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Taya2010 [7]
4 years ago
9

Cedar point is an amusement park located in Sandusky, OH. It's collection of 112 rides is the largest in the world. Of the rides

, 2/7 are roller coasters. How many roller coasters are in cedar point's collection of rides?
Mathematics
1 answer:
Agata [3.3K]4 years ago
8 0

Answer:

 32 Roller Coasters

Step-by-step explanation:

There are a total of 112 rides in Cedar Point.

\frac{2}{7} of these rides are roller coasters.

In Algebraic Word Problems, the term "OF" means Multiplication.

Number of Roller Coasters = \frac{2}{7} of 112

                                          =\frac{2}{7} X 112

                                          =2 x 16

                                          =32

There are 32 Roller Coasters in Cedar's point's collection of rides.

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Answer:

x = 19

Step-by-step explanation:

To solve for x, set f(x) equal to the output value, hence

- \frac{1}{3} x + 7 = \frac{2}{3}

Multiply all terms by 3 to eliminate the fractions

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To establish a driver education school, organizers must decide how many cars, instructors, and students to have. Costs are estim
mina [271]

Answer:

(a) 30,000 + 14,000x (b) 350y (c) 350y - (30,000 + 14,000x) (d) Yes

Step-by-step explanation:

(a) Total cost = 30,000 + 3,000x + 11,000x = 30,000 + 14,000x

(b) Total revenue = 350y

(c) Total profit = Total revenue - total cost = 350y - (30,000 + 14,000x)

(d) To break even, the total profit of the school should be $0 or more. If they decide to use 5 cars with 4 students assigned to each car, 16 times a year (eight times with two sessions each) then we have a total  of 20 students. Using our formula total profit is equal to 350(320) - (30,000 + 14000(5)) = $112,000 - $100,000 = $12,000 profit

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Please help! I think I have the equation set up.
ExtremeBDS [4]

\bold{\huge{\underline{ Solution }}}

<h3><u>Given :-</u></h3>

  • Here, we have given one quadrilateral that is quadrilateral ABCD
  • We also have given the angles of quadrilateral that is ( 6x + 5)° , ( 9x - 10)° , 80° and a right angle

<h3><u>To </u><u>Find </u><u>:</u><u>-</u></h3>

Here, we have to find the value of x

<h3><u>Let's </u><u>Begin </u><u>:</u><u>-</u><u> </u></h3>

We have given quadrilateral ABCD here , whose angles are as follows

  • Angle A = ( 6x + 5)°
  • Angle B = ( 9x - 10)°
  • Angle C = 80°
  • Angle D = A right angled triangle

[ The measure of right angled triangle is 90° ]

<u>We </u><u>know </u><u>that</u><u>, </u>

  • Sum of the angles of quadrilateral is equal to 360°

<u>That </u><u>is </u>

\bold{\angle{ A + }}{\bold{\angle{B +}}}{\bold{\angle{C + }}}{\bold{\angle{D + = 360{\degree}}}}

<u>Subsitute </u><u>the </u><u>required </u><u>values </u>

\sf{ ( 6x + 5){\degree} + 80{\degree}+ 90{\degree} + (9x - 10){\degree} = 360{\degree}}

\sf{  6x + 5  + 170{\degree} + 9x - 10  = 360{\degree}}

\sf{  15x - 5   =  360{\degree} - 170{\degree}}

\sf{  15x - 5   =  190 {\degree}}

\sf{  15x   =  190 {\degree} + 5 }

\sf{  15x  =  195 {\degree}}

\sf{  x =  }{\sf{\dfrac{ 195}{15}}}

\sf{  x =  }{\sf{\cancel{\dfrac{ 195}{15}}}}

\bold{  x = 13 }

Hence, The value of x is 13 .

\bold{\huge{\underline{\red{ Verification }}}}

Measure of Angle A

\sf{ = (6x + 5){\degree}}

\sf{ = (6(13) + 5 ){\degree}}

\sf{ = (78 + 5 ){\degree}}

\sf{ =  83{\degree}}

Measure of Angle D

\sf{ = (9x - 10){\degree}}

\sf{ = (9(13) - 10){\degree}}

\sf{ = (117 - 10  ){\degree}}

\sf{ =  107{\degree}}

<u>Now</u><u>, </u><u> </u><u>we </u><u>know </u><u>that</u><u>, </u>

  • Sum of angles of triangles is equal to 360°

<u>That </u><u>is</u><u>, </u>

\sf{ 83{\degree} + 80{\degree}+ 90{\degree} + 107 {\degree} = 360{\degree}}

\sf{ 163{\degree}+ 90{\degree} + 107 {\degree} = 360{\degree}}

\sf{ 253{\degree}+ 107 {\degree} = 360{\degree}}

\sf{ 253{\degree}+ 107 {\degree} = 360{\degree}}

\bold{ 360{\degree} = 360{\degree}}

\bold{ LHS = RHS }

Hence, Proved.

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