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Elina [12.6K]
3 years ago
13

Clyde rents a tuxedo for several days. Let d represent the number of additional days Clyde uses the tuxedo. Write an algebraic e

xpression to represent the total cost of the rental after d additional days.
Mathematics
1 answer:
yaroslaw [1]3 years ago
3 0

Answer:

Total cost = f + ad

Step-by-step explanation:

Given:

Number of days = d

Fixed charges = f

Cost per day = a

Find:

Equation

Computation:

Total cost = fixed cost + (Number of days)(Cost per day)

Total cost = f + ad

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1. The figure shows the regular triangular pyramid SABC. The base of the pyramid has an edge AB = 6 cm and the side wall has an
Musya8 [376]

Given:

• AB = 6 cm

,

• SM = √15 cm

Let's solve for the following:

• 1) the base elevation AM.

Given that we have a regular triangular pyramid, the length of the three bases are equal.

AB = BC = AC

BM = BC/2 = 6/2 = 3 cm

To solve for AM, which is the height of the base, apply Pythagorean Theorem:

\begin{gathered} AM=\sqrt{AB^2-BM^2} \\  \\ AM=\sqrt{6^2-3^2} \\  \\ AM=\sqrt{36-9} \\  \\ AM=\sqrt{27} \\  \\ AM=5.2\text{ cm} \end{gathered}

The base elevation of the pyramid is 5.2 cm.

• (2)., The elevation SO.

To find the elevation of the pyramid, apply Pythagorean Theorem:

SO=\sqrt{SM^2-MO^2}

Where:

SM = √15 cm

MO = AM/2 = 5.2/2 = 2.6 cm

Thus, we have:

\begin{gathered} SO=\sqrt{(\sqrt{15})^2-2.6^2} \\  \\ SO=\sqrt{15-6.76} \\  \\ SO=2.9\text{ cm} \end{gathered}

Length of SO = 2.9 cm

• (3). Area of the base:

To find the area of the triangular base, apply the formula:

A=\frac{1}{2}*BC*AM

Thus, we have:

\begin{gathered} A=\frac{1}{2}*6^*5.2 \\  \\ A=15.6\text{ cm}^2 \end{gathered}

The area of the base is 15.6 square cm.

• (4). Area of the side surface.

Apply the formula:

SA=\frac{1}{2}*p*h

Where:

p is the perimeter

h is the slant height, SM = √15 cm

Thus, we have:

\begin{gathered} A=\frac{1}{2}*(6*3)*\sqrt{15} \\  \\ A=34.86\text{ cm}^2 \end{gathered}

• (5). Total surface area:

To find the total surface area, apply the formula:

TSA=base\text{ area + area of side surface}

Where:

Area of base = 15.6 cm²

Area of side surface = 34.86 cm²

TSA = 15.6 + 34.86 = 50.46 cm²

The total surface area is 50.46 cm²

• (6). Volume:

To find the volume, apply the formula:

V=\frac{1}{3}*area\text{ of base *height}

Where:

Area of base = 15.6 cm²

Height, SO = 2.9 cm

Thus, we have:

\begin{gathered} V=\frac{1}{3}*15.6*2.9 \\  \\ V=15.08\text{ cm}^3 \end{gathered}

The volume is 15.08 cm³.

ANSWER:

• 1.) 5.2 cm

,

• 2.) 2.9 cm

,

• 3.) 15.6 cm²

,

• 4.) 34.86 cm²

,

• (5). 50.46 cm²

,

• 6). 15.08 cm³.

7 0
1 year ago
Josephine wants to put a wallpaper border around the ceiling of her room. The dimensions are 7 ft and 3 inches and 8 feet and 3
Ilya [14]
Answer:
372inches or 31feet
How to:
7feet and three inches is equal to 87 inches and 8ft and 3 inches is equal to 99 inches. Then you know that both sides have to be multiplied by two because there are four sides in the room. Meaning you have 174in and 198in. Then you add those together to get your answer which is 372. To get back to feet just divide by twelve.
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Using your knowledge of inverse operations, what does 56 - 25 - 56 equal?
Ivan

Answer:

-25

Step-by-step explanation:

Using the commutative property of addition, we can rearrange the expression to 56-56-25. 56-56 = 0, so the answer is 0 - 25 = -25.

7 0
3 years ago
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If Hank shoots from inside the three-point line, what can be said about his distance from the center of the basket?
Digiron [165]

Answer:

If Hank shoots from inside the three-point line we can say that he has to shoot 246 inches to make the ball into the hoop.

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3 years ago
What is the difference of the rational expressions below?
Korolek [52]

Answer:

in the pic

Step-by-step explanation:

answer A

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