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3 years ago

Write a two column proof.

Mathematics

1 answer:

sineoko [7]3 years ago

3 0

Step-by-step explanation:

HJ ≅ JH, by symmetric property of equality.

ΔGHJ ≅ ΔIJH, by SAS congruence.

GJ ≅ IH, corresponding parts of congruent triangles are congruent.

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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 dozen muffins costs $5. Large bottles

notka56 [123]

Answer: Option D) 3 x 5 + 4 x 2

Step-by-step explanation:

- Since a dozen muffins costs $5.

Buying 3 dozen muffins means (3 x $5)

- Since Large bottles of juice cost $2.

The cost of 4 large bottles of juice is (4 x $2)

Hence, the total cost is (3 x $5) + (4 x $2)

= $15 + $8

= $23

Now, you'll notice that "3 x 5 + 4 x 2" gives 23.

Thus, it is the only expression that could be used to find the total cost.

5 0

3 years ago

What is the answer to the equation 13=1/6y + 2x

Eddi Din [679]

13=1/6y+2x
-1/6y -1/6y
-1/6y+13=2x
-13 -13
-1/6y=2x-13
*-6 *-6
y=-12x-13

*I multiply it by -6 because -6 is the reciprocal of -1/6, and I can't divide -1/6, actually I can, but it just going to be more confusing that way, and the fastest way to get rid of the -1/6 when you solving this type of equation is multiply it by its reciprocal.

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3 years ago

Can 72/15 be simplified? Tell me what the number is in YOUR ANSWER. Please and thank you!

Snezhnost [94]

Answer:

4.8

Step-by-step explanation:

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3 years ago

Write th number of permutations in factorial form. then simplify. How many different ways can you and six of your friends sit in

kolbaska11 [484]

The answer is D. The answer is D because when It is simplified 7?49. The answer is the only possible answer could be correct since the rest of their maths don't add up.
C
A 
C 
D 
D 
B 
D 
B 
C

8 0

3 years ago