2x^2-12x+6=0 how to solve

Mathematics

1 answer:

Alona [7]2 years ago

4 0

Answer:

x=3+sqrt{6}

Step-by-step explanation:

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A student has some $1 and $5 bills in his wallet. he has a total of 1919 bills that are worth $5959. how many of each type of

uysha [10]

X = ones, y = fives

x + y = 19....x = 19 - y
x + 5y = 59

19 - y + 5y = 59
19 + 4y = 59
4y = 59 - 19
4y = 40
y = 40/4
y = 10 <=== there are 10 five dollar bills

x + y = 19
x + 10 = 19
x = 19 - 10
x = 9 <=== there are 9 one dollar bills

4 0

3 years ago

Find a vector equation and parametric equations for the line segment that joins p to q. p(1, −1, 7), q(7, 6, 1) vector equation

AleksAgata [21]

Answers:

- vector equation: r(t) = <1 + 6t, -1 + 7t, 7 - 6t>
- parametric equations:
x = 1 + 6t
y = -1 + 7t
z = 7 - 6t

Explanation:

To obtain the vector equation, we first get a vector v that is parallel to the line. To get the vector v, we subtract p from q. So,

v = q - p
= (7,6,1) - (1,-1,7)
v = (6, 7, -6)

The vector equation of the line is given by

$r(t) = v_0 + tv$

Where

$v_0$ = a point in the line (we choose point p(1,-1,7))

So, the equation of the line joining p and q is given by

$r(t) = v_0 + tv
\\ \indent = \left \langle 1, -1, 7 \right \rangle + t\left \langle 6, 7, -6 \right \rangle
\\ \indent = \left \langle 1, -1, 7 \right \rangle + \left \langle 6t, 7t, -6t \right \rangle
\\ \indent \boxed{r(t) = \left \langle 1 + 6t, 1 + 7t, 7 - 6t \right \rangle }$

In the parametric equation of the line, we just need to get the x, y and z coordinates in the vector equation.

Since the vector equation is given by

$r(t) = \left \langle 1 + 6t, 1 + 7t, 7 - 6t \right \rangle$

The parametric equations of the line are given by:

$x(t) = 1 + 6t
\\y(t) = 1 + 7t
\\z(t) = 7 - 6t$

4 0

3 years ago

The points (3,0) and (6,4) are adjacent vertices of a square, What is the area of the square, in unit squared? HELP PLS

zaharov [31]

Answer: 25

<u>Step-by-step explanation:</u>

Find the distance from (3, 0) to (6,4). That is the side length (s).

Area (A) = s²

$s=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\s^2=(x_2-x_1)^2+(y_2-y_1)^2\\\\s^2=(6-3)^2+(4-0)^2\\\\s^2=3^2+4^2\\\\s^2=9+16\\\\s^2=25\\\\\\A=s^2\\\\\large\boxed{A = 25}$