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3 years ago

2 3/4 divided by 3. What is the quotient and what is it in lowest terms?

Mathematics

1 answer:

Dmitry_Shevchenko [17]3 years ago

5 0

Answer:

11/12

Step-by-step explanation:

2 3/4 = 2·(4/4) + 3/4 = (8/4) +(3/4) = (8+3)/4 = 11/4

Then your problem becomes ...

(11/4) / 3 = (11/4) · (1/3) = (11·1)/(4·3) = 11/12

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The numerator and denominator have no common factors, so this is lowest terms.

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A triangle has two sides that measure 4ft. and 3ft. Which could be the measure of the 3rd side?

Aneli [31]

In order to form a triangle, the third side must be at least greater than the difference of the other two sides
4 - 3 = 1 So the third side must be greater than 1 foot and the third side must be less than the sum of the other two sides
4 + 3 = 7 So, the third side must be less than 7

1 < third side < 7

4 0

3 years ago

Solve The Equation <br> 4x×9y=7<br> 4x-9y=9

hoa [83]

Answer:

$\large\boxed{x=\dfrac{9}{8}-\dfrac{\sqrt{109}}{8},\ y=-\dfrac{1}{2}-\dfrac{\sqrt{109}}{18}}\\or\\\boxed{x=\dfrac{9}{8}+\dfrac{\sqrt{109}}{2},\ y=-\dfrac{1}{2}+\dfrac{\sqrt{109}}{18}}$

Step-by-step explanation:

$\left\{\begin{array}{ccc}4x\times9y=7&(1)\\4x-9y=9&(2)\end{array}\right\\\\(2)\\4x-9y=9\qquad\text{subtract}\ 4x\ \text{from both sides}\\-9y=-4x+9\qquad\text{change the signs}\\9y=4x-9\qquad\text{substitute it to (1)}\\\\4x(4x-9)=7\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\(4x)(4x)+(4x)(-9)=7\\(4x)^2-36x=7\\(4x)^2-2(4x)(4.5)=7\qquad\text{add}\ 4.5^2\ \text{to both sides}\\(4x)^2-2(4x)(4.5)+4.5^2=7+4.5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2$

$(4x-4.5)^2=7+20.25\\(4x-4.5)=27.25\to 4x-4.5=\pm\sqrt{27.25}\\\\4x-\dfrac{45}{10}=\pm\sqrt{\dfrac{2725}{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{2725}}{\sqrt{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25\cdot109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25}\cdot\sqrt{109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{5\sqrt{109}}{10}\qquad\text{add}\ \dfrac{45}{10}\ \text{to both sides}\\\\4x=\dfrac{45}{10}\pm\dfrac{5\sqrt{109}}{10}$

$4x=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 4}\\\\x=\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\\\\\text{Put the values of}\ x\ \text{to (2):}\\\\9y=4\left(\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\right)-9\\\\9y=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}-\dfrac{18}{2}\\\\9y=-\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 9}\\\\y=-\dfrac{1}{2}\pm\dfrac{\sqrt{109}}{18}$

8 0

3 years ago

What is the slope of a line that passes through the points (4,3) and (-7,1)?

Andreyy89

Answer:

-2/3

Step-by-step explanation:

If you use the formula y2-y1/x2-x1 your answer will be -2/3

5 0

3 years ago

Read 2 more answers

How to solve Which ordered pair is a solution for x − 3y = 1?

babunello [35]

There is no one answer (ordered pair) to this equation and the answer is found by graphing or trying out different values for each variable. Anyway, here are some solutions; (1,0), (4,1), (0,-1/3).

5 0

3 years ago

I'm very confused on this question and I don't know how to solve it. Any kind of help will be appreciated.

juin [17]

QP is the bisector so QPM is half NPM or

$m \angle NPM = 2 m \angle QPM$

6 0

4 years ago