A line passes through (10,-1) and has a slope of -1/2 whats the equation of the line

Mathematics

1 answer:

8090 [49]3 years ago

8 0

Answer:

Y=-1/2x+4

Step-by-step explanation:

-The slope is -1/2 so you just plug it in where the slope would go with an x in front

-all you need now is your y-intercept which can be found by plugging in the provided info to your basic form y=mx+b

-You can take the provided point at (10,-1) and work out what the intercepts is

-1=-1/2(10)-b

-1=-5-b

4=b

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Anybody know the correct answer?

earnstyle [38]

Since $\csc^2{x}=\frac{1}{\sin^2{x}}$ and $\cot^2{x}=\frac{\cos^2{x}}{\sin^2{x}}$ , we can rewrite the right side of the equation as

$\frac{1}{\sin^2{x}}-\frac{\cos^2{x}}{\sin^2{x}} =\frac{1-\cos^2{x}}{\sin^2{x}}$

Using the identity $\sin^2{x}+\cos^2{x}=1$ , we can subtract $\cos^2{x}$ from either side to obtain the identity $\sin^2{x}=1-\cos^2{x}$

substituting that into our previous expression, the right side of our equation simply becomes

$\frac{\sin^2{x}}{\sin^2{x}}=1$

We can now write our whole equation as

$3\tan^2{x}-2=1$

Adding 2 to both sides:

$3\tan^2{x}=3$

dividing both sides by 3:

$\tan^2{x}=1$

$\tan{x}=\pm1$

When 0 ≤ x ≤ π, tan x can only be equal to 1 when sin x = cos x, which happens at x = π/4, and it can only be equal to -1 when -sin x = cos x, which happens at x = 3π/4

4 0

3 years ago

PLEASE ANSWER!! I don’t understand

iVinArrow [24]

Answer:

$m\angle 2=122^{\circ},\\m\angle 1 = 58^{\circ}$

Step-by-step explanation:

By definition, tangent lines touch a circle at one point. This one point intersects the circle at a 90 degree angle.

In any circle, the measure of an inscribed angle is exactly half of the arc it forms. Since $\angle 2$ forms an arc labelled 244 degrees, the measure of angle 2 must be $\frac{244}{2}=\boxed{122^{\circ}}$ .