tomsun

AGD is 90 because it's given that BGD is a right angle, so the AGD is also a right angle considering the fact that AB is a straight line, which it is.

y=-2x^2+12x-23

a=-2 b=12 c=-23

Use formula -b/2a: -12/-4=3

x=3

Plug in 3 as x: y=-2(3)^2+12(3)-23

y=-5

(3,-5)

number of ways to select 2 freshman girls: 12 choose 2
number of ways to select 3 freshman boys: 11 choose 3

using the formula: n!/k!(n-k)!

12 choose 2 is 12!/2!10!, which is 12*11/2, and that is 66

11 choose 3 is 11!/3!8!, which is 11*10*9/6, and that is 165

...

number of ways to pick 5 students without restriction: 30 choose 5

30 choose 5 is 30!/5!25!, which is 30*29*28*27*26/120, and that is 142506

...

66*165/142506=10890/142506, which is 605/7917.

---Tom

Just to give you some hints: 

for question 1, add 11*14 with (20-11)*9

for question two do the same thing with the splitting method. 

\( 9 + \frac{27}{x} + \frac{8}{x^2} = 0\)

answer: -1/3, -8/3

Multiply both sides by x^2

and you will get \(9 x ^2 + 27 x + 8 = 0\)

which is equal to (3x+1)(3x+8)=0

set 3x+1 = 0 and solve for x.

you will get -1/3

set 3x+8=0 and solve for x

you will get -8/3

a) On each action, there are 15 possible inputs: 5 inputs consisting of a single button, and 10 inputs consisting of two different buttons.

the answer is 60.

this question is not original. 

the answer can be found on 

https://brilliant.org/problems/question-19/

27 for the rate of the boat

C=9 for the current

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.735649.html

credited to checkley79

D=RT
180=(R-C)10
180=10R-10C DIVIDE BY 2 & ADD.
180=(R+C)5
180=5R+5C
90=5R-5C
---------------
270=10R
R=270/10
R=27 MPH. ANS. FOR THE RATE OF THE BOAT.
180=(27-C)10
180=270-10C
10C=270-180
10C=90
C=90/10
C=9 MPH. ANS.FOR THE CURRENT.
PROOF:
180(27+9)5
180=36*5
180=180

credited to checkley79

Setting up 2 equations:

\(y=x+21\)

\(y=4x\)

\(4x=x+21\)

\(3x=21\)

\(x=7\)

\(y=28\)

x=time and y=distance

The answer: it takes 7 seconds and the adults go 28 meters

post deleted. 

sorry, I put the wrong answer

hint: brute force means every possible route was calculated. So, figure out how many routes are possible with seven cities, divide the time by that, and that gives you how much time it takes to calculate a single route with 7 cities.

divide the time for an individual route by 7 and that tells you how much time it takes to evaluate an individual route per 1 city.

Multiply that by 11, you get the time it takes to measure an 11 city route.

With that, all you need is the number of routes in 11 cities, multiply that by the time to calculate each route, and you're good.

I have to say that you asked too many questions.

most of the questions u asked can be easily solved by using a simple google search or a Calculator. 

\(2L + 2(L − 2.5) = 56\)

\(2L+2L-5=56\)

\(4L=64\)

\(L=16\)

OKay. Let's get started.

we will make a system of equations.

s for students.

\(6s + 27s − 45 = 1,374\)

\(27s+6s=1374+45\)-- add 45 to both sides.

\(33s=1419\)-- combine like-terms.

\(s=43\)

I *agree*, but I like to answer directly because there is always a possibility that the person doesn't know how to solve it.

As you said, this question is easy and the guest doesn't know how to do it, so that means the guest might not know how to solve the equation as well.

The answer is D.

I also explained on https://web2.0calc.com/questions/help_1360

Thank you Impasta and Guest.

I will start from the place where Impasta and the Guest left out.

\(2t+5=13\)

\(2t=13-5\)

\(2t=8\)

\(t=4\)

The answer is: Tony has 4 kills.