(x + 2) = 0
x - 4 = 0; x = 4
x + 2 =0; x = -2

answer
C) x = −2, x = 4

Answer:

First Answer - C

Second Answer B

Step-by-step explanation:

A large Pizza has a diameter of 18 inches. If each large pizza is cut into 10 equal slices, what is the approximate area of 3 slices of pizza?

Answers

--------------------------------------
Find Radius
--------------------------------------
Radius = Diameter ÷ 2
Radius = 18 ÷ 2
Radius = 9 inches

--------------------------------------
Area of the Pizza
--------------------------------------
Area = πr²
Area = π x (9)²
Area = 81π
Area = 254.47 in² (nearest hundredth)

--------------------------------------
find area of 1 slice of pizza
--------------------------------------
10 slices = 254.47 in²
1 slice = 254.47 ÷ 10
1 slice = 25.44 in² 

--------------------------------------
Find area of 3 slices of pizza
--------------------------------------
1 slice = 25.44 in²
3 slices = 25.44 x 3 
3 slices = 766.32 in²

--------------------------------------
Answer: 766.32 in²
--------------------------------------

Gaff has used 331/3 of his monthly minutes on his cell phone plan. If he already used 200 mintues, how many does he have left this month?

Answers

The first step to solve this problem is to compute for the total minutes allowable in his cell phone plan. To compute for this, you have to divide the number of minutes consumed by the fraction of the time consumed.

200 minutes / 33 1/3% = 600 minutes

To compute for the remaining minutes left for this month, you have to deduct the consumed minutes to the total allowable minutes in his plan.

600 minutes – 200 minutes = 400 minutes left

The equation of the circle whose center is at (3, 7) and whose radius is 6 is a. (x + 3)² + (y + 7)² = 6 b. (x + 3)² + (y + 7)² = 36 c. (x - 3)² + (y - 7)² = 36

Answers

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{7}{ k})\qquad \qquad radius=\stackrel{6}{ r} \\\\\\ (x-3)^2+(y-7)^2=6^2\implies (x-3)^2+(y-7)^2=36[/tex]

Helene bought 6 bottles of juice. The bottles were on sale at 10 bottles for $12. Which explanation correctly tells how to calculate the cost of 6 bottles? A. Step 1 Multiply $12 by 10 to figure out the cost of 1 bottle. Step 2 Divide that cost by 6. B. Step 1 Divide $12 by 10 to find out the cost of 1 bottle. Step 2 Multiply that cost by 6. C. Step 1 Multiply $12 by 10 to find out the cost of 1 bottle. Step 2 Multiply that cost by 6. D. Step 1 Divide $12 by 10 to find out the cost of 1 bottle. Step 2 Divide that cost by 6.

Answers

she wanted to buy 6 bottles.
the cost of 10 bottles was $12.
therefore we need to find the cost of one bottle and then find the cost for 6 bottles.                                           
if 10 bottles cost - $ 12                                                                                  
then 1 bottle costs - $ 12 / 10 bottles
                                         
here we divided 12 by 10 , cost of 1 bottle is 12/10 to find the cost of 6 bottles we have to multiply by 6 .12 / 10 x 6
                                                                                 
correct answer is therefore B. divide 12 by 10 and then mulitply by 6
Answer:

Option: B is the correct answer.

B.   Step 1:  Divide $12 by 10 to find out the cost of 1 bottle.

Step 2 :  Multiply that cost by 6.

Step-by-step explanation:

The cost of 10 bottles is: $ 12.

This means that the cost of 1 bottle is:

$ (12/10)=$ 1.2

( Since the cost of  1 bottle will be less and hence the total cost must be divided by the number of items in order to obtain the cost of 1 item)

and similarly in order to find the cost of 6 items we need to multiply the cost of 1 item by 6.

Hence, cost of 6 bottles of juice is: $ (1.2×6)=$ 7.2

Hence, the correct answer is:

B.   Step 1:   Divide $12 by 10 to find out the cost of 1 bottle.

Step 2:   Multiply that cost by 6.

Write an absolute value equation that has the solutions x=23

Answers

|x -23| = 0 has solution x=23.

An open rectangular box having a volume of 108 in.3 is to be constructed from a tin sheet. find the dimensions of such a box if the amount of material used in its construction is to be minimal. hint: let the dimensions of the box be x in. by y in. by z in. then, xyz = 108 and the amount of material used is given by

Answers

It works out the the optimum box dimensions are those that make the lateral area twice the base area. Of course, the base is a square in order to minimize the lateral area for a given base area.

That being the case, the height of the box is half the base edge length and the dimensions are
.. x = y = 6 in
.. z = 3 in

_____
If x and y are the base dimensions, the volume is
.. xyz = 108
and we want to minimize the area
.. area = xy +2(x+y)z

These equations are symmetrical in x and y, so the solution will require x=y. Making that substitution, we have
.. x^2*z = 108
.. x^2 +4xz = area = x^2 +4x(108/x^2)

That is, we want to minimize x^2 +432/x. A graphing calculator finds the minimum at x=y=6, (and z = 108/x^2 = 3).
Final answer:

Given that the volume of a rectangular box is a product of its length, breadth, and height, we define our problem using the given volume of 108 cubic inches and the formula for the surface area of an open box. To find the dimensions that will use minimal material requires the application of calculus and optimization techniques.

Explanation:

In this problem, we know that the volume of the open rectangular box is 108 cubic inches. The volume of a rectangular box can be calculated with the formula V = xyz where x, y, and z are the length, width, and height. If we let the dimensions of the box be x, y, and z inches respectively, it means that the volume V = 108 = x*y*z.

The amount of material used or the surface area S of an open box (a rectangular box without a top) is given by the formula S = xy + 2xz + 2yz. Here, our task is to minimize this surface area.

To minimize the surface area, we need to employ calculus, specifically the concept of optimal control. However to apply calculus, we need to express S in terms of one variable. We can get this by expressing y in terms of x and z using the volume formula. This leads to a complex optimization problem that involves calculus.

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Nancy builds a hollow wooden ramp for an obstacle course as part of an athletic event. The ramp and the net of the ramp are shown below. Units are in feet. The surface area of the ramp is square feet. Nancy wants to sell the wooden ramp at a price based on the surface area. If each square foot of wood of the ramp is sold for $3, the ramp would sell for $.

Answers

the answer would be $1,296

Nancy can sell the wooden ramp for $486 based on the surface area.

What is Area of Rectangle?

The area of Rectangle is length times of width.

The area of each rectangular face is length times width, so the top and bottom faces have an area of:

2 x (8 feet x 3 feet) = 48 square feet

The side faces also have an area of:

2 x (8 feet x 6 feet) = 96 square feet

The area of each triangular face is one-half the product of the base and the height, so the front and back faces have an area of:

2 x (0.5 x 3 feet x 6 feet) = 18 square feet

The total surface area of the ramp is the sum of the areas of all the faces:

48 + 96 + 18 = 162 square feet

If each square foot of wood of the ramp is sold for $3, then the ramp would sell for:

162 square feet x $3/square foot = $486

Therefore, Nancy can sell the wooden ramp for $486 based on the surface area.

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Math question help please!

Answers

It seems you have to find the ranges of the functions given: y = 3sin(x - π), y = 1 - sin(x), y = 3+4cos(x-π), y = 2+cot(x).

1) y = 3sin(x-π).

The function sine returns a value between -1 and 1, including those limits, so the range interal is [-1,1]  no matter what the input be.

Multiplying the function by the factor 3, stretches the range by that factor.

So, the range of the given function is [-3,3].

2) y = 1 - sin(x)

Againt the range of sin(x) is [-1,1], then when you subtract that from 1, the limits of 1 - sin(x) are: 1 - (-1) = 2 and 1 - 1=0, and any other value wiill be in that range.

So, the answer is [0,2]

3) y = 3 + 4cos(x - π).

The range of the cosine function is also [-1,1], so the range of cos(x - π) is [-1,1].

By multiplying by 4 you stretch the range by that factor, so the new range is [-4,4].

By adding 3, the new borders are 3 - 4 = -1 and 3 + 4 = 7, so the range of the given function is: [-1, 7].

4) y = 2+cot(x)

The range of cot(x) is (-∞,∞), so adding 2 does not modify the range

So, the range for the given function is (-∞,∞).

Be sure to understand how this work. For both functions sine and cosine the range is [-1,1], when you mutiply by a constant factor you scale the range by that factor and when you add a constant you translate the range by that number of units.

A stadium has a total of 18000 seats. Of these 7500 are field seats and the rest are grandstand seats. Write an equation that can be used to find the number of standsteats s

Answers

18000-7500=x because whatever the number "x" is would be your answer trust me.

A spinner has three sections. The table shows the results of spinning the arrow on the spinner 80 times.

What is the experimental probability of the arrow stopping over Section 1?
Section 1 Section 2 Section 3
28 36 16

Answers

Answer: [tex]\frac{7}{20}[/tex]

Step-by-step explanation:

From the given table, The number of times arrow comes results in section 1= 28

The total number of times spinner spins =80

Now, the experimental probability of the arrow stopping over Section 1 is given by:-

[tex]\text{P(Section 1)}=\frac{28}{80}=\frac{7}{20}[/tex]

Hence, the  experimental probability of the arrow stopping over Section 1 is [tex]\frac{7}{20}[/tex]

an aviary places an order for 75 pounds of bird seeds. the order is filled by mixing different kinds of seeds from Bin A Bin B and Bin C Three times as much seed was added from Bin C as Bin A.Ifx respresents the amount of seed from Bin Cwhich expression represents the amount of bird seed mixed from Bin B

Answers

Where are the options?

75 - (x + 1/3x). Thst is the answer


Mario was given some birthday money. He puts the money in an account. Every month after that, he deposits the same amount of money.The equation that models this situation is y = 75x + 50, where y is the amount of money in the account and x is the number of deposits.What does the y-intercept mean in this situation? A. He puts $75 in the account each month. B. He puts $50 in the account each month. C. He was given $75 for his birthday. D. He was given $50 for his birthday.

Answers

The y intercept in the equation y=75x+50 shows that he was given $50 for his birthday which is option D.

What is equation?

Equation is like a relationship between two variables in equal to form which is simplified in order to get the value of both variables.

How to evaluate an equation?

The given equation is y=75x+50 where y is the amount of money in the account and x is the number of deposits. Put the value of x=0 and we get y=50 means when deposit is 0 means no deposits then the amount of money in account is equal to 50 which concludes that Mario was given 50 on his birthday.

Hence y intercept in the equation y=75x+50 shows that he was given $50 for his birthday.

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In in a random survey, 8 out of every 13 students were taking Pre-Algebra, how many students out of the larger population of 8,000 students would be taking Pre-Algebra?

Answers

4923 I believe. It would be 8/13 to find the ratio and then you would multiply that by 8000

Julia has to measure an object. She does not have a ruler. Tell what Julia could do to solve her problem.

Answers

pretty much and in short, make up your own measure.

so... say you can use a tie or something with length, and use that to measure whatever object you need it for.

for example, I can just grab a string, cut it, and measure something, and the measurement may just be that the object is my string 6 times, so I know the length of the object is 6 times the length of the string I cut.

it doesn't quite matter how long the string cut was, all that matters is that is relable or referenciable for reuse.  Later on I could always just get the string measure and convert it to metric, once I found a ruler  or imperial units.

but in the short run, it doesn't really matter the length of the string cut, all that matters is that is referenciable, the object will be 6 times my string cut, here, in France, in Pluto, in Andromeda, anywhere.

bear in mind that the measure units we use today, are only usable because they're referenciable, so if I tell you 15 inches of something, you know how much 15 inches is, so that's all that matters.

please help please ..

Answers

14,400 = P*0.08*30 . . . . . fill in the given numbers

Divide by the coefficient of P to find the value of P.
14,400/2.4 = P = 6000

A building is in the shape of a square pyramid. Each side of the base is 54 meters long and the height is 260 meters.

I know is 1/3 b*h 
is that correct... google failed me before

Answers

check the picture below.

What is one way to determine if a quadrilateral has parallel sides

Answers

One way of finding it is to find the slope of the sides and if the slopes are the same then the lines are parallel.

How many MP3 players in the shipment would you predict to be damaged if 6 MP3s in the sample had been damaged

Answers

Given that there is a little information I would say all is damaged.
Substitute values into the proportion.

Substitute known values. Let x be the number of defective MP3 players in the population.

6 / 50 = x / 3500

50 x 70 = 3500, so multiply the numerator and denominator of the fraction 6/50 by 70.

(6x70) / (50x70) = x / 3500

420 / 3500 = x / 3500

420 = x

Based on the sample, we can predict that 420 MP3 players in the shipment would be defective.

The point of intersection of the diagonals of a rectangle is 4 cm further away from the smaller side than from the larger side of the rectangle. The perimeter of the rectangle is equal to 56 cm. Find the lengths of the sides of the rectangle.

Answers

we have that
If you draw a diagram, and draw perpendiculars from the intersection to the sides of the rectangle, you will see they are the mid point of each side. 

see the attached figure

If the mid point of the smaller side is ---------> x.
The mid point of the larger side will be -----------> (x + 4) 
The full length if the smaller side will be 2x and the length of the larger side will be 2(x + 4) = 2x + 8 

The perimeter = 2 times the length + 2 times the width. 
2(2x + 8) + 4x = 56 
4x + 16 + 4x = 56 
8x = 40 
x = 5 
Therefore 
length = 2x + 8 = 18cm 
width = 2x = 10cm

the answer is
the lengths of the sides of the rectangle are
length = 18cm 
width = 10cm

Answer:

length is 18 and width is 10

Which of the following is a solution to 3tan^3x=tanx?
PLEASE HELP

Answers

Answer:
0, π, 2π, π/6, 5π/6, 7π/6 and 11π/6

Explanation:
3 tan³x = tan x
3 tan³x - tan x = 0
tan x (3 tan²x - 1) = 0
either tan x = 0
This means that:
x = 0 , π or 2π ...........> I

or 3 tan²x - 1 = 0
This means that:
3 tan²x = 1
tan²x = [tex] \frac{1}{3} [/tex]
tan x = ± [tex] \frac{1}{ \sqrt{3}} [/tex]
at tan x = [tex] \frac{1}{ \sqrt{3}} [/tex]
x = π/6 or 7π/6 ...................> II
at tan x = - [tex] \frac{1}{ \sqrt{3}} [/tex]
x = 5π/6 or 11π/6 ..............> III

From I, II and III, the solutions for x would be:
0, π, 2π, π/6, 5π/6, 7π/6 and 11π/6

Hope this helps :)

Answer:

its 150 degrees i think

Step-by-step explanation:

i could be wrong though but i'm like 80% sure im right

Prove or disprove: for all integers a, b, c, if a|bc, then a|b or a|c.

Answers

it is c good luck bro

Find the value of each expression. Show your work.

18.) ₉P₃



Answers

We have to find the value of 9P3 which means the Permutations of 9 objects taken 3 at a time.

The formula of permutations is:

[tex]nPr = \frac{n!}{(n-r)!} [/tex]

In the given case n=9 and r=3. Using these values, we get:

[tex]9P3= \frac{9!}{(9-3)!} \\ \\ = \frac{9!}{6!} \\ \\ = \frac{9*8*7*6!}{6!} \\ \\ =9*8*7 \\ \\ =504 [/tex]

Thus 9P3 is equal to 504.

9! is expanded above using the following  factorial formula:

n! = n(n-1)(n-2)(n-3)....3.2.1

Answer:

The value of the expression is 504.

Step-by-step explanation:

We are given the expression [tex]9P3[/tex].

Now, [tex]9P3[/tex] represents the permutations of 9 objects which are taken 3 at a time.

Also, its value is given by,

[tex]9P3=\dfrac{9!}{(9-3)!}\\\\9P3=\dfrac{9!}{6!}[/tex],

where ! represents the factorial given by,

[tex]n!=n(n-1)(n-2)...3.2.1[/tex]

Thus, evaluating the expression, we get,

[tex]9P3=\dfrac{9!}{6!}\\\\9P3=\dfrac{9\times 8\times 7\times 6!}{6!}\\\\9P3=9\times 8\times 7\\\\9P3=504[/tex]

Thus, the value of the expression is 504.

what is the 5% of 300

Answers

15
300*5/100 =15
That's all
15.
the best way to do it is see the % as a decimal in my opinion, then plug it into a calculator. just move the decimal over to the left 2 times, then multiply the number you're taking the percent out of. So, in this case it would be:
300x.05
which is 15


Maya's penny bank is 3/10
full. After she adds 520
pennies, it is
4/5 full. How many pennies can Maya's bank hold?

Answers

Final answer:

Maya's bank can hold 1733 pennies.

Explanation:

To find out how many pennies Maya's bank can hold, we can set up an equation using the given information. Let's start with the fact that Maya's bank is 3/10 full before adding 520 pennies. This means that 3/10 of the bank's capacity is equal to 520 pennies. We can use this information to find the total capacity of the bank.

Since 3/10 of the bank's capacity is equal to 520 pennies, we can set up the equation (3/10)x = 520, where x represents the total capacity of the bank in pennies.

To solve for x, we can multiply both sides of the equation by 10/3 to cancel out the fraction. This gives us x = (10/3) * 520 = 1733.33. Since we cannot have a fraction of a penny, we round down to the nearest whole number. Therefore, Maya's bank can hold 1733 pennies.

A line has the following vector equation.
[x, y] = [2, -3] + t[5, 1]

a) State the coordinates of three other points on the line. Can you show your work please.
b) Write another vector equation of this line.

Answers

a) You can use 3 different numbers for t. How about 5, 10, 20?
.. [x, y] = [2, -3] +5[5, 1] = [27, 2]
.. [x, y] = [2, -3] +10[5, 1] = [52, 7]
.. [x, y] = [2, -3] +20[5, 1] = [102, 17]


b) You can replace t with any function of whatever parametric variable you want to use. For example, t = -3s+2.
.. [x, y] = [2, -3] +(-3s +2)[5, 1]
.. = [2 -15s +10, -3 -3s +2]

.. [x, y] = [12, -1] +s[-15, -3]

_____
The graph uses "t" instead of "s" for the parameter of the second version of the line. This is a Desmos thing: it likes "t" for parametric equations. The second equation is shown as dotted, so you can see it is the same line as the first equation (solid red).

What does the expression 12f + 24 represent?

Answers:

Answers

24 more than 12 times a number

Answer:

Option 1 : twenty four more than twelve times a number

Step-by-step explanation:

Given : 12f+24

To Find : What does the expression 12f+24 represents?

Solution:

The given expression : 12f+24

Option 1 : twenty four more than twelve times a number

The given expression 12f+24

This expression means 24 more than twelve times f

f is any number

So, we can say twenty four more than twelve times a number .

Thus Option 1 is correct

Option 2 :twenty four more than twelve plus a number

Let f be a number

So, (12+f)+24 is the obttained expression from option 2

Option 3 :twelve times the difference of number and twenty four.

Let f be a number

So, 12(24-f) is the obttained expression from option 3

Option 4 : twelve times the sum of a number plus twenty four

Let f be a number

So, 12(24+f) is the obttained expression from option 4

Thus option 1 represent the given expression 12f+24


Help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Asked and answered elsewhere.
https://brainly.com/question/9281713

check all that apply

Answers

Hi again!


You need to do the same steps I used for the other one.

x² < 81

Find the critical points of the inequality

x² = 81

Then take square root

x = [tex]\pm \sqrt{81} [/tex]

x = 9 or x = -9

Thus,


The answer is option B 9

what is the equivalent fraction of each one. 3/4 and 9/15 and24/40 and 5/7

Answers

3/4 = 6/8
9/15 = 3/5
24/40 = 3/ 5
5/7 = 10/14
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