The five men would be paid $10.41 each at the same hourly rate
Answer:
Both Scott and Tara have responded correctly.
Step-by-step explanation:
we know that
The area of a trapezoid is equal to
A=(1/2)[b1+b2]h
we have
b1=16 cm
b2=24 cm
h=8 cm -----> <em>Note</em> The height is 8 cm instead of 18 cm
substitute
A=(1/2)[16+24](8)
A=160 cm²
<em>Verify Scott 's work</em>
<em>Note</em> Scott wrote A = (1/2)(24 + 16)(8) instead of A = 2(24 + 16)(8)
Remember that the Commutative Property establishes "The order of the addends does not alter its result"
so
(24+16)=(16+24)
A = (1/2)(24 + 16)(8)=160 cm²
<em>Verify Tara's work</em>
<em>Note</em> Tara wrote A = (1/2)(16+24)(8) instead of A = (16 + 24)(8)
A = (1/2)(16+24)(8)=160 cm²
Answer:
x = 5, x = 1
Step-by-step explanation:
The quadratic equation 0 = 4(x - 3)2 - 16.
Using binomial theorem, (a - b)2 = a2 - 2ab + b2 to expand (x - 3)2.
0 = 4(x2 - 6x + 9 ) - 16.
Using distributive property to multiply 4 by x2 - 6x + 9.
0 = 4x2 - 24x + 36 - 16.
Subtract 16 from 36 to get 20.
0 = 4x2 - 24x + 20.
4x2 - 24x + 20 = 0.
Divide both sides by 4.
x2 - 6x + 5 = 0.
To solve the equation, factor and rewrite as x2 + ax + bx + 5
a + b = -6, ab = 1(5) = 5.
a = -5, b = -1.
Rewriting x2 - 6x + 5 as
(x2 - 5x) + (-x + 5)
Factor x in the first and -1 in the second group.
x(x - 5) - (x - 5)
Factor out common term
(x - 5)(x - 1)
By solving the above, we get
x = 5, x = 1
Given that 
, we have 
, so that
Take the derivative and find the critical points of 
:
Take the second derivative and evaluate it at the critical point:
Since 
is positive for all 
, the critical point is a minimum.
At the critical point, we get the minimum value 
.
