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
Alright! In order to find the answer you first have to find out how many miles you can go on one gallon of gas. To do this you divide your miles by your gallons:
[400 ÷ 15] = <span>26.6
Then you take this value and multiply it by 6.
[</span>26.6 x 6] = <span>160.
You can go 160 miles on 6 gallons of gas.</span>
Since a cube has 6 faces, just divide the total surface area by 6 to find the area of 1 face.
96 / 6 = 16
So, the answer is: The area of one face is 16 cm!
Answer:
Step-by-step explanation:
It would be 15 girls to 24 boys
<h3>
Two possible answers: 6 or -6</h3>
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Explanation:
r = common ratio
To get any term in a geometric sequence, we multiply the previous term by r.
So that means 4r is the second term, since 4 is the first term.
The third term is (4r)*r = 4r^2, which is equal to 9 as given to us.
4r^2 = 9
4r^2 - 9 = 0
(2r)^2 - (3)^2 = 0
(2r - 3)(2r + 3) = 0 ... difference of squares rule
2r-3 = 0 or 2r+3 = 0
2r = 3 or 2r = -3
r = 3/2 or r = -3/2
r = 1.5 or r = -1.5
We can use each r value to find the possible second term
S = 4r = 4*(1.5) = 6
S = 4r = 4*(-1.5) = -6
The second term is either 6 or -6.
We could have this sequence: 4, 6, 9, ...
Or we could have this sequence: 4, -6, 9, ...
