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3 years ago

Write the equation of a line that has a slope of 1/3 and a y intercept at (0,4)

Mathematics

1 answer:

Rus_ich [418]3 years ago

5 0

Answer:

y = 1/3x + 4

Step-by-step explanation:

The slope intercept form is y=mx+b so what we need to do is fill in the blanks. M is the slope and we know the 1/3 is the slope. (0,4) is basically meaning that the x-value is 0 and the y-value is 4, and when that's the case it means 4 is the y-intercept. Now we can put the information together y = 1/3x +4 is the equation.

Hope this helps and have a great day!

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Cos x cos (-x) -sin x sin (-x) = 1. Verify the Identity. Please Show All Steps.

umka21 [38]

Answer:

cos x cos (-x) -sin x sin (-x) = 1 ⇒ proved down

Step-by-step explanation:

* Lets revise the angles in the four quadrants

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tan (180 - x) = -tan x)

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tan (180 - x) = -tan x)

# -x ⇒fourth quadrant (sin (- x) = -sin x , cos (- x) = cos x

tan (- x) = -tan x)

* Lets solve the problem

∵ L. H .S is ⇒ cos x cos (-x) - sin (x) sin (-x)

- From the rules above cos x = cos(-x)

∴ cos x cos (-x) = cos x cos x

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- From the rule above sin (-x) = - sin x

∴ sin x sin (-x) = sin x [- sin x]

∴ sin x sin (-x) = - sin² x

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8 0

3 years ago

The length of a rectangle field if 7/5 of its width. if the perimeter of the field is 240 meters, what are the length and width

trasher [3.6K]

Perimeter of any figure is all its sides summed up

for a rectangle, with two equal pairs, that means, length + length + width + width or 2length + 2width, or 2(length + width)

but we know the length is 7/5 the width

width = w
perimeter = P

$\bf P=2\left(\frac{7}{5}w +w \right)\qquad P=240\implies 240=2\left(\frac{7}{5}w +w \right)
\\\\\\
120=\frac{7}{5}w +w\impliedby \textit{let's multiply both sides by 5}
\\\\\\
600=7w+5w\implies 600=12w\implies \cfrac{600}{12}=w$

and the length is 7/5 of that

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