What is the measure of

Answer:

THE SMALLEST FORMS:

- smallest prism ---> the cube with all sides 2 ==> the volume is 2*2*2 = 8 cm^3

- smallest pyramid number one ---> the pyramid with base sides 2 and the height also 2 ==> the volume is (1/3)*2*2*2 = 8/3 cm^3

- smallest pyramid number two ---> the pyramid with base sides 2 and the lateral sides also 2 ==> the radius of the base is sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 2^2 - sqrt(2)^2 = 4 - 2 = 2 ==> pyramid_height = sqrt(2) ==> the volume is (1/3)*2*2*sqrt(2) = 4*sqrt(2)/3 cm^3

- smallest cylinder --> the cylinder of diameter 2 and height also 2 ==> the radius is diameter/2 = 2/2 = 1 ==> the volume is pi*(radius^2)*height = pi*(1^2)*2 = pi*1*2 = 2*pi cm^3

The lesser volume is the volume of the smallest pyramid number two. ==> it's wax cost is approximately 0.0075 * 4 * 1.42 / 3 $ per candle = 0.014 $ per candle ==> the total cost  per candle is approximately 0.014 + 1.6 = 1.614 $ per candle.

THE BIGGEST FORMS:

- biggest prism ---> the cube with all sides 10 ==> the volume is 10*10*10 = 1000 cm^3

- biggest pyramid number one ---> the pyramid with base sides 10 and the height also 10 ==> the volume is (1/3)*10*10*10 = 1000/3 cm^3

- biggest pyramid number two ---> the pyramid with base sides 10 and the lateral sides also 10 ==> the radius of the base is 5*sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 10^2 - [5*sqrt(2)]^2 = 100 - 50 = 50 ==> pyramid_height = 5*sqrt(2) ==> the volume is (1/3)*10*10*5*sqrt(2) = 500*sqrt(2)/3 cm^3

- biggest cylinder --> the cylinder of diameter 10 and height also 10 ==> the radius is diameter/2 = 10/2 = 5 ==> the volume is pi*(radius^2)*height = pi*(5^2)*10 = pi*25*10 = 250*pi cm^3

The bigger volume is the volume of the biggest prism (the side-10 cube). ==> it's wax cost is  0.0075 * 1000 $ per candle = 7.5 $ per candle ==> the total cost per candle is 7.5 + 1.6 = 9.1 $ per candle

The range of the cost is the interval [1.614 ; 9.1]. Depending on other prices on the market,  you greed, and other factors you will put a profit margin: maybe 20% of the cost ; maybe a fixed margin like 5$. So the price per candle will be the cost per candle plus the profit margin per candle.

If I were to choose the base length I would have to say 6 because it is the arithmetic mean between 2 and 10: (2+10)/2 = 12/2 = 6. 2cm is too small, and 10cm is too big.

Also if you start with a rectangle of length 10 and width 2 and you have to find the rectangle with the largest area by being allowed to increase the width and decrease the width with the same quantity you get this:

Area of the new rectangle is (10-x)(2+x) = -x^2 + 8x + 20 = -x^2 + 8x -16 + 36 = -(x^2 - 2*x*4 + 4^2) + 36 = -(x-4)^2 + 36 = 36 - (x-4)^2 which has the maximum value of 36 because out of 36 you subtract a positive value. You get the maximum when (x-4)^2 = 0 ==> x-4=0 ==> x=4

The new length is 10-4=6 and the new width is 2+4=6.

Next I would choose the height of the prism (I like prisms :P) to be [the_golden_ratio]*[base_side] which is approximately 1.618 * 6 = 9.708 which I would round up to 10. ==> The volume would be 6*6*10 = 360 cm^3. ==> the cost would be 0.0075*360 + 1.6 = 2.7 + 1.6 = 4.3 $ per candle. And because my candle is so perfect I'd put the profit margin to be 5.69 $ per candle so I can proudly show it in the store with the price of 4.3 + 5.69 = 9.99 $ :)

Answer:

Rational numbers

Step-by-step explanation I put D on a test and I got it right

9514 1404 393

Answer:

Step-by-step explanation:

There are an infinite number of equivalent expressions. A couple of them are ...

  (1/3)/(4/5) = (1/3)(5/4) . . . . . division is multiplication by the inverse

  (1/3)/(4/5) = (5/15)/(12/15) . . . . converted to common denominators*

_____

* this latter form is useful in that the ratio is then the ratio of the numerators, 5/12

Answer:

f(3) = 7

Step-by-step explanation:

To evaluate f(3), substitute x = 3 into f(x), that is

f(3) = 2(3) + 1 = 6 + 1 = 7

X=y+16

4y-1=7

Solve on both sides

4y=8

Y=8/2

Y=4

X= (4)+16

X=20

Answer:

[tex]10\frac{14}{48}[/tex]

Step-by-step explanation:

given data:

recipe = two and one sixth cups of walnuts [tex]2\frac{1}{6}[/tex]

and eight and one eighth cups of peanuts [tex]8\frac{1}{8}[/tex]

solution:

[tex]= 2\frac{1}{6} + 8\frac{1}{8}\\\\= 10 (\frac{1}{6} + \frac{1}{8} )\\[/tex]

[tex]= 10\frac{7}{24}\\or\\= 10\frac{14}{48}[/tex]

Answer:

9x+4/x

Step-by-step explanation:

hope this helps!

Answer: m = 6

Step-by-step explanation:

first, move the terms.

4m + 3m = 49 - 7

then, collect like terms and calculate.

7m = 42

then divide both sides.

m = 6

Answer:

m=42

Step-by-step explanation:

simplifying both sides of the equation then isolating the variable.

Answer:

D. 24

Step-by-step explanation:

Plug in -14 to the equation:

f(x) = 2x - 4(x + 1)

f(-14) = 2(-14) - 4(-14 + 1)

Simplify:

f(-14) = -28 - 4(-13)

f(-14) = -28 + 52

f(-14) = 24

So, D is the correct answer.

Answer:

y=x doesent that mean 2=3 so what you do is the line that goes up thats y and the one that goes sideways thats x so at the to go to 2 then at the side go to 3

Answer:

Step-by-step explanation:

y=x doesent that mean 2=3

Answer:

m = [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Slope Formula is...

m= rise / run      or    [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Two Coordinate Points / Ordered Pair: (16,2) and (32,4)

Your rise is...

4 - 2

Your run is...

32 - 16

Together the fraction reads...

(4 - 2) / (32 - 16)

Then do the subtracting to get....

2 / 16 ( 2 over 16)

Don't forget to simplify...

*2 can go into 2 and 16

Making the equation....

1 / 8 (one over 8)

So your m (slope) is ...  [tex]\frac{1}{8}[/tex]

Answer:

True

Step-by-step explanation:

sry if it wrong

Answer:

Alternate interior angle

Step-by-step explanation:

Hope this helps.

Answer:

your answer is A ....

Answer:

5x+10

Step-by-step explanation:

Distribute:

=(5)(x)+(5)(3)+−5

=5x+15+−5

Combine Like Terms:

=5x+15+−5

=(5x)+(15+−5)

=5x+10

Answer:35

Step-by-step explanation:

take 180 and subtract those numbers and u get ur answer

Answer:153

Step-by-step explanation:

From the question, we are informed that Emilio asks his classmates what month they were born and that he finds that 15 out of 125 classmates were born in July. This gives us a fraction of 15/125 = 3/25.

If there are 1,280 students in Emilio's school, the number of students that he can expect to have birthdays in July would be:

= 3/25 × 1280

= 153.6

There will be 153 students expected

Answer:

75

Step-by-step explanation:

Answer:

3d+1=[]

Step-by-step explanation:

first collect the like terms ie 4d-d+9-8

giving you 3d+1

Answer:

1i and -19i

Step-by-step explanation:

3-2=1, therefor: 1i

-11-8=-19, therefor: -19i

Step-by-step explanation:

Enter a problem...

Algebra Examples

Popular Problems

Algebra

Expand using the Binomial Theorem (3x+2)^4

(3x+2)4(3x+2)4

Use the binomial expansion theorem to find each term. The binomial theorem states (a+b)n=n∑k=0nCk⋅(an−kbk)(a+b)n=∑k=0n⁡nCk⋅(an-kbk).

4∑k=04!(4−k)!k!⋅(3x)4−k⋅(2)k∑k=04⁡4!(4-k)!k!⋅(3x)4-k⋅(2)k

Expand the summation.

4!(4−0)!0!⋅(3x)4−0⋅(2)0+4!(4−1)!1!⋅(3x)4−1⋅(2)+4!(4−2)!2!⋅(3x)4−2⋅(2)2+4!(4−3)!3!⋅(3x)4−3⋅(2)3+4!(4−4)!4!⋅(3x)4−4⋅(2)44!(4-0)!0!⋅(3x)4-0⋅(2)0+4!(4-1)!1!⋅(3x)4-1⋅(2)+4!(4-2)!2!⋅(3x)4-2⋅(2)2+4!(4-3)!3!⋅(3x)4-3⋅(2)3+4!(4-4)!4!⋅(3x)4-4⋅(2)4

Simplify the exponents for each term of the expansion.

1⋅(3x)4⋅(2)0+4

Hope this helps!

Answer:81x^4+216x^3+216x^2+96x+16

Step-by-step explanation:cause yussss

Hey there!

• Reminder: “x” is a unknown number so will say it is an invisible 1!

x/9 = 6

• FIRST: MULTIPLY by 9 on BOTH SIDES

x/9 × 9 = 6 × 9

• CANCEL out: x/9 × 9 because that gives you 1

• KEEP: 6 × 9 because that gives the value of your “x”

• New equation:

x = 6 × 9

6 × 9 = 54

Because 54 ÷ 9 = 6

Answer:

x = 54 ☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer:

M=0

Step-by-step explanation:

Youre welcome

Answer:

y=3

Step-by-step explanation:

Answer:

I'm pretty Shure b is ur answer

Answer:

x=3

Step-by-step explanation:

3^x+3=30

3^x=27

3^3=27

x=3

Answer:

Step-by-step explanation:

3 x 3 = 9 + 3 = 12

30 divided by 12

= 2.5