5n + 3 + 4n = 30 combine the like terms on the left
9n + 3 = 30 Subtract 3 from both sides
9n = 30 - 3
9n = 27 Divide by 9
n = 27/9
n = 3
This is the concept of application of quadratic equations; To get the number of dimes and quarters we proceed as follows;
suppose there are x dimes and y quarters;
x+y=95.......i
but we know;
$0.1=1 dimes
$0.25=1 quarters
thus
0.1x+0.25y=23.45.....ii
solving equation i and ii by substitution we shall have:
from i;
x=95-y
thus substituting the value of x in equation ii we get
0.1(95-y)+0.25y=23.45
9.5-0.1y+0.25y=23.45
collecting like terms we get:
0.15y=13.95
dividing both sides by 0.15 we get;
y=13.95/0.15=93
x=95-93=2
therefore we conclude that there were 2 dimes and 93 quarters
Instead of using the quotient rule, you can first expand <em>y</em> :
<em>y</em> = (4<em>x</em> - 1)^2 / <em>x</em> ^2 = (16<em>x</em> ^2 - 8<em>x</em> + 1) / <em>x</em> ^2 = 16 - 8/<em>x</em> + 1/<em>x</em> ^2
Then the derivative is
d<em>y</em>/d<em>x</em> = -8/<em>x</em> ^2 - 2/<em>x</em> ^3
The tangent to the curve at (-1, 25) then has a slope or gradient of
d<em>y</em>/d<em>x</em> = -8/(-1)^2 - 2/(-1)^3 = -6
Answer is f(x)= (x - 17) ^2
Answer:
a) two
b) S = {Orange, Purple}
c) 50%
d) 50%
Step-by-step explanation:
a)
When a marble is drawn from the jar, there are <u>two</u> possible outcomes. Either the marble will be orange or it will be purple.
b)
A sample space is a set of all possible outcomes of an event. Thus, the sample space in this case will be:
<u>Sample Space = {Orange, Purple}</u>
c)
The probability of an event is given as the number of favorable outcomes divided by the number of total outcomes.
Therefore,
Probability of selecting orange marble = P(Orange) = 1/2
<u>P(Orange) = 0.5 = 50%</u>
d)
Probability of selecting purple marble = P(Orange) = 1/2
<u>P(purple) = 0.5 = 50%</u>
