Answer:
Z
Step-by-step explanation:
The letter 'Z' represents integers.
it comes from the german word "zahlen" which translates to "numbers"
The linear equation represents y = mx + b describes several real world situations such as
- Relation between printer and ink cartridges,
- Relationship between number of songs and how much is left on the card.
<u>Step-by-step explanation</u>:
Linear equations y = mx + b.
m is your rate of change.
b is your constant. This is the initial value of y. The value of y when x is 0.
Finally, y is the thing that depends on x.
Oh right, examples:
- I buy a printer for $100 and the ink cartridges cost $25 each. The relationship between ink cartridges and total cost.
total cost = 25(cartridges I buy) + 100 or y = 25x + 100
-
I get a $100 iTunes gift card for my birthday and then start buying $1 songs. The relationship between the number of songs I buy and how much is left on the card
amount left on card = -$1(songs bought) + 100 or y = -x +100
Answer:
The answer is all real numbers
Step-by-step explanation:
Simpify both sides of the equation: 14−(2y+5)=−2y+9
14+−1(2y+5)=−2y+9(Distribute the Negative Sign)
14+−1(2y)+(−1)(5)=−2y+9
14+−2y+−5=−2y+9
(−2y)+(14+−5)=−2y+9(Combine Like Terms)
−2y+9=−2y+9
−2y+9=−2y+9
Then add 2y to each side. −2y+9+2y=−2y+9+2y
9=9. Then subtract 9 from each side. 9-9=9-9=0. That means that all real numbers is the answer.
Answer:
-4
Step-by-step explanation:
x³ + cx + 4 divided by x + 2 has a remainder of 4, so:
(x³ + cx + 4) / (x + 2) = ax² + bx + d + 4 / (x + 2)
Multiply both sides by x + 2:
x³ + cx + 4 = (ax² + bx + d) (x + 2) + 4
Distribute:
x³ + cx + 4 = ax²(x + 2) + bx(x + 2) + d(x + 2) + 4
x³ + cx + 4 = ax³ + 2ax² + bx² + 2bx + dx + 2d + 4
x³ + cx + 4 = ax³ + (2a + b)x² + (2b + d)x + 2d + 4
Match the coefficients.
a = 1
2a + b = 0
2b + d = c
2d + 4 = 4
Solving, a = 1, b = -2, and d = 0. So c = -4.
We can also solve this using long division (see picture).
