Fill in the missing steps and justifications used to solve the given equation.

Answer:

a = [tex]\frac{11}{7}[/tex] ; b = [tex]\frac{6}{7}[/tex]

Step-by-step explanation:

[tex]\frac{3 + \sqrt{2}}{3 - \sqrt{2} } = a + b\sqrt{2} \\\\[/tex]

Rationalising [tex]\frac{3 + \sqrt{2}}{3 - \sqrt{2} }[/tex] gives :-

[tex]\frac{3 + \sqrt{2}}{3 - \sqrt{2} } = \frac{(3 + \sqrt{2})(3 + \sqrt{2})}{(3 - \sqrt{2})(3 + \sqrt{2}) } = \frac{(3 + \sqrt{2})^2}{3^2 - (\sqrt{2})^2 } = \frac{11 +6\sqrt{2} }{7}[/tex]

Comparing [tex]\frac{11 + 6\sqrt{2} }{7}[/tex] with [tex]a + b\sqrt{2}[/tex] gives

a = [tex]\frac{11}{7}[/tex] & b = [tex]\frac{6}{7}[/tex]

Answer:

[tex]\frac{11}{7}[/tex] + [tex]\frac{6}{7}[/tex] [tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given

[tex]\frac{3+\sqrt{2} }{3-\sqrt{2} }[/tex]

Multiply the numerator/ denominator by the conjugate of the denominator.

The conjugate of 3 - [tex]\sqrt{2}[/tex] is 3 + [tex]\sqrt{2}[/tex] , thus

= [tex]\frac{(3+\sqrt{2})(3+\sqrt{2}) }{(3-\sqrt{2})(3+\sqrt{2}) }[/tex] ← expand numerator/ denominator using FOIL

= [tex]\frac{9+6\sqrt{2}+2 }{9-2}[/tex]

= [tex]\frac{11+6\sqrt{2} }{7}[/tex]

= [tex]\frac{11}{7}[/tex] + [tex]\frac{6}{7}[/tex] [tex]\sqrt{2}[/tex] ← in the form a + b[tex]\sqrt{2}[/tex]

with a = [tex]\frac{11}{7}[/tex] and b = [tex]\frac{6}{7}[/tex]

Answer:

a = 2

Step-by-step explanation:

First of all you should remove parentheses by using distribution

24 + 5a = - a + 30a - 24

Then you should collect all like terms

24 + 5a = 29a - 24

After you should move the terms so the variables are only on one side.

5a - 29a = -24 - 24

Collect like terms

-24a = -48

After dividing both sides you get

a = 2

Answer:

Step-by-step explanation:

x -  9 = 17

x = 26

the answer is D

Answer:

Cost: $10.00

Number of Tickets:26

Step-by-step explanation:

Each ticket is $0.50

20*$0.50=$10.00

For the tickets:

$13.00/$0.50=26 tickets

Answer:

B-LearnCenter charges a higher membership fee but a lower rate per class.

Step-by-step explanation:

Answer:B-learning for ever

Step-by-step explanation:

Answer:

i can't see that

Step-by-step explanation:

plzz sent me a clear photo

Answer:

1. 1

2. 1  ⋅  10 ^24

3. 1000000000

4. 1

5. 1  ⋅  10 ^20

6. 1  ⋅  10 ^30

7. 1  ⋅  10 ^27

8. 10000

9. 0.01

10. 0.0001

11. 0.1

Hopefully these are right, I simplified all of the problems...sorry if they are wrong

Step-by-step explanation:

Answer:

52^8

Step-by-step explanation:

26^8 = 208827064576 + 26

Answer:

176 ounces (C)

Step-by-step explanation:

if you divide 48 by 3 it will give you 16 and there are 11 pints so u wanna multiply 16 and 11 to 176 ounces..

also i got it right on edge :P

Answer: 176

Step-by-step explanation:

Answer:

15 m

Step-by-step explanation:

The area of the circle is

A =pi r^2

A = pi 4^2 = 16 pi

The area of the sector is 30

The fraction is

30/16 pi  

Take this time 2pi which are the  radians of a circle

30 /16 pi * 2 pi = 15/4

This is the number of radians the angle is

The arc length is s = r * theta where theta is in radians

s = r  theta

  = 4 * 15/4

  = 15

Answer:

16

Step-by-step explanation:

f(-2)=4-3(-2)*2

f(-2)=4-3(-4)

f(-2)=4+12

f(-2)=16

Answer:

The cube root of a number is a special value that, when used in a multiplication three times, gives that number. Example: 3 × 3 × 3 = 27, so the cube root of 27 is 3. See: Square Root. Cubes and Cube Roots.

Answer:

C. p -> q

Step-by-step explanation:

Just did this on Edge2020. Hope this helps :)

Answer:

Step-by-step explanation:

a ) Let the volume required be v .

v x .8 + 500 x .3 / ( v + 500 ) = .7

.8 v + 150 = .7 v + 350

.1 v = 200

v = 2000 mL

b )

Let the volume of solution A  required be v . The volume of solution of B required will be 100 - v

v x .8 + ( 100 - v ) x .3 / 100 = .5

.8 v + 30 - .3 v = 50

.5 v = 20

v = 40 mL

volume of solution B = 60 mL .

c )

It is not possible because 90 % is more than 80 % the concentration of solution A . Any mixture will have concentration less than 80 % .

volume of solution B = 60 mL

Answer: x=22

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Add 9/2 to both sides.

Step 3: Multiply both sides by 4/3.

Answer:

The problem states that the answer cannot be a perfect square or have prime factors less than $50$. Therefore, the answer will be the product of at least two different primes greater than $50$. The two smallest primes greater than $50$ are $53$ and $59$. Multiplying these two primes, we obtain the number $3127$, which is also the smallest number on the list of answer choices. So we are done, and the answer is $\boxed{\textbf{(A)}\ 3127}$.

Step-by-step explanation:

Answer:

71

Step-by-step explanation:

I just did the AOPS question, you can see the attachment down below.

Hope this helped! :)

Answer:

1.65x + 2.25y ≤ 15

Step-by-step explanation:

Strawberries = $1.65 per pound Raspberries = $2.25 per pound

Amount with Christine = $15

Let

pounds of strawberries = x

pounds of raspberries = y

PxQx + PyQy ≤ 15

1.65x + 2.25y ≤ 15

The inequality which represent the situation where she buys x pounds of strawberries and y pounds of raspberries is 1.65x + 2.25y ≤ 15

1.65x + 2.25y less than or equal to 15

Answer:

the answer is -12-(-3)

Step-by-step explanation:

The expression equivalent to -18-(-9) is -12-(-3)

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.

Given is an expression, -18-(-9), we are given to find the expression equivalent to it,

-18-(-9) = -18+9 = -9

1) -18+2 = -16 (not equivalent)

2) -12-(-3) = -12+3 = -9

Therefore, we see, the value of expressions -12-(-3) and -18-(-9) are equivalent,

Hence, the expression equivalent to -18-(-9) is -12-(-3)

For more references on expressions, click;

https://brainly.com/question/14083225

#SPJ2

Answer:

2 000 miles

Step-by-step explanation:

In the first year, Mr James travels 8 x [tex]10^{3}[/tex] miles = 8 000 miles.

The second year, he traveled 1 x [tex]10^{4}[/tex] miles = 10 000 miles.

Comparing the distance covered in the two years,

10 000 miles - 8 000 miles = 2 000 miles

Therefore, Mr James travels 2 000 more miles in the second year than he did the first year.

Let's assume that Mr James conveys himself to his place of work all through the first year in his private car. But in the second year, there were some days in which the car was not available. So he had to go for his job by public transportation. This itch during those days, could cause an increase in the distance covered from his home to his place of work for the second year.

Answer:

No

Step-by-step explanation:

If you want to know whether they are equivalent or no, we will first have to find the value of both.

[tex]27x+45y[/tex]

Since there aren't any like terms here, your answer would be

[tex]27x+45y[/tex]

Let's solve for next one.

[tex]7(9x+7y)[/tex]

Let's add in parenthesis to 7.

[tex](7)(9x+7y)[/tex]

Now we will separate everything. And also you will have to add.

[tex](7)(9x)+(7)(7y)[/tex]

Now that we added we got our answer.

[tex]63x+49y[/tex]

Both values were not the same, so therefore, your answer is no, they are not equivalent.

Hope this helps!

No

Step-by-step explanation:

If you want to know whether they are equivalent or no, we will first have to find the value of both.

Since there aren't any like terms here, your answer would be

Let's solve for next one.

Let's add in parenthesis to 7.

Now we will separate everything. And also you will have to add.

Now that we added we got our answer.

Both values were not the same, so therefore, your answer is no, they are not equivalent.

Hope this helps!

Read more on Brainly.com - https://brainly.com/question/17379473#readmore

Answer:

the mistake is the addition sign. When a number is next to a parenthesis it means multiplication

Answer:

z^5

Step-by-step explanation:

z^8  * z^-3

Since we are multiplying exponents and the bases are the same, we can add the exponents

z^(8-3)

z^5

Answer:

The part that is shaded is 5/14

Step-by-step explanation:

The total circle is 1

1/2 + 1/7 + x = 1  where x is the shaded area

Multiply each side by 14 to get rid of the fractions

14(1/2 + 1/7 + x) = 1*14

7 + 2 + 14x = 14

9+14x = 14

Subtract 9 from each side

14x = 5

Divide by 14

x = 5/14

The part that is shaded is 5/14

Answer:

Acute, 40 degree angle

Step-by-step explanation:

Take 90 - 50 and you get 40

I hope this helps you :)

-KeairaDickson

Answer:

40°

Step-by-step explanation:

Count how many 10s it takes to get from 90 degrees to 50 and you get your answer...

Answer:

The interest rate is 0.79% per month.

Step-by-step explanation:

Present value of borrowed amount = $350

Future value of borrowed amount = $400

Interest amount = $50

Time duration = 18 months or 1.5 years

Now we have to find the rate of interest by using the above information. Here below is the calculation of interest rate.

Interest rate =  P×R×T

50 = 350 × R×18

R = 0.007936

Or, R = 0.79% per month.

Answer:

its \text{L}Lstart text, L, end text

Step-by-step explanation:

The sorting of the dataset and the information from the five number summary, which includes the three quartiles and the minimum and maximum values indicates that we get;

1. 2.8, 4, 4.3, 6, 7.5, 8.5, 9, 11.6, 12, 12.1

2. The interquartile range is; 7.745

The five number summary includes the first, second and third quartiles, Q₁, Q₂, and Q₃, and maximum and minimum values of the dataset, which serves to describe the characteristics of the data.

here, we have,

1. The sorted data from least to greatest can be presented as follows;

2.8, 4, 4.3, 6, 7.5, 8.5, 9, 11.6, 12, 12.1

Therefore, the original data in the question is already sorted from least to the greatest

2. The interquartile range, IQR, is the the difference between the third quartile, Q₃, and the first quartiles, Q₁, of the data.

IQR = Q₃ - Q₁

The dataset indicates that we get;

The number of datapoints in the dataset, n = 10

The first quartile = The (N + 1)/4 percentile value

First quartile, Q₁ = (10 + 1)/4 × 10 = The 2.75th value

The 2.75th value is the value 0.75 = 3/4 larger than the 2nd value, which can be found as follows;

Q₁ = The 2.75th value = 4 + (4.3 - 4) × (3/4)  = 4.225

The third quartile, Q₃ = The (N + 1) × (3/40th value, therefore;

Q₃ = The (10 + 1) × (3/4)th value = The 8.25th value (The value 0.25th more than the 8th value )

Q₃ = 11.6 + (12 - 11.6) × 0.25 = 11.7

The interquartile range, IQR = 11.7 - 4.225 = 7.475

The interquartile range = 7.475

Learn more on the interquartile range of a dataset here: brainly.com/question/13119591

#SPJ7

Complete question:

The following data points represent the volume of gas in each race car driver's tank (in liters).

Answer 2 questions about the data set.

1. Sort the data from least to greatest.

2.8

4

4.3

6

7.5

8.5

9

11.6

12

12.1

2. Find the interquartile range (IQR) of the data set.

L

Answer:

8

Step-by-step explanation:

Answer:

106 or 4x+18  

Step-by-step explanation:

Since Ray QR is a bisector you can determine that PRQ and QRS are equal angles (def. of a bisector). Then, what I chose to do is graph them and find where they intercept which was 22. We now know 22 is x so we can substitute it into the equation and solve to deterine that our answer is 106.