Can someone help me with the extra credit

x = 64√13 / 9

Step-by-step explanation:

Starting at the top triangle, the hypotenuse is found with Pythagorean theorem:

c² = a² + b²

c² = 4² + 6²

c = √52

Moving on to the 30-60-90 triangle, the hypotenuse if found with trigonometry:

sin 60 = √52 / c

c = √52 / sin 60

c = √52 / (√3 / 2)

c = 2√(52/3)

Next is the 45-45-90 triangle.  The hypotenuse is again found with trig:

sin 45 = 2√(52/3) / c

c = 2√(52/3) / sin 45

c = 2√(52/3) / (√2 / 2)

c = 4√(26/3)

The next 30-60-90 triangle:

cos 30 = 4√(26/3) / c

c = 8√(26/9)

Another 30-60-90 triangle:

sin 60 = 8√(26/9) / c

c = 16√(26/27)

A 45-45-90 triangle:

sin 45 = 16√(26/27) / c

c = 32√(13/27)

The final 30-60-90 triangle:

sin 60 = 32√(13/27) / x

x = 64√(13/81)

x = 64√13 / 9

step-by-step explanation:

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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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