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raketka [301]
3 years ago
14

A high school basketball team has a budget specifically for towels and extra basketballs. A towel costs $3 and a basketball cost

s $18. Assume the budget is $450 and that 30 towels are needed for the team for the entire season. Use a standard form equation to determine how many basketballs may be purchased by the team.
Mathematics
1 answer:
bonufazy [111]3 years ago
4 0
An equation that can be used is 3T + 18B = 450. Since they know they need 30 towels, substitute 30 for T. The equation becomes 3(30) + 18B = 450. Simplifying, 90 + 18B = 450. Subtract 90 from each side, 18B = 360. Finally, divide each side by 18, B = 20. The maximum number of basketballs that may be purchased is 20.
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In parallelogram ABCD, base AD is 15 and side AB is 8. What are the height and area of paralelogram ABCD if mDAB is 20?
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Step-by-step explanation:

✰ \underline{ \underline{ \large{ \tt{G\: I \: V \: E \: N}}}} :

  • AD = 15 , AB = 8 , \angle DAB

✰ \underline{ \underline{ \large{ \tt{T \: O \: \: F\: I \: N \: D}}}} :

  • Height & Area of the given parallelogram

✰ \underline{ \underline{ \large{ \tt{S \: O \: L \: U \: T\: I\: O \: N}}}} :

In right angled triangle ABE :

  • Hypotenuse ( h ) = 8
  • Perpendicular ( p ) = h [ height ]
  • \theta = 20°

Now , Using trigonometric ratio :

\large{ \tt{Sin \theta \:  = \:  \frac{Perpendicular}{Hypotenuse}  }}

Plug the known values :

⟶ \large{ \tt{ Sin(20)  =  \frac{h}{8} }}

⟶ \large{ \tt{0.34 =  \frac{h}{8}}}

⟶ \large{ \tt{h = 0.34 \times 8}}

⟶ \large{ \tt{h = 2.72}}

Now , We have :

  • Base ( b ) = 15
  • Height ( h ) = 2.72

Finding the area of a parallelogram whose base and height are 15 and 2.72 respectively :

❀ \underline{ \underline{ \text{Area \: of \: parallelogram =  \tt{b   *\:  h}}}}

⟶ \large{ \tt{A = 15  *2.72}}

⟶ \large{ \tt{A = 40.8 \:  {units}^{2} }}

Hence , Our final answer :

\large{ \boxed{ \sf{Height \: ( \: h \: ) = 2.72 \: units}}}

\large{ \boxed{ \sf{Area \: of \: parallelogram \: ( \:A \: ) = \: 40.8 \:  {units}^{2} }}}

Hope I helped ! ♡

Have a wonderful day / night ! ツ

# \underbrace{ \tt{Carry \: On \: Learning}} !! ✎

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3 0
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