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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.

Using it's formula, it is found that the slope of the line formed from the two given places is of [tex]\mathbf{\frac{6}{7}}[/tex]

Given two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex], the slope is given by change in y divided by change in x, that is:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this problem:

Hence, applying the formula for the slope, considering [tex](x_1, y_1) = (-1, -4)[/tex] and [tex](x_2,y_2) = (6,2)[/tex]:

[tex]m = \frac{2 - (-4)}{6 - (-1)} = \frac{6}{7}[/tex]

The slope is of [tex]\mathbf{\frac{6}{7}}[/tex]

A similar problem is given at https://brainly.com/question/5427529

Answer:

x<-3

Step-by-step explanation:

cheater bro wyd ur doing a diagnostic try ur best lol

Answer:

30/18=1 2/3 cups of popcorn in each bag

Hope This Helps!!!

Answer:

8x-24

Step-by-step explanation:

First you do:

8×x which is 8x

Then you do:

8×-3 which is -24

Then you put it into 1 expression:

8x-24

Answer:

8−24

Thank You!

Answer: I'd say the best answer is b.

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

1/4 is equal to 1.00 split into 4 equal parts. 0.25*4 = 1.00 , meaning that each 1/4 is equal to 0.25

Answer:

0.25.

Step-by-step explanation:

We divide 1 by 4:

4)  1. 00

    0.25

Step-by-step explanation:

I don't really know what demonstrating with rigid motion means, never heard that before. But a method for demonstrating it could be drawing circumferences of radius:

1) R1 = d(O,S)

2) R2 = d(O,J)

3) R3 = d(O,M)

With O being the origin of the reference system.

*Note: d(A,B) means distance between point A and point B

After you've done that you can show that the points S and P are on the same circumference, J and W are on the same circumference (different from the one of S and P), M and D are on the same circumference.

After you've done that you calculate the angle between the points on the same circumference and demonstrating that they are all the same.

Answer:

Step-by-step explanation:

Congruent

Shift right 1 unit and up 5 units

Rotate 90 degrees clockwise about (-1, 2)

Or

just rotate 90 degrees clockwise about (1, -1)

Answer:

find the vertical asymptote of the graph of f(×) = (×+3) +2.

Answer:

y = 3

x = 2

Step-by-step explanation:

-5x + 4y = 2

9x - 4y = 6

Sum both eq.

-5x + 9x = 4x

+4y - 4y = 0

2 + 6 = 8

then:

4x + 0 = 8

4x = 8

x = 8/4

x = 2

from the first eq.

-5x + 4y = 2

-5*2 + 4y = 2

-10 + 4y = 2

4y = 2 + 10

4y = 12

y = 12/4

y = 3

Check:

from the second eq.

9x - 4y = 6

9*2 - 4*3 = 6

18 - 12 = 6

The completed table showing Bianca Ramos's tax deduction and NET PAY

is presented as follows;

SOCIAL SECURITY SYSTEM = Php 1,147

MEDICARE (PHILHEALTH) = Php 268.25

PAGIBIG (FUND) = Php 370

BIR (WITHHOLDING TAX) = Php 5,509.19

Total deductions = Php 7,294.44

NET PAY = Php 11,205.56

Reasons:

Based on online search, the tax rate for the items on the table are as follows;

SOCIAL SECURITY SYSTEM = 6.20% of earnings

MEDICARE (PHILHEALTH) = 1.45% of earnings

PAGIBID (FUND) = 2% of salary

BIR (WITHOLDING TAX) = P1,342.47 + 32% over P5,479

Bianca Ramos's basic salary = 18,500.00

Which gives the deduction amount as follows;

SOCIAL SECURITY SYSTEM = 0.062 × 18,500.00 = 1,147

MEDICARE (PHILHEALTH) = 0.0145 × 18,500.00 = 268.25

PAGIBIG (FUND) = 0.02 × 18,500.00 = 370

BIR (WITHHOLDING TAX) = 1,342.47 + 0.32×(18,500 - 5,479) = 5,509.19

Total deductions = 1,147 + 268.25 + 370 + 5,509.19 = 7,294.44

NET PAY = 18,500 - 7,294.44 = 11,205.56

Her net pay = Php 11,205.56

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Answer:

39.0625

Step-by-step explanation:

15.625 times 2.5= 39.0625

You're just multiplying each value by 2.5

1 times 2.5= 2.5

2.5 times 2.5= 6.25

6.25 times 2.5= 15.625

and then 15.625 times 2.5= 39.0625

Answer:

d-7 divided by 2 or over 2

Answer:    114

Step-by-step explanation:

3/4 * 152 = 3*38 =114

Answer: I don’t know :(

Step-by-step explanation:

Answer:

8

Have an amazing day!

Answer:

Molly played 4 games

Answer:

x=-5 and y= 4

Step-by-step explanation:

To eliminate x, add up both equations

9y= 36

divide both sides by 9

y=36/9

y= 8

To eliminate y, multiply the first equation by 8

-16x + 8y = 112

2x+ 8y= 22

Subtract equation 2 from equation 1

-18x = 90

Divide both sides by -18

x= 90/-18

x= -5

Answer:

Step-by-step explanation:

If you mean length is 2½ times its width not "2½cm times its width"

      2(L + W) = 270

2(2.5W + W) = 270

      2(3.5W) = 270

              7W = 270

                W = 38.5714285714...

                W ≈ 38.57 cm

Answer:

Width = 38. 57 cm

Step-by-step explanation:

The perimeter of a Rectangle = 270 cm

Now,

Let's take x to be the width.

Length = 2½ = 5x/2

According to the formula,

The perimeter of a rectangle = 2 ( l + w )

270 = 2 ( 5x/2 + x )

270 = 5x + 2x

270 = 7x

x = 270/7

x = 38. 57 cm.

• The width of a rectangle is 38.57 cm

The capital formation of the investment function over a given period is the

accumulated  capital for the period.

Reasons:

(a) The given investment function is presented as follows;

[tex]I(t) = 100 \cdot e^{0.1 \cdot t}[/tex]

(a) The capital formation is given as follows;

[tex]\displaystyle Capital = \int\limits {100 \cdot e^{0.1 \cdot t}} \, dt =1000 \cdot e^{0.1 \cdot t}} + C[/tex]

From the end of the second year to the end of the fifth year, we have;

The end of the second year can be taken as the beginning of the third year.

Therefore,  for the three years; Year 3, year 4, and year 5, we have;

[tex]\displaystyle Capital = \int\limits^5_3 {100 \cdot e^{0.1 \cdot t}} \, dt \approx 298.87[/tex]

The capital formation from the end of the second year to the end of the fifth year, C ≈ 298.87

(b) When the capital stock exceeds $100,000, we have;

[tex]\displaystyle \mathbf{\left[1000 \cdot e^{0.1 \cdot t}} + C \right]^t_0} = 100,000[/tex]

Which gives;

[tex]\displaystyle 1000 \cdot e^{0.1 \cdot t}} - 1000 = 100,000[/tex]

[tex]\displaystyle \mathbf{1000 \cdot e^{0.1 \cdot t}}} = 100,000 + 1000 = 101,000[/tex]

[tex]\displaystyle e^{0.1 \cdot t}} = 101[/tex]

[tex]\displaystyle t = \frac{ln(101)}{0.1} \approx 46.15[/tex]

The number of years before the capital stock exceeds $100,000 ≈ 46.15 years.

Learn more investment function here:

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Answer:

333.333333333

Step-by-step explanation:

you have to divide

Answer:

the answer is number 1 !!

• correct me if I'm wrong

Answer:

18-3(n-1)

Step-by-step explanation:

In attachment I have answered this problem.

The value of x {0 < x < (π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 ​is x = π/4.

Since cos x /(cosec x + 1) + cos x /(cosec x - 1) = 2 ​

Taking the L.C.M (cosecx + 1)(cosecx - 1), we have

[cosx(cosecx - 1) + cosx(cosecx + 1)]/(cosecx + 1)(cosecx - 1) = 2

[cosxcosecx - cosx + cosxcosecx + cosx]/(cosec²x - 1²) = 2

[cosx/sinx - cosx + cosx/sinx + cosx]/(cosec²x - 1²) = 2

[cotx - cosx + cotx + cosx]/(cosec²x - 1) = 2

collecting like terms, we have

[cotx + cotx + cosx - cosx ]/(cosec²x - 1) = 2

[2cotx + 0]/(cosec²x - 1) = 2

2cotx/(cosec²x - 1) = 2

cotx/(cosec²x - 1) = 1

Since cot²x + 1 = cosec²x ⇒ cot²x = cosec²x - 1

So, cotx/(cosec²x - 1) = 1

cotx/cot²x = 1

1/cotx = 1

tanx = 1

Taking inverse tan of both sides, we have

x = tan⁻¹(1)

x = 45°

x = 45 × π/180

x = π/4

So, the value of x {0 < x < (π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 ​is x = π/4.

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Answer:

34.5 people

Step-by-step explanation:

Answer:

Percent change in the price of gas is [tex]9.85\%[/tex]

Step-by-step explanation:

Percentage change equals the change in value divided by the absolute value of the original value, multiplied by  .

[tex]\text { Percentage Change }=\frac{\Delta V}{\left|V_{1}\right|} \times 100[/tex]

Here

[tex]\Delta V=2.26-2.03\\\\=0.23\$/gallon[/tex]

[tex]V_{1}=2.03\$/gallon[/tex]

The percent change in the price of gas

[tex]=\frac{0.23}{2.03} \times100\\\\=9.85\%[/tex]

Percent change in the price of gas is [tex]9.85\%[/tex]

Answer:

0.80

Step-by-step explanation:

its the farthest away from 0.60