Answer:
(2,1)
Step-by-step explanation:
The solution is the point where the two lines cross.
Hope this helped! :)
Answer: the independent variable would be m (minutes spent talking on the phone)
Explanation: the cell phone bill will be affected by how many minutes is spent talking on the phone. However the nothing will affect how many minutes is spent on the phone.
Alright! so how do we complete the square? you're first step is to take the coefficient in front of your middle value, or 8x. 8 would we the coefficent. now, you divide that value by 2.
so we have :
8/ 2 = 4
so what do we do with 4? we square it.
4^2 = 16
okay. so I've made you do some stuff. what do we do now? we add AND SUBTRACT this value from our equation. since I both add and subtract, I haven't changed the value of my equation.
4x^2 + 8x + 23 +16 -16
now, we isolate the positive version of the number we solved for--or 16, and all the terms that have a varaible. by this I mean:
(4x^2 + 8x + 16) + 23 - 16
all I've done is move stuff around. no values have been changed. so what now? well, you factor that portion in the parenthesis.
if you don't know how to factor, I can go over r that seperately, but I'm gonna assume you can factor. when I factor this, I get:
4x^2 + 8x + 16 = (x+ 4)(x + 4) = (x + 4)^2
so now I have
(x+4)^2 + 23 - 16
I can now combine like terms, which include 23-16, which equals 7.
finally, I have:
(x+4)^2 + 7
so I have officially completed the square. ^^^that's your process of doing that. so how do I find the minimum value? well, run with me for a sec. if I just look at (x+4)^2, what type of values will I always get? well, anything squared is POSITIVE, so I will Never get a negative number. in fact, I only get numbers from 0 to infinity. so, if the lowest number I can get there is 0, the lowest value this polynomial can have overall is 0+ 7, which is 7. hope that helps!
Answer:
a. 0.69
b. 0.13
c.0.56
Step-by-step explanation:
Total number = 100
a) either means students with either option are valid
69/100 = 0.69
b) both means each student has done both math and english
=13/100 = 0.13
c) Only one means has done one subject and not both classes. We have 23 for math and 33 for english (this is according to your venn diagram)
23+33=56
one subject =56/100 = 0.56