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3 years ago

Solve for x and y:x = y =

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

5 0

Answer:

x = 15

y = 21

Step-by-step explanation:

*triangle sum theorem*

(6x - 11)° + (81)° + (x + 5)° = 180°

(7x - 6)° + (81)° = 180°

(7x)° + (75)° = 180°

(7x)° = (105)°

x = 15

________________

*vertical angle theorem* *triangle sum theorem*

(6x - 11)° + (4y - 18)° + (y + 14)° = 180°

(79°) + (4y + y) + (14 - 18)°

_________________________

(79)° + (5y - 4)° = 180°

(5y)° + (75)° = 180°

(5y)° = 105°

y = 21

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Find the value of sinY

Tatiana [17]

Answer:

$\frac{63}{65}$

Step-by-step explanation:

Please see the attached picture.

Let's find the value of the opposite side, XZ.

Applying Pythagoras' Theorem,

(XZ)² +(XY)²= (ZY)²

(XZ)² +16²= 65²

(XZ)²= 4225 -256 (bring constant to 1 side)

(XZ)²= 3969 (simplify)

Square root both sides,

XZ= $\sqrt{3969}$

XZ= 63 (simplify)

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= XZ/ ZY

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8 0

3 years ago

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

If time is four hours from now, the time left till midnight would be quarter that if it is one hour from now. What time is it no

lapo4ka [179]

Answer:

The time now is 7 pm

Step-by-step explanation:

Suppose that now is the time T.

We know that:

"if time is four hours from now, the time left till midnight would be a quarter that if it is one hour from now".

Then:

if we define midnight as 12, and we assume that T is in the pm range.

Then the "time left till midnigth, assuming that the time is four hours from now" will be written as (12 - (T + 4))

With this in mind, we can write the problem as:

12 - (T + 4) = (1/4)*( 12 - (T + 1))

Now we can solve this for T.

12 - T - 4 = (1/4)*(12 - T - 1)

8 - T = (1/4)*(11 - T)

4*(8 - T) = 11 - T

32 - 4*T = 11 - T

32 - 11 = -T + 4*T

21 = 3*T

21/3 = T

7 = T

Then T = 7 pm

The time now is 7 pm

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3 years ago

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Paha777 [63]

Answer:

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Step-by-step explanation:

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2 years ago

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Solve for x and y:x = y = ​

Solve for x and y:x = y =