Answer:
m∠W = 125°
m∠X = 55°
m∠Z = 55°
Step-by-step explanation:
The shape is parallelogram WXYZ. m∠Y = 125.
A parallelogram is a quadrilateral shape in which both opposite sides and opposite angles are equal to each other. The diagonals of a parallelogram bisect each other. Also consecutive angles in a parallelogram are supplementary.
Therefore in parallelogram WXYZ:
m∠Z + m∠Y = 180° (Consecutive angles in a parallelogram are supplementary)
m∠Z + 125 = 180
m∠Z = 180 - 125
m∠Z = 55°
m∠W = m∠Y (Opposite angles are equal)
m∠W = 125°
m∠W + m∠X = 180° (Consecutive angles in a parallelogram are supplementary)
m∠X + 125 = 180
m∠X = 180 - 125
m∠X = 55°
Answer:
Dimensions of the container:
x = 3 m
y = 6 m
h = 1.1 m
C(min) = 270 $
Step-by-step explanation:
Volume of storage container
V = 20 m³
Let "y" be the length and "x" the width then y = 2*x
V = x*y*h ⇒ V = 2*x²*h ⇒ 20 = 2*x²+h ⇒ h = 10/ x²
Costs:
Total cost = cost of base ( 5*2*x² ) + cost of side with base x ( 2*9*x*h) +
cost of side witn base y =2x (2*9*2x*h)
C(t) = 10*x² + 18*x*h + 36*x*h
C(x) = 10x² + 54*x*10/x² ⇒ C(x) 10*x² + 540 /x
Taking derivatives on both sides of the equation we get:
C´(x) = 20*x - 540/x²
C´(x) = 0 ⇒ 20*x - 540/x² = 0 ⇒ 2x - 54/x² = 0
2x³ - 54 = 0
x³ = 27 x = 3 m
Then y = 2*x ⇒ y = 2*3 y = 6 and h = 10 / x² h = 1.1 m
And the minimum cost is
C (min) = 10*x² + 540/x ⇒ C (min) = 90 + 180
C(min) = 270 $
Answer:
x = 7
Step-by-step explanation:
QY = 5x
YZ = 18
QZ = 53
Thus:
QY + YZ = QZ (segment addition postulate)
5x + 18 = 53
5x = 53 - 18 (subtraction property of equality)
5x = 35
Divide both sides by 5
x = 7
Answer:
A
Step-by-step explanation:
His speed change is the slope or -15, decreases by 15 miles/hour
when he starts, his speed is 0*-15+60 = 60 miles/hour
