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Slope, m,  of given line is -3/4       perpindicular is  - 1/m    =   4/3

A  and C have slopes of  4/3     ....   plug in 12,9   to see which equation it is.....

(6*12^0 + 10*12^1  +  4 * 12^2  + 1 * 12^3 )         -       ( 9*12^0   + 11*12^1  + 5* 12^2 )

Then convert the result  back to base₁₂

87 coins total

x = nickels

  then   87- x = quarters

value

5 x     +   25 (87-x)   = 1395            solve for 'x' = number of nickels   then quarters = 87-x

3x^2-18x+55                           divide first part  by 3

3 ( x^2-6x)   + 55                    'complete the square'

3 (x^2 -6x +9)    -9    + 55       simplify

3 ( x-3)² + 46      You can finish......

52.20254 how can I round it on 2 decimal places?

Hello Guest

\(52.20254 \approx 52.20\)

If the 3rd digit after the decimal point is \(\ge 5\), 1 is added to the 2nd digit.
If the 3rd digit after the decimal point is \(< 5\), the 2nd digit remains unchanged.

  !

"Hey, how much is 8 to the power of 0? And why?"

Perhaps this will help:

A blueprint for a cottage has a scale of 1:40

One room measures 3.4m by 4.8m.

Calculate the dimensions of the room on the blueprint.

Hello parpar!

\(w:3.4m=1:40\\ 40w=3.4m\)

\(w=\frac{3.4m}{40}\cdot \frac{100cm}{m}\)

\(w=8.5cm\)       on the blueprint

\(l=\frac{4.8m}{40}\cdot \frac{100cm}{m}\)

\(l=12cm\)         on the blueprint

greetings

  !

(5 C 3)  * 5^2 = 250 / 6^5=125 / 3,888 = 3.215%

The sum of the two parallel sides of a trapezoid is 44 cm. The segment that connects the midpoints of the two non-parallel sides divides the area of the trapezoid into two parts, in a ratio of 4:7. What is the product of the lengths of the two parallel sides?

If the height of a trapezoid is 2 cm, then the lengths of its bases are 10 cm and 34 cm.

10 * 34 = 340

(f o g)(x)   =   f( g(x) )

                                         Since  g(x) = -x + 1,  we can substitute  -x + 1  in for  g(x)

(f o g)(x)   =   f( -x + 1 )

                                         And  f(x) = x² + 2, so to find  f(-x + 1), plug  -x + 1  into

                                         the function by replacing every instance of  x  with  -x + 1

(f o g)(x)   =   (-x + 1)² + 2

                                                        Expand the squared term by multiplying it out.

(f o g)(x)   =   (-x + 1)(-x + 1) + 2

(f o g)(x)   =   x² - 2x + 1 + 2

(f o g)(x)   =   x² - 2x + 3

To start this problem, we can first calculate how much money each person makes per hour.

If Sal makes $24 in 3 hours, we can calculate the unit rate by doing 24 divided by 3.

24 ÷ 3 = 8, so we know that Sal makes $8 per hour.

Try to repeat the other two on your own. Remember, all you have to do is:

amount of money person makes ÷ number of hours it takes that person to make that amount of money

Once you've done that, it's just a comparison of numbers.

The greater the number, the more that person makes per hour.

Once you've found the greatest number, find out who makes that amount of money per hour (this part should be fairly simple if you write down your work), and that is your answer for part a.

For part b, all you have to do is multiply the amount of money the person with the highest unit rate makes (AKA what you just solved for in part a) by 8.

This is because part b is asking how much that person (your answer for part a) makes in 8 hours, and in part a you were solving for how much they make in 1 hour.

Happy solving! 

tysm for the hints! i get it now :)

This equals   (x-3-sqrt5)(x-3+sqrt5)             

  c would equal the red parts multiplied together and then multiplied by -2 ( because the x^2 has a -2 coefficient)

  b would equal the red parts added together and multiplied by -2

Vertex 'x' value is then =  -b/2a      get the y value of the vertex by putting 'x' into the equation and calculating....

Your question is not displaying properly.

Since the theater has a goal of selling 1500 tickets in the first week, and in the first 2 days it sold 30% of its ticket goal, we can do:

1500 * 30% = 450

This gives us 450, which basically stands for how many tickets were sold in the first 2 days of the first week.

Subtracting this (450) from 1500, we get:

1500 - 450 = 1050

1050 stands for the number of tickets the theater still has to sell (in the remaining 5 days) to meet its goal.

Therefore, we can find the average number of tickets the theater has to sell in the remaining 5 days by calculating:
 

1050 / 5 = 210 tickets

If you're confused, the 210 stands for the average number of tickets the theater has to sell in order to meet its ticket selling goal.

Hope this helped, if I made a mistake please let me know!

(2³)^2x  = 2¹²

^{Equate the exponents}

6x = 12

x = 2

3 = .06 x    solve for x for simple interest

if compounded annually

3 = (1+ .06)^x      solve for x

Draw it!

The centre is obviously (-3,1)   so this gives h and k 

and it is going to have a vertical axis.

\(\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1\)

c is the distance from the  centre to a focus so          \(c=\frac{\sqrt5}{4}\)

\(|PF_1-PF_2|=1=2a\\ so\;\;\;a=0.5\)

Then you have     \(c^2=a^2+b^2\)

so you can find b

Not so difficult after all.

Tytyty very much! :D I'm not too hot on probability but i get this thx :D

Nice to hear I ACTUALLY GOT A PROBABILITY/COUNTING QUESTION RIGHT!!!!

I didn't bother with the computations since that is a bit nasty and I am FAR too lazy to go onto mathway or the forum calculator. 

Ahr, thank you guest, now our answers are the same   

I only give approximations when the question asks for, or implies the need for or the benefit of, an approximation. 

If I have ever done it at other times then my answer is not as good as it could have been.

If it is a practical question then an approximate answer is most likely best.

If it is a pure mathematics question, such as this one, then the precise answer is the best one.

Cube everything in the parentheses

    and take the 4th root of that result....