Answer:
3/4
Step-by-step explanation:
Constant of Proportionality is just a fancy way of saying slope (for a line passing through (0, 0), at least).
You can find it by looking at y/x, which will be equal at any point on the line (which is why it is a "constant").
So, for multiple points on the line:
1.5 / 2 = 3/4
3 / 4 = 3/4
4.5 / 6 = 3/4
Answer:
Two dotted lines, one solid line
Step-by-step explanation:
The graph of the system of inequalities
will have two dotted lines, one solid line.
To plot the solution set to the inequality with signs < or >, we need to plot the dotted line (because the points of this line are not the solutions to the inequality).
To plot the solution set to the inequality with signs ≤ or ≥, we need to plot the solidd line (because the points of this line are the solutions to the inequality).
The system above has two inequalities with signs < and > and one inequality with sign ≥, so there will be two dotted lines, one solid line.
Answer:
60 degrees and 30 degrees
Step-by-step explanation:
let the angles be x and y
we are given that the angles are complementary (i.e they sum up to 90 degrees). Hence we can write the first equation:
x + y = 90 ------(eq 1)
we are also given that the difference between the two angles is 30 degrees). Similarly we can write
x - y = 30 ------(eq 2)
now we have a system of 2 equations with 2 unknowns, which we can solve by elimination:
eq 1 + eq 2:
(x + y) + (x - y) = 90 + 30
2x = 120 (divide both sides by 2)
x = 120/2
x = 60 deg (substitute this back into eq 1)
x + y = 90
60 + y = 90 (subtract 60 from both sides)
y = 90 - 60
y = 30 deg.
Answer:
The amount $15000 is divided as
in 2% = $7000
in 5% = $8000
Step-by-step explanation:
It is given that the total amount is $15000 and rates of interests are 2% and 5%.
<em>Let the amount invested in 2% be "x", so the amount invested in 5% is (15000 - x).</em>
The annual interest on x part is given as,
=
Similarly, The annual interest on (15000 - x) part is given as,
=
the total annual interest is given as $540
Thus, <em>540 = </em>
<em>54000 = </em>
<em>21000 = 3(x)</em>
x = = 7000
Thus the shares are $7000 and (15000 - 7000) $8000 .