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zhannawk [14.2K]
3 years ago
8

Please answer this in two minutes

Mathematics
1 answer:
inysia [295]3 years ago
7 0

Answer:

x = 5.7 units

Step-by-step explanation:

By applying Sine rule is the triangle XYZ,

\frac{\text{SinX}}{\text{WY}}=\frac{\text{SinY}}{\text{WX}}=\frac{\text{SinW}}{\text{XY}}

\frac{\text{SinX}}{\text{x}}=\frac{\text{SinY}}{\text{y}}=\frac{\text{SinW}}{\text{10}}

\frac{\text{Sin33}}{\text{x}}=\frac{\text{SinY}}{\text{y}}=\frac{\text{Sin107}}{\text{10}}

\frac{\text{Sin33}}{\text{x}}=\frac{\text{Sin107}}{\text{10}}

x=\frac{10\times(\text{Sin33})}{\text{(Sin107)}}

x = 5.69

x ≈ 5.7 units

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Right angle trigonometry
Nady [450]

Answer:

B

Step-by-step explanation:

Given

sinΘ = \frac{1}{\sqrt{2} }, then

Θ = sin^{-1}( \frac{1}{\sqrt{2} } ) = 45° → B

7 0
3 years ago
Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 60 inches long and cuts it into
Alex_Xolod [135]

Answer:

a) the length of the wire for the circle = (\frac{60\pi }{\pi+4}) in

b)the length of the wire for the square = (\frac{240}{\pi+4}) in

c) the smallest possible area = 126.02 in² into two decimal places

Step-by-step explanation:

If one piece of wire for the square is y; and another piece of wire for circle is (60-y).

Then; we can say; let the side of the square be b

so 4(b)=y

         b=\frac{y}{4}

Area of the square which is L² can now be said to be;

A_S=(\frac{y}{4})^2 = \frac{y^2}{16}

On the otherhand; let the radius (r) of the  circle be;

2πr = 60-y

r = \frac{60-y}{2\pi }

Area of the circle which is πr² can now be;

A_C= \pi (\frac{60-y}{2\pi } )^2

     =( \frac{60-y}{4\pi } )^2

Total Area (A);

A = A_S+A_C

   = \frac{y^2}{16} +(\frac{60-y}{4\pi } )^2

For the smallest possible area; \frac{dA}{dy}=0

∴ \frac{2y}{16}+\frac{2(60-y)(-1)}{4\pi}=0

If we divide through with (2) and each entity move to the opposite side; we have:

\frac{y}{18}=\frac{(60-y)}{2\pi}

By cross multiplying; we have:

2πy = 480 - 8y

collect like terms

(2π + 8) y = 480

which can be reduced to (π + 4)y = 240 by dividing through with 2

y= \frac{240}{\pi+4}

∴ since y= \frac{240}{\pi+4}, we can determine for the length of the circle ;

60-y can now be;

= 60-\frac{240}{\pi+4}

= \frac{(\pi+4)*60-240}{\pi+40}

= \frac{60\pi+240-240}{\pi+4}

= (\frac{60\pi}{\pi+4})in

also, the length of wire for the square  (y) ; y= (\frac{240}{\pi+4})in

The smallest possible area (A) = \frac{1}{16} (\frac{240}{\pi+4})^2+(\frac{60\pi}{\pi+y})^2(\frac{1}{4\pi})

= 126.0223095 in²

≅ 126.02 in² ( to two decimal places)

4 0
3 years ago
Which term best describes the expression 2x + 2dy−3?
Margarita [4]

Answer:

the term is separated by minus (-) and plus (+) .

therefore this term is trinomial.

7 0
3 years ago
Read 2 more answers
Select the answer choice that is equivalent to the expression given belon.
uranmaximum [27]

Answer:

23x - 10

Step-by-step explanation:

To the find the equivalent of 9(2x - 3) + 5x + 17, evaluate the expression. Start by opening the bracket.

9*2x - 9*3 + 5x + 17

18x - 27 + 5x + 17

Pair like terms

18x + 5x - 27 + 17

23x - 10

The equivalent of 9(2x - 3) + 5x + 17 is 23x - 10

6 0
3 years ago
10. Simplify the rational expression by rationalizing the denominator. 3 sqrt 160/sqrt 1350x A) 2 sqrt 15x/15x B) 3 sqrt 160/135
Viefleur [7K]
The simplified expression by rationalizing the denominator is (C)\frac{4 \sqrt{15x} }{15x}.

First we must simplify the expression:
\frac{3 \sqrt{160} }{\sqrt{1350x} } =  \frac{12 \sqrt{10} }{15 \sqrt{6x} } =  \frac{4 \sqrt{10} }{5 \sqrt{6x} }

Then we factor the rational parts and cancel it out:
\frac{4 \sqrt{2} \sqrt{5} }{5 \sqrt{2} \sqrt{3x} } = \frac{4\sqrt{5} }{5\sqrt{3x} }

Then we rationalize the expression:
\frac{4\sqrt{5} }{5\sqrt{3x} } * \frac{\sqrt{3x} }{\sqrt{3x} } = \frac{4 \sqrt{15x} }{5*3x} = \frac{4 \sqrt{15x} }{15x}

<span>Finally, the simplified expression by rationalizing the denominator is (C)\frac{4 \sqrt{15x} }{15x}.</span>
7 0
3 years ago
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