Elinas friend Luke said that he could make mor rectangules with 24 tiles than with Elinas 10 tiles do you agree with Luke

assuming the growth rate stays constant at 1.2%, how many doublings would take place in a 500- year period?

Juliette [100K]

9514 1404 393

Answer:

8.6

Step-by-step explanation:

The growth factor per year is 1.012, so in 500 years is ...

1.012^500

The number of doublings is the solution to ...

2^n = 1.012^500

Taking logarithms, we have ...

n·log(2) = 500·log(1.012)

n = 500·log(1.012)/log(2) ≈ 8.6046

About 8.6 doublings will take place in 500 years.

3 0

2 years ago

What is Bethany's score on the test if she got 23 out of 30 right? (Round to the nearest whole number.)

matrenka [14]

Answer:

77%

Step-by-step explanation:

23 divided by 30 is 0.766666, which percent-wise is rounded to 77% :)

3 0

2 years ago

Read 2 more answers

WILL GIVE BRAINLIEST, SUPERB RATING, AND THANKS!

Vaselesa [24]

A line on this coordinate plane is horizontal when every input (x) has the same output y).

This function always gives the same output with no matter what input you put it in.

8 0

3 years ago

What is the solution to the equation 9k = 40.5? k= 4 k= 4.5 k= 5

Scilla [17]

Answer:

k=4.5

Step-by-step explanation:

40.5/9

3 0

3 years ago

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The points A(1, 4), B(5,1) lie on a circle. The line segment AB is a chord. Find the equation of a diameter of the circle.

tangare [24]

Check the picture below.

well, we want only the equation of the diametrical line, now, the diameter can touch the chord at any several angles, as well at a right-angle.

bearing in mind that perpendicular lines have negative reciprocal slopes, hmm let's find firstly the slope of AB, and the negative reciprocal of that will be the slope of the diameter, that is passing through the midpoint of AB.

$\bf A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}\implies \cfrac{-3}{4} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{slope of AB}}{-\cfrac{3}{4}}\qquad \qquad \qquad \stackrel{\textit{\underline{negative reciprocal} and slope of the diameter}}{\cfrac{4}{3}}$

so, it passes through the midpoint of AB,

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{5+1}{2}~~,~~\cfrac{1+4}{2} \right)\implies \left(3~~,~~\cfrac{5}{2} \right)$

so, we're really looking for the equation of a line whose slope is 4/3 and runs through (3 , 5/2)

$\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{\frac{5}{2}}) \stackrel{slope}{m}\implies \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\cfrac{5}{2}}=\stackrel{m}{\cfrac{4}{3}}(x-\stackrel{x_1}{3})\implies y-\cfrac{5}{2}=\cfrac{4}{3}x-4 \\\\\\ y=\cfrac{4}{3}x-4+\cfrac{5}{2}\implies y=\cfrac{4}{3}x-\cfrac{3}{2}$

4 0

3 years ago