Switching the hypothesis and conclusion of a conditional statement<span> and negating both. For example, the </span>contrapositive<span> of "If it is raining then the grass is wet" is "If the grass is not wet then it is not raining."
It's just to negate both sides :)</span>
X^2+8x=10, has to look like ()^2 = value:
(x+4)^2 = x^2+8x+16, you match first the x^2 and term with x, okay?
Now that 16 was not there (add zero!):
x^2+8x+16-16 = (x+4)^2 -16, finish the problem:
(x+4)^2 = 11+16=27, and x+4 = +/-sqrt(27) ---> x = -4+/-sqrt(27) = -4 +/-3*sqrt(3) if you prefer.
The quadratic formula is a direct answer:
x^2+8x-11=0
x = (-8 +/- sqrt( 8^4 -4*1*(-11)) ) / 2 = (-8 +/- sqrt(108))/2
sqrt(108)=sqrt(4*9*3) = 2*3*sqrt(3) = 6*sqrt(3)-->
x = (-8+/- 6*sqrt(3))/2 = - 4 +/- 3*sqrt(3)
Lesson: completing the square is longer and requires some algebra skills but it pays off. Quadratic formula does not need us to think! But it may be cumbersome. Both are good depending on the rpoblem.
Indeed the quadratic formula was invented completing the sqaure for a*x^2+b*x+c = 0
Finally, sqrt(3)~1.73, so you may approximate the solutions as -4+/-3*1.7 = -4 +/- 5.1 = -9.1, and 1.1
Answer:
Step-by-step explanation:
If you have choices, you really should list them.
Here is the graph for y = (x + 0.25)(x - 1.75) which will look like yours. There are all sorts of variations that are possible, but at least I could reproduce a similar looking graph.
Answer:
w<4
Step-by-step explanation:
divide both sides by 8. no need to flip the sign because 8 is positive
8/8w<32/8
w<4
We know that
The equation for the eccentricity of an ellipse is
e=c/a
where
e is eccentricity, c is the distance from the foci to the center, and a is the square root of the larger of our two denominators.
To find c, we must use the equation a²−b²=c², where b is the square root of the smaller of our two denominators
case 1)
(x²/2²)+(y-2)²/4²=1
a=4
b=2
c²=16-4----> c=√12
e=c/a----> √12/4----> e=0.8660
case 2)
(x+3)²/5²+(y-1)²/3²=1
a=5
b=3
c²=25-9----> c=√16-----> c=4
e=c/a----> 4/5-----> e=0.80
case 3)
(x-5)²/3²+(y²/7²)=1
a=7
b=3
c²=49-9-----> c=√40
e=c/a-----> √40/7-----> e=0.9035
case 4)
(x-2)²/4²+(y+4)²7²=1
a=7
b=4
c²=49-16-----> c=√33
e=c/a-----> √33/7------> e=0.8207
case 5)
x²/7²+y²/6²=1
a=7
b=6
c²=49-36-----> c=√13
e=c/a-----> √13/7-----> e=0.5151
case 6)
(x-3)²/6²+y²/4²=1
a=6
b=4
c²=36-16-----> c=√20
e=c/a-----> √20/6-----> e=0.7454
case 7)
(x+4)²/5²+(y-5)²/6²=1
a=6
b=5
c²=36-25-----> c=√11
e=c/a-----> √11/6----> e=0.5528
case 8)
x²/7²+(y+7)²/2²=1
a=7
b=2
c²=49-4----> c=√45
e=c/a-----> √45/7----> e=0.9583
the answer is1) x²/7²+y²/6²=1
e=0.51512) (x+4)²/5²+(y-5)²/6²=1
e=0.55283) (x-3)²/6²+y²/4²=1
e=0.74544) (x+3)²/5²+(y-1)²/3²=1
e=0.80005) (x-2)²/4²+(y+4)²7²=1
e=0.82076) (x²/2²)+(y-2)²/4²=1
e=0.86607) (x+4)²/5²+(y-5)²/6²=1
e=0.90358) x²/7²+(y+7)²/2²=1
e=0.9583