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Pachacha [2.7K]
3 years ago
12

The frog population at a lake doubles every three weeks. The population can be modeled by f(x)=15(2)^x and f(6)=960. What does t

he 15 represent?
A- The population after six weeks
B- The starting population
C- The rate the population increases
D- The number of weeks that have passed
Mathematics
2 answers:
hammer [34]3 years ago
4 0

Answer:B- The starting population

aivan3 [116]3 years ago
3 0
We have to answer what does the 15 represent in the function : f ( x ) = 15 * 2^x, which models the increasing of the frog population at a lake. We know that the frog population doubles every 3 weeks and that: f ( 6 ) = 960. It means that: 15 * 2^ 6 = 15 * 64 = 960. And also f ( 0 ) = 15 * 2^0 = 15 * 1 = 15. Therefore it is a starting population. Answer: The 15 represents <span>B - The starting population.</span>
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anyanavicka [17]

Step-by-step explanation:

about circle R

arc angle MP = angle MRP = 78°

angle M = angle LMP.

according to the rules of inscribed angles, LMP is half of angle LRP.

LRP + MRP = 180° because together they cover the whole LM segment (half-circle).

LRP = 180 - MRP = 180 - 78 = 102°

so, LMP = angle M = 102/2 = 61°

also circle R (with arc ULNP)

the arc ULNP = arc UL + arc LN + arc NP = 160°

due to the congruent definition of JU and MP we know that arc UL = arc NP.

and we know arc LN = arc JM = 18°.

so,

160 = 2×arc NP + 18

142 = 2×arc NP

arc NP = 71° = arc UL

now, because arc MP + arc LP = 180 (half-circle),

arc MP = 180 - arc LP = 180 - arc LN - arc NP =

= 180 - 18 - 71 = 91°

about the circle R with 2 congruent chords :

the second answer : they are equidistant from R (the center of the circle).

about circle W

arc MK + arc KL = 180° (half-circle).

and we see

arc HL = arc KL = 53°.

so,

arc MK + 53 = 180°

arc MK = 180 - 53 = 127°

about circle M

arc QTS = 204°.

therefore, arc QRS = 360 - arc QTS = 360 - 204 =

= 156° = angle QMS.

according to the rules of inscribed angles

angle QTS = QMS/2 = 156/2 = 78°

4 0
3 years ago
The figure, polygon ABCD is dilated by a factor of 2 to produce A B C D with the origin as the center of dilation
cestrela7 [59]

In the polygon ABCD, the production of point A' and point D' is (-2,-2)  and (4,-2) respectively.

<h3>What is the transformation rule?</h3>

In coordinate planes, the rule of transformation involves interchanging the x and y values on the plane such that:

\mathbf{(x,y) \to  (k_x, k_y)}

where;

  • k = scale factor

From the given information:

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Now, using the coordinate vertices:

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  • D = (2, -1)

The corresponding coordinate of the image vertices is as follows:

A(-1,-1) → A'(2 × (-1), 2 × (-1))

A' = (-2,-2)

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Learn more about the transformation rule in coordinate planes here:

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