Answer: The slope is −2/3
Step-by-step explanation:
2
x
+
3
y
=
12 is the standard form for a linear equation. To determine the slope, solve the equation for y in order to convert to the slope-intercept form y
=
m
x
+
b
, where m is the slope and b is the y-intercept.
2
x
+
3
y
=
12
Subtract 2
x from both sides.
3
y
=
−
2
x
+
12
Divide both sides by
3
.
y
=
−
2
/3
x
+
12
/3
=
y
=
−
2
/3
x
+
4
The slope is
−
2
/3
Answer:
The answer is "The Parallel Postulate
".
Step-by-step explanation:
When the two lines will cross where angles of the amount are less than 180 degrees and the direct line overlaps two direct lines, that produces 2 ways the reinforcement on the same side to less than 180 degrees if extended indefinitely from the other hand. All this means that there is only one segment on the same plane parallel to a certain line at any point, not with a line.
Answer:
The equation for the nth term of the given arithmetic sequence is: ![\mathbf{a_n=13n+22}](https://tex.z-dn.net/?f=%5Cmathbf%7Ba_n%3D13n%2B22%7D)
Step-by-step explanation:
We need to write an equation for the nth term of the arithmetic sequence:
15,28,41 ....
The equation for arithmetic sequence is: ![a_n=a_1+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d)
Where
is the nth term,
is first term and d is common difference
In the given sequence we have:
a₁ = 15
a₂ = 28
We can find common difference using the formula:
![a_n=a_1+(n-1)d\\Put\: n=2, a_2=28\: and\: a_1=15\\a_2=a_1+(2-1)d\\28=15+d\\d=28-15\\d=13](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d%5C%5CPut%5C%3A%20n%3D2%2C%20a_2%3D28%5C%3A%20and%5C%3A%20a_1%3D15%5C%5Ca_2%3Da_1%2B%282-1%29d%5C%5C28%3D15%2Bd%5C%5Cd%3D28-15%5C%5Cd%3D13)
So, the common difference d is 13
Now, equation for nth term will be:
![a_n=a_1+(n-1)d\\Put\:a_1=15, d=13\\a_n=15+(n-1)13\\Solving:\\a_n=15+13n-13\\a_n=13n+2](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d%5C%5CPut%5C%3Aa_1%3D15%2C%20d%3D13%5C%5Ca_n%3D15%2B%28n-1%2913%5C%5CSolving%3A%5C%5Ca_n%3D15%2B13n-13%5C%5Ca_n%3D13n%2B2)
So, the equation for the nth term of the given arithmetic sequence is: ![\mathbf{a_n=13n+22}](https://tex.z-dn.net/?f=%5Cmathbf%7Ba_n%3D13n%2B22%7D)
where n=1,2,3..
The function
represents exponential growth with the initial value equal to 1, the decay factor equal to 0.3, and the rate equal to 0.7.
<h3>Population Growth Equation</h3>
The formula for the Population Growth Equation is:
![P_f=P_o*(1+\frac{R}{100}) ^t](https://tex.z-dn.net/?f=P_f%3DP_o%2A%281%2B%5Cfrac%7BR%7D%7B100%7D%29%20%5Et)
Pf= future population
Po=initial population
r=growth rate
t= time (years)
growth or decay factor = (1 ±r)
When 1+R > 1, the equation represents growth, while 1+R < 1 the equation represents decay.
The question gives:
, then
Pf=y
Po= 1
, thus
![(100+R}) =30\\ \\ R=-100+30\\ \\ R=-70](https://tex.z-dn.net/?f=%28100%2BR%7D%29%20%3D30%5C%5C%20%5C%5C%20R%3D-100%2B30%5C%5C%20%5C%5C%20R%3D-70)
r= -70%= -0.7
decay factor= (1-0.7)=0.3
Therefore,
1+R will be = 1+(-0.7)=1 - 0.7 =0.3
When 1+R >1, the function represents exponential growth.
Read more about the exponential function here:
brainly.com/question/8935549
C because if it was constant then for day 3 the distance would be 65.4 instead of 64.8