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Ivenika [448]
3 years ago
8

Prove the algebraic identity with the left hand side and supplying a sequence of equivalent expressions that ends with the right

hand side. X^3-x^2/x -(x-1)(x+1)=1-x
Mathematics
1 answer:
My name is Ann [436]3 years ago
4 0

Answer:

See Prove

Step-by-step explanation:

Given the expression: \dfrac{x^3-x^2}{x} -(x-1)(x+1)

To Prove: \dfrac{x^3-x^2}{x} -(x-1)(x+1)=1-x

Taking the Left-Hand side

\dfrac{x^3-x^2}{x} -(x-1)(x+1)\\=\dfrac{x(x^2-x)}{x} -[x(x+1)-1(x+1)]\\=x^2-x-[x^2+x-x-1]\\=x^2-x-x^2+1\\=-x+1\\=1-x

This is the right-hand side as required.

We have proved the given algebraic identity.

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In a circle, a 90° sector has area 64π ft2. Solve for the radius of the circle. A. 16 ft. B. 12 ft. C. 18 ft. D. 8 ft.
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3 years ago
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Which expressions are equivalent to -6n + (-12) + 4n ?
raketka [301]
The expression equivalent to the fort is a) 4(n-3) -6n, if you so the math for the first one do what is inside the parenthesis first. (think PEMDAS) Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction. So the first thing it gives you is -6n +(-12) Well, a negative + a negative = a negative! So, -6+-12= -18, then add your caroable. So, -18n. Now, you add -18n with what you have left so 4n -18+4 is -14n. So, if you do answer a) (n-3) = (1n-3)= (1-3) =-2. -2×4=-8n because a negative × a positive = a negative because they have different signs. From there you have -8n - (6) Instead of subtracting you just add a negative So, you would rewrite your problem as: -8n+(-6)= -14n the same thing you got as your orginal. Hope tj
his helped! Don't forget about adding you variables and PEMDAS!! Also d po not forget about your positive a negative rules!!!
4 0
4 years ago
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I need help please. I don't understand
Viktor [21]

Answer:

  a.  y = 0.56x -17.78 . . . . y = Celsius temperature; x = Fahrenheit temperature

  b.  37.436 °C

  c.  interpolation

  d.  83.2 °F

Step-by-step explanation:

a. In most cases, finding the linear regression equation that fits a table of data involves somewhat tedious calculations best performed by a calculator or computer. The general approach is to enter the data into the necessary list(s) or table, and invoke the necessary function.

In Microsoft Excel (and many other spreadsheet programs), you can chart the data in the usual way, then choose the option to add the regression equation to the chart.

In the Desmos calculator used here, the data can be entered into a table, and a generic equation written relating the table entries. Any unknown constants in the equation are computed by Desmos so as to maximize the correlation between the equation and the data. Using a linear equation results in a linear regression computation.

This calculator tells us what we should already know (from previous knowledge of Fahrenheit–Celsius conversion).

  y ≈ 0.56x -17.78

(We already know the actual conversion is y = (5/9)(x -32) = (5/9)x -(17 7/9). The above is what you get when the numbers are rounded to hundredths, as required by this problem.)

___

b. Using the above equation for x=98.6, we get

  y = 0.56·98.6 -17.78 = 55.216 -17.78 = 37.436 . . . °C

___

c. Since we're finding a value <em>between</em> values already in the table, the process is called interpolation. (Extrapolation is used to find values beyond those that are already in the table. The prefixes <em>inter</em>- (between) and <em>extra</em>- (beyond) can help you remember what these terms mean.)

___

d. In this part, we're asked to find x that corresponds to y=28.8. We fill in the value and solve.

  28.8 = 0.56x -17.78

  46.58 = 0.56x . . . . . . add 17.78

  46.58/0.56 = x ≈ 83.179 ≈ 83.2 . . . . . divide by the coefficient of x; round appropriately. Units are °F.

6 0
4 years ago
What is the solution of the system? Use the substitution method.
cricket20 [7]
Start by isolating one of the variables
x=-4y+2
Sub x into the other formula and solve for the y value of the solution.
3(-4y+2)+2y=11
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Sub the y value into the x formula you created.
x=-4(-1/2)+2
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x=4
Therefore the solution is (4,-1/2) I think the answer is B unless the y value is actually -12.
Hope this helps :)
8 0
3 years ago
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