Statements and reasonings 2(4x+2)=20

A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is___ units. The point (

Pachacha [2.7K]

<span>A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is 5_ units. The points(-7,5) and (-7,-1</span>) lie on this circle.

3 0

2 years ago

Read 2 more answers

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

2 years ago

A television is 28.5 inches wide and 16 inches long.

Umnica [9.8K]

Answer:

33 in

Step-by-step explanation:

The Pythagorean theorem tells you ...

diagonal² = length² +width²

diagonal² = (16 in)² +(28.5 in)² = 1068.25 in²

diagonal = √(1068.25 in²) ≈ 32.684 in

The diagonal of the television is about 33 inches.

7 0

2 years ago

780 students stand in rows and columns. each row has an equal number of students and each column has an equal number of students

Alex73 [517]

Answer:

Step-by-step explanation:

x = number of rows

780=x(x+4)

$780=x^{2} +4x$

$x^{2} +4x-780=0\\(x+26)(x-30)=0\\x=30 \\x\neq -26\\$

there are 26 rows and 30 students in each row 26*30=780

8 0

2 years ago

The commission earned on the sale of a car can be represented by the equation c(p)=250+0.02p where c represents the commission a

ch4aika [34]

Answer:

1) His total commission is $1,234.3

2) The purchase of the car is $24,790.

Step-by-step explanation:

1) 21640*0.02= 432.8+ 250= 682.8

15075*0.02= 301.5+ 250= 551.5

682.8+ 551.5= 1,234.3

2) 745.8- 250= 495.8/ 0.02= 24,790

6 0

2 years ago

Read 2 more answers