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3 years ago

Which description best describes the solution to the following system of equations?

Mathematics

1 answer:

sertanlavr [38]3 years ago

4 0

Line y = –x + 4 intersects the line y = 3x + 3., this is the right answer

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For a field trip 9 students rode in cars and the rest filled three busses. How many students were in each bus if 99 students wer

taurus [48]

Answer: 30 students per bus

Step-by-step explanation: 99-9=90

90/3=30

30 students per bus

8 0

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:

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

Solution:

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

Y=4x+1 complete the table

Tom [10]

Please refer to the attached image for the answer

3 0

2 years ago

Dal

iogann1982 [59]

Answer:a

Step-by-step explanation:

6 0

2 years ago

How do you do this? I can't remember

Hitman42 [59]

14.75 depending on if the model is 8 & the actual is 1 in the 1:8 scale factor because you would just multiply the actual by 8 because it is the scale factor. the answer could also be .23 is the model is 1 & the actual is 8 because you would divide the actual by 8! hope this helps!!

3 0

3 years ago

Read 2 more answers