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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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Rectangle A measures 10 inches by 8 inches. Rectangle B is an enlarged copy of Rectangle A. Select all of the measurement pairs
Fudgin [204]

Answer:

See Explanation

Step-by-step explanation:

Given

Rectangle A:

Length: 10\ in

Width: 8\ in

Required

Determine the possible dimensions of Rectangle B

<em>The question has missing options; however, the question can still be solved.</em>

<em></em>

Rectangle B being an enlarged copy of A implies that the dimension of A A is enlarged in equal proportion to form B

Take for instance, the measurements of Rectangle B are

Length: 15 in

Width: 12 in

Divide the corresponding lengths of B by A to get the enlargement ratio

Ratio = \frac{B}{A}

For length:

Ratio = \frac{15}{10}

Ratio = 1.5

For width

Ratio = \frac{12}{8}

Ratio = 1.5

Notice that both ratios are the same.

For this measurement of B, we can conclude that B is an enlargement of A

Assume another measurements for B

Length: 20\ in

Width: 10\ in

Calculate Ratios

Ratio = \frac{B}{A}

For length:

Ratio = \frac{20}{10}

Ratio = 2

For width

Ratio = \frac{10}{8}

Ratio = 1.25

Notice that, both ratios are not equal.

For this measurement of B, we can conclude that B is not an enlargement of A

<em>Conclusively, all you have to do is: determine the ratios of the dimensions of B to A, if the result are equal then B is an enlarged copy of A; if otherwise, then B is not an enlarged copy</em>

5 0
3 years ago
Here is a triangular pyramid and its net.
bazaltina [42]

Answer:

a) Area of the base of the pyramid = 15.6\ mm^{2}

b) Area of one lateral face = 24\ mm^{2}

c) Lateral Surface Area = 72\ mm^{2}

d) Total Surface Area = 87.6\ mm^{2}

Step-by-step explanation:

We are given the following dimensions of the triangular pyramid:

Side of triangular base = 6mm

Height of triangular base = 5.2mm

Base of lateral face (triangular) = 6mm

Height of lateral face (triangular) = 8mm

a) To find Area of base of pyramid:

We know that it is a triangular pyramid and the base is a equilateral triangle. \text{Area of triangle = } \dfrac{1}{2} \times \text{Base} \times \text{Height} ..... (1)\\

{\Rightarrow \text{Area of pyramid's base = }\dfrac{1}{2} \times 6 \times 5.2\\\Rightarrow 15.6\ mm^{2}

b) To find area of one lateral surface:

Base = 6mm

Height = 8mm

Using equation (1) to find the area:

\Rightarrow \dfrac{1}{2} \times 8 \times 6\\\Rightarrow 24\ mm^{2}

c) To find the lateral surface area:

We know that there are 3 lateral surfaces with equal height and equal base.

Hence, their areas will also be same. So,

\text{Lateral Surface Area = }3 \times \text{ Area of one lateral surface}\\\Rightarrow 3 \times 24 = 72 mm^{2}

d) To find total surface area:

Total Surface area of the given triangular pyramid will be equal to <em>Lateral Surface Area + Area of base</em>

\Rightarrow 72 + 15.6 \\\Rightarrow 87.6\  mm^{2}

Hence,

a) Area of the base of the pyramid = 15.6\ mm^{2}

b) Area of one lateral face = 24\ mm^{2}

c) Lateral Surface Area = 72\ mm^{2}

d) Total Surface Area = 87.6\ mm^{2}

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