I need help solving x^2+3xy-y^2=12 and x^2-y^2=-12

Answers

Answer 1

Answer: $substitute:x^2-y^2=-12\ to\ x^2+3xy-y^2=12\n\n3xy-12=12\n3xy=12+12\n3xy=24\ \ \ \ \ /:3\nxy=8\to x=(8)/(y)\n\nsubstitute\ to\ x^2-y^2=-12\n\n\left((8)/(y)\right)^2-y^2=-12\n\n(64)/(y^2)=y^2-12$

$(64)/(y^2)=(y^2-12)/(1)\n\ny^2(y^2-12)=64\n\ny^4-12y^2-64=0\n\nsubstitute:y^2=t > 0\n\nt^2-12t-64=0$

$a=1;\ b=-12;\ c=-64\n\Delta=b^2-4ac\to\Delta=(-12)^2-4\cdot1\cdot(-64)=144+256=400\n\nt_1=(-b-\sqrt\Delta)/(2a);\ t_2=(-b+\sqrt\Delta)/(2a)\n\n\sqrt\Delta=√(400)=20\n\nt_1=(12-20)/(2\cdot1)=(-8)/(2)=-4 < 0;\ t_2=(12+20)/(2\cdot1)=(32)/(2)=16\n\ny^2=16\Rightarrow y=\pm√(16)\Rightarrow y=-4\ or\ y=4\n\nx=(8)/(-4)=-2\ or\ x=(8)/(4)=2\n\nSolution:x=-2\ and\ y=-4\ or\ x=2\ and\ y=4$

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Answers

the answer to that would be 5 !!!!

Robin randomly selects a number between 1 and 20. What is the probability that the number selected is the square of a natural number?a.1/2
b.-3/20
c.-3/10
d.1/5
e.1/3

Answers

Answer: d. $(1)/(5)$

Step-by-step explanation:

The square number between 1 and 20 = 1,4,9,16

The number of squares between 1 and 20 = 4

The total numbers between 1 and 20= 20

The probability that the number selected is the square of a natural number is given by :-

$P=\frac{\text{square numbers}}{\text{total numbers}}\n\n\Rightarrow\ P=(4)/(20)=(1)/(5)$

Hence, The probability that the number selected is the square of a natural number is $(1)/(5)$

D is I am pretty sure

Change the radians to degrees

Answers

the method of changing a degree to a radian is to multiply with 1/180

Which of these is the algebraic expression for "nine less than some number?"Fraction 9 over k
Fraction k over 9
9 − k
k − 9

Answers

The answer is k - 9.

Answer:

K - 9

I TOOK THE TEST AND GOT IT RIGHT!!

PLSSSS HELP IF YOU TULRY KNOW THISSS

Answers

Answer:

Step-by-step explanation:

Rearrange terms: -3x+4=6-3x

-3x+4=-3x+6

Subtract 4 from both sides

-3+4-4=-3x+6-4

Subtract the numbers

=3x==3x+2

Add 3x to both sides

=3x+3x=-3x+2+3x

-3x+3x=-3x+2+3x= 0=2 which is no solution

Simplify. 17 – 6 × 10 ÷ 2 + 12

Answers

use PEMDAS.

17-(6×10÷2)+12

6×10=60 divide by 2 to get 30

now: 17-30+12
17-30=-13
-13+12=-1

Answer:-

Simplify: $17-6 * 10 / 2 +12$

PEMDAS rule acronym as

P -Parenthesis

E - Exponent

M -Multiplication

D - Division

A - Addition

S - subtraction

Now, follow the rule to simplify the expression:

$17-6 * 10 / 2 +12$

According to the PEMDAS rule,

First we multiply the numbers 6 and 10 we have;

$17-60 / 2 +12$

Now, divide the number 60 by 2 we get;

$17-30+12$

Now, Add the numbers 17 and 12 we have

$29-30$

Now, subtract the numbers 29 and 30; we get

-1

Therefore, the simplified expression of $17-6 * 10 / 2 +12$ according to the PEDMAS rule is, -1

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