Answer:
see explanation
Step-by-step explanation:
Given
x² - 3x - 40 = 0
Consider the factors of the constant term (- 40) which sum to give the coefficient of the x- term (- 3)
The factors are - 8 and + 5, since
- 8 × 5 = - 40 and - 8 + 5 = - 3, thus
(x - 8)(x + 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 8 = 0 ⇒ x = 8
x + 5 = 0 ⇒ x = 5
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Given
4x² - 81 = 0 ← this is a difference of squares and factors in general as
a² - b² = (a + b)(a - b), thus
4x² - 81
=(2x)² - 9²
= (2x + 9)(2x - 9) = 0 ← in factored form
Equate each factor to zero and solve for x
2x + 9 = 0 ⇒ 2x = - 9 ⇒ x = - 
2x - 9 = 0 ⇒ 2x = 9 ⇒ x = 
If the radio active isotope has the half life of 24100 years, then the initial quantity is 2.16 grams
The half life in years = 24100
Consider the quantity of the radio active isotope remaining
y = 
When t = 1000 the y = 1.2
y = C/2 when t = 1599
Substitute the values in the equation
C/2 = 
Cancel the C in both side
1/2 = 
Here we have to apply ln to eliminate the e terms
ln (1/2) = 24100k
k = ln(1/2) / 24100
k = -2.87× 10^-5
To find the initial value we have to substitute the value of k and y in the equation
1.2 = Ce^{1000 × -2.87× 10^-5}
C = 1.2 / e^(-0.0287)
C = 2.16 gram
Hence, the initial quantity of the radioactive isotope is 2.16 gram
Learn more about half life here
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Answer:
1. d
2. 2
Step-by-step explanation:
if it's a negative it's opposite will be a positive and vice versa
Answer:
84.3%
Step-by-step explanation:
You first find the frequency. You do this by multiplying the frequency density by the class length.
So you want to find two numbers that add up to -13 and multiply to
40. You can find the factors of 40 and find the pair that adds up to
-13. -8 and -5 multiply to 40 and add up to -13.
<span><span>(x−5)</span><span>(x−8)</span>=<span>x2</span>−13x+40</span>
You can use foil to test it
<span><span>x2</span>+<span>(−8x)</span>+<span>(−5x)</span>+40=<span>x2</span>−13x+40</span>
<span><span>x2</span>−13x+40=<span>x2</span>−13x+</span>