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3 years ago

The second largest prime factor of 38 is

Mathematics

2 answers:

viva [34]3 years ago

8 0

The second largest prime factor is 19

Kobotan [32]3 years ago

6 0

I'll post one, because I disagree with everybody so far.

All the factors of 38 are 1, 2, 19, and 38.

The primes are 2 and 19.

The second largest prime factor is 2 .

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If x+y=12 and xy=15,find the value of (x^2+y^2)

Mice21 [21]

Answer: $x^2+y^2=\dfrac{105\pm 18\sqrt6}{2}$

<u>Step-by-step explanation:</u>

EQ1: x + y = 12 --> x = 12 - y

EQ2: xy = 15

Substitute x = 12-y into EQ2 to solve for y:

(12 - y)y = 15

12y - y² = 15

0 = y² - 12y + 15

↓ ↓ ↓

a=1 b= -12 c=15

$.\ y=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\.\quad =\dfrac{-(-12)\pm \sqrt{(-12)^2-4(1)(15)}}{2(1)}\\\\\\.\quad =\dfrac{12\pm \sqrt{144-120}}{2}\\\\\\.\quad =\dfrac{12\pm \sqrt{24}}{2}\\\\\\.\quad =\dfrac{12\pm 2\sqrt{6}}{2}\\\\\\.\quad =6\pm \sqrt{6}$

Now, let's solve for x:

$xy=15\\\\x(6\pm\sqrt6)=15\\\\x=\dfrac{15}{6\pm\sqrt6}\\\\\\x=\dfrac{15}{6\pm\sqrt6}\bigg(\dfrac{6\pm\sqrt6}{6\pm\sqrt6}\bigg)=\dfrac{6\pm \sqrt6}{2}$

Lastly, find x² + y² :

$y^2=(6\pm \sqrt6)^2\quad \rightarrow \quad y^2=36\pm 12\sqrt6 +6\quad \rightarrow \quad y^2=42\pm 12\sqrt6$

$x^2=\bigg(\dfrac{6\pm \sqrt6}{2}\bigg)^2\quad \rightarrow \quad x^2=\dfrac{42\pm 12\sqrt6}{4}\quad \rightarrow \quad x^2=\dfrac{21\pm 6\sqrt6}{2}$

$x^2+y^2=\dfrac{21\pm 6\sqrt6}{2}+42\pm 12\sqrt6\\\\\\.\qquad \quad = \dfrac{21\pm 6\sqrt6}{2}+\dfrac{84\pm 24\sqrt6}{2}\\\\\\. \qquad \quad = \dfrac{105\pm 18\sqrt6}{2}$

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3 years ago

A 140-meter rope is cut into two pieces. One piece is four times as long as the other. How long is each piece?

grandymaker [24]

Answer:

28meters and 112meters

Step-by-step explanation:

one piece is x

the other is 4x

therefore; 4x+x=140

5x= 140

divide both sides by 5

x=28

4x=4(28)

=112

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2 years ago

What is x in the equation x+3=9

densk [106]

Answer:

x=6

Step-by-step explanation:

x+3=9

x+3-3=9-3

x=6

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2 years ago

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3x+6y=36 and -3x-6y=0

Anastasy [175]

Answer:

No solution

Step-by-step explanation:

3x + 6y =36

-3x - 6y =0

------------------add

0 ≠ 36

No solution

4 0

3 years ago

During the summer , you want to earn at least $150 per week. You can earn$10 per hour working for a farmer, and $5 per hour baby

almond37 [142]

X = nr. hrs working for a farmer;
y = nr. hrs. babysitting;
x + y <= 25;
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a) Solve the system => one of the solution is x =5; y = 20(babysitting)
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3 years ago

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