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Svetradugi [14.3K]
3 years ago
6

What is the length of CD

Mathematics
2 answers:
fgiga [73]3 years ago
3 0
16:30 = 30:x
16x = 900
x = 56.25
so C. is the closest answer
this solution is also know as the geometric mean of the altitude of a right triangle to the parts of the hypotenuse.
faltersainse [42]3 years ago
3 0

Answer:

Option C. 56 cm

Step-by-step explanation:

From the diagram attached, in ΔABC

By Pythagoras Theorem,

AB² = AC² + BC²

      = 16² + 30²

      = 256 +900

AB² = 1156

AB  =  34

Now sinA = \frac{BC}{AB} = \frac{30}{34}

             A = sin⁻¹  (\frac{30}{34}) = 61.93°

From ΔABD

∠A + ∠B + ∠D = 180°

61.93° + 90° + ∠D = 180°

∠D = 180 - 151.93° = 28.07°

Now tan 28.07° =\frac{BC}{CD} = \frac{30}{CD}

0.53328=\frac{30}{CD}

CD = \frac{30}{0.53328} = 56.25 cm ≈ 56 cm

Option C. 56 cm is the answer.

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Hi! Algebra two question, rational exponents.
ivanzaharov [21]

Simplifying \left(x^2+8xy+16y^2\right)^{\frac{1}{3}}.\left(x+4y\right)^{\frac{1}{3}} we get \left(x+4y\right)}

Step-by-step explanation:

We need to simplify:

\left(x^2+8xy+16y^2\right)^{\frac{1}{3}}.\left(x+4y\right)^{\frac{1}{3}}

For solving, we will first simplify the terms inside the exponent and then solve exponent

First Solving: \left(x^2+8xy+16y^2\right)}.\left(x+4y\right)}

Using the formula: (a^2+2ab+b^2)=(a+b)^2

\left(x^2+8xy+16y^2\right)}.\left(x+4y\right)}\\\left((x)^2+2(x)(4y)+(4y)^2\right)}.\left(x+4y\right)}\\\left(x+4y\right)^2}.\left(x+4y\right)}

Using exponent rule:

a^m.a^n=a^{m+n}

\left(x+4y\right)^{2+1}}\\\left(x+4y\right)^3}

Now,

(\left(x+4y\right)^3})^{\frac{1}{3}}\\Simplifiying:\\\left(x+4y\right)}^{\frac{3}{3}}\\\left(x+4y\right)}

So, simplifying \left(x^2+8xy+16y^2\right)^{\frac{1}{3}}.\left(x+4y\right)^{\frac{1}{3}} we get \left(x+4y\right)}

Keywords: Solving Rational exponents:

Learn more about Solving Rational exponents at:

  • brainly.com/question/13174254
  • brainly.com/question/13174255
  • brainly.com/question/5639299
  • brainly.com/question/729447

#learnwithBrainly

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