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3 years ago

6

State the solution: 6x + 5 - x = 2(x -2) +3x + 7

2 answers:

sveticcg [70]3 years ago

7 0

A Infinite Solution

Step-by-step explanation:

please see attached

zysi [14]3 years ago

3 0

Answer:

No solution

Step-by-step explanation:

I did the math, trust me. Mark as brainliest please

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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.

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3 years ago

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Find the percent of decrease from 6 to 5.

lozanna [386]

Answer:

Use this

Step-by-step explanation:

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3 years ago

Shade 2/5 of the 10 squares

Rina8888 [55]

Shade in 4 of the squares.

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70 = -2.5x does anybody know the answer to this?

AleksAgata [21]

X= -28

-2.5(-28) = 70

If you got this right, please make me Brainliest

6 0

4 years ago

PLEASE HELP!!!!!

KiRa [710]

$\dfrac{5}{\sqrt{13}}=\frac{5}{\sqrt{13}}\cdot\dfrac{\sqrt{13}}{\sqrt{13}}=\dfrac{5\sqrt{13}}{13}\\\\Used:\ \sqrt{a}\cdot\sqrt{a}=a$

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3 years ago