Answer:
Step-by-step explanation:
This Sequence is Geometric Progression
a = 16
r = 8/16 = 1/2
nth term = ar^(n-1) = 16*(1/2)^(n-1)
Answer:
First choice.
Step-by-step explanation:
You could plug in the choices to see which would make all the 3 equations true.
Let's start with (x=2,y=-6,z=1):
2x+y-z=-3
2(2)+-6-1=-3
4-6-1=-3
-2-1=-3
-3=-3 is true so the first choice satisfies the first equation.
5x-2y+2z=24
5(2)-2(-6)+2(1)=24
10+12+2=24
24=24 is true so the first choice satisfies the second equation.
3x-z=5
3(2)-1=5
6-1=5
5=5 is true so the first choice satisfies the third equation.
We don't have to go any further since we found the solution.
---------Another way.
Multiply the first equation by 2 and add equation 1 and equation 2 together.
2(2x+y-z=-3)
4x+2y-2z=-6 is the first equation multiplied by 2.
5x-2y+2z=24
----------------------Add the equations together:
9x+0+0=18
9x=18
Divide both sides by 9:
x=18/9
x=2
Using the third equation along with x=2 we can find z.
3x-z=5 with x=2:
3(2)-z=5
6-z=5
Add z on both sides:
6=5+z
Subtract 5 on both sides:
1=z
Now using the first equation along with 2x+y-z=-3 with x=2 and z=1:
2(2)+y-1=-3
4+y-1=-3
3+y=-3
Subtract 3 on both sides:
y=-6
So the solution is (x=2,y=-6,z=1).
Answer:
y = sqrt(29)/2 - 1/2 or y = -1/2 - sqrt(29)/2
Step-by-step explanation:
Solve for y:
y^2 + y - 7 = 0
Add 7 to both sides:
y^2 + y = 7
Add 1/4 to both sides:
y^2 + y + 1/4 = 29/4
Write the left hand side as a square:
(y + 1/2)^2 = 29/4
Take the square root of both sides:
y + 1/2 = sqrt(29)/2 or y + 1/2 = -sqrt(29)/2
Subtract 1/2 from both sides:
y = sqrt(29)/2 - 1/2 or y + 1/2 = -sqrt(29)/2
Subtract 1/2 from both sides:
Answer: y = sqrt(29)/2 - 1/2 or y = -1/2 - sqrt(29)/2
Answer:
25
Step-by-step explanation:
2<em>x</em>+10=60
2<em>x</em> =60-10
2<em>x</em> =50
<em>x</em> =50÷2
<em>x</em> =25