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Answer:
3x-4y=15
7x+y=4
Solve7x+y=4 for y:
7x+y=4
7x+y+−7x=4+−7x (Add -7x to both sides)
y=−7x+4
Step: Substitute −7x+4 for y in 3x−4y=15:
3x−4y=15
3x−4(−7x+4)=15
31x−16=15 (Simplify both sides of the equation)
31x−16+16=15+16 (Add 16 to both sides)
31x=31
(Divide both sides by 31)
x=1
Step: Substitute 1 for x in y=−7x+4:
y=−7x+4
y=(−7)(1)+4
y=−3(Simplify both sides of the equation)
Answer: x=1 and y=−3
Area of the rectangle .
Solution:
Given data:
Height of a rectangle =
Width of a rectangle =
Area of the rectangle = height × width
Multiply each term of height with the each term of width.
Adding like terms of the polynomial.
Therefore, Area of the rectangle .
5 times 6x =30x the second one is 7y+7x the third one is 8x+20y
We know that
the equation of the parabola is of the form
y=ax²+bx+c
in this problem
y=−1/4x²<span>−x+3
where
a=-1/4
b=-1
c=3
</span><span> the coordinates of the focus are
</span>
(-b/2a,(1-D)/4a)
where
D is the discriminant b²-4ac
D=(-1)²-4*(-1/4)*3-----> D=1+3---> D=4
therefore
x coordinate of the focus
-b/2a----> 1/[2*(-1/4)]----> -2
y coordinate of the focus
(1-D)/4a------> (1-4)/(-4/4)---> 3
the coordinates of the focus are
(-2,3)