help me pls asap!! it’s pass due!
Simplify the expression and rationalize the denominator.

Help Me Pls Asap!! Its Pass Due!Simplify The Expression And Rationalize The Denominator.

Answers

Answer 1

Answer: C

Step-by-step explanation:

First, take the square root of both the numerator and denominator. The numerator would then be equal to 6 a^4 b^2 and the bottom would just be sqrt7c. Since you still have a sqrt in the denominator, rationalize the fraction by multiplying sqrt7c to both the numerator and denominator to get rid of the sqrt. This would leave you with answer choice C.

Answer 2

Answer:

[tex]\frac{6a^4b^2\sqrt{7c}}{7c}[/tex]

Step-by-step explanation:

You can distribute radicals across division such that: [tex]\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}[/tex]

So you get the expression: [tex]\frac{\sqrt{36a^8b^4}}{\sqrt{7c}}[/tex]

Similarly with division, you can distribute radicals across multiplication such that: [tex]\sqrt{ab}=\sqrt{a}*\sqrt{b}[/tex], and you can do this multiple times

So our expression on top becomes: [tex]\frac{\sqrt{36}*\sqrt{a^8}*\sqrt{b^4}}{\sqrt{7c}}[/tex]

Whenever we take the square root of a base to an exponent, we simply divide the exponent by two. In general if you take the "nth" root of any base to an exponent, you divide the exponent by n, since: [tex](x^a)^b=x^{a*b}[/tex] and radicals such as: [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex], so you're just multiplying the two, which results in a division of "n" which in this case is 2.

So the square root of a^8 simplifies to a^4 after dividing the exponent by 2, which makes since: [tex]a^4*a^4=a^{4+4}=a^8[/tex] which exemplifies the very definition of a square root.

Applying this same logic to b^4 and just simplifying sqrt(36) regularly we get the following expression:

[tex]\frac{6a^4b^2}{\sqrt{7c}}[/tex]

We generally don't want square roots in the denominator, so we rationalize it by multiplying by the sqrt(7c)/sqrt(7c) which just simplifies to one, so we're not actually changing the value but it removes the sqrt(7c) from the denominator

[tex]\frac{6a^4b^2}{\sqrt{7c}} *\frac{\sqrt{7c}}{\sqrt{7c}}\\\\\frac{6a^4b^2\sqrt{7c}}{7c}[/tex]

and this turns out to be our solution!


Related Questions

A rental company charges $85 a day and 30 cents a mile for renting a truck. Michael rents a truck for 2 days, and his bill comes to $290. How many miles did he drive?

Answers

Answer:

400 miles

Step-by-step explanation:

Let m be the number of miles.

[tex]85(2) + .30m = 290[/tex]

[tex]170 + .30m = 290[/tex]

[tex].30m = 120[/tex]

[tex] m = 400[/tex]

is y-4x=9 a linear equation

Answers

Answer:

it is a linear equation

Step-by-step explanation:

Respuesta d/4, d/x = 4

The diference between two numbers is 3 their sum is 27. What is the smaller number?

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

x - y = 3

x + y = 27

add them:

2x = 30

x = 15

from x+y=27, we can see that y = 12

Draw the image of \triangle ABC△ABCtriangle, A, B, C under a dilation whose center is CCC and scale factor is 222.

Answers

The image of triangle ABC△ABC triangle, A, B, C under a dilation whose center is CCC and scale factor is 222. The dimensions of the new triangle are 8.2, 12.8, and 10.2 units. The graph of the Δ is given below.

What is a transformation of a point?

A spatial transformation is each mapping of the feature space to itself and it maintains some spatial correlation between figures.

The △ABC is given below.

The dimensions of triangle are approximately 4.1, 6.4, and 5.1.

And scale factor of the dilation is 2.

If △ABC is dilated by the scale factor of 2 as a center of C.

Then dimensions of the new △A'B'C will be

A'C = AC × 2

A'C = 4.1× 2

A'C = 8.2 units

B'C = BC × 2

B'C = 6.4 × 2

B'C = 12.8 units

B'A' = BA × 2

B'A' = 5.1 × 2

B'A' = 10.2 units

Then the dimensions of new triangle are 8.2, 12.8, and 10.2 units.

The graph of triangle is given below:

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Construct RS so that RS is bisector to PQ

Answers

To bisect is to cut into two equal parts. Therefore, in the picture below, line segment PS should be congruent to line segment QS.

See details:

Plot the following ordered pairs on the same Cartesian plane for each one.
1.(2,3)

2.(0,-7)

3.(-5,9)

Answers

A graph of the given ordered pairs has been plotted as shown in the image attached below.

What is a graph?

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

What is an ordered pair?

An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane.

In conclusion, a graph which represents the given ordered pairs shows a discrete function.

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Sebastian used his knowledge of exponents to simplify the following expression. Did he simplify correctly? If not, what mistake did
Sebastian make?
87.8-4.40
87+(-4).40
83.40
8³.0
0

Answers

Sebastian has solved the expression wrongly and the correct answer will be 536.

We are given the expression:

(87 × 8) - (4 × 40)

We need to simplify the expression.

For this, we need to follow the rule of PEMDAS.

So, we get that:

696 - 160

= 536

Sebastian has simplified it wrong as he has not followed the rule of PEMDAS and first subtracted 4 from 8.

Therefore, we get that, Sebastian has solved the expression wrongly and the correct answer will be 536.

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A scale drawing of a car is presented in the following three scales. Order the scale drawings from smallest to largest. Explain your reasoning. (There are about 1.11.1​ yards in a meter and 2.542.54​ cm in an inch)

help me please ;-;

Answers

The order of the scales from smallest to largest would be,

inch, centimeter, yard, meter

In this question, we have been given a scale drawing of a car is presented in the following three scales.

We need to order the scale drawings from smallest to largest.

We know that,

1 cm = 2.54 inch

and 1 meter = 1.1 yards

We know that the metric conversion,

1 meter = 100 centimeters

And 1 cm = 2.54 inch

So, 1 meter = 254 inches

This means, meter is the largest scale and inch is the smallest scale.

1 yd = 91.44 cm

This means, yard is greater than centimeter.

Therefore, the order of the scales from smallest to largest would be,

inch, centimeter, yard, meter

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What number makes the fractions equivalent?

Answers

different numerators and denominators but are equal to the same value.
-
if you need a specific number answer from a problem, you'd need to attach a picture

Mark wanted to know the area of his backyard. his parents told him that the yard was 4/5 of a mile wide and 1/2 of a mile long. what is the area of his yard ?

Answers

Answer:

A = 0.041138659 Sq. Mi.

Step-by-step explanation:

now I'm guessing that mark's backyard is GIGANTIC

and according to the info the question gave I know his back yard is also a Rectangle, knowing this we can safely say the formula to find the Area of a rectangle: A = LW to break this down it's like saying:

Area = length × width

the question already states that the width was 4/5 of a mile and the length was 1/2 of a mile we would convert the miles to feet

1 mile = 5,280 ft

4/5 × 5,280 = 4,224 ft

so, 4/5 of a mile would be 4,224 ft

similarly, 1/2 of a mile would be 2,640

1/2 × 5,280 = 2,640

GREAT we found our new length and width

length= 2,640 ft

width=4,224 ft

plug it in the formula

A= L×W

A= 2,640 ft · 4,224 ft

A= 1,146,880 sq. ft.

change that into square miles by dividing by 27878000

0.041138659 Square Miles

Can someone help and please hurry i don't have a lot of time

Answers

hi! i believe it’s the second and fourth one.

a library subscribes to two different weekly news magazines, each of which is supposed to arrive in wednesday's mail. in actuality, each one may arrive on wednesday, thursday, friday, or saturday. suppose the two arrive independently of one another, and for each one p(wed.)

Answers

The two come separately, and the p(wed.) value for each one is 0.0841. It is founded on likelihood on probability.

What does probability mean in math?

Probability is a way to gauge how likely something is to happen. Many things are hard to predict with complete certainty. We can only forecast how likely an event is to occur using it, or how likely it is to occur.

The probability is typically defined as the proportion of positive outcomes to all outcomes in the sample space. Probability of an event P(E) = (Number of favourable outcomes) is how it is stated (Sample space).

based on the facts provided;

p(0) = p(w,w)

= 0.29² = 0.0841

p(1) = p(t, w+t) + p(w, t)

= 2p(w,t) +p(t,t) = 2·.29·.37 + .37² = 0.3515

p(2) = p(f, w+t+f) +p(w+t, f)

= 0.16(2(.29+.37)+.16) = 0.2368

p(3) = p(s, w+t+f+s) +p(w+t+f, s)

= 0.18(2(.29+.37+.16) +.18) = 0.3276

In summary, your pmf is ...

y : p(y)

0 : 0.0841

1 : 0.3515

2 : 0.2368

3 : 0.3276

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Grace has a coupon for $2 off the regular price of each pair of jeans she buys. She buys 4 pairs of jeans with a regular price of $23 each. What is the total cost for her jeans?

Answers

The total cost for her jeans will be $84.

How to calculate the cost?

From the information, Grace has a coupon for $2 off the regular price of each pair of jeans she buys and she buys 4 pairs of jeans with a regular price of $23 each.

The total cost for her jeans will be:

= (4 × $23) - (4 × $2)

= $92 - $8

= $84

Therefore, it should be noted that the total cost is $84.

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Help me please I am in need

Answers

At 1 hour, 3 hours and 6.5 hours she travels 36 miles, 108 miles and 234 miles respectively using the concept of average speed of an object.

As per the question statement, Clare covers a distance of 0 miles, 72 miles, 144 miles and 216 miles in 0 hours, 2 hours, 4 hours and 6 hours respectively.

We are supposed to find out the distance travelled by her in 1 hour, 3 hours and 6.5 hours.

We will use the concept of average speed of an object which is as follows

average speed = total distance divided by the total time taken

average speed = 216/6 = 36 miles per hour

Hence at 1 hour, distance = 1 * 36 = 36 miles

at 3 hours, distance = 3 * 36 =108 miles

at 6.5 hours, distance = 6.5 * 36 = 234 miles

Average Speed : The overall distance the thing travels in a given amount of time is its average speed.

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jonh had 5 dish soap and shared 16 how many did he share

Answers

Answer:

16

Explanation:

It states the answer in the question. Unless you meant something else?

Hope this helps!

Have a good day :)

Answer: He shared 16.

Step-by-step explanation:

hey please help
Using the digits to (no more than once per digit), fill in the boxes to create three equivalent ratios.
You will get 15 points! or maybe even 20!

Answers

3:6=7:14=29:58 or 3:6=9:18=27:54

This equation is three equivalent ratios.

two gears, A and B. are arranged so that the teeth of one gear is mesh with the teeth of another. Gear A turns clockwise and has 54 teeth. Gear B turns counterclockwise and has 36 teeth. If gear A makes 5.5 rotations, how many turns will gear B make?

Answers

The number of turns gear B will make is 8.25 turns

How to find the number of turns gear B will make

Given data

Gear A turns clockwise and has 54 teeth

Gear B turns counterclockwise and has 36 teeth

gear A makes 5.5 rotations

One of the gears is driving the other hence the distance covered by each of the gears is constant.

The distance is the product of the number of rotations and the number of teeth and this should be a constant

Therefore, let the number of rotations of gear B be x

54 teeth * 5.5 rotations = 36 teeth * x rotations

x rotations = ( 54 teeth * 5.5 rotations ) / 36 teeth

x rotations = 54/36 * 5.5

x rotations = 1.5 * 5.5

x rotations = 8.25

We can therefore say that gear B will make 8.25 rotations

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Two fish tanks have measurements as shown.
Which tank has a greater volume? How much greater is its volume?
Use the drop-down menus to explain and show your answer.
8 ft
Choose.
Fish Tank A
The volume of fish tank A is Choose...
volume is greater by ose
Fish Tank B
Area of base: 25 ft²
Area of base: 40 ft²
4 ft
cubic feet, and the volume of fish tank B is
has a greater volume. Its
cubic feet. So fish tank Choose....
cubic feet

Answers

Step-by-step explanation:

sgshshsbhehdbdbdbsbehebebdbebd

Help I will. Give brainly

Answers

No, because there is one x value that corresponds to two y values

(5, 3) and (5, 7)

I need help pls its really hard for me rn and teach me how to do it

Answers

The sequence that contains all the given terms is:

aₙ = -18 + 6*n

Then the correct option is C.

Which sequence can be used to find the n-th term?

Here we have the elements:

a₃ = 0

a₄ = 6

a₅ = 12

a₆ = 18

a₇ = 24

So each term adds 6 to the previous one, so trivially the relation is of the form:

aₙ = aₙ₋₁ + 6

Now we need to find the first term.

We can rewrite the above equation as:

aₙ₋₁ = aₙ - 6

Then we willget:

a₂ = a₃ - 6 = 0 - 6 = -6

a₁ = a₂ - 6 = -6 - 6 = -12

a₀ = a₁ - 6 = -18

Then the sequence is:

aₙ = -18 + 6*n

Then the correct option is C.

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The first and the last terms of two Arithme- tic progressions are the same. The first A.P. has 51 terms with a common difference of 6. Find the number of terms of the 2nd A.P if its common difference is given as 4.

Answers

The number of terms of the 2nd A.P if its common difference is given as 4 is 76.

What is common difference?

The difference between consecutive integers in an arithematic sequence is a frequent distinction. Simply subtract the first word from the second term, or the second from the third, or anything similar, to find it. See how we have to add 8 each time to reach the following term? Thus, our common difference is eight.

1st A.P

Let 1st term be a d = 6

Therefore T51 = a + ( 51 - 1 )6

= a + 300

Now 2nd A.P

let the 1st term be a

Therefore for n no. of terms,

lats term,  a + ( n - 1 )4

But according to the question:

 a + ( n - 1 )4 =  a + 300

n - 1 = 300/4

n = 75 + 1

n = 76

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What are the y-intercept and the slope of the graph of the following equation? 3x+4y=12

Answers

[tex]3x+4y=12\implies 4y=-3x+12\implies y=\cfrac{-3x+12}{4} \\\\\\ y = \cfrac{-3x}{4}+\cfrac{12}{4}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{4}}x+\stackrel{\stackrel{b}{\downarrow }}{3}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

3) Mr. G. was once offered a job as a car salesperson. Below is a partial compensation table they used to calculate monthly pay. (10 points)
Number cars sold 5 6 7 8 9 10
Salary 2750 3200 3650 4100 4550 5000

a. Is this linear? How do you know?
b. Suppose Mr. G thought he could sell 23 cars during one month. What would his total monthly pay be? Show your work!
c. If the gross pay is $6,800, how many cars were sold? Show your work!

Answers

The relation on the table of values is a linear model,

The total monthly pay is $10850 when he sells 23 cars in one monthThe number of cars is 14 if the gross pay is $6,800

How to determine if the relation is linear?

The table of values is given as

Number cars sold 5 6 7 8 9 10

Salary 2750 3200 3650 4100 4550 5000

On the table of values, we can see that:

As the number of cars increase by 1, the salary increases by 450

This means that the table has a constant rate of 450

Relations that have a constant rate are  linear relations

Hence, the table of values is a linear relation

The total monthly pay

In (a), we have

Slope, m = 450

A linear equation is represented as

y = m(x - x1) + y1

So, we have

y = 450(x - 5) + 2750

Evaluate

y = 450x + 500

When the number of cars is 23, we have

y = 450 x 23 + 500

Evaluate

y = 10850

Hence, the total monthly pay is $10850

The number of cars

Here, we have

y = 6800

This gives

450x + 500 = 6800

This gives

450x = 6300

Evaluate

x = 14

Hence, the number of cars is 14

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What is 3.68086257145 divided by 6.533 * 4,085,0811

Answers

When  3.68086257145 divided by 6.533 * 4,085,0811 we get 1.379228624370833401829E-8

The methods of division are of three types according to the difficulty level. These are the chunking method or division by repeated subtraction, short division method or bus stop method and long division method.

The division of two numbers can be calculated using the following formula:

Dividend / Divisor = Quotient + Remainder.

The number that is being divided in this case is known as the dividend. The number that divides the number (dividend) into equal parts is known as the divisor.

The quotient is the result of the division operation.

The remainder is the leftover number in the division operation.

We have been given that

3.68086257145 divided by 6.533× 4,085,0811

First we simplify multiplication part

6.533× 4,085,0811  = 266878348.263

Now

3.68086257145 divided by 266878348.263

3.68086257145 ÷ 266878348.263

= 1.379228624370833401829E-8

Hence , 1.379228624370833401829E-8 is the result of the 3.68086257145 divided by 6.533× 4,085,0811 .

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Which of the following functions has an amplitude of 4 and a phase shift of pi over 4

Answers

The cosine function that has an amplitude of 4 and a phase shift of pi over 4 is given by:

f(x) = 4cos(2x - π/4) + 4.

How the cosine function is defined?

The cosine function is defined as follows, considering it's coefficients:

y = acos(bx - c) + d.

The meaning of the coefficients is given as follows:

Coefficient a is the amplitude of the cosine function.Coefficient 2π/b gives the period of the cosine function.Coefficient c gives the phase shift of the cosine function.Coefficient d gives the vertical shift of the cosine function.

In this problem, we want an amplitude of 4, hence coefficient a has a value of:

a = 4.

We also want a phase shift of π/4, hence the coefficient c has a value of:

c = π/4.

Among the given options, the one that gives a cosine function with the desired amplitude and phase shift is:

f(x) = 4cos(2x - π/4) + 4.

Which is the first option.

What is the missing information?

The options are missing, and are given by the image at the end of the answer.

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Number 21… please explain I don’t know how to do this

Answers

Answer:

The lengths of the sides are 18 ft, 18 ft, and 24 ft.

Your friend has $80 when he goes to the fair. He spends $4 to enter the fair and $12 on food. Rides at the fair cost $1.25 per ride.

The function f(x) = -1.25x + 64 can be used to determine how much money he has left over after x rides? What does f(17) represent?

Group of answer choices

Your friend paid for 17 rides and spent $42.75.

Your friend paid for 17 rides and had $37.25 left over.

Your friend paid for 17 rides and had $42.75 left over.

Your friend paid for 17 rides and spent $37.25.

Answers

The function f(17) represent your friend paid for 17 rides and had $42.75 left over.

What is an equation?

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

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let f(x) represent the amount that the rider has left over after x rides.

f(x) = -1.25x + 64

f(17) = -1.25(17) + 64 = 42.75

f(17) = $42.75

f(17) represent the money left

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4p−5(p+6) Help plssss

Answers

Answer: -p - 30

Step-by-step explanation:

         We will simplify the expression.

   Given:

4p - 5(p + 6)

   Distirubte the negative 5:

4p - 5p - 30

   Combine like terms:

-p - 30

What is the total surface area??

Answers

Check the picture below.

[tex]\stackrel{\textit{\LARGE Areas}}{ \stackrel{\textit{two triangles}}{2\left[\cfrac{1}{2}(\underset{b}{8})(\underset{h}{6}) \right]}~~ + ~~\stackrel{\textit{three rectangles}}{(14)(6)~~ + ~~(14)(8)~~ + ~~(14)(10)}} \\\\\\ 48~~ + ~~84~~ + ~~112~~ + ~~140\implies \text{\LARGE 384}~cm^2[/tex]

Convert 0.17 to a fraction in simplest form and a percent.

Answers

Answer: 17/100, which would be 17%

Step-by-step explanation:

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