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kati45 [8]
3 years ago
8

May someone solve and give explanation

Mathematics
1 answer:
torisob [31]3 years ago
7 0

Answer:

x = 15.7945

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Trigonometry</u>

  • [Right Triangles Only] SOHCAHTOA
  • [Right Triangles Only] sinθ = opposite over hypotenuse

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify variables</em>

Angle θ = 33°

Opposite Leg = <em>x</em>

Hypotenuse = 29

<u>Step 2: Find Angle</u>

  1. Substitute in variables [sine]:                                                                           sin33° = x/29
  2. [Multiplication Property of Equality] Multiply 29 on both sides:                    29sin33° = x
  3. Rewrite:                                                                                                             x = 29sin33°
  4. Evaluate:                                                                                                           x = 15.7945
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2. Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large
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Answer:

\boxed {\boxed {\sf 98 \ Small \ Cups}}\\\\\boxed {\boxed {\sf 57 \ Large \ Cups}}

Step-by-step explanation:

Let's make a system of equations.

First, define the variables.

Let s= small cups and g= large cups

Next, make 2 equations. 1 for the money and 1 for the number of cups.

<u>Money</u>

  • A small cup costs 1.25 and a large cup costs 2.50. The total money made is 265.
  • 1.25s+2.50g=265

<u>Number</u>

  • A total of 155 cups of lemonade were sold. The sum of small cups and large cups sold will equal 155.
  • s+g=155

Here is our system of equations:

1.25s+2.50g=265 \\s+g=155

Now, solve. Let's isolate a variable in the 2nd equation, so we can plug it in after.

  • Subtract g from both sides of the equation.
  • s+g=155
  • s+g-g=155-g
  • s=155-g

Now we know that s is equal to 155-g. We can substitute (155-g) in for s in the first equation.

1.25s +2.50g=265

1.25(155-g)+2.50g=265

Distribute the 1.25

  • 1.25(155-g)= (1.25*155)+ (1.25*-g)= 193.75-1.25g

193.75-1.25g+2.50g=265

Work to isolate the variable. Subtract 193.75 from both sides of the equation and combine like terms on the left.

193.75-1.25g+2.50g=265-193.75       (Subtract 193.75)

-1.25g+2.50g=265-193.75      

1.25g=71.25      (Combine like terms).

1.25 and g are being multiplied. The inverse of multiplication is division. Divide both sides by 1.25

1.25g/1.25=71.25/1.25\\g=71.25/1.25\\g=57

Now we know that 57 large cups were sold. Plug 57 back into the original second equation to find the small cups.

s+g=155

s+57=155

Subtract 57 from both sides of the equation to isolate the variable, s.

s+57-57=155-57\\s=155-57\\s=98

Ashley sold 57 large cups and 98 small cups.

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