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Korvikt [17]
3 years ago
12

Solve the equation with special factors. (Please show all steps) 16q^2 - 81 = 0

Mathematics
2 answers:
steposvetlana [31]3 years ago
6 0

Answer:

q = ± \frac{9}{4}

Step-by-step explanation:

16q² - 81 = 0 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

16q² - 81 = 0

(4q)² - 9² = 0

(4q - 9)(4q + 9) = 0

Equate each factor to zero and solve for q

4q - 9 = 0 ⇒ 4q = 9 ⇒ q = \frac{9}{4}

4q + 9 = 0 ⇒ 4q = - 9 ⇒ q = - \frac{9}{4}

guapka [62]3 years ago
5 0

Answer: q=\frac{\sqrt{81}}{16}

Step-by-step explanation:

16q^2-81=0\\16q^2=0+81=81\\16q=\sqrt{81} \\q=\frac{\sqrt{81}}{16}

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1.2%

Step-by-step explanation:

We know that for every 500 computers, 6 are defective. So, to know what percentage of computers are defective on average, we can do a rule of three:

500 computers -> 6 defective

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500/100 = 6/X

X = 100 * 6 / 500 = 1.2

So, in average, for every 100 computers, 1.2 are defective, so the percentage is 1.2% (1.2 for every 100)

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9x-18=5x+2

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Step-by-step explanation:

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sdas [7]

Answer:

Based on the model, the length of the wall is \frac{9}{8} ft, the width of the wall is \frac{1}{2} ft,  and the height of the wall is \frac{11}{8} ft. The volume of the portion of security wall that  Tim has constructed so far is \frac{99}{128}  cu ft.

Step-by-step explanation:

Given:

The figure constructed shows a rectangular prism made up of small wooden cubes of length \frac{1}{8}\ ft.

Width of the prism = \frac{1}{2}\ ft.

To find length , height and volume of the figure.

Solution:

From the figure we can conclude that :

Length side of the prism counts 9 cubes.

Thus, length of the prism will be given as :

⇒ \textrm{Length of each cube}\times \textrm{Number of cubes}

⇒ \frac{1}{8}\ ft\times 9

⇒ \frac{9}{8}\ ft  (Answer)

Height side of the prism counts 11 cubes.

Thus, height of the prism will be given as :

⇒ \textrm{Length of each cube}\times \textrm{Number of cubes}

⇒ \frac{1}{8}\ ft\times 11

⇒ \frac{11}{8}\ ft (Answer)

Volume of the prism can be given as :

⇒ Length\times width\times height

⇒ \frac{9}{8}\ ft\times \frac{1}{2}\ ft\times \frac{11}{8}\ ft

⇒ \frac{99}{128}\ ft^3 (Answer)

7 0
3 years ago
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