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Anon25 [30]
2 years ago
5

From which store should Dylan make his purchase if he wants to get the best price per unit?

Mathematics
1 answer:
KATRIN_1 [288]2 years ago
6 0

Answer:

Store 1

Step-by-step explanation:

Given

See attachment

Required

Determine the store with the best price per unit

It should be noted that the store with the best has the least price per unit.

So, we have:

<u>Store 1</u>

Quantity = 10\ ft

Price = \$2.50

The unit rate is:

Rate = \frac{Price}{Quantity}

Rate = \frac{\$2.50}{10\ ft}

Rate = $0.250 per feet

<u>Store 2</u>

Quantity = 2\ yd

Price = \$1.85

Convert quantity to feet

Quantity = 2 * 3ft = 6ft

The unit rate is:

Rate = \frac{Price}{Quantity}

Rate = \frac{\$1.85}{6\ ft}

Rate = $0.308 per feet

<u>Store 3</u>

Quantity = 12\ ft

Price = \$3.40

The unit rate is:

Rate = \frac{Price}{Quantity}

Rate = \frac{\$3.40}{12\ ft}

Rate = $0.283 per feet

<u>Store 4</u>

Quantity = 5\ yd

Price = \$4.00

Convert quantity to feet

Quantity = 5 * 3ft = 15ft

The unit rate is:

Rate = \frac{Price}{Quantity}

Rate = \frac{\$4.00}{15\ ft}

Rate = $0.267 per feet

From the calculations above; store 1 has the least unit rate.

Hence, store 1 has the best price per unit

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If ΔACB is an isosceles triangle, then ∠A ≅ ∠B and AC ≅ CB

Since ∠C = 120° and ∠A + ∠B + ∠C = 180°, then ∠A = 30° and ∠B = 30°

Next, look at ΔADB.  ∠A + ∠D + ∠B = 180°, so ∠A + 90° + 30° = 180° ⇒ ∠A = 30°

Now look at ΔADC.  Since ∠A = 30° in ΔACB, and ∠A = 60° in ΔADB, then ∠A = 30° in ΔADC <em>per angle addition postulate.</em>

Now that we have shown that ΔADB and ΔADC are 30-60-90 triangles, we can use that formula to calculate the side lengths.

CD = 4 cm (given) so AC = 2(4 cm) = 8 cm

Since AC ≅ BC, then BC = 8 cm. Therefore, BD = 4 + 8 = 12 <em>by segment addition postulate.</em>

Lastly, look at ΔBHD.  Since ∠B = 30° and ∠H = 90°, then ∠D = 60°. So, ΔBHD is also a 30-60-90 triangle.

BD = 12 cm, so HD = \frac{12}{2}cm = 6 cm

Answer: 6 cm



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A block of sugar maple wood has a mass of 82.8 g and density of 0.69 ​g/cm3​. The block is a rectangular prism with a length of
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3. The backyard of a home is a rectangle 25m by 30m. A garden of uniform width is to be
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Answer:

Part A

The width of the garden is approximately 3.987 meters

Part B

Please find attached the drawing of the solution

Step-by-step explanation:

Part A

The given parameters are;

The dimensions of the backyard of the home = 25 m by 30 m

The width of the garden to be built in the yard = Uniform width

The shape of the grass left inside = Rectangular

The area of the grass at the center = The area of the garden

Let 'x' represent the width of the garden, we have;

The length of the rectangular grass area at the center, l = 30 - 2·x

The width of the rectangular area of grass at the center, w = 25 - 2·x

The area of the rectangular backyard, A = 30 m × 25 m = 750 m²

The area of the rectangular backyard, A = (The area of the garden) + (The area of the rectangle of grass inside)

The area of the rectangle of grass, GA = (30 - 2·x)·(25 - 2·x) = The area of the garden

The area of the rectangular backyard, A = 750 = (30 - 2·x)·(25 - 2·x) + (30 - 2·x)·(25 - 2·x)  = 2 × (30 - 2·x)·(25 - 2·x) = 8·x² - 220·x + 1,500

∴ 750 = 8·x² - 220·x + 1,500

8·x² - 220·x + 1,500 - 750 = 0

8·x² - 220·x + 750 = 0

x = (220 ± √(220² - 4 × 8 × 750))/(2 × 8)

x ≈ 23.513, or x = 3.987

When x = 25.513, the width of the rectangle of grass inside, w = 25 - 2 × 23.513 = -22.026, which is not a natural (physically possible)

Therefore, the possible width of the garden, x ≈ 3.987

Part B

The drawing of the solution created with MS Visio is attached

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2 years ago
Ok I’m actually dumb lol help me please.
mezya [45]

Answer:

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Step-by-step explanation:

As a line is 180 degrees

So 7x + 40 would be 180, which would lead us with the equation:

7x+40=180

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=x =20 (divide both sides by 7)

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