The given line passes through the points and (4,1).

Mathematics

1 answer:

Dominik [7]3 years ago

7 0

Hey there! :)

Answer:

y -3 = -2(x + 4).

Step-by-step explanation:

Begin by calculating the slope of the line shown in the graph. Use the slope formula:

$m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$

Plug in two coordinates:

$m = \frac{1-(-3)}{4-(-4)}$

Simplify:

$m = \frac{4}{8}$

$m = \frac{1}{2}$

Therefore, the slope of the line is 1/2.

A line that is perpendicular contains a slope that is the negative reciprocal. Therefore:

1/2 --> -2.

Plug the slope into the point-slope formula:

y -3 = -2(x + 4). This is your equation in point-slope form!

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3 years ago

In ΔQRS, the measure of ∠S=90°, the measure of ∠R=29°, and SQ = 5.8 feet. Find the length of RS to the nearest tenth of a foot.

taurus [48]

Answer:

10.5 ft

Step-by-step explanation:

In ΔQRS,

m∠S=90°
m∠R=29°,
SQ = 5.8 feet.

See the diagram below.

The triangle is a Right Triangle,

Using trigonometric ratios,

$Tan R=\dfrac{|SQ|}{|RS|} \\Tan 29^\circ=\dfrac{5.8}{|RS|}\\$Cross multiply$\\|RS|XTan 29^\circ=5.8\\|RS|=\dfrac{5.8}{Tan 29^\circ}\\$=10.5 ft (to the nearest tenth of a foot)$