Answer: D
Step-by-step explanation:
Given that Svana wants to solve the equation 1/2x - 1.0675 = 3x - 4145.
This equation is a system of equations which can be solved by using simultaneous equation methods.
But if she uses a graphing program to graph the equations y = 1/2x - 1.0675 and y = 3x - 4.145
The solution of 1/2x - 1.0675 = 3x - 4.145. Will be the point of intersection of the two equation.
Trace the point of intersection to the x - axis and also to the y - axis.
The solution to the system of equations is ( 1.231, - 0.452 )
1) slope = (y₂-y₁)/(x₂-x₁)
Let A and B be A(4,-6) and B(0,2) ;
m = [2-(-6)]/[0-4) = (2+6)/(-4) → m = -2
2) Midpoint = value of x of the midpoint = (x₁+x₂)/2
value of y of the midpoint = (y₁+y₂)/2
x(midpoint) = (4+0)/2 → x= 2
y(midpoint) = (-6+2)/2 → y= - 2, so Midpoint M(2,-2)
3) Slope of the perpendicular bisector to AB:
The slope of AB = m = -2
Any perpendicular to AB will have a slope m' so that m*m' = -1 (or in other term, the slope of one is inverse reciprocal of the second, then if m =-2, then m' = +1/2 ; Proof [ (-2)(1/2) = -1]
4) Note that the perpendicular bisector of AB passes through the midpoint of AB or M(2,-2). Moreover we know that the slope of the bisector is m'= 1/2
The equation of the linear function is :
y = m'x + b or y = (1/2)x + b. To calculate b, replace x and y by their respective values [in M(-2,2)]
2= (1/2).(-2) + b → 2 = -1 + b → and b= 3, hence the equation is:
y = (1/2)x + 3
Answer:
I believe it's the one on the bottom left
Step-by-step explanation:
I'm still taking my test so I'll come back later to tell you if it's correct.
Answer:
Sum of volumes = (16.6 ± 0.03) cm³
Difference of volumes = (3.8 ± 0.03) cm³
Step-by-step explanation:
Solution
V₁ = (10.2 ± 0.02) cm³ and V₂ = (6.4 ± 0.01) cm³.
∆V = ± (∆V₁ + ∆V₂)
= ± (0.02 + 0.01) cm³
= ± 0.03 cm³
V₁ + V₂ = (10.2 + 6.4) cm³ = 16.6 cm³ and
V₁ - V₂ = (10.2 - 6.4) cm³ = 3.8 cm³
Hence, sum of volumes = (16.6 ± 0.03) cm³
and difference of volumes = (3.8 ± 0.03) cm³
<u>-TheUnknownScientist</u>
Number of red marbles in bag = r. b = 10-rProbability of first marble being red: r/10Second marble being red: (r-1)/9total probability = 2/15 = (r-1)*r/90r = 4b = 6
