Solve for x.
16x^2- 9=0

Answer:

16

Step-by-step explanation:

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:

13) 28

14) 22

15) 24

16)13

Step-by-step explanation:

13) Because they all lie on the same line, AC would be AB+BC, or 16+12, or 28.

14) Same thing as 13, 13+9=22

15) Same thing as others but make an equation

-1+2x+11=3x+3

Simplifying the equation, we get x=7. Now, we plug in x=7 to 3x+3 to get AC.

3(7)+3=21+3=24

16) build the equation:

x+14+x+10=22

2x+24=22

2x=-2

x=-1

Now plug in x=-1 to x+14.

-1+14=13

Answer:

Yes students should be confident in addition before they proceed to mulplication.This is because addition is the base of multiplication and requires mastery before you start,so It would be much easier to solve

Answer:

512 ounces

Step-by-step explanation:

Answer:

512

Step-by-step explanation:

multiply the volume value by 128

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: 21 cupcakes and 33 cookies were sold.

Step-by-step explanation:

Let x= Number of cupcakes

y = Number of cookies

As per given,

x+y= 54       (i)

Cost: 2.25x+0.25y=55.50          (ii)

Multiply 0.25 to (i0, we get

0.25x+0.25y = 0.25(54)

⇒0.25x+0.25y = 13.5         (iii)

subtract (iii) from (ii), we get

2x=42

Divide both sides by 2, we get x= 21

Put this in (i) , we get 21+y =54 ⇒ y= 54-21= 33

Hence, 21 cupcakes and 33 cookies were sold.

Answer:

0

Step-by-step explanation:

Everything multiplied by 0 is 0.

Answer:

[tex]his \: reasoning \: is \: correct.[/tex]

Step-by-step explanation:

[tex]since \: the \: ratio \: of \: the \: glass \: to \:that \\ \: of \: the \: thermos \: is \: in \: the \: fraction : \\ \frac{2 7 0 mL }{1mL} \: which \: is \:270 mL : 1mL \\ then \: the \: keem \: is \: right.[/tex]

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:

1.125 or 9/8

Step-by-step explanation:

Answer:

15.51

Step-by-step explanation:

Answer:

$9.50

Step-by-step explanation:

Answer:

-5 yards

Step-by-step explanation:

4 - 9

= -5

in that two plays:

loss 5 yards

Answer:

x=12

Step-by-step explanation:

6x+7=8x-17

-6x     -6x

7=2x-17

+17    +17

24=2x

÷2   ÷2

12=x

x=12

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:

B i think

Step-by-step explanation:

Answer:

y = 2x

Step-by-step explanation:

y-int = 0

slope = 2

Answer:

$22.37

Step-by-step explanation:

Answer:

$22.37

Step-by-step explanation:

6.99(3.2)

Step-by-step explanation:

(1200-700)/5

=500/5

=

The expression results to 100.

Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

Given:

divide the difference between 1200 and 700 by 5

so, mathematically

(1200- 700)/5

= 500 /5

= 100

Hence, the expression results to 100.

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ5

Answer:

The answer is C

Step-by-step explanation:

Both f(x) and g(x) have a domain of [0,infinite). and a range of [0, infinite).

Answer:

It costs $42.43

Step-by-step explanation:

Answer:

$1.35

Step-by-step explanation:

7.5÷ 5/6=0.25

0.25x4 7/5=1.35

Answer:

x=-6

Step-by-step explanation:

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:

15 (50*0.3)

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

0.3*50 = 15

Answer:

if u could include a photo it may help more ..thanks

Answer: 0.00002163799

Step-by-step explanation:

Answer:

46,215

Step-by-step explanation:

you just have to divide the bigger number first and then the smallest