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2 years ago

What is the slope of the line in this diagram? what is the y-intercept

Mathematics

1 answer:

rusak2 [61]2 years ago

7 0

Where's the diagram?

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I don’t know how to solve for Q.

Naya [18.7K]

Answer:

∠Q = 75°

Step-by-step explanation:

Start by recognizing that the triangle is isosceles (the long sides are marked as being equal-length). That means angles Q and R have the same measure.

Next, you use the fact that the sum of angles is 180° to write an equation.

∠R +∠P +∠Q = 180°

(2x +15)° +x° +(2x +15)° = 180° . . . . substitute the known values

5x +30 = 180 . . . . . . . . . . . . . . . . divide by °, collect terms

5x = 150 . . . . . . . . subtract 30

x = 30 . . . . . . . divide by 5

Then angle Q is ...

∠Q = (2x +15)° = (2×30 +15)°

∠Q = 75°

8 0

2 years ago

zubka84 [21]

Answer:

See Explanation Below

Step-by-step explanation:

Given

$(sin x - cos x)^2 = sec^2x - tan^2x - 2sinx.cos x.$

Required

Prove

To start with; we open the bracket on the left hand side

$(sin x - cos x)^2 = (sin x - cos x)(sin x - cos x)$

$(sin x - cos x)^2 = (sin x )(sin x - cos x)- (cos x)(sin x - cos x)$

$(sin x - cos x)^2 = sin^2 x -sinx cos x - sin xcos x + cos^2 x$

$(sin x - cos x)^2 = sin^2 x -2sinx cos x + cos^2 x$

Reorder

$(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x$

From trigonometry;

$sin^2x + cos^2x = 1$

So;

$(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x$

becomes

$(sin x - cos x)^2 = 1 - 2sinx cos x$

Also from trigonometry;

$sec^2x - tan^2x = 1$

So,

$(sin x - cos x)^2 = 1 - 2sinx cos x$

becomes

$(sin x - cos x)^2 = sec^2x - tan^2x - 2sinx cos x$

Proved

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3 years ago

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I think this would be sometimes true

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