Answer. 2(x-4)
Step-by-step explanation:
common factor
2x-8
2(x-4)
Answer:
x= -9
Step-by-step explanation:
-x+3=2(x+15)
-x+3=2x+30
-x-2x+3=30-3
-3x=30-3
-3x=27
x= -9
This is the question:
A
bicycle manufacturing company makes a particular type of bike.
Each
child bike requires 4 hours to build and 4 hours to test.
Each
adult bike requires 6 hours to build and 4 hours to test.
With
the number of workers, the company is able to have up to 120 hours of building
time and
100 hours of testing time for a week.
If
c represents child bikes and a represents adult bikes,
determine
which system of inequality best explains whether the company can build 10 child
bikes and 12 adult bikes in the week
Now you
can state the system of inequalities from the statements
1) First inequality based on the hours availble
to buiding
Each
child bike requires 4 hours, e<span>ach
adult bike requires 6 hours to build and </span>the company is able to have up to 120 hours of building =>
4c + 6a ≤ 120
2) Second inequality based of the hours available to testing.
Each
child bike requires 4 hours to test, each
adult bike 4 hours to test and the company is able to have up 100 hours of testing time for a week =>
4c + 4a ≤ 100
Then the two inequalities are:
4c + 6a ≤ 1204c + 4a ≤ 100<span>
The answer is Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100Which you can verify by replacing in both equations 10 for c and 12 for a. Look:
1) 4(10) + 6(12) = 40 + 72 = 112 ≤ 1202) 4(10) + 4(12) = 40 + 48 = 88 ≤ 100</span>
The intercepts and the graph on your worksheet are not correct. Please see below for details:
has solutions at x=-1 and x=3 (use the quadratic formula to solve). That means these are the x-intercepts, namely points:
(-1,0) and (3,0).
The y-intercept comes from setting x=0 and calculating the y value:
so the y-intercept is (0,-3).
Now to the graph: Based on the form of the function we can see this is a quadratic function and its graph will be a parabola. You can reformat the expression in the following form
and that will indicate that the apex of the parabola (open up) will be at the point (1,-4).
Knowing the apex, the x intercepts, and the y intercept, we can graph it now.
Graph is in the image attached.
