Show that the cosine law simplifies to the Pythagorean theorem when the contained angle between the two known sides is 90°.

See Below.

Step-by-step explanation:

We want to show that the Law of Cosines simplifies to the Pythagorean Theorem when the contained angle between the two known sides is 90°.

The Law of Cosines is given by:

Where a and b are the two known sides, and C is the angle between them.

If C is 90° then we will have:

Recall that the cos(90°)=0. Hence:

Simplify:

So, we acquire the Pythagorean Theorem as desired.

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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