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evablogger [386]
3 years ago
9

If AC = 40, find the length of JK.

Mathematics
2 answers:
lesantik [10]3 years ago
8 0

Answer:

JK = 24

Step-by-step explanation:

Δ BKJ and Δ BCA are similar triangles and ratios of corresponding sides are equal, that is

\frac{JK}{AC} = \frac{BK}{BC} , substitute values

\frac{JK}{40} = \frac{3}{5} ( cross- multiply )

5JK = 120 ( divide both sides by 5 )

JK = 24

eduard3 years ago
8 0

the triangles are all similar, because they have proportional sides and equal angles.

if you assume the smallest, equal part of side to be x

the biggest triangle has "5 parts" so BC=5x and BK has 3 parts so BK=3x .

since they're similar, ratio of their corresponding sides is constant or equal.

{BK\over BC}={JK \over AC}

BK/BC=3/5

and AC=40

so JK = 40*3/5=24

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The equation of function h is h... PLEASE HELP MATH
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Answer:

Part A: the value of h(4) - m(16) is -4

Part B: The y-intercepts are 4 units apart

Part C: m(x) can not exceed h(x) for any value of x

Step-by-step explanation:

Let us use the table to find the function m(x)

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∵ At x = 8, m(x) = 2

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∵ 2 = \frac{1}{2} (8) + b

∴ 2 = 4 + b

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∴ -2 = b

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Now let us answer the questions

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∵ h(x) = \frac{1}{2} (x - 2)²

∴ h(4) = \frac{1}{2} (4 - 2)²

∴ h(4) = \frac{1}{2} (2)²

∴ h(4) =  \frac{1}{2}(4)

∴ h(4) = 2

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∴ m(16) =  \frac{1}{2} (16) - 2

∴ m(16) = 8 - 2

∴ m(16) = 6

- Find now h(4) - m(16)

∵ h(4) - m(16) = 2 - 6

∴ h(4) - m(16) = -4

Part B:

The y-intercept is the value of h(x) at x = 0

∵ h(x) = \frac{1}{2} (x - 2)²

∵ x = 0

∴ h(0) = \frac{1}{2} (0 - 2)²

∴ h(0) =  \frac{1}{2} (-2)² =  

∴ h(0) = 2

∴ The y-intercept of h(x) is 2

∵ m(x) = \frac{1}{2} x - 2

∵ x = 0

∴ m(0) = \frac{1}{2} (0) - 2 = 0 - 2

∴ m(0) = -2

∴ The y-intercept of m(x) is -2

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Compare this form with the form of h(x)

∵ h = 2 and k = 0

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<em>Look to the attached graph for more understand</em>

The blue graph represents h(x)

The green graph represents m(x)

The blue graph is above the green graph for all values of x, then there is no value of x make m(x) exceeds h(x)

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So lets just think of a full day as 6 hours.

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This is 4284(total passangers) divided by 6(total hours):

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So each hour, there are 714 passangers.

Hope this helps!

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