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uysha [10]
3 years ago
12

A dance studio offers ballet and hip-hop classes. The studio has 8 ballet classes for every 12 hip-hop classes. How many hip-hop

classes are there for each ballet class
Mathematics
2 answers:
LiRa [457]3 years ago
8 0
There are 1 1/2 hip hop classes for 1 ballet class.
ElenaW [278]3 years ago
4 0
For every hip hop class, there are:

12:8

Simplify.

3:2

For every 3 hip hop classes, there are 2 ballet classes.

Hope this helped!
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Find an equation for the line perpendicular to y=−15x+3 with x-intercept at x = 3.
Alex Ar [27]

bearing in mind that perpendicular lines have negative reciprocal slopes, let's find the slope of the provided line then

\bf y=\stackrel{\stackrel{m}{\downarrow }}{-15}x+3\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} \\\\[-0.35em] ~\dotfill

\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-15\implies -\cfrac{15}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{1}{15}}\qquad \stackrel{negative~reciprocal}{+\cfrac{1}{15}\implies \cfrac{1}{15}}}

well, we know the x-intercept is at x = 3, recall when a graph intercepts the x-axis y = 0, so this point is (3 , 0).  Then we're really looking for the equation of a line whose slope is 1/5 and runs through (3 , 0).

\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{0})~\hspace{10em} slope = m\implies \cfrac{1}{5} \\\\\\ \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-0=\cfrac{1}{5}(x-3)\implies y=\cfrac{1}{5}x-\cfrac{3}{5}

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4 years ago
100 POINTS!!!!!
Oksanka [162]

Answer:

a. Ratio of their circumference = 2:3

b. The ratio of their surface areas = 2:3

c. The ratio of their volume = 4:9

Step-by-step explanation:

Let the cylinders be labelled as A and B respectively.

Diameter of cylinder A = 6 in,

its radius = \frac{diameter}{2}

                = \frac{6}{2} = 3 in

Diameter of cylinder B = 9 in,

its radius = \frac{diameter}{2}

               = \frac{9}{2}  = 4.5 in

Thus,

a. circumference of a circle = 2\pir

Circumference of cylinder A = 2\pir

                                               = 2 x \pi x 3

                                            = 6\pi in

Circumference of cylinder B = 2\pir

                                              = 2 x \pi x 4.5

                                              = 9\pi

Ratio of their circumference = \frac{circumference of cylinder A}{circumference of cylinder B}

                                               = \frac{6\pi }{9\pi }

                                               = 2:3

b. The surface area of a cylinder = 2\pirh

the surface area of cylinder A = 2\pirh

                                                  = 6\pih

the surface area of cylinder B = 2\pirh

                                                = 9\pih

The ratio of their surface areas = \frac{surface area of cylinder A}{surface area of cylinder B}

                                                 = \frac{6\pi h}{9\pi h}

                                                 = 2:3

c. Volume of a cylinder = \pir^{2}h

volume of cylinder A = \pir^{2}h

                                = \pi x 3^{2} x h

                                = 9\pih

volume of cylinder b = \pir^{2}h

                                    = \pi x 4.5^{2} x h

                                    = 20.25\pih

The ratio of their volume = \frac{volume of cylinder A}{volume of cylinder B}

                                         = \frac{9\pi h}{20.25\pi h}

                                         = 4:9

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Answer:

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2 years ago
Solve the inequality.
DedPeter [7]
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Find the measure of angle x in the figure below: A triangle is shown. At the top vertex of the triangle is a horizontal line ali
anastassius [24]

Answer:

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Step-by-step explanation:

The three angles 51° , 56° and y form a straight angle.

This means that:

51 + 56 + y = 180

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y = 180 - 107

y = 73°

7 0
3 years ago
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