Answer:
Input:
14 x^2 + 57 x - 27
Plots:
Geometric figure:
parabola
Alternate forms:
(7 x - 3) (2 x + 9)
x (14 x + 57) - 27
14 (x + 57/28)^2 - 4761/56
Roots:
x = -9/2
x = 3/7
Polynomial discriminant:
Δ = 4761
Properties as a real function:
Domain
R (all real numbers)
Range
{y element R : y>=-4761/56}
Derivative:
d/dx(14 x^2 + 57 x - 27) = 28 x + 57
Indefinite integral:
integral(-27 + 57 x + 14 x^2) dx = (14 x^3)/3 + (57 x^2)/2 - 27 x + constant
Global minimum:
min{14 x^2 + 57 x - 27} = -4761/56 at x = -57/28
Definite integral:
integral_(-9/2)^(3/7) (-27 + 57 x + 14 x^2) dx = -109503/392≈-279.344
Definite integral area below the axis between the smallest and largest real roots:
integral_(-9/2)^(3/7) (-27 + 57 x + 14 x^2) θ(27 - 57 x - 14 x^2) dx = -109503/392≈-279.344
Step-by-step explanation:
S=sullivan's age
d=daughter's age
in 3 years time (s+3 and d+3)
sulivan is 3 times as old as daughter
s+3=3(d+3)
6 years ago (s-6 and d-6)
he was 6 times as old
s-6=6(d-6)
expand
s+3=3d+9
s-6=6d-36
for 2nd equation, add 6 to both sides
s=6d-30
sub 6d+30 for s in other equation
6d-30+3=3d+9
6d-27=3d+9
minus 3d both sides
3d-27=9
add 27 both sides
3d=36
divide both sides by 3
d=12
sub back
s=6d-30
s=6(12)-30
s=72-30
s=42
Mr. Sullivan is 42 now
Daughter is 12 now
Step-by-step explanation:
let jasmine age b
so the equation is
n=4*(n-10)
Answer: OPTION C.
Step-by-step explanation:
The systems of linear equations can have:
1. <u>No solution:</u> When the lines have the same slope but different y-intercept. This means that the lines are parallel and never intersect, therefore, the system of equations has no solution.
2. <u>One solution</u>: When the lines have different slopes and intersect at one point in the plane. The point of intersection will be the solution of the system
3. I<u>nfinitely many solutions</u>: When the lines have the same slope and the y-intercepts are equal. This means that the equations represents the same line and there are infinite number of solution.
Therefore, based on the explained above, the conclusion is: Systems of equations with different slopes and different y-intercepts <em><u>never</u></em> have more than one solution.
X^2 - 10x + 8 =0
x^2 - 10 + (-10/2)^2 - (-10/2)^2 + 8 = 0
(x - 5)^2 - 25 + 8 = 0
(x - 5)^2 - 17 = 0
To be honest , this is the final step for this equation. It seems like there is no any suitable answer for this question..
To me , I think the best answer will be the third option.
x - 5 =0
x = 5
2x-10 = 0
2x = 10
x = 5
I guess this answer seems like legit.. So I will choose the third option.
