Find the roots

solve
we use hmm, completing the suare
2(x²-1.5x)=4
divide both sides by 2
x²-1.5x=2
take 1/2 of linear coeiftn and square it
-1.5/2=-0.75, (-0.75)²=0.5625
add that to both sides
x²-1.5x+0.5625=2+0.5625
factor perfect squaer trinomial
(x-0.75)²=2.5625
square root both sides, remember to take positive and negative square roots
x-0.75=+/-√2.5625
add 0.75 to both sides
x=0.75+/-√2.5625

the roots are x=0.75+√2.5625 and x=0.75-√2.5625

1/a and 1/b
1/(0.75+√2.5625) and 1/(0.75-√2.5625)

if the roots of a quadratic equation are r1 and r2 then it factors to
(x-r1)(x-r2)
so then we can factor our equation to be
$(x-\frac{1}{0.75+\sqrt{2.5625}})(x-\frac{1}{0.75-\sqrt{2.5625}})$

if we were to try and expand it, we would get
x²+0.75x-0.5
that's the simpliest equation with roots 1/a and 1/b where a and b are he roots of 2x²-3x=4

x²+0.75x-0.5 is answer

8 0

3 years ago

AABC is reflected across the x-axis. What is the new location of point B? A (-4, -2) C (4, -2) B (-4,2) D (4,2)

Molodets [167]

Answer:

D (4,2)

Step-by-step explanation:

you just change the y value to the opposite sign hehe

7 0

3 years ago

Question

Gnoma [55]

Given parameters:

y varies directly as w;

This interpreted implies that as y increases, we increases by a certain factor or amount;

So, y ∝ w

y = kw

where k is the constant of proportionality

Now, given that y = 8 and w = 2

Input in the equation to solve for k;

8 = k x 2

Solving k gives, k = 4

Now to the second part,

if v is directly proportional to w;

v = k w

So v = 4w

The equation that relates v to w is v = 4w

3 0

3 years ago