Answer:
Make use of your knowledge of the maximum and minimum of the cosine function. Then scale and translate according to the way that function is scaled and translated to make f(x).
Step-by-step explanation:
f(x) is the cosine function, multplied by 4 and with 9 added to the result.
The minimum of the cosine function is -1. Multiplying that by 4 gives -4, and adding 9 gives 5.
The maximum of the cosine function is +1. Multiplying that by 4 gives +4, and adding 9 gives 13.
The minimum and maximum of f(x) are 5 and 13, respectively.
Answer:
y = 9 + -1x + 5x2
Step-by-step explanation:
Simplifying
4y + -7 = 5x2 + -1x + 2 + 3y
Reorder the terms:
-7 + 4y = 5x2 + -1x + 2 + 3y
Reorder the terms:
-7 + 4y = 2 + -1x + 5x2 + 3y
Solving
-7 + 4y = 2 + -1x + 5x2 + 3y
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-3y' to each side of the equation.
-7 + 4y + -3y = 2 + -1x + 5x2 + 3y + -3y
Combine like terms: 4y + -3y = 1y
-7 + 1y = 2 + -1x + 5x2 + 3y + -3y
Combine like terms: 3y + -3y = 0
-7 + 1y = 2 + -1x + 5x2 + 0
-7 + 1y = 2 + -1x + 5x2
Add '7' to each side of the equation.
-7 + 7 + 1y = 2 + -1x + 7 + 5x2
Combine like terms: -7 + 7 = 0
0 + 1y = 2 + -1x + 7 + 5x2
1y = 2 + -1x + 7 + 5x2
Reorder the terms:
1y = 2 + 7 + -1x + 5x2
Combine like terms: 2 + 7 = 9
1y = 9 + -1x + 5x2
Divide each side by '1'.
y = 9 + -1x + 5x2
Simplifying
y = 9 + -1x + 5x2
The factored form of the quadratic equation x² - 2x - 3 = 0 is (x - 3)(x + 1)
<h3>How to factor quadratic equation?</h3>
The quadratic equation can be factored as follows;
x² - 2x - 3 = 0
Therefore, let's find the numbers we can multiply to get -3 and add to get -2.
x² + x - 3x - 3
x(x + 1) - 3(x + 1)
Therefore,
(x - 3)(x + 1)
Therefore, the factored form of x² - 2x - 3 = 0 is (x - 3)(x + 1)
learn more on quadratic equation here: brainly.com/question/18427257
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Answer:
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Step-by-step explanation:
First you solve the brackets;
68+7 = 75
Then you add the 93;
75+93 = 168
