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3 years ago

Which of the Following is a solution to 7x-6y=19 (-5,-3) ,(7,5), (-4,0) (1,-2)

Mathematics

1 answer:

Korolek [52]3 years ago

4 0

Answer:

(1,-2)

Step-by-step explanation:

Choose any value for x that is in the domain to plug into the equation.

Choose 0 to substitute in for x to find the ordered pair.

(0, -19/6)

Choose 1 to substitute in for x to find the ordered pair.

Remove parentheses.

y= -19/6 + 7(1)/6

Simplify

y=2

Use the

x and y values to form the ordered pair.

(1,−2)

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Answer:

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3 years ago

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3 years ago

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

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3 years ago

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PIT_PIT [208]

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3 years ago

Read 2 more answers

Which equation in point-slope form contains the point (–3, 5) and has slope –1? y + 3 = –1(x – 5) y – 5 = –1(x + 3) y – 3 = –1(x

andreev551 [17]

Answer:

y - 5 = -1(x + 3)

Step-by-step explanation:

Point slope form

y - y1 = m(x - x1) where m = slope and passing through point (x1 , y1)

In this case if the equation in point-slope form contains the point (–3, 5) and has slope –1 then the equation should be:

y - 5 = -1(x - (-3))

y - 5 = -1(x + 3)

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3 years ago