A) I would make the positive integer x and then form an equation.
x + 30 = x^2 - 12
x + 42 = x^2
0 = x^2 - x - 42 this can be factorised
(x - 7) ( x + 6) Therefore x = 7 or x = -6
Since the question asks for a positive integer the answer is 7.
B) two positive numbers x and y.
X - y = 3
x^2 + y^2 = 117
Use these simultaneous equations to figure out each number.
Rearrange the first equation
x = y + 3
Then substitute it into the second equation.
(y+3)^2 + y^2 = 117
y^2 + 6y + 9 + y^2 = 117
2y^2 + 6y - 108 = 0
then factorise this.
(2y - 12) (y + 9)
This means that y = 6 or y = -9 but it’s 6 because that’s the only positive number.
Use y to find x
x = y + 3
x = 6 + 3
x = 9
So the answers are x = 9 and y = 6.
Answer:StartFraction 2 over 13 End fraction
Step-by-step explanation:
Probability = number of possible outcomes/ total number of outcomes
P (Yellow marble) = 2/ 13
Step 1: Make sure that the trinomial is written in the correct order; the trinomial must be written in descending order from highest power to lowest power.
Step 2 : Decide if the three terms have anything in common, called the greatest common factor or GCF. If so, factor out the GCF. Do not forget to include the GCF as part of your final answer.
Step 3 : Multiply the leading coefficient and the constant, that is multiply the first and last numbers together.
Step 4 : List all of the factors from Step 3 and decide which combination of numbers will combine to get the number next to x.
Step 5 : After choosing the correct pair of numbers, you must give each number a sign so that when they are combined they will equal the number next to x and also multiply to equal the number found in Step 3.
Step 6 : Rewrite the original problem with four terms by splitting the middle term into the two numbers chosen in step 5.
Step 7 : Now that the problem is written with four terms, you can factor by grouping.
Answer:
Julie need to sell at least 45 shirts to break even.
Step-by-step explanation:
The selling cost of each shirt = $ 20
Cost of each shirt = $6
The fixed cost per month = $420
Number of shirts she can make = 80
Hence, the <u>cost of making 80 shirts</u> = 80 x $6 = $480
So, her total capital investment of the month
= Cost of shirts made + Fixed cost = $420 + $480 = $900
Now, let us assume she sell k number of shirts.
⇒ $20 x k = $900
or, k = 900 / 20 = 45
or, k = 45
Hence, Julie need to sell at least 45 shirts to break even.
All three numbers have to have a equal multiple.
