Answer:
Step-by-step explanation:
Define ...
z = 3x+2
Substitute for that expression in the given quadratic:
z^2 +7z -8 = 0 . . . . . . your equivalent quadratic
_____
This equation is easily solved by factoring:
(z +8)(z -1) = 0
z = -8 or +1
Then x can be found from z:
(z -2)/3 = x
(-8 -2)/3 = x = -10/3
(+1 -2)/3 = x = -1/3
The answer is the one on the top
Problem
Write the slope-intercept form of the line described in the following:
Parallel to 4x + 5y=20
and passing through (12,4)
Solution>
For this case we need to have the same slope, and if we write the equation given we see:
5y = 20 -4x
y = 4 -4/5 x
then the slope m = -4/5
and we also know a point given x= 12, y= 4 and we can do the following:
4 = -4/5 (12) +b
4 = -48/5 + b
And if we solve for the intercept we got:
b= 4 +48/5= -28/5
And our equation would be given by:
y = -4/5 x -28/5
By understanding and applying the characteristics of <em>piecewise</em> functions, the results are listed below:
- r (- 3) = 15
- r (- 1) = 11
- r (1) = - 7
- r (5) = 13
<h3>How to evaluate a piecewise function at given values</h3>
In this question we have a <em>piecewise</em> function formed by three expressions associated with three respective intervals. We need to evaluate the expression at a value of the <em>respective</em> interval:
<h3>r(- 3): </h3>
-3 ∈ (- ∞, -1]
r(- 3) = - 2 · (- 3) + 9
r (- 3) = 15
<h3>r(- 1):</h3>
-1 ∈ (- ∞, -1]
r(- 1) = - 2 · (- 1) + 9
r (- 1) = 11
<h3>r(1):</h3>
1 ∈ (-1, 5)
r(1) = 2 · 1² - 4 · 1 - 5
r (1) = - 7
<h3>r(5):</h3>
5 ∈ [5, + ∞)
r(5) = 4 · 5 - 7
r (5) = 13
By understanding and applying the characteristics of <em>piecewise</em> functions, the results are listed below:
- r (- 3) = 15
- r (- 1) = 11
- r (1) = - 7
- r (5) = 13
To learn more on piecewise functions: brainly.com/question/12561612
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