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Trava [24]
4 years ago
11

Starla bought cloth napkins at an outlet store for $4.25 each, and she also used a $20 off coupon. In the equation below, x repr

esents the number of napkins, and y represents the cost before tax.
y = $4.25x - $20

If Starla paid $43.75 before tax, how many napkins did she buy?
Mathematics
1 answer:
mars1129 [50]4 years ago
5 0

Solution:

Given data in the question-

Price of per piece of napkin at an outlet store - $4.25

Discount coupon used a $20 off coupon.

y = 4.25x - 20

In the equation , x represents the number of napkins, and y represents the cost before tax.

She paid $43.75 before tax, which means y=43.75

=> 43.75 = 4.25x-20\\= >43.75+20 =4.25x\\=>x=\frac{63.75}{4.25} = 15

Starla bought 15 napkins

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4 years ago
The angles of depression of two ships from the top of the light house are 45° and 30° towards east. If the ships are 200 m apart
azamat

Answer:

273 meters

Step-by-step explanation:

See image attached for the diagram I used to represent this scenario.

The distance between the ships, at angles 30 and 45, is 200 meters. The distance between the left ship and the lighthouse is x meters.

We can use trigonometric ratios to solve this problem. We can use the tangent ratio \big{(} \frac{\text{opposite}}{\text{adjacent}} \big{)} to create an equation with the two angles.

  • \displaystyle \text{tan(45)} = \frac{h}{x}
  • \displaystyle \text{tan(30)} = \frac{h}{x+200} }

Let's take these two equations and solve for x in both of them.

<h2>\textbf{Equation I}</h2>
  • \displaystyle \text{tan(45)} = \frac{h}{x}  

tan(45) = 1, so we can rewrite this equation.

  • \displaystyle 1=\frac{h}{x}

Multiply x to both sides of the equation.

  • \displaystyle x = h
<h2>\textbf{Equation II}</h2>
  • \displaystyle \text{tan(30)} = \frac{h}{x+200} }

Multiply x + 200 to both sides and divide h by tan(30).

  • \displaystyle \text{x + 200} = \frac{h}{\text{tan (30)}}  

Subtract 200 from both sides of the equation.

  • \displaystyle \text{x} = \frac{h}{\text{tan (30)}} - 200

Simplify h/tan(30).

  • x=\sqrt{3}h - 200  
<h2>\textbf{Equation I = Equation II}</h2>

Take Equation I and Equation II and set them equal to each other.

  • h=\sqrt{3}h-200

Subtract √3 h from both sides of the equation.

  • h-\sqrt{3}h=-200

Factor h from the left side of the equation.

  • h(1-\sqrt{3}) =-200

Divide both sides of the equation by 1 - √3.

  • \displaystyle h=\frac{-200}{1-\sqrt{3} }

Rationalize the denominator by multiplying the numerator and denominator by the conjugate.

  • \displaystyle h=\frac{-200}{1-\sqrt{3} } \big{(} \frac{1+\sqrt{3} }{1+\sqrt{3}} \big{)}
  • \displaystyle h=\frac{-200+200\sqrt{3} }{1-3}
  • \displaystyle h =\frac{-200+200\sqrt{3} }{-2}

Simplify this equation.

  • \displaystyle h=100+100\sqrt{3}
  • h=273.20508075

The height of the lighthouse is about 273 meters.

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