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3 years ago

Math picture, please help

Mathematics

1 answer:

Sergeu [11.5K]3 years ago

5 0

the sum of all interior angles in a polygon is 180(n - 2), where n = number of sides.

well, this is a quadrilateral, so it has 4 sides so it has a total of interior angles of 180(4-2) = 360°, since this is a kite, then one pair of opposite angles are congruent, namely ∡C = ∡A.

360° - 45° - 100° = 215°, and ∡C and ∡A split that evenly, so ∡C = 107.5°.

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Simplify the trigonomic expression 1/1+ sin

Softa [21]

Answer:

$\sec^2\theta-\tan\theta\sec\theta$

Step-by-step explanation:

We have to simplify the trigonometric expression $\frac{1}{1+\sin\theta}$

Let us multiply the numerator and denominator by $1-\sin\theta$

$\frac{1}{1+\sin\theta}\times\frac{1-\sin\theta}{1-\sin\theta}$

In the denominator apply the formula for difference of squares

$a^2-b^2=(a+b)(a-b)$

Thus, the denominator will become

$(1+\sin\theta)(1-\sin\theta)=1-\sin^2\theta$

Thus, the expression is

$\frac{1-\sin\theta}{1-\sin^2\theta}$

Using the relation $1-\sin^2\theta=\cos^2\theta$

$\frac{1-\sin\theta}{\cos^2\theta}$

We can rewrite this expression as

$\frac{1}{\cos^2\theta}-\frac{\sin\theta}{\cos^2\theta}$

Finally, the simplified expression is

$\sec^2\theta-\tan\theta\sec\theta$

6 0

3 years ago

Read 2 more answers

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Delvig [45]

Answer:

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Step-by-step explanation:

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2 years ago

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irga5000 [103]

Answer:

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Step-by-step explanation:

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3 years ago

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lord [1]

Answer:

2(W - 5) ≤ -29

Step-by-step explanation:

"Twice the difference of a number and 5 is at most -29" can be expressed symbolically as follows:

2(W - 5) ≤ -29

Further explanations:

"the difference of a number and 5" is W - 5, and thus "Twice the difference of a number and 5" is 2(W - 5).

"x ≤ -29" states "x is at most -29."

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