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A rectangular pool has dimensions of 40 ft. and 60 ft. The pool has a patio area around it that is the same width on all sides.I

ladessa [460]

Area of pool edge = Area of big rectangle - Area of the pool

Area of pool edge = Area of the pool = 40 × 60 = 2400 ft²

2400 = Area of big rectangle - 2400
Area of big rectangle = 2400 + 2400
Area of big rectangle = 4800

Length × width = 4800

From the diagram, we need the length to be [x + x] more than the length of the pool, where x is the distance from the pool edge to the patio edge.

We also need the width of the big rectangle to be [[x + x] more than the width of the pool.

Length = 60 + 2x
Width = 40 + 2x

Length × Width = [60+2x] × [40+2x]
4800 = 2400 + 120x + 80x + 4x²
0 = 4x² + 200x - 2400
0 = 4[x² + 50x - 600]
0 = x² + 50x - 600
0 = [x - 60] [x + 10]

x - 60 = 0 OR x + 10 = 0
x = 60 OR x = -10

We can only use the positive value of x since the context is length

Hence, x = 60

7 0

4 years ago

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Solve the Equation 3x + 5x - 5 = 19

Mila [183]

Answer:

x=3

Step-by-step explanation:

8 0

3 years ago

Find the measure of angle B

amid [387]

Answer:

64°

Step-by-step explanation:

Angles in a straight line add up to 180° so 180° - 116° = 64°

7 0

3 years ago

Given right triangle ABCABC with altitude \overline{BD}

Alex

Answer:

$x = 2\sqrt{11}$

Step-by-step explanation:

AD = 4

AC = 11

DC = 11 - 4 = 7

First, find BD using the right triangle altitude theorem:

$BD = \sqrt{AD*DC}$

Plug in the values

$BD = \sqrt{4*7}$

$BD = 2\sqrt{7}$

Use pythagorean theorem to find x:

x² = AD² + BD²

Plug in the values

$x^2 = 4^2 + (2\sqrt{7})^2$

$x^2 = 16 + (4*7)$

$x^2 = 16 + 28$

$x^2 = 44$

Take the square root of both sides

$\sqrt{x^2} = \sqrt{44}$

$x = \sqrt{44}$

$x = \sqrt{4 * 11}$

$x = 2\sqrt{11}$

6 0

3 years ago

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A group of 55 football players were polled about which synthetic grass they like to play on, Chemstrand or Chemgrass. The data f

IrinaVladis [17]

From the Venn diagram: 15 players like Chemstrand, 17 players like Chemgrass, 13 players like both Chemstrand and Chemgrass while 10 players like neither Chemstrand nor Chemgrass.

The missing values in the frequency table are x - representing the number of players that like both Chemstrand and Chemgrass, y - representing the number of players that like Chemgrass but do not like Chemstrand and z - representing the number of players likes Chemstrand but do not like Chemgrass.

The number of players that like both Chemstrand and Chemgrass is 13. The number of players that like Chemgrass but do not like Chemstrand is 17. The number of players likes Chemstrand but do not like Chemgrass is 15.

Therefore, x = 13, y = 17 and z = 15

8 0

3 years ago

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Please help as soon as possible ​

Please help as soon as possible