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3 years ago

-4x + (-2) = 3x + (-5)

Mathematics

1 answer:

slamgirl [31]3 years ago

7 0

Answer:

Let x = 1

LHS: -4(1)+(-2)=-4+(-2)=-6

RHS:3(1)+(-5)=3+(-5)=-2

Therefore -4x+(-2) is not equal to 3x+(-5)

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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)

4 0

3 years ago

Use the reference angles to find the exact value of the expression cot -11 pi/6. Do not use a calculator

laiz [17]

Answer:

$\sqrt{3}$

Step-by-step explanation:

cot(-11pi/6)=cot(-pi-5pi/6)= -cot(5pi/6)=cot(pi/6)= $\sqrt{3}$ ≈1.73

7 0

3 years ago

Twice the sum of 15 and a number

pashok25 [27]

2(15+N)

replace a number by N

replace the sum of 15 and N by (15+N)

and lastly, replace twice by 2

So your answer is 2(15+N)

7 0

3 years ago

Read 2 more answers

Does anyone know how to do this?

xeze [42]

Answer:

Step-by-step explanation:

6 0

3 years ago

What is the area , in square meters of the shaded part of the rectangle below

Licemer1 [7]

Answer:

123.5 m^2

Step-by-step explanation:

The area of the whole rectangle is 9 x 19 = 171 m^2

The area of the region that isn't shaded is (5 x 19)/2 = 47.5 m^2 because the height of the triangle is 5 (9 - 4) and the area of a triangle is

(height x length)/2

171 - 47.5 = 123.5 m^2

4 0

3 years ago