9514 1404 393
Answer:
x -y = -5
3x +y = -11
Step-by-step explanation:
We assume you want two linear equations. Since you know a point on each line, the only thing you need to choose is the slope of the two lines through that point. We can make the slopes be +1 and -3, for example. Then the point-slope equations are ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -1 = +1(x +4)
y -1 = -3(x +4)
We can use these equations "as is", or put them in whatever form you like. I personally prefer "standard form:" ax+by=c.
<u>First equation</u>:
y -1 = x +4 . . . . . . eliminate parentheses
-5 = x -y . . . . . . . keep positive x term, put x and y together, separate from the constant
x - y = -5 . . . . . . standard form
<u>Second equation</u>:
y -1 = -3x -12 . . . . eliminate parentheses
3x +y = -11 . . . . . . add 3x+1 to both sides
__
A system of equations with solution (-4, 1) is ...
Answer:
729.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Now sum of infinite series is
a
1
−
r
and if first three term are removed, fourth term becomes the first term i.e. first term becomes
a
r
3
and
sum of infinite series becomes
a
r
3
1
−
r
As
a
1
−
r
=
27
×
a
r
3
1
−
r
27
r
3
=
1
or
r
3
=
1
27
and
r
=
1
3
and hence
Common ratio is
1
3
Answer:
He is not correct because he made a sign error.
Step-by-step explanation:
-2 |8-x| - 6 = -12
-2 |8-x| = -12 + 6
-2 |8-x| = - 6
2 |8-x| = 6
|8-x| = 3
2 possible solutions:
8-x = 3 ----> x = 5
or
8-x = -3 ----> x = 11
Comparing the answer choices, we can see that Johan got the sign of x = 11 wrong.
Hence the correct answer is:
He is not correct because he made a sign error.
Find rates of change until you find a constant.
dy/dx=1,2,3,4,5,6
d2y/dx2=1,1,1,1,1
So the acceleration, d2y/d2x, is constant. This means that this is a quadratic sequence of the form a(n)=an^2+bn+c. So we can set up a system of equations to solve for the values of a,b, and c. Using the first three points, (1,1), (2,2), and (3,4) we have:
9a+3b+c=4, 4a+2b+c=2, and a+b+c=1 getting the differences...
5a+b=2 and 3a+b=1 and getting this difference...
2a=1, so a=1/2 making 5a+b=2 become:
2.5+b=2, so b=-1/2, making a+b+c=1 become:
1/2-1/2+c=1, so c=1 so the rule is:
a(n)=0.5x^2-0.5x+1 or if you prefer to not have decimals
a(n)=(x^2-x+2)/2
