3 years ago

Find the value of r so that the line through (8,r) and (4,5) has a slope of -4

Mathematics

1 answer:

Ratling [72]3 years ago

7 0

Answer:

r = - 11

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to - 4

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (4, 5) and (x₂, y₂ ) = (8, r)

m = $\frac{r-5}{8-4}$ = $\frac{r-5}{4}$ = - 4 ( multiply both sides by 4 )

r - 5 = - 16 ( add 5 to both sides )

r = - 11

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to avoid a large shallow reef a ship set a course from point a and traveled 24 miles east to point b . the ship them turn and tr

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First, we are going to find the distance traveled by the ship adding the tow distances:
Distance traveled= 24 mi +33 mi=57 mi

Next, we are going to use the Pythagorean theorem to find the distance from $a$ to $c$ :
$d^2=24^2+33^2$
$d^2=576+1089$
d^2=1665
$d= \sqrt{1665}$
$d=40.8$ mi

Finally, we are going to subtract the two distances:
57 mi -40.8 mi= 16.2 mi

We can conclude that <span>if the ship could have traveled in a straight lime from point a to point c, it could have saved 16.2 miles.</span>