Statement 1: If √12 - √8 = a, then √12 + √8 is equal to 4/a.
Statement 2: a + √b is called the rationalizing factor of c + √d if their product is 1.

• Statement 1 is true; Statement 2 is true; Statement 2 is the correct explanation of Statement 1.

• Statement 1 is true; Statement 2 is true; 2 is not the correct explanation of Statement 1.

• Statement 1 is true; Statement 2 is false.

• Statement 1 is false; Statement 2 is true.

It is an assertion-reasoning question. Please help me to solve this. Need step-by-step explanation as well. Thank you.​

Answers

Answer 1

Answer:

Statement 1 is true; Statement 2 is false.

Step-by-step explanation:

Statement 1:

√12 - √8 = a

Let's use the given value of √12 + √8 ,that is, 4/ a.

If we multiply both the expressions such that their Left Hand Sides get multiplies together and Right Hand Sides together:

=> (√12- √8)(√12 + √8) = a × 4/a

On the LHS,

identity used:

(a-b)(a+b) = a²-b²

On the RHS:

a gets canceled due to its presence in both the numerator as well as the denominator.

=> 12 - 8 = 4

=> 4 = 4

That's it!

We got LHS = RHS, that approves the existence of the given statement.

___________________

Statement 2:

"a + √b is called the rationalizing factor of c + √d if their product is 1"

That's not entirely right!

The correct statement would be:

" a + √b is called the rationalizing factor of c + √d if their product is a rational number ."

Since, rationalizing has got nothing to do with 1, (1 is just another rational number), even if we get 2 by their multiplication, it will be called rationalizing as long as we're getting a rational number.

___________________

Answer:

Hence, I'd say:

Statement 1 is correct but Statement 2 isn't.

That's the third option.


Related Questions

what is the slope of y-3=-2(x+5)

Answers

Answer: slope (m) = -2

Step-by-step explanation:

y-3=-2(x+5)

put it into y=mx+b

use PEMDAS-Parantheses, Exponents, Mult. Div. Add. Sub. for your order of operations.

first, parantheses.

-2(x+5)

-2 times x = -2x

-2 times 5 = -10

your new equation is y-3 = -2x-10

now, to get y by itself, cancel out the -3 by adding a positive 3 to both sides.

you final equation will be y=-2x-7

in the form y=mx+b, m is your slope.

therefore, -2 is your answer, or slope.

The value of √42 Is a rational or an irrational number. ​

Answers

Answer:

irrational

Step-by-step explanation:

Answer:

Irrational.

Step-by-step explanation:

When we simplify √42, we get:

6.48074069841 (Calculator Used)

And 6.48074069841 is an irrational number.

Hoped this helped.

[tex]GeniusUser[/tex]

PART B: Uber was also available for Mike to use to get home from the airport. Uber
does not have an initial fee; it charges $3.45 per mile. Which would be a better deal
the taxi or Uber for Mike's trip home?

Answers

Answer:

taxi

Step-by-step explanation:

you would take the taxi because it would cost less than Uber

The taxi would be the better deal because of the price

Evaluate the expression please.
Evaluate the expression.

3–

10÷

2+1

Answers

Answer:

-7

Step-by-step explanation:

-3-(-10)/-2+1

-3-5+1

-8+1

-7

Answer:

Step-by-step explanation:

Expert-Verified Answer

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jayilych4real

Some useful tips to help you write a five-paragraph essay are:

Choose a topic

Make suitable claims

Make use of supporting details

Make use of rhetorical appeals

Make use of counterclaims and rebuttals

Restate your main points

Conclude.

What does a fraction represent

Answers

A fraction represents a part of a whole or any numbers of equal parts


What is mL BCD ?









THANK U <3

Answers

m∠BCD= m∠ACB ÷ 2 = 134.76° ÷ 2 = 67.38°

Ok done. Thank to me :>

Please help, I’m having trouble

Answers

Answer:

z=13

Step-by-step explanation:

SU         1

------   = ------

WV          2

z             1

-----   = ----------

z+13        2

Using cross products

2z = z+13

Subtract z from each side

2z-z = z+13-z

z = 13

Divide. Write the answer in simplest form. 14/27÷7=

Answers

Answer:

[tex]\frac{2}{27}[/tex]

Step-by-step explanation:

hope this helps! :D

have a MIRACULOUS day!! <3

Answer:

2/27

Step-by-step explanation:

14/27÷7

Convert The element to fraction: 7=7/1

=14/27 ÷ 7/1

Apply the fraction rule:

=14/27 x 1/7

Cross- cancel common factor: 7

2/27

What is the surface area of the rectangular prism?
2 m
10 m
5 m

Answers

Answer:

10m

Step-by-step explanation:

what are the first 100000000000000000000 digits of pie

Answers

Answer:

The first 10 digits of pi (π) are 3.1415926535. The first million digits of pi (π) are below, got a good memory? Then recite as many digits as you can in 30 ...

Step-by-step explanation:

After Lois picks a value for b, Clark must solve the equation 2x + 7 - x = 4x + 2b – 3x - 3b.

Clark uses Lois's b, then tries to solve the equation by repeatedly guessing values of x until he guesses
the right one. However, for every x he picks, the left side is always 3 more than the right side. What
value of b did Lois give Clark?

Answers

The value of b that Lois give Clark will be -7

Given the expression 2x + 7 - x = 4x + 2b – 3x - 3b.

First, we need to find the value of b from the expression.

Rearrange;

2x + 7 - x = 4x + 2b – 3x - 3b.

x + 7 = x + 2b - 3b

2b - 3b = 7

-b = 7

b = -7

Substitute b = -7 into the expression and find the value of x;

2x + 7 - x = 4x + 2(-7) – 3x - 3(-7)

x + 7 = 4x - 3x - 14 + 21

x + 7 = x + 7

Since for every x he picks, the left side is always 3 more than the right side, the equation becomes;

x + 7 = x + 3x + 7

x + 7 = 4x + 7

x - 4x = 0

-3x = 0

x = 0

Hence the value of b that Lois give Clark will be -7

Learn more on equations here: https://brainly.com/question/16450098

what situation can be represented by this equation 15 + x = 63.75

Answers

315 the answer

15 + x = 63.75

Answer:

63.75 minus 15 equal to 48.75

Using a phone card to make a long distance call costs a flat fee of $0.57 plus $0.31 per minute starting with the first
minute. Find the total cost of a phone call which lasts 27 minutes.
O A. $27.18
OB. $15.7
O C. $8.37
OD. $8.94

Answers

Answer:

it's d

Step-by-step explanation:

multiply 0.31 by the amount of minutes used (27) and add the flat fee to it.

0.31×27+(0.57)= 8.94

Mario Andretti drives his race car 500 miles in 2.5 hours. What is his speed?

Answers

Answer:

His speed was 200.

Step-by-step explanation:

500/2.5 is 200.

Answer:

The speed of Mario Andretti's race car is 200 m/h.

Step-by-step explanation:

Speed = Distance/Time=> Speed = 500 miles/2.5 hours=> Speed = 200 miles/1 hour

Conclusion:

Therefore, the speed of Mario Andretti's race car is 200 m/h.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

need help with this dividing whole numbers thing

Answers

Answer:

72 : n = 18. n x 18 = 72

n : 18 = 72. 72 x 18 = n

72 : 18 = n

Step-by-step explanation:

The table below shows a proportional relationship.
X
-4
-2
0
2
4
у
-14
-7
7
14
What is the constant ratio k, Y ?
2

Answers

Answer: I think it is -7 and +7

The area of a regular pentagon is 600 cm². Calculate the length of one side of the pentagon.

Answers

Answer:

18.675cm

just search it

Rhian sat at a maths test and an English test
In the Maths test she scored 14 out of 17
In the English test she scored 31 out of 39
In which test did she do better

Answers

Answer: She did better in the Math test

Step-by-step explanation:

find the ratios of each by saying 14/17 = 0.82 then multiply by 100 to see it from 100 then you will get 82%

Now do the same thing for the other:

31/39 = 0.79 x 100 = 79%

In the end she got better in the math test!

Hope that helps :)

What is an expression that represents 5 times the value of Y plus 4

Answers

Answer:

5y+4

Step-by-step explanation:

Answer:

2 plus 5 times n

Step-by-step explanation:

2. Find the total purchase price. Frank bought a pair of jeans for $55 and some sunglasses
for $249. The tax rate is 7% in the state of Nevada. What is the total cost of Frank's order?

Answers

Frank paid a total of $304 ($55+249). You multiply $304 by 0.07 to get $21.28 (To convert a number to a percentage, multiply it by 100. So, 0.07 as a percent is equal to 7%). You add this to $304 to get to your answer: $325.28.

The total would be $325.28 if the sunglasses were $249. Hope it helped!

Consider this problem: 2+3(3)+5(2+3)+2(-5)
a.
How many terms are in the expression?

Answers

Answer:

[tex]5[/tex]

....,,,✨✨✨✨✨✨✨

What is the solution for -10 < x - 9?
x > -19
x < -1
x < -19
x > -1

Answers

-10 < x - 9

Reverse the equation to get x on the left side"

x-9>-10

Add 9 to both sides:

X >-1

Answer: x > -1

Can someone answer this for me 9- 6x -8

Answers

Answer:

Combine like terms

Step-by-step explanation:

-6x + 1

Topic: Determining if given values are solutions to a two variable equation

Answers

Answer:

2. a & c

3. a, b & c

Step-by-step explanation:

Substitute each solutions to the question to see if you get the answer

a. 5(2)-0=10 -- so (2,0) is the solution

b. 5(3)-0=15 -- (3,0) is not the solution

c. 5(0)-(-10)=10 -- (0,-10) is the solution

d. 5(1)-(1)=4 -- (1,1) is not the solution

a. -(-4)+ 6(1) = 10 -- so (-4,1) is the solution

b. -(-22)+ 6(-2) = 10 -- so (-22,-2) is the solution

c. -(2)+ 6(2) = 10 -- so (2,2) is the solution

d. -(10)+ 6(0) = - 10 -- so (10,0) is not the solution

Mrs. Palmer's famous peanut butter cookies call for 1 cup of peanut butter for every
1
2
of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil. How much peanut butter should she use?

Answers

Answer:

2 cups

Step-by-step explanation:

if she uses 1/2 cup of oil per 1 cup of peanut butter

then she should use the ratio PB(peanut butter)= 2O(oil)

so if oil is 1 then PB must be 2 cups

What is the perimeter of triangle ABC with coordinates of A(3,4), B(3,11), C(27,4)

Answers

Answer:

Is there supposed to be a picture or no?

Step-by-step explanation:

working together two mathletes solve 32 math problems in a certain amount of time how many problems will 3 mathletes solve if they together at the same rate for the same amount of time

Answers

If they together at the same rate for the same amount of time, they will solve 48 math problems,

From the question, we can see that two mathletes solve 32 math problems in a certain amount of time, this can be written as:

2 mathletes = 32 math problems

In order to determine the number of problems for 3 mathletes, this is expressed as:

3 mathletes = x

DIvide both expressions:

2/3 = 32/x

Cross multiply

2x = 3* 32

x = 3 * 16

x = 48math problems

Hence if they together at the same rate for the same amount of time, they will solve 48 math problems,

Learn more on proportion here: https://brainly.com/question/1496357

Please help me solve these problems ASAP

Answers

Answer:

imagine having this

Step-by-step explanation:

can't relate

just times by 2 k:)))))))))

Craig sells cabinets at a 600% percent markup from the cost of materials. He spent $2000.00 on the materials for cabinets he just built. What will be the price he sells those cabinets for?

Answers

Answer:

3781

Step-by-step explanation:

80 hours × $18=$1440 for labor. 1440+15%(1440×.15)=$216.00 + material cost=$2125

(2125.00+1440.00+216=3781)

Karla is reading about a type of single-celled microorganism that can live inside the human body. This type of organism can be either harmful or harmless to people, depending on the type. One harmless type lives in the intestines and helps the body digest food. One harmful type can cause strep throat. Which type of organism is Karla most likely reading about?

Answers

Bacteria.

Bacteria is unicellular. Bacteria can either be harmful to the human body or it can do nothing; meaning it can be harmless.
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