How are algebraic properties applied in the steps to solving equations?
1 answer:
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Vertex form is
y=a(x-h)^2+k
vertex is (h,k)
axis of symmetry is x=4, therfor h=4
y=a(x-4)^2+k
we have some points
(3,-2) and (6,-26)
input and solve for a and k
(3,-2)
-2=a(3-4)^2+k
-2=a(-1)^2+k
-2=a(1)+k
-2=a+k
(6,-26)
-26=a(6-4)^2+k
-26=a(2)^2+k
-26=a(4)+k
-26=4a+k
we have
-2=a+k
-26=4a+k
multiply first equation by -1 and add to second
2=-a-k
<u>-26=4a+k +</u>
-24=3a+0k
-24=3a
divide both sides by 3
-8=a
-2=a+k
-2=-8+k
add 8 to both sides
6=k
the equation is
y=a(x-h)^2+k
vertex is (h,k)
axis of symmetry is x=4, therfor h=4
y=a(x-4)^2+k
we have some points
(3,-2) and (6,-26)
input and solve for a and k
(3,-2)
-2=a(3-4)^2+k
-2=a(-1)^2+k
-2=a(1)+k
-2=a+k
(6,-26)
-26=a(6-4)^2+k
-26=a(2)^2+k
-26=a(4)+k
-26=4a+k
we have
-2=a+k
-26=4a+k
multiply first equation by -1 and add to second
2=-a-k
<u>-26=4a+k +</u>
-24=3a+0k
-24=3a
divide both sides by 3
-8=a
-2=a+k
-2=-8+k
add 8 to both sides
6=k
the equation is
Answer:
The net profit rate on the book is 5.41
Step-by-step explanation:
Given as :
The marks up percentage of book = m = 40%
The overhead rate is 16% of selling price
The cost price of book = c.p = $18.10
Let The profit = $p
Let The selling price = s.p
<u>Now, According to question</u>
mark up percentage =
I.e 40% =
Or, + 1 =
Or, =
Or, s. p =
∴ s.p = $25.34
So, selling price of book = s.p = $25.34
Now, The overhead percentage = 16%
i.e overhead rate =
Or, estimated cost = 16% × 25.34
I,e estimated cost = 0.16 × 25.34
∴ estimated cost = $4.05
Now,
Profit = selling price of book - estimated book cost
I.e p = $25.34 - $4.05
∴ p = $21.29
So, The profit rate% =
I.e The profit rate% =
∴ profit rate %= 5.41
So, The profit rate = p = 5.41
Hence, The net profit rate on the book is 5.41 Answer