Answer:
8
Step-by-step explanation:
Step-1 : Multiply the coefficient of the first term by the constant 1 • -16 = -16
Step-2 : Find two factors of -16 whose sum equals the coefficient of the middle term, which is 6 .
-16 + 1 = -15
-8 + 2 = -6
-4 + 4 = 0
-2 + 8 = 6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 8
p2 - 2p + 8p - 16
Step-4 : Add up the first 2 terms, pulling out like factors :
p • (p-2)
Add up the last 2 terms, pulling out common factors :
8 • (p-2)
Step-5 : Add up the four terms of step 4 :
(p+8) • (p-2)
Which is the desired factorization
This is hard in mathematical language, but there is only this way to present it. Let us denote by A the consentration of the substance and by A' its rate.
We have that b/A= t+c where c is a constant.
Hence A=b/(c+t)
By differentiating, we get that A'=-b/(C+t)^2
Then, we have that -(A)^2=A'/b
Hence at any point, we have that if we make the concentration 17 times, we have that there is a 17 times bigger , the rate will become bigger by 17*17, hence 289 times faster.
SOLUTION
Write out the equation
To solve this system of equation, the aprropriate method will be substitution
Substitute the expression for y into the second equation for y, we have
Expand the paranthesis we have
Divide both sides by 4, we have
Since the value of x has been obtained, we substitute into the first equation
Therefore
x = -3, y= -4
Okay, we know that the expenses for the day is 210.
Knowing this, and the price of the taco, we write the inequality:
3.25t > 210
t = number of tacos
Now divide both sides by 3.25:
t > 64.62 (rounded)
Because a taco stand can't sell a fraction of a taco, we know that the taco stand has to sell more than 65 tacos for a profit.
Answer:
(7, 1)
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define systems</u>
x = 2y + 5
x/3 - y = 4/3
<u>Step 2: Solve for </u><em><u>y</u></em>
- Substitute: (2y + 5)/3 - y = 4/3
- Multiply 3 on both sides: 2y + 5 - 3y = 4
- Combine like terms: -y + 5 = 4
- Isolate <em>y</em> term: -y = -1
- Isolate <em>y</em>: y = 1
<u>Step 3: Solve for </u><em><u>x</u></em>
- Define: x = 2y + 5
- Substitute: x = 2(1) + 5
- Multiply: x = 2 + 5
- Add: x = 7
And we have our final answer!
