Well, if the two angles are complementary, then that means that

(2x -9)° + (x + 30)° = 90°

$\bf 3x+21=90\implies 3x=69\implies x=\cfrac{69}{3}\implies x=23$

4 0

4 years ago

Write an equation to describe the amount of income tax paid on an income of x dollars if the income tax rate is 4%

Wittaler [7]

if your income i 10000 x 4% intrest rate it would be 400

3 0

3 years ago

A man on the deck of a ship is 14 ft above water level. He observes that the angle of elevation of the top of a cliff is 40 degr

topjm [15]

Answer:

The distance of the ship from the cliff is 38.465 feet

The height of the cliff is 46.28 feet.

Step-by-step explanation:

As shown in the figure attached $d$ is the distance from the ship to the cliff, and $h$ is the height of the cliff from the ship.

From trigonometry

$tan(20^o)=\frac{14}{d}$

$d=\frac{14}{tan(20^o)}=38.465\:feet.\\\\\boxed{d=38.465ft}$

This is the distance to the cliff.

And we have

$tan(40^o)=\frac{h}{d}$

since $d=38.465ft$

$h=d*tan(40^o)=38.465*tan(40^o)=32.28ft$

Ad the height of the cliff is just $14+h$ or

$32.28+14=46.28 ft\\\\\boxed{height=46.28ft}$

Which is the height of the cliff.

4 0

4 years ago

A cone with volume 2880 m³ is dilated by a scale factor of 1/4. What is the volume of the resulting cone?

labwork [276]

The volume of the cone is 2880 m3.
The scale factor is 1/4.
The volume of the cone has the formula (1/3)π r² h.
A scale factor of 1/4 will reduce the dimensions by 1/4 which will result to a total volume reduction of (1/4)³ = 1/64
The new volume will be 45 m3

5 0

3 years ago

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