Which of the following is the same as 2.3 times 10 to the third power

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

Find the leg (in inches) of the triangle whose hypotenuse is 10 inches and whose other leg is 3.25 inches. Round to the nearest

alekssr [168]

Answer:

Other Side (B) = 9.45 inches

Step-by-step explanation:

Given:

Hypotenuse = 10 inches

Other Side (A) = 3.25 inches

Find:

Other Side (B) = ?

Computation:

According to Pythagoras theorem:

$Hypotenuse^2= (Perpendicular)^2+(Base)^2\\\\Hypotenuse^2= (A)^2+(B)^2\\\\10^2= (3.25)^2+(B)^2\\\\100=10.5625 +(B)^2\\\\89.4375 = (B)^2\\\\B=\sqrt{89.4375}\\\\B=9.4571$

Other Side (B) = 9.45 inches

7 0

3 years ago

Which of the expressions are equivalent to the one below? Check all that

garik1379 [7]

Hi hi!!

So, A is correct because it is the same equation just (3+4) is in the front. D is also correct because it is the same question because when a number is for example like 10(3+4) it mean multiplication and in this case you are multiplying. B and C are incorrect because they do not have a total of 70. The original equation, 10x(3+4) = 10x7 = 70.

Correct answers:

A. (3+4)x10
D. 10(4+3)

4 0

3 years ago

In how many ways can 100 identical chairs be distributed to five different classrooms if the two largest rooms together receive

Eva8 [605]

Answer:

There are 67626 ways of distributing the chairs.

Step-by-step explanation:

This is a combinatorial problem of balls and sticks. In order to represent a way of distributing n identical chairs to k classrooms we can align n balls and k-1 sticks. The first classroom will receive as many chairs as the amount of balls before the first stick. The second one will receive as many chairs as the amount of balls between the first and the second stick, the third classroom will receive the amount between the second and third stick and so on (if 2 sticks are one next to the other, then the respective classroom receives 0 chairs).

The total amount of ways to distribute n chairs to k classrooms as a result, is the total amount of ways to put k-1 sticks and n balls in a line. This can be represented by picking k-1 places for the sticks from n+k-1 places available; thus the cardinality will be the combinatorial number of n+k-1 with k-1, ${n+k-1 \choose k-1}$ .

For the 2 largest classrooms we distribute n = 50 chairs. Here k = 2, thus the total amount of ways to distribute them is ${50+2-1 \choose 2-1} = 51$ .

For the 3 remaining classrooms (k=3) we need to distribute the remaining 50 chairs, here we have ${50+3-1 \choose 3-1} = {52 \choose 2} = 1326$ ways of making the distribution.

As a result, the total amount of possibilities for the chairs to be distributed is 51*1326 = 67626.

7 0

3 years ago

It is not B so plz help me

11111nata11111 [884]

Answer:

The picture is blocked out D:

Step-by-step explanation:

6 0

3 years ago

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