Combine the radicals. 2√24+5√54 A) 53√6 B) 5√6 C) 19√6 D) 93√6

Answers

Answer 1

Answer:

The answer is option C

Step-by-step explanation:

2√24 + 5√54

To combine the radicals first make sure the radicals have the same square root

That's

For 2√24

[tex]2 \sqrt{24} = 2 \sqrt{4 \times 6} = 2 \times 2 \sqrt{6} [/tex][tex] = 4 \sqrt{6} [/tex]For 9√54

[tex]5 \sqrt{54} = 5 \sqrt{9 \times 6} = 5 \times \sqrt{9} \times \sqrt{6} [/tex][tex] = 5 \times 3 \times \sqrt{6} [/tex][tex] = 15 \sqrt{6} [/tex]

Since they have the same square root we can combine them

That's

[tex]4 \sqrt{6} + 15 \sqrt{6} = (4 + 15) \sqrt{6} [/tex]

We have the final answer as

[tex]19 \sqrt{6} [/tex]

Hope this helps you


Related Questions

A square has a perimeter of 24cm. Work out its area.​

Answers

Answer:

A = 36 cm^2

Step-by-step explanation:

The perimeter of a square is given by

P =4s

24 = 4s

Divide by 4

24/4 = 4s/4

6 =s

The area of a square is

A =s^2

A = 6^2

A = 36 cm^2

please help me for the homework

Answers

Answer:

refer to the pic attached

0.21212121 as a fraction

Answers

Answer:

21212121/100000000

Step-by-step explanation:

21212121/100000000 cannot be simplified

Hope this helps!

Answer:

0.21212121 Cannot be converted into a fraction

what is the method or solution to this question (3)x-1=81x

Answers

[tex]3x-1=81x\\78x=-1\\x=-\dfrac{1}{78}[/tex]

Answer:

[tex]\large \boxed{\displaystyle x=- \frac{1}{78}}[/tex]

Step-by-step explanation:

[tex]3x-1=81x[/tex]

Subtract 3x from both sides of the equation.

[tex]-1=78x[/tex]

Divide both sides of the equation by 78.

[tex]\displaystyle \frac{-1}{78} =x[/tex]

Kapil deposited Rs. 1600 in a bank on 1st January 2005. Find the amount in his bank account on 1st January 2006, if the bank pays interest at 8% per annum and the interest is calculated every year on 30th June and 31st December.

Answers

Answer:

SI=PRT/100

=10000*5*42/12*100

=1750

SI=1750

TOTAL AMOUNT=PRINCIPLE+SI

=10000+1750

=101750

Which products result in a difference of squares? Select three options. A. (x minus y)(y minus x) B. (6 minus y)(6 minus y) C. (3 + x z)(negative 3 + x z) D. (y squared minus x y)(y squared + x y) E. (64 y squared + x squared)(negative x squared + 64 y squared)

Answers

Answer:

C D E

Step-by-step explanation:

Edg

Out of the given options, options C, D and E are a difference of squares.

What is the difference of squares?

Difference of Squares, two terms that are squared and separated by a subtraction sign.

Given are, options,

D) (y squared minus x y)(y squared + x y) = (y²-xy)(y²+xy) = y⁴-(xy)²

E) (64 y squared + x squared)(negative x squared + 64 y squared) = (64y²+x²)(64y²-x²) = (64y)⁴-x⁴

C) (3 + x z)(negative 3 + x z) = (3+xz)(3-xz) = 3²-(xz)²

Hence, out of the given options, options C, D and E are a difference of squares.

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please help :) Respecting and understanding different opinions promotes fill in the blank . answer choices : (value/tolerance)

Answers

Answer:

Tolerance

Step-by-step explanation:

Value in this situation doesn't make sense and you can search up the definition of tolerance on the web to verify.

Also, this doesn't seem like a math related question so you should have answered this in English or something.  

Order the expressions from least to greatest.
2^3 - 2^1 , 2^1 + 3^1 , 3^2

Answers

Answer:

2¹ + 3¹, 2³ - 2¹, 3²

Step-by-step explanation:

2³ - 2¹ = 8 - 2 = 6

2¹ + 3¹ = 2 + 3 = 5

3² = 9

At the beginning of the day the stock market goes up 60 1/2 points and stays at this level for most of the day. At the end of the day the stock market goes down 100 1/4 points from the high at the beginning of the day. What is the total change in the stock market from the beginning of the day to the end of the day?

Answers

Answer: it would be 40/2 or 20, but im not sure.

Step-by-step explanation: so what I did was: 100 1/4 - 60 1/2: 100 - 60 = 40 and then I subtracted 1-1 which is 0 then 4-2 which is 2, and got 40/2 or just simplify which will be equal to 20

Two shaded identical rectangular decorative tiles are first placed (one each) at the top and at the base of a door frame for a hobbit's house, as shown in Figure 1. The distance from W to H is 45 inches. Then the same two tiles are rearranged at the top and at the base of the door frame, as shown in Figure 2. The distance from Y to Z is 37 inches. What is the height of the door frame, in inches?

Answers

Answer:

41 inches

Step-by-step explanation:

Let the point at the top of the door on the left be x

Wx + xH = 45

Let the point at the top of the door  on the right be c

Yc + cZ = 37

We know the door is

xH +  plus the width of the tile

The width of the tile is Yc

xH + Yc

On the right door

cZ +  the height of the tile

cZ + Wx

Add the two doors together

xH + Yc + cZ + Wx = 2 times the height of the door

Rewriting

xH +  Wx +  Yc + cZ = 2 times the height of the door

45+ 37 = 2 times the door height

82 = 2 times the door height

Divide by 2

41 = door height

Someone pls HELP MEEEE i’m giving the rest of my points away . i have like 20 mins to turn this in

Answers

Answer:

1) 27.89

2) 20

Step-by-step explanation:

#1)

9.5x + 75 --> 340

340 - 75 --> 265

265 / 9.5 = 27.89

#2)

120 / 6 =

20 minutes

Chuck goes to a community college there is an enrollment fee of 207.55 plus 223.07 per credit hour which eqaution shows C the total cost of attending the community college for x credit hour

Answers

Answer:

C = 207.55 + 223.07x

Step-by-step explanation:

Given the following :

Cost of community college:

Enrollment fee = 207.55

Fee per credit hour = 223.07

Attending the community College for 'x' credit hours can be represented by:

Total cost = C

[Enrollment fee + (fee per credit hour * number of credit hours)]

Number of credit hours = x

C = [207.55 + (223.07 * x)]

C = 207.55 + 223.07x

Therefore, the total cost 'C' of attending the community college for 'x' credit hour:

C = 207.55 + 223.07x

Answer ASAP, Will give brainliest!!

Answers

Answer:

First. 115°

Second. 65°

Third. 65°

Fourth. 7

Fifth. 425.25

First

angle DAB = angle ADC (since this is an isosceles trapezoid)

Second

In a trapezoid adjacent angle are supplmentary (that is their sum is 180°)

180-115 is 65°

Third

(Same reason as second)

Fourth

The side 3x+4 is same as the opposite side

So 3x + 4 = 25

on solving you get x = 7 in

Fifth

[tex]area \: = \frac{1}{2} \times length \: of \: the \: perpendicular \: (b1 + b2)[/tex]

area = 1/2 × 13.5 (20+43)

area = 1/2 × 13.5 × 63

Thus area is 425.25

Answer:

Step-by-step explanation:

1)As ABCD is isosceles trapezium,

∠ADC= ∠DAB

∠ADC = 115°

2) AD //BC

∠ADC + ∠DCB = 180°   {co interior angles}

115 + ∠DCB = 180

 ∠DCB = 180 - 115

 ∠DCB = 65°

3) As ABCD is isosceles trapezium,

∠CBA = ∠DCB

∠CBA = 65°

4) As ABCD is isosceles trapezium, non parallel sides are congruent.

AB = DC

3x + 4 = 25 in

3x = 25 - 4

3x = 21

x = 21/3

x = 7 in

5) height = 13.5 in

a= 43 in

b= 20 in

Area of trapezium = [tex]\frac{(a+b)*h}{2}\\[/tex]

                   [tex]= \frac{(43 +20)*13.5}{2}\\\\=\frac{63*13.5}{2}\\\\\\= 425.25 in^{2}[/tex]

Evaluate the expression when c = 4 and x = -2.
-C+ 6x

Answers

Answer:

-16

Step-by-step explanation:

We are given the expression:

-c+6x

and asked to evaluate when c=4 and x=-2. Therefore, we must substitute 4 in for c and -2 in for x.

-(4)+6(-2)

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Addition, Subtraction.

First, multiply 6 and -2.

6 * -2= -12

-(4)+ -12

-(4) -12

Distribute the negative sign.

-4 -12

Subtract 12 from -4.

-16

The expression -c+6x when c=4 and x= -2 is -16.

Answer:

-16

Step-by-step explanation:

Start with -C+ 6x.  Replace C with '4' and x with '-2'

This comes out to -(4) + 6(-2) = -4 - 12 = - 16

I need help fast please

Answers

Answer:

Difference : 4th option

Step-by-step explanation:

The first thing we want to do here is to factor the expression x² + 3x + 2. This will help us if it is similar to the factored expression " ( x + 2 )( x + 1 ). " The denominators will be the same, and hence we can combine the fractions.

x² + 3x + 2 - Break the expression into groups,

( x² + x ) + ( 2x + 2 ) - Factor x from x² + x and 2 from 2x + 2,

x( x + 1 ) + 2( x + 2 ) - Group,

( x + 2 )( x + 1 )

This is the same as the denominator of the other fraction, and therefore we can combine the fractions.

x - 1 / ( x + 2 )( x + 1 )

As you can see this is not any of the options present, as we have not expanded ( x + 2 )( x + 1 ). Remember previously that ( x + 2 )( x + 1 ) = x² + 3x + 2. Hence our solution is x - 1 / x² + 3x + 2, or option d.

3. E, F and G are collinear points. E is between F and G.
If FE = 3 in., and FG = 7 in., what is the length of EG?
a. 4
c. 3
I
b. 10
d. 21

Answers

Answer:

A. 4 in

Step-by-step explanation:

Collinear points are points that lies on the same straight line. If the points E, F and G are collinear points, then the three points lies on the same straight line.

If E is between F and G, the FE+EG = FG

EG = FG - FE

Given FE = 3 in and FG = 7 in

On substituting into the expression above to get EG;

EG = 7in - 3in

EG = 4in

Hence the length of EG is 4in

QUICK IT IS FOR, NOW!!! I WILL GIVE BRAINLIESTS AND 10 POINTS
When p2 – 4p is subtracted from p2 + p – 6, the result is: -3p-6, 5p-6 or 4p+6. To get p – 9, subtract: 4p+3, 4p-15 or 4p+12 from this result.

Answers

Step-by-step explanation:

p² - 4p is subtracted from p² + p - 6 is written as

p² + p - 6 - (p² - 4p)

Remove the bracket and simplify

That's

p² + p - 6 - p² + 4p

p² - p² + 4p + p - 6

We have the answer as

5p - 6

Let the unknown expression be x

Subtract x from the expression to get p - 9

That's

5p - 6 - x = p - 9

x = 5p - p - 6 + 9

x = 4p + 3

The expression is

4p + 3

Hope this helps you

Of the students at Milton Middle School, 120 are girls. If 50% of the students are girls, how many total students are there at Milton Middle school

Answers

Answer- 240 students
Explanation-multiply the amount of girls by two because they make up 50% of the school.

You check 20 batteries.Fourteen of the batteries do not have a charge. What is the experimental probability that the next battery you check does not have a charge?

Answers

Answer:

[tex]\dfrac{7}{10}[/tex]

Step-by-step explanation:

Given that

Number of batteries that do not have a charge = 14

Total number of batteries = 20

To find:

Experimental probability that the next battery checked does not have a charge = ?

Solution:

First of all, let us learn about the definition of experimental probability.

Probability is the chances of happening of an event.

Formula for probability of happening of an event E is given as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Here we have to find the probability of checking a battery that has no charge.

So, number of favorable cases = Number of batteries that do not have a charge = 14

AND

Total Number of cases = Total number of batteries to be checked = 20

So, the required probability is:

[tex]\dfrac{14}{20} = \bold{\dfrac{7}{10}}[/tex]

What is the product of complex conjugates? (1 point)

the product of complex conjugates is a difference of two squares and is always a real number

the product of complex conjugates may be written in standard form as a+bi where neither a nor b is zero

the product of complex conjugates is the same as the product of opposites

the product of complex conjugates is a sum of two squares and is always a real number ​

Answers

Answer:

A. the product of complex conjugates is a difference of two squares and is always a real number

Step-by-step explanation:

Given a complex number z1 = x+iy where x is the real part and y is the imaginary part.

The conjugate of a complex number is the negative form of the complex number z1 above i.e z2= x-iy (The conjugate is gotten by mere changing of the plus sign in between the terms to a minus sign.

Taking the product of the complex number and its conjugate will give;

z1z2 = (x+iy)(x-iy)

z1z2 = x(x) - ixy + ixy - i²y²

z1z2 = x² - i²y²

.since i² = -1

z1z2 = x²-(-1)y²

z1z2 = x²+y²

The product gave a real function x²+y² since there is no presence of complex number 'i'

It can also be seen that the product of the complex numbers z1z2 is like taking the difference of two square. An example of difference of two square is that of two values a and b which is (a+b)(a-b).

From the above solution, it can be concluded that the product of complex conjugates is a difference of two squares and is always a real number.

sinθ/(1-〖cos〗^2 θ)=cosecθ

Answers

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x

cosec x = [tex]\frac{1}{sinx}[/tex]

Consider the left side

[tex]\frac{sin0}{1-cos^20}[/tex]

= [tex]\frac{sin0}{sin^20}[/tex] ← cancel sinΘ on numerator/denominator

= [tex]\frac{1}{sin0}[/tex]

= cosecΘ = right side

Write an expression that represents an increase of 5% over the
original cost of $d as both a sum and product of d.

Answers

Answer:

Sum equation: [tex]d + 0.05d[/tex]

Product equation: [tex]1.05d[/tex]

Step-by-step explanation:

If we have an increase in 5% of d, that means that 5% of d ([tex]0.05\cdot d[/tex]) will be the total amount of money added to it.

However, we need to still count the original price of d, if we increase it by 5%!

So we add d to 0.05d.

[tex]d + 0.05d[/tex] is the sum equation.

Now, we can create the product equation for d by expanding the coefficients for the previous equation,  [tex]d + 0.05d[/tex].

[tex]1d + 0.05d[/tex]

We can add like terms here: [tex]1 + 0.05 = 1.05[/tex]! So we can just multiply this by d for our product equation.

[tex]1.05d[/tex]

Hope this helped!

2500 feet is to how many meters

Answers

Answer:  is 762 meters

Step-by-step explanation:

One foot is equal to 0.3048 meters so multiply 2500 by 0.3048 to find how many meters there are.

2500 * 0.3048 = 762

Answer:762.5 meters

Step-by-step explanation:

1 foot =0.305 m

Hence,0.305×2500=762.5 metres as the answer.

represent 1/3 and 5/2 on the same number line​

Answers

Answer:

Picture below

Step-by-step explanation:

● 5/2 is 2.5 so just divide the space between 3 by 2

● for 1/3 divide the space between 0 and by 3

Use the first four terms of the binomial theorem to approximate 2.2^7

A. 248.96
B. 248.4688
C. 23.424
D. 249.4357888
please explain the steps to how you got your answer thank you!!

Answers

The answers is choice d .

Answer:

248.96.

Step-by-step explanation:

We write  it as:

(2 + 0.2)^7 = 2^7 + 7*2^6*0.2 + 7C2*2^5*(0.2)^2 + 7C3*2^4(*(0.2)^3

= 128 + 89.6 + 26.88 + 4.48

= 248.96.

Your mother has left you in charge of the annual family yard sale. Before she leaves you to your entrepreneurial abilities, she explains that she has made the job easy for you: everything costs either $1.50 or $3.50. She asks you to keep track of how many of each type of item is sold, and you make a list, but it gets lost sometime throughout the day. Just before she’s supposed to get home, you realize that all you know is that there were 150 items to start with (your mom counted) and you have 41 items left. Also, you know that you made $227.50. Write a system of equations that you could solve to figure out how many of each type of item you sold.

A) x + y = 109
(1.5)x + 227.50 = (3.5)y
B) x + y = 109
(3.5)x + 227.50 = (1.5)y
C) x + y = 41
(1.5)x + 227.50 = (3.5)y
D) x + y = 109
(1.5)x + (3.5)y = 227.50
E) x + y = 150
(1.5)x + (3.5)y = 227.50
F) x + y = $3.50
(1.5)x + (3.5)y = 227.50

Answers

Answer:

[tex]D)\ x + y = 109\\(1.5)x + (3.5)y = 227.50[/tex]

Step-by-step explanation:

Let the items sold with price $1.5 = [tex]x[/tex]

Let the items sold with price $3.5 = [tex]y[/tex]

Initially, total number of items = 150

Items left at the end of the day = 41

So, number of items sold throughout the day = Total number of items - Number of items left

Number of Items sold = 150 - 41 = 109

So, the first equation can be written as:

[tex]\bold{x+y = 109} ....... (1)[/tex]

Now, let us calculate the sales done by each item.

Sales from item with price $1.5 = Number of items sold [tex]\times[/tex] price of each item

= (1.5)[tex]x[/tex]

Sales from item with price $3.5 = Number of items sold [tex]\times[/tex] price of each item

= (3.5)[tex]y[/tex]

Total sales = [tex]\bold{(1.5)x+(3.5)y = 227.50} ....... (2)[/tex]

So, the correct answer is:

[tex]D)\ x + y = 109\\(1.5)x + (3.5)y = 227.50[/tex]

Oliver completed his project in no more than twice the amount of time it took Karissa to complete her project. Oliver spent 4 and one-fourth hours on his project. If k represents the amount of time that it took Karissa to complete her project, which inequality can be used to represent the situation?

Answers

Answer:

4 1/4 <_ 2K

Step-by-step explanation:

The inequality that represents the situation is k ≥ 2.125 hours.

What is Inequality ?

Inequality is the statement where two algebraic expressions are equated using an inequality operator, <, >, <> etc.

Karissa takes k time to complete the project.

Oliver takes ≤ 2k

The time spent by Oliver is 4 1/4 = 17/4 = 4.25 hours

2k ≥ 4.25

k ≥ 2.125 hours

Therefore, the inequality that represents the situation is k ≥ 2.125 hours.

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Find the area of a circle with a diameter of 4.
Either enter an exact answer in terms of it or use 3.14 for 7 and enter your answer as a decimal.
units?

Answers

area of circle =22/7×4=12.56

Answer: 12.56

Explanation:

Find area of a circle:

Form: A = pi x d^2/4
d = 4 (given)
Pi = 3.14

=> A =3.14 x 4^2/4
A = 3.14 x 4
A = 12.56

It costs $0.0015 to leave a lightbulb on for an hour. How much would it cost
to have a lightbulb on for a month? (Helpful conversions: There are 24 hours
in a day, and there are 30 days in a month).

Answers

the answer would be $1.08

The total cost for a bucket of popcorn and 4 movie tickets is $56. The total cost for the same size bucket of popcorn and 6 movie tickets is $80. The cost of a bucket of popcorn is $8. Which equation represents the relationship between y, the total cost of the popcorn and movie tickets, and x, the number of movie tickets that are purchased?

Answers

Answer: y=12x+8

Step-by-step explanation:

The relationship between y, the total cost of the popcorn and movie tickets, and x, the number of movie tickets that are purchased will be y = 12x + 8.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's suppose the cost of popcorn is P and the cost of movie tickets is M then

P + 4M = 56

P + 6M = 80

Given that P =$8 hence by putting it to the equation 1

8 + 4M = 56

4M = 48

M = 12 now

Let x number of movie have watch then

y = 12x + 8 will be the formation of the equation.

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