Answer:
The given system of equations has solutions below:
1) The solution is (2,3)
2) The solution is (
)
3) The solution is infinitely many solutions
4) No solution
Step-by-step explanation:
Given system of equation are
To solve equation by using elimination method
Multiply eqn (2) into 2
Now subtracting (1) and (3)
_________________
7x=14
x=
Substitute x=2 in equation (1)
-2+2y=4
2y=4+2
y=3
Therefore the solution is (2,3)
2) Given equation is
4y-4=x
Rewritting as below
To solve equation by using elimination method
multiply (2) into 2
Adding (1) and (3)
-2x+y=3
2x-8y=-8
________
-7y=-5
substitute in (1)
Therefore the solution is (
)
3) Given equation is 
equation (1) can be written as
2(3x+y)=10
3x+y=5
Therefore equations (1) and (2) are same therefore it has infinitely many solutions
4) Given equation is 
multiply equation (1) into 2
To solve equation by using elimination method
subtracting (2) and (3)
-2x-4y=28
-2x-4y=12
_______
therefore it has no solution
16-4=12
12x5=60
I'm putting together assumptions as this isn't really clear to me, I apologize.
It looks like you might have intended to say the roots are 7 + i and 5 - i, judging by the extra space between 7 and i.
The simplest polynomial with these characteristics would be
but seeing as each of the options appears to be a quartic polynomial, I suspect f(x) is also supposed to have only real coefficients. In that case, we need to pair up any complex root with its conjugate to "complete" f(x). We end up with
which appears to most closely resemble the third option. Upon expanding, we see f(x) does indeed have real coefficients:
(a) the given triangle is a isosceles triangle, therefore the two leg sides will be congruent, as well as the two base angles. It is given that one of the base angles ∠XYW is 70°, therefore, due to the law of a isosceles triangle, the measurement of ∠XWY is also 70°. Remember, a triangle's interior angles add up to 180°, so:
180 - (70 + 70) = 180 - 140 = 40
40° is your answer.
m∠X = 40°
(b) All sides are congruent, making it a equilateral triangle. If it is a equilateral triangle, then all the angles also have the same measurement. The total of the interior angle's measurement is 180°. Divide by the amount of angles, 3:
180/3 = 60
60° is your answer.
m∠V = 60°
~
volume cylinder
=3.14×3^2×5
=141.3 cubic inches
volume sphere
=4/3×3.14×3^3
=113.04 cubic inches
difference between volume of cylinder and sphere
=141.3-113.04
=28.26 cubic inches
