38. In a right triangle, if one acute angle has measure 8x + 5 and the other has measure 4x + 9, find the larger of these two angles.
55.67
62.4
57.92
64.61
None of the above

Angle 1 = ( 8x + 5 ) ...(i)

Angle 2 = ( 4x + 9 ) ...(ii)

Angle 3 = 90° ( ∵ it is a right-angled triangle )

The value of the larger angle of the two acute angles.

. ✅

We know that,

➪ ∠ 1 + ∠ 2 + ∠ 3 = 180°

➪ 8x + 5 + 4x + 9 + 90° = 180°

➪ 12x + 104° = 180°

➪ 12x = 180° - 104°

➪ 12x = 76°

➪ x =

➪ x = 6.333°

The value of x is 6.333°.

Now,

Substituting the value of x in eq. (i) & (ii), we have

Angle 1 = 8x + 5

= 8 x 6.333 + 5

= 50.666 + 5

= 55.67°

Angle 2 = 4x + 9

= 4 x 6.333 + 9

= 25.332 + 9

= 34.332°

Clearly, angle 1 is greater than angle 2.

Therefore, the value of the larger angle of the two acute angles is 55.67°.

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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