Answer:
When y=276, x= 23
Step-by-step explanation:
Since they're directly proportional, when divided they have to equal the same.
180/15= 12 and 276/23= 12
The equations and the number of hotdogs and sodas sold are: x+ y = 126 and 2.25x + 1.50y = 225.75 ; 49 hot dogs and 77 sodas.
Two equations can be derived from this question:
2.25x + 1.50y = 225.75 equation 1
x + y = 126 equation 2
Where:
x = number of hotdogs sold
y = number of soda sold
In order to determine the value of y, multiply equation 2 by 2.25
2.25x + 2.25y = 283.50 equation 3
Subtract equation 1 from 3
57.75 = 0.75y
y = 77
Substitute for y in equation 2
x + 77 = 126
x = 49
To learn more about simultaneous equations, please check: brainly.com/question/23589883
Answer: The correct option is (A) 
Step-by-step explanation: Given that Raymond has 120 books on his bookshelf that he has not read. He plans on reading 3 books per week until there are only 24 books that he still needs to read.
We are to find the equation that can be used to determine the number of weeks it will take Raymond to have only 24 books left.
Also, we are to find the number of weeks.
The number of weeks it will take Raymond to have only 24 books left is represented by 'w'.
We have
number of books read by Raymond is 1 week = 3.
So, number of books read by Raymond is w weeks = 3w.
Since, there are total 120 books on his bookshelf, so the number of books left to read after w weeks will be
According to the given information, we get
thus, the required equation is 
and number of weeks is 32.
Option (A) is correct.
Remember PEMDAS is the order of operations. parenthesis,exponents,multiply,divide,add,subtract. so -8x-4x is -12x. now simplified the problem is 3(9-12x) + 8(3x+4)=11 . now I would distribute the numbers before the parentheses and it becomes 27-36x + 24x+32 =11 . now combine like terms. 59-12x =11 . subtract 59 on both sides. -12x=-48. divide -12 on both sides. x=4. :-)
Answer:
C
Step-by-step explanation:
In this technique, if we have to factorise an expression like ax2+bx+c, we need to think of 2 numbers such that:
N1⋅N2=a⋅c=1⋅−12=−12
AND
N1+N2=b=−1
After trying out a few numbers we get N1=3 and N2=−4
3⋅−4=−12, and 3+(−4)=−1
x2−x−12=x2−4x+3x−12
x(x−4)+3(x−4)=0
(x+3)(x−4)=0
Now we equate the factors to zero.
x+3=0,x=−3
x−4=0,x=4
