## Forum Replies Created

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- July 21, 2021 at 4:04 pm in reply to: Enter the maximum number of electrons in each type of sublevel (s, p, d, and f, respectively). #10712July 21, 2021 at 8:28 pm in reply to: What are the solutions of the equation x^4 + 95x^2 – 500 = 0? Use factoring to solve. #10821::
**Answer :**Option C

x = ±√5, x = ±10i**Explanation :**

Given equation,

x^4 + 95x^2 – 500 = 0By

**factoring**the above equation we get,

x^4 + 100x^2 – 5x^2 – 500 = 0

x^2(x^2 + 100) – 5(x^2 + 100) = 0

(x^2 – 5)(x^2 + 100) = 0solving the equation,

x^2 = 5, x^2 = 100Therefore,

**x = ±√5, x = ±10i**- This reply was modified 3 years, 2 months ago by ProtonsTalk.

::**Solution:**To find the inverse equation,**interchange**x and y variables,

x = 100 – y²

Then find roots of y,

y² = 100 – x

y = ±√(100 – x)

Therefore, the inverse equation for*y = 100 – x^2*

is,**y = ±√(100 – x)**- This reply was modified 3 years, 2 months ago by suseelk.
- This reply was modified 3 years, 2 months ago by ProtonsTalk.

July 21, 2021 at 9:41 pm in reply to: Which equation is y=3(x-2)^2-(x-5)^2 rewritten in vertex form? #10838::**Answer : Option D****Explanation :**

=> y = 3(x – 2)^2 – (x – 5)^2

=> y = 3(x – 2)(x – 2) – (x – 5)(x – 5)

=> y = 3(x(x – 2) – 2(x – 2)) – (x(x – 5) – 5(x – 5))

=> y = 3(x(x) – x(2) – 2(x) + 2(2)) – (x(x) – x(5) – 5(x) + 5(5))=> y = 3(x^2 – 2x – 2x + 4) – (x^2 – 5x – 5x + 25)

=> y = 3(x^2 – 4x + 4) – (x^2 – 10x + 25)

=> y = 3(x^2) – 3(4x) + 3(4) – (x^2) + (10x) – (25)

=> y = (3x^2 – 12x + 12) + (-x^2 + 10x – 25)

=> y = (3x^2 – x^2) + (-12x + 10x) + (12 – 25)

=> y = 2x^2 – 2x – 13add 13 on both sides

=> y + 13 = 2x^2 – 2x + 1/2y + 13 + 1/2 = 2(x^2 – x + 1/4)

=> y + 27/2 = 2(x^2 – 1/2x – 1/2x + 1/4)

=> y + 27/2 = 2(x(x) – x(0.5) – 0.5(x) + 0.5(0.5))

=> y + 27/2 = 2(x(x – 1/2) – 1/2(x – 1/2))

=> y + 27/2 = 2(x – 1/2)(x – 1/2)

=> y + 27/2 = 2(x – 1/2)^2subtract 13.5 on both sides

Hence, y = 2(x – 1/2)^2 – 27/2

- This reply was modified 3 years, 2 months ago by ProtonsTalk.

July 21, 2021 at 10:03 pm in reply to: What is the greatest common factor of 4k, 18k^4, and 12? #10843July 21, 2021 at 3:50 pm in reply to: What is the slope of the line represented by the equation y = x – 3? #10703::The Slope of line,

*y = x – 3*is 1.**Explanation**:

the**standard equation**of the line in the slope-y intercept form is**y = m.x + c**

where,

m is slope of the line

c is the y-intercept of lineBy comparing the above equation with standard form

y = (1)x – 3Therefore,

**the Slope of line, y = x – 3 is 1.**- This reply was modified 3 years, 2 months ago by ProtonsTalk.

July 21, 2021 at 8:11 pm in reply to: Using the quadratic formula to solve 2x^2 = 4x – 7, what are the values of x? #10818::**Answer:**x = (2 ± √10 i)/2**Explanation :**

**Standard Quadratic Expression :**ax^2 + bx + c = 0

Using**quadratic formula**, expression for roots,

x = [ -b ± √(b2 – 4ac) ] / 2aBy comparing,

=> x = [ -(-4) ± √{(-4)2 – 4(2)(7)} ] / 2(2)

=> x = [ 4 ± √{16 – 56} ] / 4

=> x = [ 4 ± √(-40) ] / 4

=> x = [ 4 ± 2√10 i ] / 4

=> x = (2 ± √10i)/2Therefore, the roots of x are : (2 + √10 i)/2 and (2 – √10 i)/2

- This reply was modified 3 years, 2 months ago by ProtonsTalk.

July 21, 2021 at 9:25 pm in reply to: If h(x) is the inverse of f(x), what is the value of h(f(x))? #10832::**Solution:**

Given,

f(x) is a function and h(x) is inverse of f(x),Hence,

**h(x) = f^-1(x)**

Then, h(f(x)) will be,

**f^-1(f(x)) = x**- This reply was modified 3 years, 2 months ago by ProtonsTalk.

July 21, 2021 at 9:54 pm in reply to: If f(x) = 8 – 10x and g(x) = 5x + 4, what is the value of (fg)(–2)? #10841::**Answer : Option 2) -168****Explanation :**

=> (fg)(−2) = f(−2)×g(−2).

=> f(−2) = 8−10(−2) = 8+20 = 28

=> g(−2) = 5(−2)+4 = −10+4 = −6Then,

**(fg)(−2) = 28×−6 = −168**- This reply was modified 3 years, 2 months ago by ProtonsTalk.

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