If x and y are positive real numbers, which expression is equivalent to the expression below?
(49x^2y)^1/2(27x^6y^3/2)^1/3


A.) 21x/^3y
B.) 10x^2y
C.) 10x^3y
D.) 21x^3y^2

Answer:

12 kg

Step-by-step explanation:

15%×80 =

= 15×80/100

= 15×8/10

= 120/10

= 12 kg

Answer:

[tex]\fbox{\begin{minipage}{13em}Option D: 2(3x + 4)(3x - 4)\end{minipage}}[/tex]

Step-by-step explanation:

      [tex]A = 18x^{2} - 32\\[/tex]

Find the sharing components:

<=> [tex]A=2*9*x^{2} - 2*16[/tex]

Apply the inverse of associative property:

<=> [tex]A = 2(9x^{2} - 16)[/tex]

Identify two square components inside the parenthesis:

<=> [tex]A = 2((3x)^{2} - 4^{2} )[/tex]

Factorize:

<=> [tex]A = 2(3x + 4)(3x - 4)[/tex]

=> Option D is correct

Hope this helps!

:)

Answer:

Im pretty sure its the 1st one

Step-by-step explanation:

Answer:

option 3 π

Step-by-step explanation:

Circumference = πd

Circumference : diameter = πd : d

                                            = π : 1 = π

Answer:

Ace Electronics buys 30, Hi-Fi Stereo buys 50, and CD World buys 115

Step-by-step explanation:

Let x represent the number of items Ace Electronics buys

Let y represent the number of items Hi-Fi Stereo buys

Let z represent the number of items CD World buys

Since Ace Electronics, Hi-Fi Stereo, and CD World buy a total of 195 DVD players:

x + y + z = 195   (1)

Since CD World buys 35 more units than the other two stores combined:

z = x + y + 35   (2)

If you substitute z in equation 1 from equation 2:

x + y + (x + y + 35) = 195

2(x + y) = 195- 35

x + y = 80   (3)

Since z = x + y + 35:

z = 80 + 35

z = 115

Since CD World's cost is $160 per unit, Hi-Fi 's cost is $165 per unit and Ace Electronics's cost is $170 per unit and the total payment received is $31,750

170x + 165y + 160z = 31750   (Substitute x from equation 3 and z as 115)

170(80-y) + 165y + 160(115) = 31750

13600 - 170y  + 165y + 18400 = 31750

32000 - 5y = 31750

5y = 250

y = 50

Since x + y = 80:

x + 50 = 80

x = 30

Answer: x= -3 + 2[tex]\sqrt{2\\}[/tex] or -3 -2 [tex]\sqrt{2}[/tex]

Step-by-step explanation:

First you want to get the quadratic formula

in this case a=1 b=6 and c=1

plug it in and solve the equations

(sorry don't know how to put in equations here)

Answer:

Answer: x= -3 + 2\sqrt{2\\} or -3 -2 \sqrt{2}

Step-by-step explanation:

First you want to get the quadratic formula

in this case a=1 b=6 and c=1

plug it in and solve the equations

Answer: 60

Step-by-step explanation:

Cost of 1 cup = 80

Actual cost of 6 cups = 80 x 6 = 480

1/2 dozen cups were bought for 420

Discount 480 - 420 = 60

Answer:

Its 2!

Step-by-step explanation:

Just got it correct on edge 2020

The projectile is on the ground for 2 seconds.

A projectile is an object this is propelled via the application of external pressure and then movements freely underneath have an impact on gravity and air resistance.

Learn more about projectile here https://brainly.com/question/12870645

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Answer:

2:3

Step-by-step explanation:

We know that there are 24 red and black cards in the 48 pack because their ratio is 1:1. When 8 red cards are removed we have 16 red and 24 black cards. The ratio of this is 16:24 which simplifies to 2:3.

The ratio of the number of red cards in the pack to the number of black cards in the pack = 1:1

The total amount of cards (red or black) in the pack is = 48

The ratio of the number of red cards to the number of black cards is = 1:1

The number of cards removed from the pack = 8

Therefore the total number of cards( red or black = 48 -8

= 40 cards

But to calculate the number of red card

= 1+1 = 2

40/2 = 20 red cards

The number of black cards

1+1 = 2

40/2 = 20 black cards

The ratio of red is to black cards = 20:20 or 20/20 = 1:1 or 1/1

Therefore the ratio of the number of red cards in the pack to the number of black cards in the pack = 1:1

Learn more about ratio here:

https://brainly.com/question/2328454

Answer:

  a.  75%

Step-by-step explanation:

Let "p" represent the probability that Jeffrey will eat pizza, and "c" represent the probability that he will drink cola.

We are given ...

  P(p) = 0.40

  P(p&c) = 0.30

The conditional probability of interest is ...

  P(c|p) = P(p&c)/P(p) = 0.30/0.40 = 0.75

The probability Jeffrey will drink cola, given that he eats pizza, is about 0.75.

Answer:

No ABC is not a triangle

Step-by-step explanation:

Perimeter = 22 cm

AB = 8 cm ; BC = 8 cm

AC = 22 - ( 8 + 8 ) = 6 cm

But all those sides doesn't follow Pythagorean Theorem(AB^2 + BC^2 = AC^2) ....because 8^2 + 8^2 isn't equal to 6^2 ......

Had it followed the theorem , it could have been a right angle triangle...

Answer:

The width of the rectangle is k+4 inches

Step-by-step explanation:

you have [tex]k^{2}+19k+60[/tex] which can be factorized to (k+4)(k+15)

if the length of the rectangle is k-5 that would mean that we can write [tex]k^{2}+19k+60[/tex] as (k-5)n which we know is false, so the only one that applies is k+4

The true statement is:

"The width of the rectangle is k + 4"

Remember that for a rectangle of length L and width W, the area is given by:

A = L*W

So we want to factorize the area equation, which is a quadratic equation, into a product of two terms.

A = k^2 + 19k + 60

The two zeros are given by Bhaskara's formula:

[tex]k = \frac{-19 \pm \sqrt{19^2 - 4*1*60} }{2} \\\\k = \frac{-19 \pm 11 }{2}[/tex]

So we have two zeros, these are:

k = (-19 - 11)/2 = -15

k = (-19 +11)/2 = -4

So we can factorize the area as:

A = (k - (-15))*(k - (-4)) = (k + 15)*(k + 4).

From this, the only statement that can be true is:

"The width of the rectangle is k + 4"

If you want to learn more about quadratic equations, you can read:

https://brainly.com/question/1480401

tan X = |YZ| / |XZ| = 20/8 = 5/2

X = arctan(5/2) = 68.2°

Answer: 68.2°

The size of angle ∠YXZ is 68.3° given that sides YZ=20cm and XZ=8cm by using trigonometric ratios.

In a right angled triangle, if A is an angle other than right angle then trigonometric ratios are

sin A =[tex]\frac{opposite side}{hypotenuse}[/tex]

cos A=[tex]\frac{adjacent side}{hypotenuse}[/tex]

tan A =[tex]\frac{opposite side}{adjacent side}[/tex]

Given YZ=20cm and XZ=8cm

Since the triangle is right angled, and opposite side and adjacent side are given we can find tan(∠YXZ )

tan (∠YXZ ) =20/8 =2.5

∠YXZ = arctan (2.5) =68.2°

Hence the size of angle ∠YXZ is 68.2° given that sides YZ=20cm and XZ=8cm.

Learn more about trigonometric ratios here :

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Answer:

Step-by-step explanation:

We can setup the equation as

x/28 = 1/8

Cross multiplying we get

8x = 28

Dividing by 8 we get

x = 28/8 = 7/2

Answer:

The width is 2x+1

Step-by-step explanation:

10x^2 +5x

Divide this by 5x

10x^2 /5x = 2x

+

5x/5x =1

Add this together

2x+1

The width is 2x+1

Answer:

( 2x + 1 )

Step-by-step explanation:

10x^2 + 5x

it could also be;

5x (2x + 1)

so, the width is( 2x +1)

Answer:

x=5

Step-by-step explanation:

7/5=(2x-3)/x

5(2x-3)=7x

3x=15, x=5

Answer:

90.80

Step-by-step explanation:

6x+4

= (6)(13)+4

= 78+4

=82

3x

=(3)(13)

= 39

So we know the sides are 39 and 82

Pythagoras theorem in triangles

= a2+b2= c2

Now, we know the value of a and B but not c (the hypotenuse)

Therefore,

c2 = (39)^2 + (82)^2

= 1521+ 6724

= 8245

so, c = √8245

= 90.80 unitd

Answer: 5/8

Step-by-step explanation:

Answer:

k = [tex]\frac{5}{8}[/tex]

Step-by-step explanation:

The standard form of an equation representing proportion is

y = kx ← k is the constant of proportionality

y = [tex]\frac{5}{8}[/tex] x ← is in this form

with k = [tex]\frac{5}{8}[/tex]

Answer: Irrational numbers

Answer:

Total time  ≈ 100(nearest minutes)

Step-by-step explanation:

The rates at which each student writes names per minutes can be calculates as follows.

First student

6 minutes = 7 names

1 minute = 7/6 names

second student

10 minutes = 17 names

1 minute = 17/10 names

Third student

15 minutes = 23 names

1 minute = 23/15 names

Total time = 440/total rate

Total time = 440/1.17 + 1.7 + 1.53

Total time = 440/4.403

Total time = 99.931

Total time  ≈ 100(nearest minutes)

Answer: The equation is 45-10=x the answer is 35

Step-by-step explanation: To make the equation you need to have and = sign so, we can do what he has (45) and subtract what he gives away (10) which would equal what he has left (x)

Answer:

45 (initial amount) - 10 (given to brother) = x (number of cd's left)

Equation:

    45 - 10 = x

Answer:

    35 CDs

Answer: A. SSS

Step-by-step explanation:

The two triangles are congruent through SSS which means Side-Side-Side. This is because each side of the triangle correlates between the two of them. They both have a 8, 6, and 3 side.

Answer:

SSS

Step-by-step explanation:

The given triangles have 3 equal sides: 3, 6 and 8

So the answer is SSS (side-side-side)

Answer:

number of students who ate soup = 60

number of students who didn't ate soup

= 300-60

= 240

60/240 = 1/4

Answer:

6m/16 = 3m/8

Step-by-step explanation:

since the fractions have the same denominator, just take out the operation on the numerators of the 2 fractions. So, 7m +(-m).

7m +(-M) is the same as 7m - m, so that is 6,

when you put it back together, you get 6m/16, simplify it to 3m/8

Answer:

A line in form of y = ax + b passes (0, 2)

=> 2 = 0x + b => b = 2

This line also passes (4, 6)

=> 6 = 4x + 2 => x = 1

=> Equation of this line: y = x + 2

=> Option C is correct

Hope this helps!

:)

Answer:

A line in form of y = ax + b passes (0, 2)

=> 2 = 0x + b => b = 2

This line also passes (4, 6)

=> 6 = 4x + 2 => x = 1

=> Equation of this line: y = x + 2

=> Option C is correct

Hope this helps!

:)

Step-by-step explanation:

Answer:

62 degrees

Step-by-step explanation:

all triangles equal 180 degrees so you would add both angles together then subtract the sum of that by 180

Answer:

[tex]x=62^o[/tex]

Step-by-step explanation:

Since the addition of all internal angles of a triangle should add up to [tex]180^o[/tex], then, the missing angle can be found by subtracting the two known angles from [tex]180^o[/tex]:

[tex]x=180^o-68.5^o-49.5^o=62^o[/tex]

Answer:

The new length is 13.5 meters

Step-by-step explanation:

Here, we are interested in calculating the new length of the cloth she wants to use

What we know from the question is that she is making a reduction of 10% from an initial of 15 meters

Thus, the length she is to use can be calculated by first getting what 10% of 15 meters is

Mathematically, that would be ;

10/100 * 15 = 1.5 meters

We now subtract this from the total of 15 meters

= 15 meters - 1.5 meters = 13.5 meters

Answer:

a₆ = 6

Step-by-step explanation:

There is a common ratio r between consecutive terms in the sequence, that is

r = [tex]\frac{216}{-1296}[/tex] = [tex]\frac{-1296}{7776}[/tex] = [tex]\frac{7776}{-46656}[/tex] = - [tex]\frac{1}{6}[/tex]

This indicates the sequence is geometric.

To obtain any term in the sequence, multiply the previous term by r, thus

a₅ = 216 × - [tex]\frac{1}{6}[/tex] = - 36

a₆ = - 36 × - [tex]\frac{1}{6}[/tex] = 6

Answer:

It's 6

Step-by-step explanation:

Got it right!

1 –46,656

2 7,776

3 –1,296

4 216

5 36

6 6

divided by 6 every time

Answer:

x^3   +  3x^2    +   9x    +  27   +   88 / [x - 3]

Step-by-step explanation:

x ^4 + 7 by x - 3 x^3   +  3x^2    +   9x        +  27 x - 3  [  x^4  +   0x^3    +   0x^2    +   0x    +   7   ]. x^3  -    

3x^3 ________________________________ 3x^3   +     0x^2 3x^2  

-     9x^2 ______________ 9x^2      +   0x 9x^2

   -    27x ____________ 27x    +   7 27x  

 -  81 _________ 88 S

Answer:  So the result is :      x^3   +  3x^2    +   9x    +  27   +   88 / [x - 3]

Please mark me brainliest

Hope this helps.