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lina2011 [118]
3 years ago
11

Can you help me with number. 9

Mathematics
1 answer:
Ymorist [56]3 years ago
6 0
All you have to do is subtract the two degrees to get your answer
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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}

5 0
3 years ago
Cynthia ran 4 laps in 40 minutes. Which ratio represents the number of laps ran to minutes?
poizon [28]
4:40 simplifies into 1:10
4 0
3 years ago
Write the equation of a horizontal line that passes through the point (3,-3)
Artist 52 [7]
Y= mx+b

Since this line is horizontal it's slope = 0 ==> the y=b

It passes by the point (3,-3) that means b=-3 & the equation is y=-3
3 0
3 years ago
Can anyone help me answer this?
netineya [11]
We need to know how much tax she must pay based on her taxable income ,
Since un the table it states that taxable incomes that range between $0-$132000have a tax rate of 18% of each $1 .
We already know her taxable income that is = 129000, which ranges between 0 and 132000.
Hence we know how much tax she must pay .
First , we need to calculate how much 18% of $1 is
= 18/100 x 1 = $0.18
Per annum/year = $0.18 x $129,000 = $23,220

Per month = $23,220 / 12 = $1,935

Hope you found this helpful , good luck !
7 0
2 years ago
Read 2 more answers
Brittany is at a restaurant. Her bill is $48 plus 15%. She gave an $100. How much did she get back?
DanielleElmas [232]
She got 44.80 dollars back
4 0
3 years ago
Read 2 more answers
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