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otez555 [7]
4 years ago
12

What is the name for a statement that shows two expressions are equal?

Mathematics
2 answers:
Serggg [28]4 years ago
4 0

A mathematical equation

Semmy [17]4 years ago
3 0
An equation is a statement that shows that 2 expressions are equal.
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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
4 years ago
Yan has four more apples than xavier
ollegr [7]

yan has 4 xavier has zero

8 0
4 years ago
A species of phytoplankton measures about 2 × 10−6 in. A grain of sand measures about 1 × 10−4 in. About how many times longer i
Gennadij [26K]

Answer:

B. 50 times greater

Step-by-step explanation:

Given;

size of phytoplankton = 2 × 10⁻⁶ in

size of sand grain = 1 × 10⁻⁴ in

Determine how many times longer the grain of sand is than the phytoplankton.

Divide the sand size by the phytoplankton size, to find out how much greater the sand is.

This can be done by equating it as follows;

2 × 10⁻⁶ (y)  = 1 × 10⁻⁴

y = \frac{1*10^{-4}}{2*10^{-6}} \\\\y = 50

Therefore, the grain of sand is 50 times greater than the phytoplankton

B. 50 times greater

7 0
3 years ago
Gabriel determined that his total cost would be represented by 2.5x + 2y – 2. His sister states that the expression should be x
meriva

✨ SAMPLE ANSWER ✨

The entire expression should be subtracted from 30. To subtract the quantity, distribute the negative sign, which changes the signs on the terms. So, the –2 changes to positive and gets added to 30 instead of subtracted from it.

If this helped, please thank me!

5 0
3 years ago
The combined area of two squares is 45 square centimeters. Each side of one square is twice as long as a side of the other squar
vladimir2022 [97]
Let the side of  one square be x.    Area = x*x = x²

Then the side of other square  would be 2x ,   Area = 2x*2x = 4x²

Combined area = x² + 4x²  = 5x²

This combined area = 45 cm²

Therefore  5x²  = 45   Divide both sides by 5
                  x²  =  45/5
                  x²  = 9        Take square root of both sides
                  x   =  √9
                  x  = 3

Length of larger square is 2x  = 2*3 = 6 cm
Length of larger square = 6cm
4 0
3 years ago
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