Let
x-------> the original price of the bed sheets
we know that
Nancy purchased some bed sheets for $ they were on sale
% off
so
%-
%=
%
%=
therefore
the answer is
the original price of the bed sheets was $
Find the surface area of the pyramid shown to the nearest whole number. 6ft 5ft 5ft
1 answer:
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Remark
The reason you are not getting many replies to this is an uncertainty about f(x). We do not know if you mean f(x) = 2/(x - 6) or f(x) = (2/x) - 6. We'll try it both ways.
First Way f(x) = 2/(x - 6)
f(x = y = 2/(x - 6) Interchange x and y
x = 2 / (y - 6) Multiply both sides by y - 6
x(y - 6) = 2 Divide by x
y - 6 = 2/x Add 6 to both sides.
y = 2/x + 6 Which is close to g(x) but it is not the same thing, even if you use x as a common denominator. That would give you
Second Way: f(x) = (2/x) - 6
f(x) = y = (2/x) - 6 Interchange x and y
x = (2/y) - 6 Add 6 to both sides
x + 6 = 2/y Multiply both sides by y
y(x + 6) = 2 Divide by sides by (x + 6)
y = 2/(x + 6)
Comment
These do not look anything alike so g(x) and f(x) are not inverses.
Answer:
x = -3, 0, or 7
Step-by-step explanation:
After removing common factors, the remaining quadratic can be factored by comparison to the factored form of a quadratic.
__
<h3>Step 1</h3>Write the equation in standard form.
4x³ -16x² -84x = 0
<h3>Step 2</h3>Factor out the common factor from all terms.
= 4x(x² -4x -21) = 0
<h3>Step 3</h3>Compare to the factored form of a quadratic:
(x +a)(x +b) = x² +(a+b)x +ab
This tells you the constants 'a' and 'b' in the factors can be found by considering ...
(a+b) = -4 . . . . the coefficient of the x term of the quadratic
ab = -21 . . . . . the constant term of the quadratic
It is often helpful to list factor pairs of the constant:
-21 = (-21)(1) = (-7)(3) . . . . integer pairs that have a negative sum
The sums of these pairs are -20 and -4. We are interested in the latter. We can choose ...
a = -7, b = 3
<h3>Step 4</h3>Put it all together.
4x³ -16x² -84 = (4x)(x -7)(x +3) = 0 . . . . . factored form of the equation
<h3>Step 5</h3>Apply the zero product rule. This rule tells you the product of factors will be zero when one or more of the factors is zero:
4x = 0 ⇒ x = 0
x -7 = 0 ⇒ x = 7
x +3 = 0 ⇒ x = -3
Solutions to the equation are x ∈ {-3, 0, 7}.
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<em>Additional comment</em>
What we did in Step 3 is sometimes referred to as the X-method of factoring a quadratic. The constant (ab product) is put at the top of the X, and the sum (a+b) is put at the bottom. The sides of the X are filled in with values that match the product and sum: -7 and 3. The method is modified slightly if the coefficient of x² is not 1.
A graphing calculator often provides a quick and easy method of finding the real zeros of a polynomial.
