Answer:
try 36?
Step-by-step explanation:
Q6.
The slope-intercept form: y = mx + b
m - slope
b - y-intercept
We have: slope m = 3, y-intercept (0, 4) → b= 4
<h3>Answer: y = 3x + 4</h3>
Q7.
2x + 4y = 4 |subtract 2x from both sides
4y = -2x + 4 |divide both sides by 4
y = -0.5x + 1
Only second graph has y-intercept = 1.
<h3>Answer: The second graph.</h3>
Q8.
The point-slope form:

We have

Substitute:

<h3>Answer: The first equation.</h3>
Q9.
It's a vertical line. The equation of a vertical line is x = <em>a</em>, where <em>a</em> is any real number.
<h3>Answer: x = -4</h3>
<span>We can safely assume that 1212 is a misprint and the number of seats in a row exceeds the number of rows by 12.
Let r = # of rows and s = # of seats in a row.
Then, the total # of seats is T = r x s = r x ( r + 12), since s is 12 more than the # of rows.
Then
r x (r + 12) = 1564
or
r**2 + 12*r - 1564 = 0, which is a quadratic equation.
The general solution of a quadratic equation is:
x = (-b +or- square-root( b**2 - 4ac))/2a
In our case, a = 1, b = +12 and c = -1564, so
x = (-12 +or- square-root( 12*12 - 4*1*(-1564) ) ) / 2*1
= (-12 +or- square-root( 144 + 6256 ) ) / 2
= (-12 +or- square-root( 6400 ) ) / 2
= (-12 +or- 80) / 2
= 34 or - 46
We ignore -46 since negative rows are not possible, and have:
rows = 34
and
seats per row = 34 + 12 = 46
as a check 34 x 46 = 1564 = total seats</span>
Answer:
a) (8,8,-6)
b) 4x+4y+3z = -3
Step-by-step explanation:
a)
The surface is given by the equation
f(x,y,z) = 0 where
The gradient of this function is the vector
If we evaluate it in the point P = (-2,2,1) we obtain the point
(8,8,-6)
b)
The vectors with their tails at P are of the form
(-2,2,1)-(x,y,z) = (-2-x, 2-y, 1-z)
as they must be orthogonal to the gradient, they must be orthogonal to the vector (8,8,6) so their inner product is 0
and the equation of the desired plane is
4x+4y+3z = -3