Which is an equation of the line that passes through (–1, –5) and (–3, –7)?

Mathematics

1 answer:

babymother [125]3 years ago

6 0

Answer:

y = x - 4

Step-by-step explanation:

The line passes through (-1,-5) and (-3,-7)

The slope of a line is given by; change in y ÷ change in x

i.e slope = $\frac{-7 - -5}{-3 - -1}$ = $\frac{-2}{-2}$ = 1

Taking another point (x,y) on the line.

Slope will be; $\frac{y - -5}{x - -1}$ = 1

Cross multiplying gives; y + 5 = x + 1

Simplifying this equation gives us the equation of our line which is;

y = x - 4

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A surveyor, Toby, measures the distance between two landmarks and the point where he stands. He also measured the angles between

vagabundo [1.1K]

What we know so far:
Side 1 = 55m
Side 2 = 65m
Angle 1 = 40°
Angle 2 = 30°

What we are looking for:
Toby's Angle = ?
The distance x = ?

We need to look for Toby's angle so that we can solve for the distance x by assuming that the whole figure is a SAS (Side Angle Side) triangle.

Solving for Toby's Angle:
We know for a fact that the sum of all the angles of a triangle is 180°; therefore,
180° - (Side 1 + Side 2) = Toby's Angle
Toby's Angle = 180° - (40° + 30°)
Toby's Angle = 110°

Since we already have Toby's angle, we can now solve for the distance x by using the law of cosines r² = p²+ q²<span>− 2pq cos R where r is x, p is Side1, q is Side2, and R is Toby's Angle.
</span>
x² = Side1² + Side2² - 2[(Side1)(Side2)] cos(Toby's Angle)
x² = 55² + 65² - 2[(55)(65)] cos(110°)
x² = 3025 + 4225 -7150[cos(110°)]
x² = 7250 - 2445.44
x = √4804.56
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∴The distance, x, between two landmarks is 69.31m

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3 years ago

Find the missing measure in a right triangle if a= 9 ft and b = 12 ft.

Lena [83]

Answer:

c = 15 ft

Step-by-step explanation:

a^2 + b^2 = c^2

9^2 + 12^2 = c^2

c^2 = 225

c = √225

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