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4 years ago

What is the equation for a line that passes through the points (-3,-3) and (6,21)?

1 answer:

5 0

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -3 &,& -3~) 
% (c,d)
&&(~ 6 &,& 21~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{21-(-3)}{6-(-3)}\implies \cfrac{21+3}{6+3}$

$\bf \cfrac{24}{9}\implies \cfrac{8}{3}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-3)=\cfrac{8}{3}[x-(-3)]
\\\\\\
y+3=\cfrac{8}{3}(x+3)\implies y+3=\cfrac{8}{3}x+8\implies y=\cfrac{8}{3}x+5$

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3 years ago

At the zoo, for every 6 adult camels, there are 5 baby camels. There are a total of 44

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3 years ago

Match the function in the left column with its period in the right column.

kiruha [24]

The results for the matching between function and its period are:

Option 1 - Letter D
Option 2 - Letter A
Option 3 - Letter C
Option 4 - Letter B

<h3>What is a Period of a Function?</h3>

If a given function presents repetitions, you can define the period as the smallest part of this repetition. As an example of periodic functions, you have: sin(x) and cos(x).

$\mathrm{Period\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}$

$\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}$

The period of sin(x) and cos(x) is 2π.

For solving this question, you should analyze each option to find its period.

1) Option 1

$\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}\\ \\ \mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{2\pi }{\frac{1}{2} }=4\pi$

Thus, the option 1 matches with the letter D.

2) Option 2

$\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}\\ \\ \mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{4} =\frac{\pi }{2}$

Thus, the option 2 matches with the letter A.

3) Option 3

Thus, the option 3 matches with the letter C.

4) Option 4

Thus, the option 4 matches with the letter B.

Read more about the period of a trigonometric function here:

brainly.com/question/9718162

#SPJ1

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