Answer:
The solutions are x = 1.24 and x = -3.24
Step-by-step explanation:
Hi there!
First, let´s write the equation:
log[(x² + 2x -3)⁴] = 0
Apply the logarithm property: log(xᵃ) = a log(x)
4 log[(x² + 2x -3)⁴] = 0
Divide by 4 both sides
log(x² + 2x -3) = 0
if log(x² + 2x -3) = 0, then x² + 2x -3 = 1 because only log 1 = 0
x² + 2x -3 = 1
Subtract 1 at both sides of the equation
x² + 2x -4 = 0
Using the quadratic formula let´s solve this quadratic equation:
a = 1
b = 2
c = -4
x = [-b± √(b² - 4ac)]/2a
x = [-2 + √(4 - 4(-4)·1)]/2 = 1.24
and
x = [-2 - √(4 - 4(-4)·1)]/2 = -3.24
The solutions are x = 1.24 and x = -3.24
Have a nice day!
Answer:
1/7, 3/7, 4/7, 6/7
Step-by-step explanation:
There's like denominators(bottom number) so you would list the numerators(top number) from least to greatest.
Answer:
Step-by-step explanation:
x-the original price
y- the discounted price
y= the original price - 25 % discounted from x = x- (.25*x) = x( 1-.25) = .75x
equation is y= .75x
The equation should only be in the first quadrant because the prices can only be positive numbers.
<h3>Answer:</h3>
Yes, ΔPʹQʹRʹ is a reflection of ΔPQR over the x-axis
<h3>Explanation:</h3>
The problem statement tells you the transformation is ...
... (x, y) → (x, -y)
Consider the two points (0, 1) and (0, -1). These points are chosen for your consideration because their y-coordinates have opposite signs—just like the points of the transformation above. They are equidistant from the x-axis, one above, and one below. Each is a <em>reflection</em> of the other across the x-axis.
Along with translation and rotation, <em>reflection</em> is a transformation that <em>does not change any distance or angle measures</em>. (That is why these transformations are all called "rigid" transformations: the size and shape of the transformed object do not change.)
An object that has the same length and angle measures before and after transformation <em>is congruent</em> to its transformed self.
So, ... ∆P'Q'R' is a reflection of ∆PQR over the x-axis, and is congruent to ∆PQR.
There are 20 cassettes.
Step-by-step explanation:
Given,
Ratio of cassette to compact disc = 10:3
Let,
the number of cassettes = 10x
Number of compact disc = 3x
According to given statement;
the number of cassettes is 10 less than 5 times the number of compact discs.
10x = 5(Number of CD) - 10
Dividing both sides by 5
Number of cassettes= 10x = 10(2) = 20
There are 20 cassettes.
Keywords: variable, ratio
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