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3 years ago

Mathy math. Domain and range. Functions

Mathematics

1 answer:

iogann1982 [59]3 years ago

6 0

Answer:

Its A

Step-by-step explanation:

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

Mice21 [21]

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

Step-by-step explanation:

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

A baker is making croissants. He has 18 pounds of dough. Each croissant is made from 1/6 pounds of dough. How many croissants ca

Black_prince [1.1K]

Answer:The baker can make 144 croissants

Step-by-step explanation:

Lets solve your question

Divide the total amount of lbs of dough (18 lbs) by the total amount of dough for each croissant (1/8 lbs)

First divide 18(lbs) by 1/8 (lbs)

18/1/8= 18*8=144 croissants

7 0

2 years ago

Find the coordinates of the midpoint of (x,y) for A(9,1) and B(3,7)

tekilochka [14]

9514 1404 393

Answer:

(6, 4)

Step-by-step explanation:

The midpoint is found as the average of the coordinates of the end points.

M = (A +B)/2

M = ((9, 1) +(3, 7))/2 = (9+3, 1+7)/2 = (12, 8)/2

M = (6, 4)

The midpoint of segment AB is (x, y) = (6, 4).

5 0

3 years ago

You want to order a new computer. The manufacturer is offering a discount of 12% off the original price of the computer for stud

Scorpion4ik [409]

Answer:

x - 0.12x = 924 dollars

0.88x = 924

x = 924/0.88

x = $1050 (original price)

4 0

3 years ago

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2x+5y=10 x intercept= y intercept=

Stells [14]

Answer:

x= 0/-8

y= 0/5

Step-by-step explanation:

Brain-List?

5 0

3 years ago