Let's start b writing down coordinates of all points:
A(0,0,0)
B(0,5,0)
C(3,5,0)
D(3,0,0)
E(3,0,4)
F(0,0,4)
G(0,5,4)
H(3,5,4)
a.) When we reflect over xz plane x and z coordinates stay same, y coordinate changes to same numerical value but opposite sign. Moving front-back is moving over x-axis, moving left-right is moving over y-axis, moving up-down is moving over z-axis.
A(0,0,0)
Reflecting
A(0,0,0)
B(0,5,0)
Reflecting
B(0,-5,0)
C(3,5,0)
Reflecting
C(3,-5,0)
D(3,0,0)
Reflecting
D(3,0,0)
b.)
A(0,0,0)
Moving
A(-2,-3,1)
B(0,-5,0)
Moving
B(-2,-8,1)
C(3,-5,0)
Moving
C(1,-8,1)
D(3,0,0)
Moving
D(1,-3,1)
Answer:
a) The discriminant of the equation = - 44
b)The nature of the roots will be imaginary.
c) 
Step-by-step explanation:
Here, the given expression is 
or, 
Now the discriminant (D) of a quadratic equation 
D = 
Hence, the discriminant of the equation = - 44
As D< 0, so the roots will be imaginary.
Now,by quadratic formula : 
So, here 
So, either 
or,
Answer:
a = 4
Step-by-step explanation:
y = 2x + 1 ......(1)
Going through y - y1 = m(x - x1)
m is slope and it is 2
y1 = 9 and x1 = a
y - 9 = 2(x - a)
y - 9 = 2x - 2a
y = 2x - 2a + 9 ........(2)
Equating (1) and (2)
2x + 1 = 2x - 2a + 9
Collecting like terms
2x - 2x + 2a = 9 - 1
2a = 8
a = 8/2
a = 4
<u> 4 x² = 64</u>
Divide each side by 4 : x² = 16
Take the square root
of each side: x = √16
x = <em>+ 4</em>
and
x = <em>- 4</em> .
P / 100 = 25 / 75;
p = 2500 / 75 ;
p = 33.33;
p% = 33.33%
