Solve for x???????????

Answer:

1,680

Step-by-step explanation:

n!/(n-r)!

in this case n= 8 and r= 4

so 8!/(8-4)! = 1,680

The possible permutation of 8 objects taken at 4 a time will be 1680.

The linear arrangement of the set of the orders or the linear arrangements of the numbers is called the permutation.

The number of possible permutations of 8 objects taken 4 at a time will be:-

[tex]^8C_4=\dfrac{8!}{(8-4)!}[/tex]

[tex]^8C_4=\dfrac{8!}{(4)!}[/tex]

[tex]^8C_4=\dfrac{8 \times 7\times 6\times 5\times 4\times 3\times 2}{4\times 3\times 2}=1680[/tex]

Therefore the possible permutation of 8 objects taken at 4 a time will be 1680.

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Answer:

a^2 +3a-2

Step-by-step explanation:

Given the expression:

g(x) =  x^2 +3x-2

We are to find f(a). To get this, we will simply replace x with a in the expression as shown;

g(a) = a^2 +3a-2

hence the required domain is expressed as g(a) = a^2 +3a-2

The length of RS is 55 unit.

The addition axiom states that when two equal quantities are added to two more equal quantities, their sums are equal. Thus, if a = b and y = z, then a + y = b + z.

We have, ST = 15 and RT = 40

Then RS can be get by adding the value ST + RT.

Apply Axiom of addition

then, RS

= RT + ST

= 40 + 15

= 55 unit.

thus, the length of RS is 55 unit.

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Answer:

9x+4/x

Step-by-step explanation:

hope this helps!

Answer:

I'm pretty Shure b is ur answer

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:

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:

25

Step-by-step explanation:

90+x+2x+15=180

3x=75

x=25

Answer:

M=0

Step-by-step explanation:

Youre welcome

Answer:

y=3

Step-by-step explanation:

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:hi

Step-by-step explanation:

Answer:It is 100 times as great in the ZIP code than it is in the area code

Step-by-step explanation:

step 1

Veronica 's uncle ZiP CODE = 89507 = The value of 5 here, represents 5 Hundred-----500

Veronica 's uncle Area code= 775 = The value of 5 here  represents 5 units--5

it will take a 100 times the value of 5 in the area code to be same as the value of 5 in the ZIP code

Step 2:

Therefore, we can say that the value of 5 is 100 times as great as the ZIP code than it is in the area code.

Answer:

Step-by-step explanation:

the 3rd one

Answer:

[tex]a_{52}[/tex] = -541

Step-by-step explanation:

Answer:

C.$60.00

Step-by-step explanation:

Answer:

Inequality = 6 + x ≤ 10

x(Number of hours more of television Sarah can still watch this week) = 4 hours

Step-by-step explanation:

Define a variable, set up an inequality and solve that inequality to determine how many more hours of television Sarah can watch this week.

We are told in the question that:

Sarah is allowed to watch no more than 10 hours of television each week.

This means :

Sarah can watch tv for less than or equal to 10 hours in a week. Sarah has already watched 6 hours of television.

Hence:

The number of hours left that Sarah can watch television in a week is represented as x

Our Inequality Equation =

6hours + x hours ≤ 10 hours

6 + x ≤ 10

Solving the inequality

x ≤ 10 - 6

x ≤ 4 hours

This means Sarah still has no more than (less than or equal to) 4 hours or television left to watch in this week

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: D

Step-by-step explanation: Just solve for perimeter of a rectangle by just plugging the side length in with these equations.

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

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

Answer:

True

Step-by-step explanation:

sry if it wrong

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:

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:

1i and -19i

Step-by-step explanation:

3-2=1, therefor: 1i

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

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:

1. 24th 2. 140

Step-by-step explanation:

1. To figure out this problem, you would have to list the multiples of both 6 and 8.  

6 (6, 12, 18, 24)

8 (8, 16, 24) because both have 24, that would be the answer.

2. There are 8 windows, all with the same perimeter. Each window's perimeter is 17.5 (17 1/2) so 8 windows would be 140 ft. (17.50 x 8 = 140)

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