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3 years ago

Please help with two geometry questions!!!

Mathematics

1 answer:

V125BC [204]3 years ago

4 0

Answer:

2879.4 m

Step-by-step explanation:

The sine of an angle in a right triangle is the ratio of the side opposite to the hypotenuse. Here the interior angle at lower right is an "alternate interior angle" where the diagonal "transversal" crosses the parallel horizontal lines. Alternate interior angles are congruent, so the lower right interior angle is 10°. (Basically, the angle of elevation is equal to the angle of depression.)

Using the sine relation, we have ...

sin(10°) = (500 m)/x

Multiplying by x/sin(10°) gives us the solution ...

x = (500 m)/sin(10°)

x ≈ 2879.4 m

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The diagonals of a kite have lengths of x inches and 18x inches. The area of the kite is given by A=9x^2. Identify the equation(

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3 years ago

Write the equation of each line using the given information.

Marat540 [252]

A. The equation of the line is y = -0.2 x + 1.9

B. The equation of the line is y = 4 x + 3

C. The equation of the line is y = -8

D. The equation of the line is y = 2 x + 4

Step-by-step explanation:

The slope-intercept form of the equation of a line is y = m x + b, where

m is the slope of the line and b is the y-intercept

The formula of the slope of a line which passes through points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
The slope of a horizontal line whose equation y = b is zero
The y-intercept means the line intersect the y-axis at point (0 , b)

∵ The line passes through points (2 , 1.5) and (-5 , 36.5)

∴ $x_{1}$ = 2 and $x_{2}$ = -5

∴ $y_{1}$ = 1.5 and $y_{2}$ = 36.5

∵ $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∴ $m=\frac{-5-2}{36.5-1.5}=\frac{-7}{35}=\frac{-1}{5}$

∴ m = -0.2

∵ y = m x + b

∵ m = -0.2

∴ y = -0.2 x + b

- To find b substitute x and y in the equation by the coordinates of

one of the two given points

∵ x = 2 and y = 1.5

∴ 1.5 = -0.2(2) + b

∴ 1.5 = - 0.4 + b

- Add 0.4 to both sides

∴ 1.9 = b

∴ y = -0.2 x + 1.9

The equation of the line is y = -0.2 x + 1.9

∵ m = 4

∵ y = m x + b

∴ y = 4 x + b

∵ Point (3 , 15) lies on the line

- To find b substitute x and y in the equation by the coordinates

of the given point

∵ x = 3 and y = 15

∴ 15 = 4(3) + b

∴ 15 = 12 + b

- Subtract 12 from both sides

∴ 3 = b

∴ y = 4 x + 3

The equation of the line is y = 4 x + 3

∵ The line has the same slope of line y = 1

- The line whose equation y = 1 is a horizontal line

∵ The slope of the line y = 1 is zero because it is a horizontal line

∴ m = zero

∵ y = m x + b

∴ The equation of the line is y = (0)x + b

∴ y = b

∵ The line passes through point (3 , -8)

- In the horizontal line the y-coordinates of all point lie on the line

are equal

∴ The line intersect the y-axis at point (0 , -8)

∴ b = -8

∴ y = -8

The equation of the line is y = -8

∵ m = 2

∵ y-intercept is at point (0 , 4)

∴ b = 4

∵ y = m x + b

∴ y = 2 x + 4

The equation of the line is y = 2 x + 4

Learn more:

You can learn more about the linear equations in brainly.com/question/4326955

#LearnwithBrainly

6 0

3 years ago