Let
be any integer. Then
In other words:
(1) If
is a multiple of 4, then
.
(2) If dividing
by 4 leaves a remainder of 1, then
, since
for some integer
, and from (1) we know that
(because, obviously,
is a multiple of 4).
(3) If instead you get a remainder of 2, then
. This follows from (1) as well.
.
(4) Finally, if you get a remainder of 3, then
.
Answer:
Step-by-step explanation:
11) First write in decreasing exponential terms and fill in blanks with zeros.
Our goal is to eliminate all term in the dividend by subtraction
________________
2v - 2 | 2v³ - 16v² + 0v + 13
we see that 2v needs to be multiplied by 1v² to eliminate the first term
<u> v² </u>
2v - 2 | 2v³ - 16v² + 0v + 13
<u>- (2v³ - 2v²)</u>
0 - 14v²
multiply your estimate by your divisor and subtract from the dividend.
bring down the next term and repeat.
<u> v² -7v </u>
2v - 2 | 2v³ - 16v² + 0v + 13
<u>- (2v³ - 2v²)</u>
0 - 14v² + 0v
<u>-(-14v² + 14v)</u>
- 14v
repeat again
<u />
<u> v² - 7v - 7 </u>
2v - 2 | 2v³ - 16v² + 0v + 13
<u>- (2v³ - 2v²)</u>
0 - 14v² + 0v
<u>-(-14v² + 14v)</u>
- 14v + 13
<u>-(-14v + 14)</u>
-1
and remainder gets put over the divisor and appended
v² - 7v - 7 - 1/(2v - 2)
13) Same process
<u> </u>
5a + 1 | 40a³ - 12a² - 39a - 5
<u> 8a² </u>
5a + 1 | 40a³ - 12a² - 39a - 5
<u>-(40a³ + 8a²)</u>
-20a² - 39a
<u> 8a² - 4a </u>
5a + 1 | 40a³ - 12a² - 39a - 5
<u>-(40a³ + 8a²)</u>
-20a² - 39a
-(-<u>20a² - 4a)</u>
-35a - 5
<u> 8a² - 4a - 7 </u>
5a + 1 | 40a³ - 12a² - 39a - 5
<u>-(40a³ + 8a²)</u>
-20a² - 39a
-(<u>20a² - 4a)</u>
-35a - 5
-<u>(-35a - 7)</u>
2
8a² - 4a - 7 + 2/(5a + 1)
-2/3a-6=12a
-6=12a+2/3a
-6=38/3a
3/38*-6=a
-18/38=a
a=-9/19
a=-0.47
I hope this helps you
perimeter of square =4x
4x=equilateral triangle perimeter
4x=3.1
x=3/4
Answer:
The Answer is: 12.
Step-by-step explanation:
Let n = number.
The number times three plus 24 is equal to five times the number.
3n + 24 = 5n
24 = 5n - 3n
2n = 24
n = 12
Proof:
3(12) + 24 = 36 + 24 = 60
5(12) = 60
Hope this helps! Have an Awesome Day!! :-)
