All categories

3 years ago

Factor each expression

1 answer:

8 0

1 -since everything includes 4a, we can factor that to get 4a(a-4b^3+2b^2c)
2 - since 5 and 3 add to 8 and multiply to 15, we can do (n+5)(n+3)
3 - since -5 and -4 add to -9 and multiply to 20, we can do (g-5)(g-4)
4 - since -10 and 3 add to -7 and multiply to 30, we can do (z-10)(z+3)
5 - we can factor out 4y to get 4y(y^2-9).

I got the numbers in 2, 3, and 4 with a guesstimating and checking approach

You might be interested in

Which equation best represents the data shown in the scatter plot below?

ELEN [110]

Answer:

Step-by-step explanation:

6 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

4 years ago

Which of the following Statements are true?

choli [55]

Answer: Only Statement 1 is True.

Step-by-step explanation:

A box is essentially a rectangular prism, which has 8 corners. Tubes, pipes, and cans are cylinders because the corss-section of them are circular and the connection between the bases are parallel.

8 0

2 years ago

A garden has a width of 24 feet and a diagonal length of 51 feet. What is the perimeter of the garden ( in feet )?

bekas [8.4K]

Answer:

1,224 feet

Step-by-step explanation:

Multiply 51 feet times 24 feet and then you get 1,224 ft.

3 0

3 years ago

Which expresses 1050 : 2000 in decimal form

MatroZZZ [7]

Answer: 10.5 : 20.2

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers