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Kryger [21]
3 years ago
15

You order two tacos and a salad. The salad costs $2.50. You pay 8% sales tax and leave a $3 tip. You pay a total of $13.80. How

much does one taco cost?
Mathematics
1 answer:
Mnenie [13.5K]3 years ago
3 0
Price of one taco = x; price of 2 tacos = 2xPrice of salad = $2.50Sales tax = 8% of the combined price of two tacos and a salad, namely .08(2x + 2.50)Tip = constant fee = $3.00Total bill = $13.80 Therefore the equation becomes

2x + 2.50 + .08(2x + 2.50) + 3 = 13.80 Step 3:  Solve for x; isolate the variable 2x + 2.50 + .16x + .20 + 3 = 13.80 (using the distributive property to multiply 2x and 2.5 by .08).2.16x + 2.70 + 3 = 13.80 (combining like terms)2.16x + 5.70 = 13.80 (combining like terms)2.16x + 5.70 = 13.80 - 5.70 (subtraction property of equality)2.16x = 8.10x = 8.10/2.16 = 3.75 (division property of equality) Step 4: Interpret mathematical answer in context of original word problem. The cost of a single taco is $3.75 Step 5: Verify that answer makes sense for problem. 2 Tacos would cost $7.501 Salad would cost $2.50Food bill subtotal would be $10.00Sales tax is 8% of $10 or 80 centsTip is $3 Confirm 7.5 + 2.5 + .8 + 3 = $13.80
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9514 1404 393

Answer:

  a) BE = 5; DE = 6; EF = 4

  b) ∠EFC ≅ ∠DA.F ≅ ∠BDE  or  <em>b = e = f = i</em>

Step-by-step explanation:

Each short segment is the same length as the marked one it is parallel to.

  E is the midpoint of BC, so BE = EC = 5.

  ADEF is a parallelogram, so DE = A.F = 6.

  D is the midpoint of AB, so AD = DB = 4. ADEF is a parallelogram, so ...

     EF = AD = 4

__

As we have noted, AB║EF and DE║A.F, so corresponding angles and alternate interior angles are congruent. <em>b = e = f = i</em>

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2. Consider the circle x² + y2 = 1, given in figure. Let OP makes an angle 30° with the x axis.
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The equation of the tangent line to the circle passing through the point P is; y = (1/√3)x ± 2/√3

<h3>How to find the equation of the tangent?</h3>

I) We are given the equation of the circle as;

x² + y² = 1

Since angle of inclination is 30°, then slope is;

m = tan 30 = 1/√3

Then equation of the tangent will be;

y = (1/√3)x + c

Put  (√3)x + c into the given circle equation to get;

x² + ((1/√3)x + c)² = 1

x² + ¹/₃x² +  (2/√3)cx + c² = 1

⁴/₃x² +  (2/√3)x + (c² - 1) = 0

Since we need to find value of c for equation to become tangent, then the above quadratic equation must have real and equal roots.

Thus;

((2/√3)c)² - 4(⁴/₃)(c² - 1) = 0

⁴/₃c² - ¹⁶/₃(c² - 1) = 0

⁴/₃c² - ¹⁶/₃c² + ¹⁶/₃ = 0

4c² = ¹⁶/₃

c² = ⁴/₃

c = √⁴/₃

c = ±²/√3

Thus, equation of tangent is;

y = (1/√3)x ± 2/√3

II) Radius from the given equation is 1. Thus, we will use trigonometric ratio to find the x and y intercept;

x-intercept is at y = 0;

0 = (1/√3)x ± 2/√3

-(1/√3)x = ±2/√3

Intercept is positive. Thus;

x = (2/√3)/(1/√3)

x = 1

y - intercept is positive at x = 0;

y = (1/√3)0 ± 2/√3

y = 2/√3

Read more about Equation of tangent at; brainly.com/question/17040970

#SPJ1

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