What is the length of LN in the right triangle below?

Answer:   [tex]\boldsymbol{-25+18\sqrt{2}}[/tex]

The expression is in the form [tex]a+b\sqrt{2}[/tex] where a = -25 and b = 18

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Work Shown:

Let [tex]x = 3\sqrt{2}[/tex] and then square both sides

[tex]x = 3\sqrt{2}\\\\x^2 = \left(3\sqrt{2}\right)^2\\\\x^2 = \left(3\right)^2*\left(\sqrt{2}\right)^2\\\\x^2 = 9*2\\\\x^2 = 18\\\\[/tex]

We'll use both x and x^2 later on.

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The denominator is in the form 4+x. We'll multiply top and bottom by 4-x to then use the difference of squares rule. This will allow us to eliminate the square root in the denominator.

[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}}\\\\\frac{8-x}{4+x}\\\\\frac{(8-x)(4-x)}{(4+x)(4-x)}\\\\\frac{32-8x-4x+x^2}{16-x^2} \ \text{ difference of squares rule}\\\\\frac{32-12x+x^2}{16-x^2}\\\\[/tex]

[tex]\frac{32-12*3\sqrt{2}+18}{16-18} \ \text{ plug in } x = 3\sqrt{2} \text{ and } x^2 = 18\\\\\frac{50-36\sqrt{2}}{-2}\\\\\frac{-2(-25+18\sqrt{2})}{-2}\\\\\boldsymbol{-25+18\sqrt{2}}[/tex]

Therefore,

[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}}=\boldsymbol{-25+18\sqrt{2}}[/tex]

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Checking the answer:

Use a calculator to find that,

[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}} \approx 0.45584412271571 \\\\-25+18\sqrt{2} \approx 0.45584412271571[/tex]

We get the same decimal approximation, which helps confirm the correct answer.

Or you could use the idea that if M = N, then M-N = 0 to subtract the original expression M and the final result N. You should get 0 or very close to it.

Answer:

2,572,800

Step-by-step explanation:

I hope this helps!

Answer: 40 x 40 x 402 x 2 x 2 =128,640

Answer:

y= -x-6/2

Step-by-step explanation:

Given,

x+2y=-6

or,2y=-x-6 (cross multiplication)

or,y= -x-6/2

Answer:

$0.05

Step-by-step explanation:

1.25/25=0.05

Answer:

the data that is shown represents a function

Step-by-step explanation:

the easiest way to know is by looking at the x-variable. Each y-variable needs one x-variable. the x-variable should not be seen paired with another y-variable.

Answer:

Each shelf can hold 20 boxes of cereal.

Step-by-step explanation:

Start with 80 boxes of cereal: (80)

There are 4 shelves for each box of cereal: (x/4)

Thus, we get the expression: 80/4=

(You may want to simplify this; giving you the answer of 20.)

Answer: 8.26

Step-by-step explanation:

Should I Explain How I got it?

132.16 divided by 16 is equal to 8.26.

Here, we have,

given that,

132.16 divided by 16

so, we have, 132.16 ÷ 16

To find the quotient of 132.16 divided by 16,

we can perform long division:

    8.26

____________

16 | 132.16

112

____________

20

Therefore, 132.16 divided by 16 is equal to 8.26.

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Answer:

[tex]horizontal : 76 \\ \\ \\ vertical : 33 \\ \\ pls \: check \: this \: answer \\[/tex]

Answer Interest rate = 12.3%

The compound interest formula is given by:

Where

A = Future amount

P = Present amount (Principal amount)

r = Interest rate in decimal form

n = No. of times compounded per year

t = time in years.

We can say that if:

Present amount = P

Future amount = 3P

r = 12.3/100 = 0.123

n = 1

t = ?

Substitute the values in the formula of compound interest:

Taking log on both sides.

Round off to nearest option

t ≅ 9 years

113

Hope this helped you- have a good day bro cya)

Answer:

42

Step-by-step explanation:

Answer:

Marci answered 40 out of 50

Marci answered 2 more questions correctly.

Step-by-step explanation:

Donovan got 38 out of 50

Marci got 80% which means 40 out of 50

40-38 = 2

Given points are P(4,m) and Q(-2,4)

Let (x1, y1) = P(4,m)

Where, • x1 = 4 and • y1 = m

Let (x2, y2) = Q(-2,4)

Where, • x2 = -2 and • y2 = 4

We know that

The coordinates of the mod point of the linesegment joining the points (x1, y1) and (x2, y2)

is M(x,y) = ( {x1+x2}/2 , {y1+y2}/2 )

Mid point of the linesegment PQ

⇛M(x,y) = ( { 4+(-2)}/2 ,{m+4}/2)

⇛M(x,y) = {(4-2)/2 , {m+4}/2)

⇛M(x,y) = (2/2,{m+4}/2)

⇛M(x,y) = (1,{m+4}/2)

According to the given problem

Mid point of PQ = C(n,-1)

M(x,y) = C(n,-1)

(1,{m+4}/2) = (n,-1)

On Comparing both sides then

1 = n and (m+4)/2 = -1

n = 1 and m+4 = -2

n = 1 and m = -2-4

n = 1 and m = -6

Hence, the value of m&n will be (1&-6) respectively.

Additional comment:

The coordinates of the mod point of the linesegment joining the points (x1, y1) and (x2, y2)

is M(x,y) = ( {x1+x2}/2 , {y1+y2}/2 )

also read similar questions: Given that rectangle LMNO with coordinates L(0,0), M(3,0), N(3,7), O(0,7), P is the midpoint of LM⎯⎯⎯, and Q is the midpoint of NO⎯⎯⎯, which of the following pr...

https://brainly.com/question/25188846?referrer

We have:   2log₃(8) - 3log₃(2) = 2log₃(8) - log₃(2³)

= 2log₃(8) - log₃(8) =  log₃(8)

= 1,892789261 ≈ 1,9

ok done. Thank to me :>

Answer:

~1.8928 or 3log_3 (2)

Step-by-step explanation:

change 8 to 2^3 and move to front

=2*3log_3 (2) -3log_3 (2)

=6log_3 (2) -3log_3 (2)

with subtraction

=3log_3 (2)

approx with calculator

~1.8928

Answer:

y=2x-5/2

Step-by-step explanation:

f(x)=(2x+5)/4

y=(2x+5)/4

-----------------

x=(2y+5)/4

2y+5=4*x

2y+5=4x

2y=4x-5

y=4/2x-5/2

y=2x-5/2

Answer:

c. m < 13

Step-by-step explanation:

13 - 7 is equal to 6 so m must be less than 13 to be less than 6.

Answer:

it is (3/8)( -5/7)(-1/4)

if ot it should be the one that is all postitive

The inequalities which the number lines represent are as follows;

While writing inequalities represented on a number line;

We must observe the direction of the line; and also observe the shading on the starting point of the line.

In case 1:

In case 2:

The number line to represent the street sign is as in the attached image;

Read more on number line and inequalities:

https://brainly.com/question/1478009

Answer:

it would have snowed 1 2/5 feet more the previous day than the current day.

[tex]4x^2-9x = 2x^2 -2x -4\\\\\implies 4x^2 -9x -2x ^2 +2x +4 =0\\\\\implies 2x^2 -7x +4=0\\\\\text{Apply quadratic formula,}~ x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}.\\\\\text{In this case,} ~a =2, b = -7 ~ \text{and}~ c =4\\\\\\x =\dfrac{-(-7) \pm \sqrt{(-7)^2 - 4 \cdot 2 \cdot 4}}{2(2)}\\\\\\\implies x = \dfrac{7 \pm \sqrt{17}}4\\\\\\\text{Hence,}~ x = \dfrac{7 +\sqrt{17}}4~ \text{and}~x = \dfrac{7 -\sqrt{17}}4[/tex]

Therefore, the answer is 3/10.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer:

9x + 1 = 7x - 8x + 4

9x + 1 = -x + 4

9x + 1 - 1 = -x + 4 - 1

9x = -x + 3

9x + x = -x + 3 + x

10x = 3

x = 3/10

Answer:

6

Step-by-step explanation:

If p = 14

rewrite the equation

so replace the variable with 14.

now do basic subtraction.

14 - 8

= 6

The measure for angle W is 80 degree.

A unrestricted polygon or figure with four sides, four corners, and four angles is called a trapezium. Each brace of a trapezium's opposing sides is resemblant to the other.

Similar to other quadrilaterals, the trapezium's four angles add up to 360°. Two of the sides of a trapezium are parallel, and the other two are not. Regular trapezium diagonals cut each other in half.

Given:

We have angles <X= 100, <Y = 130 and <Z= 66.

As, we know that in Trapezium the sum of adjacent angle is 180.

So, <X + <W = 180

100 + <W =180

<W= 180- 100

<W = 80 degree.

Learn more about Trapezium here:

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