This equation is an example of a Limacon with inner loop. By using the symmetry tests where:
POLAR AXIS/HORIZONTAL:
replace a) θ by -θ, b) r by -r and θ by π-<span>θ
VERTICAL AXIS:
replace a) </span>θ by π-θ, b) r by -r and θ by -<span>θ
POLE:
replace a) </span>θ by π+<span>θ, b) r by -r
If any of these rules, after replacing it in the equation, results to the original equation (making it the equivalent) then it is symmetrical to that axis.
In this case, it is only symmetrical about the polar/horizontal axis. </span>
Jack's mom is purchasing thirteen tickets at a price of $11 each. This
equals a total of $143 in total spent. If Jack's mom has a credit card
limit of $500, then after purchasing $143 with the card, her available
amount to purchase additional things is $357. This impact on her
available credit is due to credit cards working on an available balance
system. When Jack's mom first received her credit card, a set balance or
total amount she could purchase with the card was set. In this example,
her total amount she could purchase with the card was $500. After her
purchase of the tickets for $143 was completed, she subtracted that
amount from her total available of $500 and that is why her available
amount to purchase is now $357.
Answer:
equation: y=-2x+2
a=-3
b=-8
Step-by-step explanation:
we need to find the equation of the line containing the point (3,-4) and has the slope (m) of -2
slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
we can plug what we know into the equation:
y=-2x+b
we need to find b though
since the point will pass through the point (3,-4) we can subsitute it into the equation to find b
-4=-2(3)+b
-4=-6+b
2=b
the y intercept is 2
so the equation is y=-2x+2
the line also contains the points (a,8) and (5,b)
first, let's find a
a is the x value of the point
we know the value of y (8)
substitute y as 8 and solve for x
8=-2x+2
subtract
6=-2x
-3=x=a
so a is -3
now find b
b is the y value of the point
we know the x value (5)
substitute x as 5 and solve for y
y=-2(5)+2
y=-10+2
y=-8=b
so b is -8
hope this helps!
Answer:
n=4
Step-by-step explanation:
Given equation: \[\frac{1}{n-4}-\frac{2}{n}=\frac{3}{4-n}\]
Simplifying the Left Hand Side of the equation by taking the LCM of the denominator terms:
\[\frac{n}{n*(n-4)}-\frac{2*(n-4)}{n*(n-4)}=\frac{3}{4-n}\]
=> \[\frac{n - 2*(n-4)}{n*(n-4)}=\frac{3}{4-n}\]
=> \[\frac{n - 2n + 8}{n*(n-4)}=\frac{3}{4-n}\]
=> \[\frac{8 - n}{n*(n-4)}=\frac{3}{4-n}\]
=> \[(8-n)*(4-n) =n*(n-4)*3\]
=> \[n-8 =3n\]
=> \[2n =8\]
=> n = 4
