Answer:
a. 6, b. 99, c. 63
Step-by-step explanation:
A) The function s(t) is in the vertex form. The standard vertex form is a(x-h)+k where the vertex is (h,k). The vertex is the highest (or lowest in some cases) point of the graph, so if we use s(t) to get the vertex we get that h=6 and k=99. This means that for a student to get a perfect score they need to study 6 hours
B) We can just take the k value from the first question because that's the highest value for s(t), so the highest score will be 99
C) For this one just plug in 0 for time, so -(0-6)^2+99. This equals -(-6)^2+99, which equals 99-36 =63
ANSWER:
- x – 3y = 2 ...(1)
- 2x – 6y = 6 ...(2)
On solving eq(1), we get
Plug the value of x in eq(2)
- 2x – 6(x - 2/3) = 6
- 2x – 2(x – 2) = 6
- 2x – 2x + 4 = 6
- 0 = 6 – 4
- 0 ≠ 2
So, given system of equations is not correct.
Part A:
A coefficient can be either '15' or '25'.
A variable can be either 'w' or 'm'.
A constant is 65.
Part B:
Simply substitute, or plug-in, the numbers and solve.
***Step 1:
65+15w+25m --> 65+15(20)+25(3)
You do this because you are substituting the 'w' for the number
of weeks that Jaxon saved up for, which is 20, and the 'm' for the number
of times that Jaxon mowed the lawn, which is 3.
***Step 2:
65+15(20)+25(3) --> 65+300+75
Begin to solve, using PEMDAS, or whichever acronym you learned.
Remember, if you are using PEMDAS, recall that the order is Parenthesis,
Exponents, Multiplication/Division (whichever comes first), and
Addition/Subtraction (whichever comes first). Here, I checked for parenthesis.
I did find parenthesis, however, they do not have any expressions inside of
them, meaning that these parenthesis are for multiplying, and not for stating
order. So, you skip parenthesis. Next, you check for exponents, which you
find none of, so you skip over that. Now, we get to multiplying/dividing, so
you multiply the 15 and the 20 to get 300, and the 25 and 3 to get 75.
***Step 3:
65+300+75 --> 440
Now, we get to addition. You simply add everything up to get your final
answer: $440.
Part C:
If Jaxon had $75, then yes, the coefficients would change.
By subtracting $65 from $75, we can see that the total amount of money
from Jaxon's deposits and his lawn-mowing money is $10. Jaxon already
deposits $15 a week, meaning that, while using the current equation, Jaxon
CANNOT have $75 in his bank account. We can change the equation
so that Jaxon is able to have $75 in his savings account. You can change
the coefficient of 15 to 10, and the other coefficient of 25 to 0.
Now Jaxon is able to have $75 in his savings account.
Answer:
-3
4 - 7 = -3.
-3 + 7 = 4.
They are in a fact family.
The answer is -3.
Hope it helps!
