Alison’s age is 16 more than half of Sam’s age. Using S to represent Sam’s age, write an expression that represents Alison’s age

Answer:

j = 12

Step-by-step explanation:

j + (-3) = 9

j = 12

Answer:

Her cousin is 12

Step-by-step explanation:

Use division

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:

D : { -3, 3, 12}

Step-by-step explanation:

I would suggest substituting the range for the function and solving for x like so.

i.e -6 = 1x-3, -6 + 3 = 1x -3 + 3, -3 = x, x = -3.

0 = 1x - 3, 0 + 3 = 1x - 3 + 3, 3 = x, x = 3.

9 = 1x - 3, 9 + 3 = 1x -3 + 3, 12 = x, x = 12

Answer:

i think its B

sorry if its wrong im not really sure by my answer

Answer:

50%

Step-by-step explanation:

Percent change = {(New-Old)/(Old)}*100%

So,

{(45-30)/(40)}*100

=(15/30)*100

=50%

Answer:

17

Step-by-step explanation:

Use BODMAS Method

B - Brackets

O - Power

D - Division

M - Multiplication

A - Addition

S - Subtraction  

24 - 8 + 8/3 - 8/9 + 8/27 - 8/81

First division

8/3 = 2.66666666667

8/9 = 0.88888888888

8/27 = 0.29629629629

8/81 = 0.09876543209

Then Subtract

24 - 8 = 15

2.66666666667 - 0.88888888888 = 1.77777777779

0.29629629629 - 0.09876543209 = 0.1975308642

Then lastly add

15 + 1.77777777779 + 0.1975308642 = 16.975308642

In these type of questions, the answer have decimals, so we have to round it to near whole number.

So nearest whole number is 17

Answer = 17

Hope you understand

:-)

Answer:

let me see the drop box options !! it helps alot!

Answer:

There is No solution to the question above.

Answer:

103

Step-by-step explanation:

Since x= 10, we need to use the second piece of the function x^2+3

f(x) = x^2 +3

Let x=10

f(10) = 10^2 +3

       = 100 +3

       = 103

Answer:

no solution

Step-by-step explanation:

Answer:

8 and 16

Step-by-step explanation:

Answer:

I have 8 and 16

Answer:

(✿◠‿◠)

I put the link in the comments!

A graph of the line with a slope of -7 and y-intercept of 6 is shown in the image below.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided about this line, the y-intercept is 6 and the slope is -7.

In this context, we can logically deduce that a linear equation that models the line is given by;

y = mx + b

y = -7x + 6

Read more on slope-intercept here: brainly.com/question/7889446

#SPJ6

Answer:

a

f

L

v

o

r

t

e

Step-by-step explanation:

Answer:

Check explanation.

Step-by-step explanation:

y > 3x - 4 = F

y < - 1/2x + 9 = L

y > 3x + 2 = U

y > 5 = R

y < - 2/3x = I

y > 1/3x + 3 = T

These are all the ones I can find, call me back if you still need help.

9514 1404 393

Answer:

Step-by-step explanation:

Let x and y represent the numbers of YuuMi and ZBox consoles, respectively. The inventory cost must be at most 70,000, so that constraint is ...

  250x +400y ≤ 70000

The number sold will be at most 250 units, so that constraint is ...

  x + y ≤ 250

Additionally, we require x ≥ 0 and y ≥ 0.

__

A profit of 295-250 = 45 is made on each YuuMi, and a profit of 450-400 = 50 is made on each ZBox. So, if we want to maximize profit, our objective function is ...

  profit = 45x +50y

__

A graph is shown in the attachment. The vertex of the feasible region that maximizes profit is (x, y) = (200, 50).

200 YuuMi and 50 ZBox consoles should be stocked to maximize profit. The maximum monthly profit is $11,500.

Answer:

2 gallons

Step-by-step explanation:

You have to find the pattern of adding and draining water for 15 days. To get there you need to subtract 2 and add 1 but keep the negative/positives the same i.e. (this is for the 10ths of gallons)

13-2=11

11+1=10

keeping the pattern for 15 days:

+13, 11,+12,-10,+11,-9,+10,-8,+9,-7,+8,-6,+7,-5,+6 = 20 (10ths of gallons)

20/10 = 2

Answer:

x>10

Step-by-step explanation:

2x - 8 >12

2x>12 +8

2x >20

x >20 :2

x>10

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:

1.125 or 9/8

Step-by-step explanation:

Answer:

Samantha payed 12.71$ for her purchase.

Step-by-step explanation:

I may have misunderstood the question, but it looks like you can use a calculator for this!

6.19 + 2.85 + 2.29 + 1.38 =

12.71

Answer:

18

Step-by-step explanation:

.2x15=3

3+15=18

Answer:

18$

Step-by-step explanation:

Answer:

Para sumar o restar decimales se colocan los números decimales uno debajo del otro, haciendo que coincidan las unidades en la misma columna. De esta manera, también tienen que coincidir las décimas, las centésimas… y la coma.

Step-by-step explanation:

Answer:

[tex]>[/tex]

Step-by-step explanation:

[tex]13 + 7 = 20[/tex]

[tex]20 > 11[/tex]

I know this because if 13 + 7 is 20, thats bigger than 11.

Ex of greater than 4:

10 > 4

-BBBM

Answer:

Step-by-step explanation:

The first one is going to be a less than symbol and the steps you would need to take is add 13 and 7. the second problem, you could do 5=4 and your answer would be greater than four. The steps you would take is 5=4 which is 9 and 9 is greater than 4

Answer:

0.6 of a serving is 225

3.85 servings are 1350

Answer: 207

Step-by-step explanation:

Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below.

Step 1: Use the algorithm method.

Step 2: Therefore, 476 − 269 = 207.

207

~I hope I helped you! :)~

Answer:

2.86666667

Step-by-step explanation:

Answer:

1 18/25

Step-by-step explanation:

4 2/3-1 4/5

=14/3-9/5

LCM is 15

=(70-27)/15

=43/25

Answer:

I think it's 92.88

Step-by-step explanation:

add up 20 and 9 to get a total of 29%

then multiply .29 and 72 to get 20.88

then add 20.88 and 72 to get the total cost including tips and tax

Answer:

150 degrees

Step-by-step explanation:

A triangle adds to 180 degrees.

48 + 102= 150

180-150 = 30

Then the angle x in total adds to 180

180-30= 150 degrees

Answer:

c, or 8

Step-by-step explanation:

Answer:

D

It would be either C or D because anything greater than 5, you move the next number up 1 digit.

Step-by-step explanation:

Answer:

a number plus five times two

Step-by-step explanation:

a number plus five times two

Answer:

hs=d

Step-by-step explanation:

Answer:

hs= d

Step-by-step explanation: