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irinina [24]
2 years ago
12

The cost of cabin lodging is $25 per lodger. The equation y = 25x relates the total lodging cost (y) to the number of lodgers (x

). Identify the unit rate in the equation.
Mathematics
1 answer:
dalvyx [7]2 years ago
5 0

Answer: The unit rate is $25

Step-by-step explanation: We know that the cost of cabin lodging is 25 dollars per lodger.

Then the equation y = 25x models this relation.

Here the cost is y, and the number of lodgers is x.

We want to find the unit rate.

The actual equation should be in dollars, and the number of lodgers is just a scalar number.

so the equation should be:

y = $25*x

Now, the unit rate is defined as the rate with 1 in the denominator, in this case, is the price for each unit of x (lodgers) so is the price per lodger.

We already know that the price per lodger is $25, so the unit rate is $25.

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Find the equation of a line passing through (-4,-3) and perpendicular to<br> 3 x + 2 y = 14.
Reil [10]

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

3x+2y=14\implies 2y=-3x+14\implies y=\cfrac{-3x+14}{2}\implies y = \cfrac{-3x}{2}+\cfrac{14}{2} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{2}}x+7\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}

so therefore

\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-3}\implies \cfrac{2}{3}}}

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

(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad \qquad \stackrel{slope}{m}\implies \cfrac{2}{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}{(-3)}=\stackrel{m}{\cfrac{2}{3}}(x-\stackrel{x_1}{(-4)}) \implies y+3=\cfrac{2}{3}(x+4) \\\\\\ y+3=\cfrac{2}{3}x+\cfrac{8}{3}\implies y=\cfrac{2}{3}x+\cfrac{8}{3}-3\implies y=\cfrac{2}{3}x-\cfrac{1}{3}

3 0
2 years ago
Help please for 50 points
Montano1993 [528]

Answer and Step-by-step explanation:

347

7 0
3 years ago
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The length of a rectangular garden is three feet less than twice it’s width. If the perimeter of the garden is 42 feet, what is
zzz [600]
<h3><u>The length is equal to 13.</u></h3><h3><u>The width is equal to 8.</u></h3>

l = 2w - 3

2l + 2w = 42

Because we have a value for l, we can plug it into the second equation to solve for w.

2(2w - 3) + 2w = 42

Distributive property.

4w - 6 + 2w = 42

Combine like terms.

6w - 6 = 42

Add 6 to both sides.

6w = 48

Divide both sides by 6.

w = 8

Now that we have a value for w, we can solve for the exact value of l.

l = 2(8) - 3

l = 16 - 3

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2 years ago
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ser-zykov [4K]

Answer:

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Step-by-step explanation:

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the pillars of a temple are cylindrically shaped.of each pillar has a circular base of radius 280 cm and height of 10 m how much
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Answer:

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Step-by-step explanation:

280 cm=2.8 m

S=πr²×h×14

  =3.14×2.8²×10×14

  =3446.464 m³

5 0
3 years ago
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