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Vikki [24]
2 years ago
7

Sam and Andre shared a number of pennies in the ratio 8:3. They received a total of 671 pennies. How many more pennies did Sam r

eceive than Andre?
Mathematics
1 answer:
motikmotik2 years ago
8 0

Answer:

Sam had 488

Andre had 183

488:183

please mark brainllest

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Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$
horrorfan [7]

Answer:

A +B+C+D  = 3 is the correct answer.

Step-by-step explanation:

Given:

$\frac{5}{2+\sqrt{6}}$

To find:

A+B+C+D = ? if given term is written as following:

$\frac{A\sqrt{B}+C}{D}$

<u>Solution:</u>

We can see that the resulting expression does not contain anything under \sqrt (square root) so we need to rationalize the denominator to remove the square root from denominator.

The rule to rationalize is:

Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.

Applying this rule to rationalize the given expression:

\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \   (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}

Comparing the above expression with:

$\frac{A\sqrt{B}+C}{D}$

A = 5, B = 6 (Not divisible by square of any prime)

C = -10

D = 2 (positive)

GCD of A, C and D is 1.

So, A +B+C+D = 5+6-10+2 = \bold3

5 0
3 years ago
How to change 50/12 to a mixed number?
11111nata11111 [884]
A mixed number is one that has an integer along with a proper fraction, so that would be (for this improper fraction):

50/12 = 4 1/6

12 goes into 50, 4 times with a remainder of 2

you get: 4 and 2/12, but 2/12 can be reduced further to 1/6

so that's how i got the answer of 4 1/6
7 0
3 years ago
Solve -1 3/8 K equals 2/3
guajiro [1.7K]

Answer:

  K = -16/33

Step-by-step explanation:

For a problem like this, it is convenient to write the mixed number as an improper fraction:

  -11/8 K = 2/3

Now, multiply the equation by the reciprocal of the coefficient of K.

  K = (-8/11)(2/3)

  K = -16/33

8 0
3 years ago
What is the result of the first step when simplifying 13-4(x-5)
Maksim231197 [3]
I don't really get this question but simply put, if you are in college syntax matters very much. (13-4) = 9 *(x-5) = 9x-45.. although in this case. since there isn't a bracket around 13-4. you'd multiply by the -4 first, giving you, 4x-20+30 =4x-10
8 0
3 years ago
The table below represents a function.
skelet666 [1.2K]

Answer:

i am pretty sure it is A/the graph is a straight line that has a slope of 6

Step-by-step explanation:

8 0
3 years ago
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