The property that best matches the equation is the associative property.
<h3>What is an associatve property?</h3>
It should be noted that the associative property simply implies that the way the factors are grouped in a multiplication problem doesn't change the product.
In this case, since it's illustrated that (5 × 3) × 2 = (2 × 3) × 5. They both will give a value of 40.
In this case, the associative property is illustrated.
The complete question is:
Write the property that best matches the following: (5 × 3) × 2 = (2 × 3) × 5.
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We know that: sin Ф = cos(π/2 - Ф) ↔ sin Ф = cos(90° - Ф)
Then:
sin 42° = cos(90° - 42°) = cos 48°
IF sin 42° = 2/3, the cos 48° = 2/3
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Answer:
(x, y) = (4, 9)
Step-by-step explanation:
Perhaps the ordered pair you want is the one that satisfies both equations.
We can find that by equating the expressions for y:
x +5 = 3x -3
8 = 2x . . . . . . . . add 3-x to both sides
4 = x . . . . . . . . . divide by 2
y = 4+5 = 9
The ordered pair is (x, y) = (4, 9).
Answer:
Choices 1 and 4 are correct.
Step-by-step explanation:
We first need to find what the slope of the line is. That way, we can find out which possible answers are perpendicular to it:
Since we now have the slope, we need the negative reciprocal of it. Remember: if x is the slope, it's negative reciprocal will be . Therefore, if the line's slope is 3, then we need to find answers with a slope of.
The first answer is correct, as you have marked. The second answer, while written a little weirdly, does show the slope as 3, which we know as wrong. The third choice is not correct, however. This equation is written in point-slope form, where. The only variable we have to worry about is m, which, in the third choice, is 3. The fourth answer is correct, which sounds weird at first. Let's put that equation into slope-intercept form:
Equations like these can be real sneaky, so it's important not to jump to conclusions with them.
From the calculation, the growth rate is 0.88.
<h3>What is the growth rate?</h3>
To find the relative growth rate
P1 = Poe^rt
P2 = Poe^rt
Thus;
1920 = Poe^4r ------ (1)
1966080 =Poe^12r -------(2)
P2/P1 gives;
1966080/1920 = Poe^12r/Poe^4r
1024 = e^12r/e^4r
1024 =e^8r
1024 = (e^r)^8
2^10 = (e^r)^8
e^r = 2^1.25
e^r = 2.38
r = ln(2.38)
r = 0.88
The initial size of the culture is;
1920 = Poe^(0.88 * 4)
Po = 1920/e^(0.88 * 4)
Po = 57
The expression for the exact number of bacteria after t hours is
P(t) = 57e^0.08t
The growth (in bacteria per hour) after 9.5 hours is
P(t) = 57e^(0.88 * 9.5)
P(t) = 243544
For the number to reach 72,000;
72,000 = 57e^0.88t
72,000/57 = e^0.88t
ln 126 = ln[e^0.88t]
4.8 = 0.88t
t = 4.8/0.88
t = 5.5 hours
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