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3 years ago

If segment FD = 20 units and segment DE = 52 units, what is the value of b? Round the solution to the nearest hundredth.

Mathematics

1 answer:

Readme [11.4K]3 years ago

7 0

Answer:

b = $22.62^{o}$

Step-by-step explanation:

Since the triangle is a right angled triangle, the appropriate trigonometric function can be applied to determine the value of b.

Thus, to determine the value of b;

Sin θ = $\frac{opposite}{hypotenuse}$

Sin b = $\frac{20}{52}$

= $\frac{20}{52}$

= 0.38462

⇒ b = $Sin^{-1}$ 0.38462

= 22.6202

b = $22.62^{o}$

The measure of angle E (= b) is $22.62^{o}$ .

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What is one of the solutions to the following system of equations? y2 x2 = 53 y − x = 5 (−10, −5) (−7, −2) (7, 2) (5, 10).

Aliun [14]

The solution of the system of equation is (-7, -2).

<h2>Given</h2>

The system of the equations;

$\rm y^2 + x^2 = 53 \\\\y -x = 5$

From equation 1

$\rm y -x=5\\\\y = 5+x$

Substitute the value of y in equation 1

$\rm y^2+x^2=53\\\\(5+x)^2+x^2=53\\\\25+x^2+10x+x^2=53\\\\2x^2+10x+25-53=0\\\\2 x^2 + 10x - 28 = 0 \\\\Divide \ by \ 2 \ both \ side \ the \ equation\\\\x^2 + 5x - 14 = 0\\\\x^2-7x+2x-14=0\\\\x(x-7) + 2(x-7) =0\\\\(x-7) \ (x+2)=0\\\\x-7=0 \ \ x = 7\\\\x +2 =0 \ \ x=-2$

The value of x= 2 is rejected because x = 2 not satisfy the equation.

Substitute 2 for the value of x in equation II

y − x = 5

y – 2 = 5

y = 5 +2

y = 7 (x =2, y =7) … Not included in the options

If x = -7

Substitute the value of x = -7 in the equation

$\rm y -x=5\\\\y - (-7)=5\\\\y +7= 5\\\\y = 5-7\\\\y = -2$

Hence, the solution of the system of equation is (-7, -2).

To know more about System of Equation click the link given below.

brainly.com/question/1495351

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2 years ago

What would y equal if you substituted 2 in y+2x=3

Ivahew [28]

Answer:

-1

Step-by-step explanation:

Given the equation:

$y+2x=3$

Substitute $x=2$ into this equation:

$y+2\cdot 2=3\\ \\y+4=3$

Subtract 4:

$y+4-4=3-4\\ \\y=-1$

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3 years ago

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nignag [31]

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umka2103 [35]

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Step-by-step explanation:

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AlexFokin [52]

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3 years ago