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Y_Kistochka [10]
2 years ago
7

Rewrite the subtraction expression as an addition expression, and then simplify (find the sum). -2 -3

Mathematics
1 answer:
Vinvika [58]2 years ago
6 0

Answer: -2 + (-3) = -5

Step-by-step explanation:

You might be interested in
100 points! simplify write as a product compute
Rom4ik [11]

Answer:

a) \sqrt{61 - 24 \sqrt{5} }  =  - 4  + 3 \sqrt{5}

b)( \sqrt{ ( {c}^{2}   -  1) ({b}^{2}    -  1) } - {2 \sqrt{bc} }) (\sqrt{ ( {c}^{2}   -  1) ({b}^{2}    -  1) }  + {2 \sqrt{bc}  } )

c) \frac{ \sqrt{9 - 4 \sqrt{5} } }{2 -  \sqrt{5} }  =   - 1

Step-by-step explanation:

We want to simplify

\sqrt{61 - 24 \sqrt{5} }

Let :

\sqrt{61 - 24 \sqrt{5} }  = a - b \sqrt{5}

Square both sides of the equation:

(\sqrt{61 - 24 \sqrt{5} } )^{2}  =  ({a - b \sqrt{5} })^{2}

Expand the RHS;

61 - 24 \sqrt{5} =  {a}^{2}  - 2ab \sqrt{5}  + 5 {b}^{2}

Compare coefficients on both sides:

{a}^{2}  + 5 {b}^{2}  = 61 -  -  - (1)

- 24 =  - 2ab \\ ab = 12 \\ b =  \frac{12}{b}  -  -  -( 2)

Solve the equations simultaneously,

\frac{144}{ {b}^{2} }  + 5 {b}^{2}  = 61

5 {b}^{4}  - 61 {b}^{2}  + 144 = 0

Solve the quadratic equation in b²

{b}^{2}  = 9 \: or \:  {b}^{2}  =  \frac{16}{5}

This implies that:

b =  \pm3 \: or \: b =  \pm  \frac{4 \sqrt{5} }{5}

When b=-3,

a =  - 4

Therefore

\sqrt{61 - 24 \sqrt{5} }  =  - 4  + 3 \sqrt{5}

We want to rewrite as a product:

{b}^{2}  {c}^{2}  - 4bc -  {b}^{2}  -  {c}^{2}  + 1

as a product:

We rearrange to get:

{b}^{2}  {c}^{2}   -  {b}^{2}  -  {c}^{2}  + 1- 4bc

We factor to get:

{b}^{2} ( {c}^{2}   -  1)  -  ({c}^{2}   -  1)- 4bc

Factor again to get;

( {c}^{2}   -  1) ({b}^{2}   -  1)- 4bc

We rewrite as difference of two squares:

(\sqrt{( {c}^{2}   -  1) ({b}^{2}   -  1) })^{2} - ( {2 \sqrt{bc} })^{2}

We factor the difference of square further to get;

( \sqrt{ ( {c}^{2}   -  1) ({b}^{2}    -  1) } - {2 \sqrt{bc} }) (\sqrt{ ( {c}^{2}   -  1) ({b}^{2}    -  1) }  + {2 \sqrt{bc}  } )

c) We want to compute:

\frac{ \sqrt{9 - 4 \sqrt{5} } }{2 -  \sqrt{5} }

Let the numerator,

\sqrt{9 - 4 \sqrt{5} }  = a - b \sqrt{5}

Square both sides of the equation;

9 - 4 \sqrt{5}  =  {a}^{2}  - 2ab \sqrt{5}  + 5 {b}^{2}

Compare coefficients in both equations;

{a}^{2}  + 5 {b}^{2}  = 9 -  -  - (1)

and

- 2ab =  - 4 \\ ab = 2 \\ a =  \frac{2}{b}  -  -  -  - (2)

Put equation (2) in (1) and solve;

\frac{4}{ {b}^{2} }  + 5 {b}^{2}  = 9

5 {b}^{4}   - 9 {b}^{2}  + 4 = 0

b =  \pm1

When b=-1, a=-2

This means that:

\sqrt{9 - 4 \sqrt{5} }  =  - 2 +  \sqrt{5}

This implies that:

\frac{ \sqrt{9 - 4 \sqrt{5} } }{2 -  \sqrt{5} }  =  \frac{ - 2 +  \sqrt{5} }{2 -  \sqrt{5} }  =  \frac{ - (2 -  \sqrt{5)} }{2 -  \sqrt{5} }  =  - 1

3 0
3 years ago
Read 2 more answers
Answer this if you can 37÷264
docker41 [41]
.1401515152 is not the answer
6 0
3 years ago
Read 2 more answers
If 1 gram = 100 centigrams and 1 centigram = 10 milligrams, how many
Alja [10]

Answer:

1,420 milligrams

Step-by-step explanation:

We know there are 100 centigrams in 1 gram, and there are 10 milligrams in a centigrams. That would mean there are 1,000 milligrams in 1 gram (100 * 10 = 1000).

As a result, all you need to do is multiply 1.42 by 1000 to get the amount of milligrams.

1.42 * 1000

Alternatively, to make 1.42 a whole number first, multiply by 100, then add a zero. (That's the other 10!)

(1.42 * 100) * 10

142 * 10

There are 1,420 milligrams in 1.42 grams.

3 0
2 years ago
Read 2 more answers
The area of a parallelogram is 5 cm Squared. explain why you can find the area without knowing the dimensions of the parallelogr
Ivan

Answer:

because a square always has the same length on each side so yo just see what number multiplies to that.

Step-by-step explanation:

6 0
3 years ago
The Wall Street Journal reported that the median salary for middle-level manager jobs was approximately $85,000 (The Wall Street
vredina [299]

Answer:

Median = $80,000 ; Mean = $84,000 ; Q1 = 67,000 ; Q3 = 106,000

Step-by-step explanation:

Given the data :

108 83 106 73 53 85 80 63 67 75 124 55 93 118 77

Reorderd data :

53, 55, 63, 67, 73, 75, 77, 80, 83, 85, 93, 106, 108, 118, 124

The median salary:

1/2(n+1)th term

Sample size, n = 15

1/2 (15 + 1)th term

1/2(16)th term

8th term = 80

Median is $80,000

Median reported by Wall Street Journal approximately $85000

The obtained and reported values are close

The mean annual salary :

ΣX / n = 1260 / 15 = 84

Mean annual salary = $84,000

Mean is the average of all earnings combined, median is the mid value of he data.

First and third quartile :

Q1 = 1/4(n+1)th term

Q1 = 1/4(16)th term

Q1 = 4th term = 67

Third quartile:.

Q3 = 3/4(n+1)th term

Q3 = 3/4(16)th term

Q3 = 12th term = 106

3 0
3 years ago
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