<h3>
Answer: Rhombus</h3>
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Reason:
Let's find the distance from A to B. This is equivalent to finding the length of segment AB. I'll use the distance formula.
Segment AB is exactly 
units long, which is approximately 4.1231 units.
If you were to repeat similar steps for the other sides (BC, CD and AD) you should find that all four sides are the same length. Because of this fact, we have a rhombus.
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Let's see if this rhombus is a square or not. We'll need to see if the adjacent sides are perpendicular. For that we'll need the slope.
Let's find the slope of AB.
Segment AB has a slope of 1/4.
Do the same for BC
Unfortunately the two slopes of 1/4 and 4 are not negative reciprocals of one another. One slope has to be negative while the other is positive, if we wanted perpendicular lines. Also recall that perpendicular slopes must multiply to -1.
We don't have perpendicular lines, so the interior angles are not 90 degrees each.
Therefore, this figure is not a rectangle and by extension it's not a square either.
The best description for this figure is a <u>rhombus</u>.
The missing values represented by x and y are 8 and 20, that is
(x, y) = (8, 20)
The function y = 16 + 0.5x is a linear equation that can be solved graphically. This means the values of both variables x and y can be found on different points along the straight-line graph.
The ordered pairs simply mean for every value of x, there is a corresponding value of y.
The 2-column table has values for x and y which all satisfy the equation y = 16 + 0.5x. Taking the first row, for example, the pair is given as (-4, 14).
This means when x equals negative 4, y equals 14.
Where y = 16 + 0.5x
y = 16 + 0.5(-4)
y = 16 + (-2)
y = 16 - 2
y = 14
Therefore the first pair, just like the other four pairs all satisfy the equation.
Hence, looking at the options given, we can determine which satisfies the equation
(option 1) When x = 0
y = 16 + 0.5(0)
y = 16 + 0
y = 16
(0, 16)
(option 2) When x = 5
y = 16 + 0.5(5)
y = 16 + 2.5
y = 18.5
(5, 18.5)
(option 3) When x = 8
y = 16 + 0.5(8)
y = 16 + 4
y = 20
(8, 20)
From our calculations, the third option (8, 20) is the correct ordered pair that would fill in the missing values x and y.
To learn more about the straight line visit:
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Sometimes when you’re doing math, it’s easier to line your numbers up when you have your ratio as a decimal! Hope it helped
Answer:
log3 (500)
Step-by-step explanation:
3 log3 (5) * log3(4)
We know that a log b(c) = log b(c^a)
log3 (5)^3 * log3(4)
We know that log a(b) * log a (c) = loga( b*c)
log3 ((5)^3 * 4)
log3 (125*4)
log3 (500)
Answer: Hello there!
We know that the culture has 2000 bacteria initially (at t = 0 min), and it doubles when t = 40min, again at t = 80 min, and so on
And the rate of grouth is proportional to the population, then we can obtain an expression of the form:
P(t) = 2000*k(t) where k(t) is the factor that defines the growth of the population:
we know that:
p(0) = 2000*k(0) = 2000
p(40) = 2000*k(40) = 2000*2 = 4000
p(80) = 2000*k(80) = 2000*2*2 = 8000
etc
then we can see that k(t) = 2^(t/40)
where k(0) = 1, k(40) = 2, k(80) = 2*2, etc
then the function that models the population of the culture is:
p(t) = 2000*2^(t/40)
where t is in minutes.
