The price of a smart watch is $109.99 and the sales tax is 6.5%.
2 answers:
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Answer:
BC = 3.6
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
=
, substitute values
=
( cross- multiply )
1.5 BC = 5.4 ( divide both sides by 1.5 )
BC = 3.6
Answer:
The speed of the bus is 74.242 kilometers per hour.
Step-by-step explanation:
Let suppose that bus runs at constant speed and that speed is measured in kilometers per hour. Then, the speed of the bus (), in kiometers per hour, is determined by following kinematic expression:
(1)
Where:
- Travelled distance, in kilometers.
- Time, in hours.
If we know that and
, then the speed of the bus is:
The speed of the bus is 74.242 kilometers per hour.
Answer:
-2, 8/3
Step-by-step explanation:
You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...
A = (1/2)(f(a) +f(4))(4 -a)
= (1/2)((3a -1) +(3·4 -1))(4 -a)
= (1/2)(3a +10)(4 -a)
We want this area to be 12, so we can substitute that value for A and solve for "a".
12 = (1/2)(3a +10)(4 -a)
24 = (3a +10)(4 -a) = -3a² +2a +40
3a² -2a -16 = 0 . . . . . . subtract the right side
(3a -8)(a +2) = 0 . . . . . factor
Values of "a" that make these factors zero are ...
a = 8/3, a = -2
The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.
_____
<em>Alternate solution</em>
The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.
