Is it true that a plane consists of an infinite set of lines?

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baherus [9]

Answer:

19)A 20)A 21)A 22)C 23)D 24)D 25)B 26) A 27)B

28) A 29)B 30)A 31) The surface area of Tina's shoebox is 184a..

u can check the answers if u wantt !! :)

4 0

3 years ago

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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.

5 0

3 years ago

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For this item, any answers that are not whole numbers should be entered as decimals, rounded to the hundredth.

IrinaK [193]

we'll proceed along the same lines as the previous one.

the cost of the boots is 90.10 and that includes 6.25% sales tax, so if "x" is the 100%, then 90.10 is really the 106.25%, because is including the extra 6.25%.

$\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 90.10&106.25\\ x&100 \end{array}\implies \cfrac{90.10}{x}=\cfrac{106.25}{100} \\\\\\ 9010=106.25x\implies \cfrac{9010}{106.25}=x\implies 88.8=x$

so if that's the cost of each boot, without tax, then the markup will be 88.8 - 50.88 = 37.92.

if the 100% is 88.8, how much is 37.92 off of it in percentage?

$\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 88.8&100\\ 37.92&x \end{array}\implies \cfrac{88.8}{37.92}=\cfrac{100}{x} \\\\\\ 88.8x=3792\implies x=\cfrac{3792}{88.8}\implies \stackrel{\%}{42.7}\approx x$

6 0

4 years ago

What is the answer to this 8x+14y=4<br> -6x-7y=-10

cestrela7 [59]

Answer:

14x=4-21y

Step-by-step explanation:

8 0

3 years ago

Find the value of x in the triangle shown below.<br><br> X=____<br><br> Please help!!

Misha Larkins [42]

Answer:

62

Step-by-step explanation:

the sum of all angles in a triangle should be 180°

180-56= 124

124÷2= 62

x= 62

8 0

3 years ago

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