Answer: D
Explanation:
The equation of a line in the point slope form is expressed as
y - y1 = m(x - x1)
where
m represents slope
x1 and y1 represents coordinates of the point that the line passes.
From the information given, the equation of the path of the old route is
y = 2x/5 - 4
Recall, the equation of a line in the slope intercept form is expressed as
y = mx + c
By comparing both equations,
slope, m = 2/5
If two lines are parallel, it means that they have the same slope. Given that the new route is to be parallel to the old route and will go through point (Q, P), then
m = 2/5
x1 = Q
y1 = P
The equation of the new route be
y - P = 2/5(x - Q)
9514 1404 393
Explanation:
∠MRQ ≅ ∠NQR . . . . given
QR ≅ RQ . . . . reflexive property
∠PQR ≅ ∠PRQ . . . . property of isosceles triangle PQR
ΔQNR ≅ Δ RMQ . . . . ASA postulate
Volume of cube, V = edge^3
Let edge of cube#1 = (x-4) m, therefore volume of cube#1, v1 = (x-4)^3 m
Let edge of cube#2 = x m, therefore volume of cube#2, v2 = x^3 m
Diff. in volume (in m) = 1216 = v2-v1 = [ x^3 - (x-4)^3 ]
= x^3 - [(x-4)(x-4)(x-4)]
= x^3 - [<span>x^2 - 8x +16(x - 4)]
= </span> x^3 - [ x^3 - 12x^2 + 48x - 64 ]
= 12x^2 - 48x + 64
= 4 (3x^2 - 12x + 16)
Therefore 4 (3^2 - 12x + 16) = 1216
3x^2 - 12x + 16 = 1216/4 = 304
3x^2 - 12x - 288 = 0
3 (x^2 - 4x - 96) = 0
(x^2 - 4x - 96) = 0
(x - 12) (x + 8) =0
(x-12) = 0
Therefore x = 12 m
Edge of cube#2 = x m = 12m
Edge of cube#1 = (x-4) m = 8m
Answer:
"unchanged"
Step-by-step explanation:
Congruence transformations (translation, rotation, reflection) do not change lengths, angles, area (of 2D figures), or volume (of 3D figures). The area would remain unchanged.
