5. What is the quotient if you divide 9/12 - 1/6​

Answer:

9

Step-by-step explanation:

steps for dividing mixed numbers.

Change every mixed number to an improper fraction.

Multiply the reciprocal of the divisor, simplifying if possible.

Put answer in lowest terms (or simpliest form)

Check to be sure the answer makes sense.

The constant is 18

To find distance (d) you would multiply the constant by the time(t).

D = 18t

Distance is speed x time, so the given constant would be the speed of the ant.

Answer:

The dimensions of the aquarium that minimize the cost of the materials:

[tex]x=y=\sqrt[3]{\frac{2V}{5}}\\z=\sqrt[3]{\frac{25V}{4}}[/tex]

Step-by-step explanation:

Let x, y and z be the dimensions of aquarium .

Surface area of an aquarium = xy+2yz+2xz

Volume of aquarium V=[tex]Length \times Breadth \times Height=xyz[/tex]  ----A

We are given that slate costs five times as much (per unit area) as glass

So, Cost function : C=5xy+2yz+2xz

Now we will use langrage multiplier to find the dimensions of the aquarium that minimize the cost of the materials.

[tex]\nabla C =\lambda \nabla V[/tex]

[tex](\frac{\partial C}{\partial x},\frac{\partial C}{\partial y},\frac{\partial C}{\partial z})= \lambda (\frac{\partial V}{\partial x},\frac{\partial V}{\partial y},\frac{\partial V}{\partial z})[/tex]

[tex](5y+2z,5x+2z,2y+2x)=\lambda(yz,xz,xy)[/tex]

So,

[tex]5y+2z=\lambda yz[/tex]   ----1

[tex]5x+2z=\lambda xz[/tex] -----2

[tex]2y+2x=\lambda xy[/tex]  ----3

Multiply 1 ,2 and 3 by x,y and z respectively.

[tex]5xy+2xz=\lambda xyz[/tex]   ----4

[tex]5xy+2yz=\lambda xyz[/tex] -----5

[tex]2yz+2xz=\lambda xyz[/tex]   ----6

Now equate 4 and 5

5xy+2xz=5xy+2yz

x=y

Substitute y=x in 5 and 6 and equate them

[tex]5x(x)+2(x)z=2(x)z+2xz\\5x^2=2xz\\5x=2z\\\frac{5}{2}x=z[/tex]

Substitute the values in A

[tex]V = xyz = x \times x \times \frac{5}{2}xV=\frac{5}{2}x^3\\\sqrt[3]{\frac{2}{5}V}=x\\x=y=\sqrt[3]{\frac{2}{5}V}\\z=\frac{5}{2}x=\frac{5}{2}(\sqrt[3]{\frac{2}{5}})=\sqrt[3]{\frac{25V}{4}}[/tex]

Hence,

The dimensions of the aquarium that minimize the cost of the materials:

[tex]x=y=\sqrt[3]{\frac{2V}{5}}\\z=\sqrt[3]{\frac{25V}{4}}[/tex]

Answer:

comparing rates.. use the formula  d = r * t    where d= distance , r = rate or speed  and t = time  ofc.  :)

Step-by-step explanation:

we know the distance  and the time but not the rate.. find that  r ....

d/t = r    4/30 = r    = 0.13333333333  this is in Km per minute,   b/c the 4 is Km and the 30  is in minutes.  Units are not to important other than keeping track of what they are.  

Now we can answer the question  can Marlene run 6 Km in 45 mins. b/c we know her rate , or speed,   so at her rate of 0.133333333  Km/min  and using that d = r * t formula  what is her distance in 45 minutes..  so  multiply 45 * 0.133333= 6     so she runs exactly 6 Km in 45 minutes.. so the math answer is yes

Answer:

i think 6

Step-by-step explanation:

2/3 divided by 1/9 then , 2 times 9 then.  3 times 9 = 18/3 if you simplifying the answer is 6  

Answer:

See Below

Step-by-step explanation:

(x-3)-2 ≤ 1                                              (x-3)-2 ≥ -1

      +2  +2                                                    +2  +2

x-3 ≤ 3                                                x-3 ≥  1

+3   +3                                                 +3  +3

x ≤ 6                          and                       x ≥ 4

Step-by-step explanation:

This is mean domain is all real numbers

Answer:

d. x = 7

Step-by-step explanation:

32/8 = 28/x

simplify the fraction

4/1 = 28/x

cross multiply:

4x = 28

divide both sides by 4:

x = 7

Answer:

Since it is a to-scale model,

the ratio of the wingspan to the length of both the airplanes must be equal

wingspan1 = 200 ft               wingspan2 = 30 cm

length1 = 240 ft                     length2 = x cm

wingspan1 / length1 = wingspan2/length2

replacing the variables

200 / 240 = 30 / x

x = 30 * 240/200

x = 36 cm

Therefore, the length of Emma's airplane is 36 cm

Answer:

Step-by-step explanation:

Answer:

Plus-or-minus one-fifth, plus-or-minus1, plus-or-minus eleven-fifths, plus-or-minus11

Step-by-step explanation:

According to the Rational Root Theorem, the potential roots of f(x) = 5x² – 7x + 11 are; Plus-or-minus one-fifth, plus-or-minus1, plus-or-minus eleven-fifths, plus-or-minus11.

The given function is; f(x) = 5x² – 7x + 11

On this note; Using the rational Root Theorem while determining the root; we have;

f(x) = 0 = x² -7/5x + 11/5.

The possible roots are therefore the factors of the constant, 11/5 and are as follows;

Read more on Rational Root Theorem;

https://brainly.com/question/4251786

Answer:

x=-6

Step-by-step explanation:

Answer:

10 i sqrt 2

Step-by-step explanation:

i indicates that it is an imaginary number. this is because 200 is negative.

The simplified form of the given square root number is 10i√2. Therefore, the correct answer is option D.

The given square root number is √-200.

The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.

Here, 200 = 2×2×2×5×5

Thus, √-200=√-2×2×2×5×5

=2×5×i√2

= 10i√2

Therefore, the correct answer is option D.

To learn more about the square root of a number visit:

https://brainly.com/question/8971086.

#SPJ6

Answer:

-8

Step-by-step explanation:

First, write it out in standard form:

2 x (-4)

Then multiply!

Answer:

-8

Step-by-step explanation:

it is basically 2 x -4 and a negative times a positive is a negative which makes it -8

Answer:

9

Step-by-step explanation:

Answer:

512 ounces

Step-by-step explanation:

Answer:

512

Step-by-step explanation:

multiply the volume value by 128

Answer:

Sorry i have no idea hahha

Step-by-step explanation:

Good luck

Answer:7

Step-by-step explanation:

Answer:

$22.37

Step-by-step explanation:

Answer:

$22.37

Step-by-step explanation:

6.99(3.2)

Answer:

473 tickets

Step-by-step explanation:

8,500/18=472.2222222 but, since you can’t sell only part of a ticket, you’ll round up to get 473 tickets.

Answer:

B i think

Step-by-step explanation:

Answer:

13  ( x  +  y ) /  6

Answer:

15.51

Step-by-step explanation:

Answer:

-2,-7/4, 1/2, square root of 5, 2.4

Step-by-step explanation:

Answer:

-2, -1.75, 1/2, [tex]\sqrt{5}[/tex], 2.4

Step-by-step explanation:

1/2

-2

√5≈2.24

-1.75

2.4

-2, -1.75, 1/2, [tex]\sqrt{5}[/tex], 2.4

Answer:

y = 2x

Step-by-step explanation:

y-int = 0

slope = 2

Answer:

-11.9166666667

Step-by-step explanation:

Answer:

-11.9166666667

Step-by-step explanation: I just seached it up

Answer:

∡BEN=122

x=17

Step-by-step explanation:

Since you know that when two sides are congruent like this then the to angles are congruent then you know that angle BNE equals 29.

Once you know that since we know that 180 is the sum of all three angles set an equation like this:

180=29+29+(11x-65)

Take off parentheses since you can't simplify in them.

180=29+29+11x-65

Combine like terms.

180=11x-7

Solve for x.

187=11x

x=17

Plug that in to (11x-65) to find angle BEN

angle BEN = 11(17)-65

angle BEN=122

Answer:

0

Step-by-step explanation:

Everything multiplied by 0 is 0.