the work must of your highest quality. assessment therefore you need to show all your work and use rulers and/or graph paper where necessary. - you must hand in these assignment questions, otherwise it will not be marked. - round all your answers to the nearest hundredth, if necessary. - be sure to include units where required. arking scheme: question 1 2 3 4 5 total marks 6 6 7 5 6 e edmonton elks uses mathematics every day. they encounter a number of problems that can be lved using the concepts learned in math 10c. in this assignment you will use your knowledge of math c to help the team solve their problems. 1) on the outside of commonwealth stadium the edmonton elks would like to place a large, rectangular sign to reveal their new name and logo. the approximate area of the sign can be represented by the trinomial ( x^2 - 7x + 6 ). a) factor the area to find the binomials that represent the length and width of the sign. b) if ( x ) represents 14m, find the length and width of the sign, in metres. c) if the sign costs $60/m², calculate how much the team will have to pay. d) the team decided that they want the sign to be a square instead of a rectangle. state what gi an example of a trinomial that could represent the area. what do we call this type of trinomi e) if the area of the square sign is to be ( x^2 - kx + 625 ), find the binomial factor that would represent the side length of this area and determine the value of ( k ), if the trinomial is factor over the integers?

Question

Accepted Answer

(a) - Factoring the Trinomial
# Explanation:
## Step 1: Identify $a$, $b$, $c$
For $x^2 - 7x + 6$, $a = 1$, $b=-7$, $c = 6$. We need two numbers that multiply to $ac=6$ and add to $b=-7$.
## Step 2: Find the numbers
The numbers are $-1$ and $-6$ (since $(-1)\times(-6)=6$ and $-1 + (-6)=-7$).
## Step 3: Factor the trinomial
Rewrite the middle term: $x^2 - x - 6x + 6$. Group: $(x^2 - x)+(-6x + 6)=x(x - 1)-6(x - 1)$. Factor out $(x - 1)$: $(x - 1)(x - 6)$.
# Answer: $(x - 1)(x - 6)$

### Part (b) - Length and Width when $x = 14$ m
# Explanation:
## Step 1: Substitute $x = 14$ into the factors
From part (a), the factors are $(x - 1)$ and $(x - 6)$.
For $x - 1$: $14 - 1 = 13$ m.
For $x - 6$: $14 - 6 = 8$ m.
# Answer: Length = $13$ m, Width = $8$ m

### Part (c) - Cost Calculation
# Explanation:
## Step 1: Calculate the area
Area = length $\times$ width = $13\times8 = 104$ $m^2$.
## Step 2: Calculate the cost
Cost = area $\times$ cost per $m^2$ = $104\times60 = 6240$ dollars.
# Answer: $\$6240$

### Part (d) - Perfect Square Trinomial Example
# Explanation:
A perfect square trinomial has the form $(x + a)^2=x^2 + 2ax + a^2$ or $(x - a)^2=x^2 - 2ax + a^2$. For example, if $a = 5$, then $(x + 5)^2=x^2 + 10x + 25$ (or any perfect square trinomial like $x^2 + 8x + 16=(x + 4)^2$ etc.).
# Answer: Example: $x^2 + 10x + 25$ (or other perfect square trinomials)

### Part (e) - Find $k$ for $x^2 - kx + 625$
# Explanation:
## Step 1: Recognize the perfect square
$625 = 25^2$, so the perfect square trinomial is $(x - 25)^2$ (since the middle term is negative).
## Step 2: Expand $(x - 25)^2$
$(x - 25)^2=x^2 - 50x + 625$. Comparing with $x^2 - kx + 625$, we see $k = 50$.
# Answer: Binomial factor: $(x - 25)$, $k = 50$

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QUESTION IMAGE

Question

Explanation:

Step 1: Identify \(a\), \(b\), \(c\)

Step 2: Find the numbers

Step 3: Factor the trinomial

Step 1: Substitute \(x = 14\) into the factors

Step 1: Calculate the area

Step 2: Calculate the cost

Answer:

Part (b) - Length and Width when \(x = 14\) m