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4 years ago

Factor completely: 2x^3 – 32x

Mathematics

1 answer:

anastassius [24]4 years ago

7 0

$2x^3-32x= \\
2x(x^2-16)= \\
2x(x^2-4^2)= \\
\boxed{2x(x+4)(x-4)} \Leftarrow
\hbox{answer B}$

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3 years ago

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Factor completely 2x2 + 28x + 96.

Evgesh-ka [11]

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2x²+28x+96

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4 years ago

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how much antifreeze 25% antifreeze and 50% antifreeze should be combined to give 40 gallon of 30% antifreeze?

VARVARA [1.3K]

32 gallons of 25 % antifreeze should be combined with 8 gallons of 50 % antifreeze to get 40 gallon of 30% antifreeze

<h3><u>Solution:</u></h3>

From given,

Final mixture is 40 gallon

Let "x" be the gallon of 25 % antifreeze

Then, (40 - x) is the gallon of 50 % antifreeze

Therefore, according to question,

"x" gallons of 25 % antifreeze should be combined with (40 - x) gallons of 50 % antifreeze to get 40 gallon of 30% antifreeze

<h3><u>Therefore, we frame a equation as:</u></h3>

25 % of x + 50 % of (40 - x) = 30 % of 40

Solve for "x"

$\frac{25}{100} \times x + \frac{50}{100} \times (40-x) = \frac{30}{100} \times 40\\\\0.25x + 0.5(40-x) = 12\\\\0.25x + 20 - 0.5x = 12\\\\0.25x - 0.5x = 12 - 20\\\\-0.25x = -8\\\\0.25x = 8\\\\Divide\ both\ sides\ by\ 0.25\\\\x = 32$

Thus, 32 gallons of 25 % antifreeze is used

Then, (40 - x) = (40 - 32) = 8

Thus 8 gallons of 50 % antifreeze is used

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3 years ago

Afla un numar,stiind ca: a)jumatatea treimii lui este 25; b)sfertul jumatatii lui este 48; c)treimea sfertului sau,marita cu 17

aalyn [17]

Answer:

(a) 150

(b) 384

(c) 84

(d) 261

(e ) 480

Step-by-step explanation:

(a)

Let 'a' be a number such that the half of his third is 25; i.e.

$\dfrac{1}{2}\times(\dfrac{1}{3}a)=25\\\\\dfrca{1}{2\times3}a=25\\\\\dfrac{1}{6}\times a=25\\\\a=25\times6\\\\a=150$

Hence, the number is 150.

(b)

Let 'b' be the number such that the quarter of his half is 48 i.e.

$\dfrac{1}{4}(\dfrac{1}{2}b)=48\\\\\dfrac{1}{8}b=48\\\\b=48\times8\\\\b=384$

Hence the number is 384.

(c)

Let 'c' be the number such that the third quarter or, increased by 17 is 80.

$\dfrac{3}{4}c+17=80\\\\\dfrac{3}{4}c=80-17\\\\\dfrac{3}{4}c=63\\\\c=\dfrac{63\times4}{3}\\\\c=\dfrac{252}{3}\\\\c=84$

Hence, the number is 84.

(d)

Let 'd' be the number such that its triplet, reduced by 28 is 755

$3d-28=755\\\\3d=755+28=783\\\\d=\dfrac{783}{3}\\\\d=261$

Hence the number is 261.

Let 'e' be the number such that double his third, increased by 80 is 400.

$\\2\dfrac{1}{3}e+80=400\\\\\dfrac{2}{3}e=400-80=320\\\\e=\dfrac{320\times 3}{2}\\\\e=\dfrac{960}{2}\\\\e=480$

Hence, the value of the number is 480.

4 0

4 years ago