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3 years ago

The sum of a rational number and an irrational number produces an irrational number.

Mathematics

2 answers:

nikklg [1K]3 years ago

7 0

Answer:

True. By definition, an irrational number in decimal form goes on forever without repeating (a non-repeating, non-terminating decimal). By definition, a rational number in decimal form either terminates or repeats. If you add a non-repeating, non-terminating decimal to a terminating decimal, you still have a non-repeating, non-terminating decimal. If you add a non-repeating, non-terminating decimal to a repeating decimal, you will no longer have a repeating decimal, so the result is irrational.

sashaice [31]3 years ago

6 0

Answer:

True

Step-by-step explanation:

Example: sqrt(5) (which decimals continue forever) will mean that if you did 5+sqrt(5) it would still have those decimals.

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How do i do 3 part a ?

WINSTONCH [101]

In general the binomial expansion is

$(a+b)^n = {n \choose 0} a^0 b^n + {n \choose 1} a^1 b^{n-1} + {n \choose 2} a^2 b^{n-2} + ... + {n \choose n} a^n b^0$

So in our case, because we want ascending powers of x we'll write,

$(-3x + 1)^{11} = {11 \choose 0} (-3x)^0 1^{11} + {11 \choose 1} (-3x)^{1} 1^{10} + {11 \choose 2} (-3x)^{2} 1^9 + {11 \choose 3 } (-3x)^3 1^8 + ...$

We need to calculate the binomial coefficients:

${11 \choose 0} = 1$

${11 \choose 1} = 11$

${11 \choose 2} = \dfrac{11 \times 10}{2} = 55$

${11 \choose 3} = \dfrac{11 \times 10 \times 9}{3 \times 2} = 165$

$(-3x+1)^{11} = 1 (-3x)^0 1^{11} + 11(-3x)^{1} 1^{10} + 55 (-3x)^2 1^{9} + 165 (-3x)^3 1^8 + ...$

$(1-3x)^{11} = 1 -33 x + 495 3x^2 - 4455 x^3+ ...$

6 0

3 years ago

A bake sale has 5 brownies for sale. Each brownie was cut into 4 slices. Each slice was sold for $7. What was the total amount e

Alona [7]

Answer:

the answer is $140

Step-by-step explanation:

5x4=20 20x7=140

4 0

3 years ago

Read 2 more answers

Use the distributive property to remove the parentheses.

nlexa [21]

Answer:

Step-by-step $12c^{3} -40c^{8}$ explanation:

8 0

3 years ago

Which of the following is equivalent to

enot [183]

Answer:

Option (2) is correct.

$18-\sqrt{-25}=18-5i$

Step-by-step explanation:

Given expression $18-\sqrt{-25}$

We have to find an equivalence value to the expression.

<u> Radical rule</u>,

$\sqrt{-a}=\sqrt{-1} \sqrt{a}$

Also, $i=\sqrt{-1}$

Consider the given expression,

$18-\sqrt{-25}$

Applying radical rule to $\sqrt{-25}$

$\sqrt{-25}=\sqrt{-1}\sqrt{25}=5i$

Thus, the expression becomes,

$18-\sqrt{-25}=18-5i$

Thus, option (2) is correct.

6 0

3 years ago

Read 2 more answers

Solve the system by substitution.<br> [-2.5x+y = 13.5<br> 12.25x - y=-12.25

IrinaK [193]

Answer:

x = 5/39 , y = 539/39

Step-by-step explanation:

Solve the following system:

{y - 2.5 x = 13.5

12.25 x - y = -12.25

In the first equation, look to solve for y:

{y - 2.5 x = 13.5

12.25 x - y = -12.25

y - 2.5 x = y - (5 x)/2 and 13.5 = 27/2:

y - (5 x)/2 = 27/2

Add (5 x)/2 to both sides:

{y = 1/2 (5 x + 27)

12.25 x - y = -12.25

Substitute y = 1/2 (5 x + 27) into the second equation:

{y = 1/2 (5 x + 27)

1/2 (-5 x - 27) + 12.25 x = -12.25

(-5 x - 27)/2 + 12.25 x = 12.25 x + (-(5 x)/2 - 27/2) = 9.75 x - 27/2:

{y = 1/2 (5 x + 27)

9.75 x - 27/2 = -12.25

In the second equation, look to solve for x:

{y = 1/2 (5 x + 27)

9.75 x - 27/2 = -12.25

9.75 x - 27/2 = (39 x)/4 - 27/2 and -12.25 = -49/4:

(39 x)/4 - 27/2 = -49/4

Add 27/2 to both sides:

{y = 1/2 (5 x + 27)

(39 x)/4 = 5/4

Multiply both sides by 4/39:

{y = 1/2 (5 x + 27)

x = 5/39

Substitute x = 5/39 into the first equation:

{y = 539/39

x = 5/39

Collect results in alphabetical order:

Answer: {x = 5/39 , y = 539/39

5 0

3 years ago