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Mariana [72]
3 years ago
11

Write an equation that could be used to find the value of x using the interior angles of ∆BDC, then solve it.

Mathematics
1 answer:
Alecsey [184]3 years ago
6 0

9514 1404 393

Answer:

  x = 16

Step-by-step explanation:

Either or both of the right triangles can be used to find x. Or, triangle ABC could be used. All numbers are assumed to be degrees.

<u>Using ∆ABD</u>

  55 +90 +2x+3 = 180

  2x = 32 . . . . . . subtract 148

  x = 16

<u>Using ∆BCD</u>

  50 +90 +2x+8 = 180

  2x = 32 . . . . . . subtract 148

  x = 16

<u>Using ∆ABC</u>

  55 +(2x +3) +50 +(2x +8) = 180

  4x = 64 . . . . . . . subtract 116

  x = 16

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Take into account, that in general, a cosine function of amplitude A, period T and vertical translation b, can be written as follow:

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In the given case, you have:

A = 4

T = 3π/4

b = -3

By replacing you obtain:

\begin{gathered} f(x)=4\cos (\frac{2\pi}{\frac{3\pi}{4}}x)-3 \\ f(x)=4\cos (\frac{8}{3}x)-3 \end{gathered}

Hence, the answer is:

f(x) = 4cos(8/3 x) - 3

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11 months ago
Find the next three terms in the geometric sequence: 400, 200, 100, 50
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It's dividing by 2. 

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An expression is shown below: 2x3y + 18xy − 10x2y − 90y Part A: Rewrite the expression by factoring out the greatest common fact
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Answer:

Part A : 2y( x³ + 9x - 5x² - 45 ), Part B : 2y( x - 5 )( x² + 9 )

Step-by-step explanation:

Part A : Let's break every term down here to their " prime factors ", and see what is common among them,

2x³y + 18xy − 10x²y − 90y -

2x³y  = 2 * x³ * y,

18xy = 2 * 3 * 3 * x * y,

− 10x²y = 2 * - 5 * x² * y, - so as you can see for this example I purposely broke down - 10 into 2 and - 5. I could have placed the negative on the 2, but as that value was must likely common among all the terms, I decided to place it on the 5. The same goes for " − 90y. " I placed the negative there on the 5 once more.

− 90y = 2 * - 5 * 3 * 3 * y

The terms common among each term are 2 and y. Therefore, the GCF ( greatest common factor ) is 2x. Let's now factor the expression using this value.

2y( x³ + 9x - 5x² - 45 )

Part B : Let's simply factor this entire expression. Of course starting with the " factored " expression : 2y( x³ + 9x - 5x² - 45 ),

2y\left(x^3+9x-5x^2-45\right) - Factor out " (x^3+9x-5x^2-45\right)) " by grouping,

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9\left(x-5\right)+x^2\left(x-5\right) - Factor out common term x - 5,

\left(x-5\right)\left(x^2+9\right) - And our solution is thus 2y( x - 5 )( x² + 9 )

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The hypotenuse would be square root of 41
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