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Evgen [1.6K]
3 years ago
10

Rationalize the denominator.

Mathematics
1 answer:
mel-nik [20]3 years ago
3 0

Answer:

7sqrt(15) - 5sqrt(6)

------------------------------

45

Step-by-step explanation:

7 -sqrt(10)

-----------------------

3 sqrt(5) *sqrt(3)

7 -sqrt(10)

-----------------------

3 sqrt(15)

Multiply the top and bottom by sqrt(15)/ sqrt(15)

7 -sqrt(10)               sqrt(15)

----------------------- * ------------

3 sqrt(15)                 sqrt(15)


(7 -sqrt(10))* sqrt(15)

-----------------------------------

3 *15

Distribute


7sqrt(15) - sqrt(150)

------------------------------

45

sqrt(ab) =sqrt(a) sqrt(b)

150 = 25*6

7sqrt(15) - sqrt(25)sqrt(6)

------------------------------

45

7sqrt(15) - 5sqrt(6)

------------------------------

45

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Find an equation of the line through these points (15,2.2) (5,1.6). Write answer in a slope-intercept form
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Answer:

y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}

Step-by-step explanation:

Hi there!

Slope-intercept form: y=mx+b where m is the slope and b is the y-intercept (the value of y when x is 0)

<u>1) Determine the slope (</u><u><em>m</em></u><u>)</u>

m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1} where two given points are (x_1,y_1) and (x_2,y_2)

Plug in the given points (15,2.2) and (5,1.6):

m=\frac{\displaystyle 1.6-2.2}{\displaystyle 5-15}\\\\m=\frac{\displaystyle -0.6}{\displaystyle -10}\\\\m=\frac{\displaystyle 0.6}{\displaystyle 10}\\\\m=\frac{\displaystyle 0.3}{\displaystyle 5}\\\\m=\frac{\displaystyle 3}{\displaystyle 50}

Therefore, the slope of the line is \frac{\displaystyle 3}{\displaystyle 50}. Plug this into y=mx+b:

y=\frac{\displaystyle 3}{\displaystyle 50}x+b

<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>

y=\frac{\displaystyle 3}{\displaystyle 50}x+b

Plug in a given point and solve for b:

1.6=\frac{\displaystyle 3}{\displaystyle 50}(5)+b\\\\1.6=\frac{\displaystyle 3}{\displaystyle 10}+b\\\\1.6-\frac{\displaystyle 3}{\displaystyle 10}=\frac{\displaystyle 3}{\displaystyle 10}+b-\frac{\displaystyle 3}{\displaystyle 10}\\\\\frac{\displaystyle 13}{\displaystyle 10}=b

Therefore, the y-intercept is \frac{\displaystyle 13}{\displaystyle 10}. Plug this back into y=\frac{\displaystyle 3}{\displaystyle 50}x+b:

y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}

I hope this helps!

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