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stiks02 [169]
3 years ago
12

If 5 + 2root3/7 + root3 = a-root3b find a and b where a and b are rational no

Mathematics
1 answer:
mariarad [96]3 years ago
8 0

Answer:

a = 29/46

b= - 9/46

Step-by-step explanation:

<u>Given:</u>

  • (5 + 2√3)/(7 + √3) = a - √3b

<u>Rationalizing the left side:</u>

  • (5+2√3)(7-√3)/(7+√3)(7-√3) =
  • (35 + 14√3 - 5√3 - 2√3²)/(7² - √3²) =
  • (35 - 6 + 9√3)/(49 - 3) =
  • (29 + 9√3)/46 =
  • 29/46 + √3 (9/46)

<u>Comparing the left and right sides:</u>

  • a - √3b = 29/46 + √3 9/46
  • a = 29/46
  • b = - 9/46

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Find the value of the variable.
melamori03 [73]

Answer:

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Step-by-step explanation:

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3 years ago
PLEASE HELP ASAP. SOLVE FOR X AND Y. SHOW ALL WORK.
ss7ja [257]

The solution to the system of equations is (-3.88, 0.66) and (3.04, 1.09)

<h3>How to determine the solution to the system of equations?</h3>

The system of equations is given as:

x^2y + yx^2 = 20

1/x + 1/y = 5/4

Multiply through the equation 1/x + 1/y = 5/4 by 4xy

So, we have:

4x + 4y = 5xy

So, we have the following system of equations

4x + 4y = 5xy

x^2y + yx^2 = 20

Next, we plot the graph of the system of equations

4x + 4y = 5xy

x^2y + yx^2 = 20

See attachment for the graph of the system

From the attached system, we have the point of intersection to be

(x, y) = (-3.88, 0.66) and (3.04, 1.09)

Hence, the solution to the system of equations is (-3.88, 0.66) and (3.04, 1.09)

Read more about system of equations at

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2 years ago
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Nataly_w [17]

Answer:

n = 80

Step-by-step explanation:

Plug in 80 for n to check:

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3 years ago
Question
dezoksy [38]

Answer:

  The equations of the lines are y=3 and y=8.

  Parallel lines have equal slopes, so if the slopes are opposites, the slopes must be 0.

  A line with this slope and passing through (7, 3) has equation y=3.

Step-by-step explanation:

The above answer statements pretty much speak for themselves. The only opposite numbers that are equal are 0 and -0 = 0, so the slopes must be 0.

A line with a zero slope has a constant y-value, so is of the form ...

  y = constant

If it goes through a point with a y-coordinate of 3, then the constant must be 3. The line is ...

  y = 3

___

If the sum of two numbers is 11 and one of them is 3, the other is 8. So, the parallel line has equation y = 8.

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4 years ago
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