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2 years ago

While you're in the parking lot, you realize that both the lightbulbs and the light switches

Mathematics

1 answer:

Romashka [77]2 years ago

4 0

Cost of Lightbulb = x

cost of switch is x-8

9x + 4(x-8) = 520.50

Use distributive property:

9x + 4x -32 = 520.50

Simplify:

13x -32 = 520.50

Add 32 to both sides:

13x = 552.50

Divide both sides by 13

X = 42.50

A lightbulb costs $42.50

A switch costs 42.50-8 = $34.50

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What is the perimeter of polygon ABCDEF

MissTica

47 is the perimeter

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3 years ago

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One of the tallest buildings in a country is topped by a high antenna. The angle of elevation from the position of a surveyor on

irina1246 [14]

Answer:

a. distance of the surveyor to the base of the building = 2051.90 ft

b. height of the building = 1384 ft

c. Angle of elevation from the surveyor to the top of the antenna = 38.31°

d. Height of antenna = 237.08 ft

Step-by-step explanation:

The picture above is a illustration of the described event.

a = the height of the flag

b = the height of the building

c = distance of the surveyor from the base of the building

the angle of elevation from the position of the surveyor on the ground to the top of the building = 34°

distance from her position to the top of the building = 2475 ft

distance from her position to the top of the flag = 2615 ft

(a) How far away from the base of the building is the surveyor located?

using the SOHCAHTOA principle

cos 34° = c/2475

c = 0.8290375726 × 2475

c = 2051.8679921

c = 2051.90 ft

(b) How tall is the building

The height of the building = b

sin 34° = opposite /hypotenuse

0.5591929035 = b/2475

b = 0.5591929035 × 2475

b = 1384.0024361

b = 1384.00 ft

(c) What is the angle of elevation from the surveyor to the top of the antenna?

let the angle = ∅

cos ∅ = adjacent/hypotenuse

cos ∅ = 2051.90/2615

cos ∅ = 0.784665392

∅ = cos-1 0.784665392

∅ = 38.310258303

∅ = 38.31°

(d) How tall is the antenna?

height of the antenna = a

sin 38.31° = opposite/hypotenuse

sin 38.31° = (a + b)/2615

sin 38.31° × 2615 = (a + b)

(a + b) = 0.6199159917 × 2615

(a + b) = 1621.0803182

(a + b) = 1621. 08 ft

Height of antenna = 1621. 08 - 1384.00 = 237.08031822 ft

Height of antenna = 237.08 ft

8 0

3 years ago

over six games, a hockey team scored 18 goals. On average, how many goals did the team score each game

Ede4ka [16]

Answer:

Step-by-step explanation:

Average = total sum of all numbers/number of items in set

Average = 18/6

Average = 3

4 0

3 years ago

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A rectangular tank that is 5324 ft cubed with a square base and open top is to be constructed of sheet steel of a given thicknes

marishachu [46]

Answer:

Side of 22 and height of 11

Step-by-step explanation:

Let s be the side of the square base and h be the height of the tank. Since the tank volume is restricted to 5324 ft cubed we have the following equation:

$V = s^2h = 5324$

$h = 5324 / s^2$

As the thickness is already defined, we can minimize the weight by minimizing the surface area of the tank

Base area with open top $s^2$

Side area 4sh

Total surface area $A = s^2 + 4sh$

We can substitute $h = 5324 / s^2$

$A = s^2 + 4s\frac{5324}{s^2}$

$A = s^2 + 21296/s$

To find the minimum of this function, we can take the first derivative, and set it to 0

$A' = 2s - 21296/s^2 = 0$

$2s = 21296/s^2$

$s^3 = 10648$

$s = \sqrt[3]{10648} = 22$

$h = 5324 / s^2 = 5324 / 22^2 = 11$

4 0

3 years ago

the sum of the digits of a certain two-digits number is 7.Reversing its digits increases the number by 9.What is the number

rusak2 [61]

Unit digit=y
tens digit=x
the number: 10x+y

We suggest this system of equations:
x+y=7
(10y+x)=(10x+y)+9
we solve it by substitution method.
x=7-y
10y+(7-y)=(10(7-y)+y)+9
9y+7=70-10y+y+9
9y+10y-y=70+9-7
18y=72
y=72/18=4

x=7-y
x=7-4=3

number=10x+y=10*3+4=30+4=34

solution: the number: 34

To check:
3+4=7
43=34+9

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3 years ago

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