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3 years ago

Factor as a product of two binomials x2-x-72

Mathematics

1 answer:

Natasha_Volkova [10]3 years ago

4 0

Answer:

(x - 9)(x + 8)

Step-by-step explanation:

Given

x² - x - 72

Consider the factors of the constant term (- 72) which sum to give the coefficient of the x- term (- 1)

the factors are - 9 and + 8, since

- 9 × 8 = - 72 and - 9 + 8 = - 1, thus

x² - x - 72 = (x - 9)(x + 8)

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3 years ago

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A truck is being filled with cube-shaped packages that have side lengths of 1/4 foot. The part of the truck that is being filled

n200080 [17]

Answer:

24000 pieces.

Step-by-step explanation:

Given:

Side lengths of cube = $\frac{1}{4} \ foot$

The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.

Question asked:

What is the greatest number of packages that can fit in the truck?

Solution:

First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.

$Volume\ of\ cube =a^{3}$

$=\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot$

Length = 8 foot, Breadth = $6\frac{1}{4} =\frac{25}{4} \ foot$ , Height = $7\frac{1}{2} =\frac{15}{2} \ foot$

$Volume\ of\ rectangular\ prism =length\times breadth\times height$

$=8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot$

The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube

The greatest number of packages that can fit in the truck = $\frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube$

Thus, the greatest number of packages that can fit in the truck is 24000 pieces.

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3 years ago

Hund’s rule of maximum multiplicity specifies that _____. A. electrons will fill orbitals of lower energy first, pairing up only

djverab [1.8K]

Answer:

A. electrons will fill orbitals of lower energy first, paring up only after each orbital of the same energy already has one electron

Step-by-step explanation:

The rule states that for a given electron configuration, the lowest energy term is the one with the greatest value of spin multiplicity. This implies that if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pairs.

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4 years ago

The area of the triangle below is 8.91 square inches. What is the length of the base?

Studentka2010 [4]

Answer:

8.1 inches

Step-by-step explanation:

Area of a triangle = ½ × base × height = Area

Rearranged =

$\frac{area}{ \frac{1}{2} \times height}$