A flagpole casts a shadow that is 12 ft long. A 6-ft tall man casts a shadow

Mathematics

1 answer:

Vikentia [17]2 years ago

4 0

Answer:

9ft

Step-by-step explanation:

Since the triangles are similar, the corresponding sides are proportional.

Let the height of the flag pole be x feet.

$\frac{x}{6} = \frac{12}{8}$

We multiply both sides by 6 to get:

$x = \frac{12}{8} \times 6$

We reduce the fraction to get:

$x = \frac{3}{2} \times 6$

We now simplify

$x = 3 \times 3$

$x = 9ft$

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Guests at an amusement park must be at least 54 inches tall to be able to ride the roller coaster. Which graph represents the se

Gre4nikov [31]

Given:

Guests at an amusement park must be at least 54 inches tall to be able to ride the roller coaster.

To find:

The graph that represents the set of heights that satisfy this requirement.

Solution:

Let x be the height required for the ride.

Guests must be at least 54 inches tall to be able to ride the roller coaster. It means required height is greater than or equal to 54.

$x\geq 54$

So, 54 and all values above 54 are in the solution set.

Since, 54 is included in the solution set, therefore there is a closed circle at 54. All values above 54 are in the solution set, so everything to the right of the circle is shaded.

Therefore, the correct option is C.

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2 years ago

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2 years ago

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Ivenika [448]

$\overline{XS}\cong\overline{YT}\Rightarrow 3m+7=4.2m+5\ \ \ |-7\\\\3m=4.2m-2\ \ \ \ |-4.2m\\\\-1.2m=-2\ \ \ \ |:(-1.2)\\\\m=\dfrac{2}{1.2}\\\\m=\dfrac{20}{12}\\\\m=\dfrac{5}{3}\to m=1\dfrac{2}{3}$

$\overline{YS}\cong\overline{XT}\Rightarrow3\dfrac{1}{2}r+2=2r+5\ \ \ \ |-2\\\\3\dfrac{1}{2}r=2r+3\ \ \ \ |-2r\\\\1\dfrac{1}{2}r=3\ \ \ |\cdot2\\\\3r=6\ \ \ \ |:3\\\\r=2$