Answer:
A.
Step-by-step explanation:
Graph B must be incorrect as this is a directly proportional relationship. Likewise, graph C shows an inversely proportional relationship.
Between graph A and D, only graph A passes through the origin, which is true because if length is zero, perimeter is zero.
Hence the answer is Graph A.
Answer:
y = 3/2 x + 3
Step-by-step explanation:
2/3 x + y = -14/3
y = -2/3 x − 14/3
The slope of this line is -2/3. So the perpendicular slope is the opposite of the inverse:
m = -1 / (-2/3)
m = 3/2
We know the slope of the line and a point on the line, so using point-slope form:
y − 0 = 3/2 (x − (-2))
Simplifying into slope-intercept form:
y = 3/2 (x + 2)
y = 3/2 x + 3
Answer:
Step-by-step explanation:
Open the brackets first:
Simplify:
It is determined that this can't be factored, so rewrite the equation so you can complete the square.
Take the square of 1.5 and add it to both sides:
Factor:
or 
So
or
Answer:26.83
Step-by-step explanation:
We will be solving this question using integration. The question has been solved in the diagram
Answer:
60 professors and 168 lecturers
Step-by-step explanation:
What you have is a 2 equations system with 2 unknown variables.
Let X be the number of professors and Y be the number of lecturers. As the total of both is 228:
X + Y = 228
Then, as there are 5 professors for every 14 lecturers:
5 X = 14 Y or X = (14/5) Y
Replacing this last value of X on the first equation:
(14/5) Y + Y = 228
(14/5) Y + (5/5) Y = 228
(19/5) Y = 228
Y = 228 * (5/19)
Y = (228*5)/19
Y = 1140 / 19
Y = 60
Then we can find X:
X = (14/5) Y = (14/5) * 60 = 168
X = 168
:)
