These are linear equations that can be solved simultaneously;
5m+3n=41
3m-6n=9 (multiplying the first equation by 3 and the second by 5)
15m+9n=123
15m-30n= 45 (subtracting the two equations)
39n = 78
n = 2,
and for m, 3m = 9+6(2)
= 21
m = 7
Therefore, n=2 and m=7
Answer:
- 224/5
Step-by-step explanation:
DECIMEL FORM = -44 4/5
Answer
The vertex is at point (-3, -1)
The axis of symmetry is x = -3
Explanation
We are asked to find the vertex and axis of symmetry of the equation given.
f(x) = x² + 6x + 8
The vertex of a quadratic equation is the point where the graph of the quadratic equation changes from sloping negatively to sloping positively and vice-versa.
The axis of symmetry represents the straight line that divides the graph of the quadratic equation into two mirror parts that are similar to and are mirror images of each other. This axis of symmetry usually passes through the vertex.
To find the vertex, it is usually at the turning point where the first derivative of the quadratic equation is equal to 0.
(df/dx) = 0
f(x) = x² + 6x + 8
(df/dx) = 2x + 6
At the vertex
(df/dx) = 2x + 6 = 0
2x = -6
Divide both sides by 2
(2x/2) = (-6/2)
x = -3
We then insert this into the equation to get the corresponding f(x) value.
f(x) = x² + 6x + 8
f(-3) = (-3)² + 6(-3) + 8
= 9 - 18 + 8
= -1
Hence, the vertex is at point (-3, -1)
And since the axis of symmetry has to pass through the vertex,
The axis of symmetry is x = -3
Hope this Helps!!!
Answer:
Cathy was right ( kinda)
Step-by-step explanation:
let the dimension of the small one be 2a : 2b : 2c
then the dimension of the big one be 3a : 3b : 3c
volume of small: 2a*2b*2c = 8 abc
volume of big: 3a*3b*3c = 27 abc
volume ratio: big/ small = 27/8 = 3.375
-> big one hold 237.5% more than small
-> Cathy was right ( kinda)
