find the value of a and b of a+root5 is (root5+root3)(root5-root3)​

Answers

Answer 1

Given:

Consider the value of [tex]a+b\sqrt{5}[/tex] is [tex](\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})[/tex].

To find:

The values of a and b.

Solution:

According to the given information,

[tex]a+b\sqrt{5}=(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})[/tex]

[tex]a+b\sqrt{5}=(\sqrt{5})^2-(\sqrt{3})^2[/tex]            [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]a+b\sqrt{5}=5-3[/tex]

[tex]a+b\sqrt{5}=2[/tex]

It can be written as

[tex]a+b\sqrt{5}=2+0\sqrt{5}[/tex]

On comparing both sides, we get

[tex]a=2,b=0[/tex]

Therefore, the value of a is 2 and the value of b is equal to 0.


Related Questions

Guy please help me out so this is the question 3.  Last Sunday, the temperature at 8:00 a.m. was -3०C.  Between 8:00 a.m and 1:00 p.m., the temperature rose by 5०C.  By 6:00 p.m. the temperature was 2०C colder than it was at 1:00p.m.  Then, the temperature dropped 3०C each hour between 6:00 p.m. to 10:00 p.m.  What was the temperature at 10:00 p.m.? I got the answer -1 is that correct?​

Answers

Answer:

ayuda necesito lo mismo

Step-by-step explanation:

por favor algún voluntario

Answer:

-9C

Step-by-step explanation:

-3+5-2-3(3)=-9C

i think you made a mistake on "it got colder by 2C." If temperatures get colder, they drop, meaning you subtract it.

also, it said between the hours of 6-10pm, which is three hours, the temperature drops each hour by 3C. so, you multiply 3 to -3, and come up with -9

Witch of the following equations have z=4
9z+22=26
7z-1=27
46-8z=14
5z+40=62

Answers

Answer:

b

Step-by-step explanation:

17 >n +4
I rlly need help now

Answers

Answer:

n=13

Step-by-step explanation:

Step 1: Flip the equation.

Step 2: Subtract 4 from both sides.

Tell weather each pair is parallel, perpendicular, or neither: 8x – 2y = 3
x + 4y = -1

Answers

Neither. 8x-2y=3 is y=4x-3/2 and x+4y=-1 is y=1/4x-1/4. To be perpendicular the slopes need to be opposite and reciprocal. the slopes in this question are only reciprocals.

Find x and y. please help​

Answers

Answer:

[tex] x = 4 \sqrt{2} [/tex]

[tex] y = 4 \sqrt{6} [/tex]

Step-by-step explanation:

[tex] \sin 45 \degree = \frac{x}{8} \\ \\ x = 8 \sin 45 \degree \\ \\ x = 8 \times \frac{1}{ \sqrt{2} } \\ \\ x = \frac{8 \sqrt{2} }{2} \\ \\ x = 4 \sqrt{2} \\ \\ \\ \tan 30 \degree = \frac{x}{y} \\ \\ \frac{1}{ \sqrt{3} } = \frac{4 \sqrt{2} }{y} \\ \\ y = 4 \sqrt{6} [/tex]

A yellow ball, a red ball, a white ball and a
black ball are placed in a barrel. Two balls
are drawn out of the barrel at random. What is the probability
that the yellow ball is drawn first?

Answers

Answer:

1/4 chance (this is equal to 25% as a percentage or 0.25 as a decimal)

Step-by-step explanation:

There are 4 balls and only one can be first. As there is only 1 yellow ball, there is 1/4 chance that the yellow ball is picked first.

Yoli survey 100 people in your school and ask them if
thely feel your school has adequate parking. Only 30%
of the sample feels the school has enough parking. If
you have 728 students total in your school, how many
would you expect out of all the student body that felt
there was enough parking?

Answers

Answer:es, theoretically you would expect to roll only eight 5s. 3. You survey 100 people in your school and ask them if they feel your school has adequate parking. Only. 30% of the sample feels the school has enough parking. If you have 728 students total in your school, how many would you expect out of all the student body that ...

Step-by-step explanation:

Which point on the number line best represents 166 ?
A
B
C
D
7
9
8
B at 7.9
Cat 8.1
D at 8.8
A at 7.3

Answers

Answer:

a and  b

Step-by-step explanation:

well i dk b

secA-tanA/secA+tanA=cos^2A/(1+sin^2A)​ could somebody prove this pls......

Answers

9514 1404 393

Answer:

  it cannot be proven

Explanation:

You cannot prove what isn't true.

We know you know how to use parentheses, so we take the left-side expression at face value. The left-side and right-side functions are different, so cannot be proved to be the same, except at specific angles.

Help me please I am a idiot who doesn’t get math

Answers

To calculate the cuboid's volume, use height×width×length which is 11×11×16

For the cylinder's volume, use πr²h. in this case, it is 3.14×4²×9

Add up the two answers you get and that's the solution

The price of a television is $567.31. The state sales tax rate is 8.3%.

What is the total cost of the television?

Answers

8.3%= 0.083

567.31 * .083 = 47.086 = 47.09

567.31+47.09= $614.40

Total cost is $614.40

Answer:

[tex]2.64957x10 [/tex]

[tex]8547 \times 31[/tex]

[tex] = 264951[/tex]

3.3 - 3.7n - 2n + 8 nnnnnnnnnnnnnnnnnn

Answers

Answer:

-5.7n + 11.3

Step-by-step explanation:

3.3 - 3.7n - 2n + 8 = -3.7n - 2n + 3.3 + 8 = -5.7n + 11.3

enejjennnenenswatehd

Posts are 4 1/4 feet in length. Posts must be installed 7/8 feet below ground level, What will be the height of fence?

Answers

Answer:

Step-by-step explanation:

4 1/4x7/8

I think 119/32

The height of fence will be "[tex]\frac{41}{8}[/tex]".

According to the question,

Length of posts,

= [tex]4\frac{1}{4} \ feet[/tex]

Length of posts below ground level,

= [tex]\frac{7}{8} \ feet[/tex]

Now,

→ The height of the fence will be:

=  [tex]4\frac{1}{4} +\frac{7}{8}[/tex]

=  [tex]\frac{17}{4}+\frac{7}{8}[/tex]

=  [tex]\frac{34}{8}+\frac{7}{8}[/tex]

=  [tex]\frac{34+7}{8}[/tex]

=  [tex]\frac{41}{8}[/tex]

Thus the above is the right answer.

Learn more:

https://brainly.com/question/24395658

1. When x is 1, what value of y makes the equation true?

Answers

Answer:

Step-by-step explanation:

-0.5

Step-by-step explanation:

If x is 1, plug it into the equation.

So, y=-3(1) + 2.5

-3(1) = -3

now add.

-3+2.5 = -0.5

so that should give you y = -0.5

which one pls help me i’ll give extra points

Answers

Answer:

C

Step-by-step explanation:

Answer:

A. The doctors will give Charlie an operation

Step-by-step explanation:

need help in this show working please​

Answers

this is what i got hope it helps

AB, BC and CD are three sides of a regular polygon with centre o.
ABX is a straight line.
Angle BCD = 140°
0 Calculate the size of each of the angles marked v, w, x, y and z.


Pls help 10 points

Answers

Answer:

Step-by-step explanation:

Since, BC and DC are the sides of a regular polygon,

m(DC) = m(BC)

Opposite angles of these equal sides will be equal in measure.

m∠DBC = m∠CDB = v

By triangle sum theorem,

m∠DBC + m∠CDB + m∠DCB = 180°

v + v + 140° = 180°

2v = 40°

v = 20°

Since angle 'x' is an exterior angles of ΔBCD,

x = m∠BDC + m∠CBD [By the property of exterior angles]

x = v + v

x = 40°

Since, angles v, w and x are the linear angles,

v + w + x = 180°

20° + w + 40° = 180°

w = 120°

Since, measure of exterior angle = [tex]\frac{360}{n}[/tex]

n = Number of sides

40° = [tex]\frac{360}{n}[/tex]

n = 9

Sum of angles formed at the center by joining vertices of the polygon = 360°

Measure of each angle at the center of a polygon with 9 sides = [tex]\frac{360}{9}[/tex]

= 40°

Since, z = 3 × (Measure of central angle formed at the center)

             = 3 × 40°

             = 120°

In ΔOAB,

m∠OAB + m∠OBA + m∠AOB = 180°

y + y + 40° = 180° [m∠OAB = m∠OBA, Opposite angles of the equal sides OA and OB]

2y = 140°

y = 70°

Drew has more than 4 times as many baseball cards as mark. Katie has fewer than half as many cards as mark. Mark has m baseball cards

Answers

Answer:

Cards with Mark = 30

Cards with Drew  = 120

Cards with Katie = 12

Step-by-step explanation:

The complete question is

Drew has 4 times as many baseball cards as Mark. Katie has 3 fewer than than half as many cards  as Mark. In all they have 162 baseball cards. How many does each have?

Solution -

Let the number of cards with Mark be "X"

Number of cards with Drew = 4 *X = 4X

Number of Cards with Katies = 0.5 X -3

Sum of all the cards is equal to 162

X+4X + 0.5 X -3 = 162

5.5 X = 165

X = 30

Cards with Mark = 30

Cards with Drew = 4 * 30 = 120

Cards with Katei = 15-3 = 12

16,-8,4...;6th term
The 6th term of the sequence is______.

Answers

Answer:

- [tex]\frac{1}{2}[/tex]  

Step-by-step explanation:

1) 16

2) 16 ÷ ( - 2) = - 8

3) - 8 ÷ ( - 2) = 4

4) 4 ÷ ( - 2) = - 2

5) - 2 ÷ ( - 2) = 1

6) 1 ÷ ( - 2) =  - [tex]\frac{1}{2}[/tex]

7.1 added to a number equals 10.3?​

Answers

The answer is 3.2. If you subtract 10.3 and 7.1, then you get 3.2.

12. (8x+15) + 45 + (18x+15) + 45

Answers

2 ( 13x + 60 ) or 26x + 120 is the correct answer
Yea that what I got so he’s right

The sum of two integers is - 5 and their difference is 11.
What are the two numbers

Answers

Can help I’m not in that math still

A game and a controller are on sale for 45% off. The regular price of the game is $80. The regular price of the controller is $120. What is the sale price for the game

Answers

It is 36

Explanation:
80/100 = 0.8
0.8*45 = 36

Please find the measure of angle F

Answers

Answer:

98º

Step-by-step explanation:

I need to figure out whether or not this is a solvable equation. HELP

Answers

Answer:

its not

Step-by-step explanation:

Answer:

yeah this question i s solvable

Step-by-step explanation:

[tex] \frac{1}{3} (4 + 2) = - \frac{2}{5} (4 - 9)[/tex]

[tex] \frac{1}{3} \times 6 = - \frac{2}{5} \times ( - 5)[/tex]

please try ti do it on thi way

PLEASE MARK ME AS BRAINLIEST

Uri has 22 same-sized circles that are divided into different numbers of equal-sized parts. He shades 1/5 of the first circle. The second circle has three times as many parts as the first circle. Uri shades an equivalent fraction of the second circle. What fraction of the second circle does Uri shade?

Answers

Answer:

The fraction of the second circle does Uri shade = [tex]\frac{1}{15}[/tex]

Step-by-step explanation:

As given,

Total number of same sized circle = 22

In first circle :

He shades [tex]\frac{1}{5}[/tex] of the first circle.

⇒ He divide the first circle in 5 parts and shaded 1 part.

Now,

The second circle has three times as many parts as the first circle.

⇒Total parts of second circle = 3 × 5 = 15

Now,

Given that  Uri shades an equivalent fraction of the second circle.

⇒Uri shade second circle = [tex]\frac{1}{15}[/tex]

∴ we get

The fraction of the second circle does Uri shade = [tex]\frac{1}{15}[/tex]

Natalie read 3/4 of a book that was 120 pages long. how many pages does she have left?

Answers

Answer:

120/3 = 40   40x2 =80  120-80=40  the answer is 40 pages

Step-by-step explanation:

one less than twice a number equals 9?

Answers

Answer:

X x 2 = 9 - 1 is your expression I am pretty sure

Find the slope of the line y = –7 2 x − 5 8 . Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Answer:

Slope = -7/2

Step-by-step explanation:

The standard equation of a line is expressed as y = mx+c

m is the slope

c is the y-intercept

Given the equation y = -7/2 x - 5/8

Compare with the general equation

mx = -7/2x

Divide both sides by x

mx/x = -7x/2x

m = -7/2

Hence the slope of the line is -7/2

pa help po need lang ipasa ngayon​

Answers

1.

[tex] \frac{3}{5} \times \frac{5}{6} = \frac{15}{30} = \frac{1}{2} [/tex]

2.

[tex] \frac{3}{5} \times \frac{3}{15} = \frac{9}{75} = \frac{3}{25} [/tex]

3.

[tex] \frac{5}{8} \times \frac{4}{10} = \frac{20}{80} = \frac{1}{4} [/tex]

4.

[tex] \frac{5}{12} \times \frac{3}{8} = \frac{15}{96} = \frac{5}{32} [/tex]

5.

[tex] \frac{12}{20} \times \frac{5}{6} = \frac{60}{120} = \frac{1}{2} [/tex]

6.

[tex] \frac{4}{5} \times \frac{8}{3} = \frac{32}{15} = 2 \frac{2}{15} [/tex]

7.

[tex] \frac{3}{8} \times \frac{16}{7} = \frac{6}{7} [/tex]

8.

[tex] \frac{11}{2} \times \frac{18}{7} = \frac{198}{14} =14 \frac{1}{7} [/tex]

9.

[tex] \frac{14}{6} \times \frac{18}{5} = \frac{252}{30} = 8 \frac{2}{5} [/tex]

10.

[tex] \frac{4}{3} \times \frac{5}{2} = \frac{20}{6} = 3 \frac{1}{3} [/tex]

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