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3 years ago

Help. Please And Thank u <3

Mathematics

2 answers:

ozzi3 years ago

7 0

Step-by-step explanation:

α = α

x = 96°

Answer → x = 96° (degree)

Eduardwww [97]3 years ago

7 0

Answer:

96 Degrees

Step-by-step explanation:

If we look at the problem, we know that due to the fact that they are adjacent that they MUST be equal.

Here is the proof:

We'll assign each angle a letter as following

A B C D with A being the top left and D being the bottom right!

Now that we know that, first off, A has to be equal to 180-96 due to them being Supplementary Angles.

Therefore, A is 84 degrees.

Now to find x, we can use Supplementary Angles again.

x has to be 180-84 which is 96 degrees proving the theorum.

Have a nice day!

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Determine the equation of each line

katovenus [111]

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

(a)

here m = - $\frac{3}{4}$ and c = 6, hence

y = - $\frac{3}{4}$ x + 6 ← equation of line

(b)

here m = 6, hence

y = 6x + c ← is the partial equation

to find c substitute (2, - 6 ) into the partial equation

- 6 = 12 + c ⇒ c = - 6 - 12 = - 18

y = 6x - 18 ← equation of line

(c)

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

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m = $\frac{7-3}{4+1}$ = $\frac{4}{5}$ , hence

y = $\frac{4}{5}$ x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

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3 years ago

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Step-by-step explanation:

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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)

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