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2 years ago

Please factor completely: 20x^2 - 102x + 54

Mathematics

1 answer:

Temka [501]2 years ago

5 0

Answer:

The answer to your question is 2(x - 9/2)(x - 3/5)

Step-by-step explanation:

Polynomial 20x² - 102x + 54

Process

1.- Find the Greatest Common Factor

20 102 54 2

10 51 27 2

5 51 27 3

5 17 9 3

5 17 3 3

5 17 1 5

1 17 17

GCF = 2

2.- Factor 2

2(10x² - 51x + 27)

3.- Factor 10x² - 51x + 27

Use the general formula to solve this equation

x = $\frac{-b +- \sqrt{b^{2} - 4ac}}{2a}$

a = 10 b = -51 c = 27

x = $\frac{51 +- \sqrt{51^{2} -4(10)(27)}}{2(10)}$

-Simplification

x = $\frac{51 +- 39}{20}$

-Result

x₁ = 9/2 x₂ = 3/5

(x - 9/2) (x - 3/5)

4.- Answer

2(x - 9/2)(x - 3/5)

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Mary walks from comer D to comer E to comer F on a city block that measures 264 feet wide and 900 feet long. Kate walks

Y_Kistochka [10]

Answer:

Difference between the distances traveled by Mary and Kate = 226 feet

Step-by-step explanation:

By applying Pythagoras theorem in right ΔDEF,

(DE)² + (EF)² = (DF)²

By substituting DE = 264 feet and EF = 900 feet

(264)² + (900)² = (DF)²

DF = √(69696+810000)

= √879696

= 937.92

Distance traveled by Kate diagonally = 938 feet

Distance traveled by Mary = DE + EF

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= 1164 feet

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= 1164 - 937.92

= 226.07

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3 0

2 years ago

Question in attachment

sdas [7]

Answer:

a₁ = 6

Step-by-step explanation:

The sum to n terms of a geometric sequence is

$S_{n}$ = $\frac{a_{1}(r^{n}-1) }{r-1}$

where a₁ is the first term and r the common ratio

Here $S_{8}$ = 1530 and r = 2, thus

$\frac{a_{1}(2^{8}-1) }{2-1}$ = 1530 , that is

a₁ (256 - 1) = 1530

255a₁ = 1530 ( divide both sides by 255 )

a₁ = 6

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3 years ago

At noon Joyce drove to the lake at 30 miles per hour. but she made the long walk back home at 4 miles per hour. How long did she

mars1129 [50]

Answer:

60 miles

Step-by-step explanation:

let d = distance to the lake

Using: time = distance ÷ speed

Create expressions for the time it takes for each journey:

Drive: $t_1=\dfrac{d}{30}$

Walk: $t_2=\dfrac{d}{4}$

If total time = 17 hours

$\implies t_1+t_2=17$

$\implies \dfrac{d}{30}+\dfrac{d}{4}=17$

$\implies \dfrac{17d}{60}=17$

$\implies 17d=1020$

$\implies d=\dfrac{1020}{17}$

$\implies d=60$

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