Answer:
18x^2 + 27x - 35
Step-by-step explanation:
f(g(x)) means function f times function g. substitute for f and g, which gets you (3x+7)(6x-5). Now, multiply using the distributive property.
3x * 6x = 18x^2
3x * -5 = -15x
7*6x = 42x
7 * -5 = -35
The equation then becomes 18x^2 - 15x + 42x - 35. Simplify the equation.
18x^2 stays, -15x and 42x combine to make 27x, and the -35 stays too.
Finally, you get the equation, 18x^2 + 27x -35.
The answer is: " <span>1.045 * 10¹⁰ " .</span>
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Explanation:
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"5.5 million = 5,500,000 = 5.5 * 10 ⁶ " ;
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"1.9 thousand = 1,900 = 1.9 * 10³ " ;
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So; "<span>5.5 million * 1.9 thousand" ;
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= (</span>5.5 * 10 ⁶) * (1.9 * 10³) = 5.5 * 10⁶ * 1.9 * 10³ ;
= 5.5 * 1.9 * 10⁶ * 10³ ;
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Note the following properties of exponents:
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xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾ ;
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As such, " 10⁶ * 10³ = 10⁽ ⁶ ⁺ ³⁾ = 10⁹ " ;
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So; rewrite:
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5.5 * 1.9 * 10⁶ * 10³ ;
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= 5.5 * 1.9 * 10⁹ ;
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5.5 * 1.9 = 10.45 ;
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Rewrite as: " 10.45 * 10⁹ " ;
In scientific notation, we need to rewrite as an single digit integer, followed by a decimal and other values (if applicable); following by * 10 raised to the appropriately adjusted exponential power.
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As such, we write the value as:
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" 1.045 * 10¹⁰ " .
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Answer:
y(s) =
we will compare the denominator to the form
comparing coefficients of terms in s
1
s: -2a = -10
a = -2/-10
a = 1/5
constant:
hence the first answers are:
a = 1/5 = 0.2
β = 5.09
Given that y(s) =
we insert the values of a and β
=
to obtain the constants A and B we equate the numerators and we substituting s = 0.2 on both side to eliminate A
5(0.2)-53 = A(0.2-0.2) + B((0.2-0.2)²+5.09²)
-52 = B(26)
B = -52/26 = -2
to get A lets substitute s=0.4
5(0.4)-53 = A(0.4-0.2) + (-2)((0.4 - 0.2)²+5.09²)
-51 = 0.2A - 52.08
0.2A = -51 + 52.08
A = -1.08/0.2 = 5.4
<em>the constants are</em>
<em>a = 0.2</em>
<em>β = 5.09</em>
<em>A = 5.4</em>
<em>B = -2</em>
<em></em>
Step-by-step explanation:
- since the denominator has a complex root we compare with the standard form
- Expand and compare coefficients to obtain the values of a and <em>β </em>as shown above
- substitute the values gotten into the function
- Now assume any value for 's' but the assumption should be guided to eliminate an unknown, just as we've use s=0.2 above to eliminate A
- after obtaining the first constant, substitute the value back into the function and obtain the second just as we've shown clearly above
Thanks...
Answer:
-10, -8, -6, -4
Step-by-step explanation:
Our smallest integer is -10, it then follows that our integers are
-10, -8, -6, -4