.1 Simplify: 5n(2n3+n2+8)+n(4-n).
Solution:
5n(2n3+n2+8)+n(4-n).
= 5n × 2n3 + 5n × n2 + 5n × 8 + n × 4 - n × n.
= 10n4 + 5n3 + 40n + 4n – n2.
= 10n4 + 5n3 + 44n – n2.
= 10n4 + 5n3 – n2 + 44n.
Answer: 10n4 + 5n3 – n2 + 44n
<span>Carol noticed that 7/10 of the children playing soccer were girls. Which statement could be correct?
A. There were 28 girls and 12 boys playing soccer.
28 : x% = 40 (the total number of children) : 100%
40x = 28 * 100
40x = 2800
x = 2800 / 40
x = 70%
There were 70% of girls in the class.
70 / 100 = 0.7
7/ 10 = 0.7
This is why A is the correct answer.
</span>
9514 1404 393
Answer:
y +6 = (-1/3)(x +6)
Step-by-step explanation:
Given a point and a slope, it is appropriate to use the point-slope form to represent the equation:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
For your point and slope, the equation is ...
y -(-6) = -1/3(x -(-6))
y +6 = -1/3(x +6)
__
Of course, this can be rearranged to whatever form you need.
y = -1/3x -8 . . . . slope-intercept form
x +3y = -24 . . . . standard form
Answer:
Ans A). The graph is shown.
Ans B). 18.3333 C temperature when F is 65 temperature
Ans C). 32 F when the line crosses the horizontal axis
Ans D). Slope of line C=
is 
Step-by-step explanation:
Given equation is C=
Ans A).
For the table,
Take the four value of F as 32,41,50,59.
For F = 32.
The value of C is
C=
C=
C=0.
For F = 41.
The value of C is
C=
C=
C=05
For F = 50.
The value of C is
C=
C=
C=10
For F = 59.
The value of C is
C=
C=
C=15
<em>Note: The figure shows a graph of given equation with points.</em>
Ans B). Estimate temperature in C when the temperature in F is 65
For F = 65.
The value of C is
C=
C=
<em>C=18.333333.</em>
Ans C). At what temperature, graph lien cross the horizontal axis
When the line crosses the horizontal axis, C=0
Therefore,
C=
0=
0=
F=32 Temperature.
Ans D). Slope of the line C=
The slope of line is given by s= 
Take points from the table of answer A.
let (32,0) and (41,5) using for slope.
s= 
s= 
s= 
Slope of line C=
is 
<span>Ayesha's right. There's a good trick for knowing if a number is a multiple of nine called "casting out nines." We just add up the digits, then add up the digits of the sum, and so on. If the result is nine the original number is a multiple of nine. We can stop early if we recognize if a number along the way is or isn't a multiple of nine. The same trick works with multiples of three; we have one if we end with 3, 6 or 9.
So </span>

<span>has a sum of digits 31 whose sum of digits is 4, so this isn't a multiple of nine. It will give a remainder of 4 when divided by 9; let's check.
</span>

<span>
</span>Let's focus on remainders when we divide by nine. The digit summing works because 1 and 10 have the same remainder when divided by nine, namely 1. So we see multiplying by 10 doesn't change the remainder. So

has the same remainder as

.
When Ayesha reverses the digits she doesn't change the sum of the digits, so she doesn't change the remainder. Since the two numbers have the same remainder, when we subtract them we'll get a number whose remainder is the difference, namely zero. That's why her method works.
<span>
It doesn't matter if the digits are larger or smaller or how many there are. We might want the first number bigger than the second so we get a positive difference, but even that doesn't matter; a negative difference will still be a multiple of nine. Let's pick a random number, reverse its digits, subtract, and check it's a multiple of nine:
</span>