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MrRa [10]
3 years ago
15

Standard Form: 3x+4y=−16

Mathematics
1 answer:
Gnesinka [82]3 years ago
8 0

Answer:

i know the answer

Step-by-step explanation:

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A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all arou
Arisa [49]

Complete question :

A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all around the patio.The perimeter of the patio after it is expanded is 74 feet. The equation which represents x, the width of the border is 2[(12+2x)+15+2x)]=74. What is the width of the border?

1) 2 1/2 feet

2) 3 feet

4) 5 feet

5) 8 1/2 feet

Answer:

2.5

Step-by-step explanation:

Solving for X in the perimeter equation :

2[(12+2x)+15+2x)]=74

Open the bracket

2[(12 + 2x + 15 + 2x)] = 74

2(27 + 4x) = 74

54 + 8x = 74

8x = 74 - 54

8x = 20

x = 20/8

x = 2.5

Hence, width fo border = 2.5

5 0
2 years ago
The area of a room is 600 square feet. The length is (x + 5) feet and the width is (x + 4) feet. Find the dimensions of the room
tangare [24]
I'm going to assume that the room is a rectangle.

The area of a rectangle is A = lw, where l=length of the rectangle and w=width of the rectangle. 

You're given that the length, l = (x+5)ft and the width, w = (x+4)ft. You're also told that the area, A = 600 sq. ft. Plug these values into the equation for the area of a rectangle and FOIL to multiply the two factors:
A = lw\\
600 = (x+5)(x+4)\\
600 =  x^{2} + 9x + 20


Now subtract 600 from both sides to get a quadratic equation that's equal to zero. That way you can factor the quadratic to find the roots/solutions of your equation. One of the solutions is the value of x that you would use to find the dimensions of the room:
600 = x^{2} + 9x + 20\\
x^{2} + 9x - 580 = 0\\
(x + 29)(x - 20) = 0\\
x + 29 = 0, \:\: x - 20 = 0\\
x = -29, x = 20

Now you know that x could be -29 or 20. For dimensions, the value of x must give you a positive value for length and width. That means x can only be 20. Plugging x=20 into your equations for the length and width, you get:
Length = x + 5 = 20 + 5 = 25 ft.
Width = x + 4 = 20 + 4 = 24 ft.

The dimensions of your room are 25ft (length) by 24ft (width).
8 0
3 years ago
Read 2 more answers
A package of 30 Oreos cost $3.60. Kennedy says the unit rate is 0.12. Mason says the unit rate is 8.33. Who is right?
Alekssandra [29.7K]

Answer:

360 \div 30 = 12

Step-by-step explanation:

so Kennedy is right

8 0
2 years ago
Choose the solution to this inequality. <br><br> 4/3 &lt; − 8/3y
Yuliya22 [10]

Answer:

Rewrite so y is on the left side of the inequality.

−83y>43

Multiply each term by −38 and simplify.

Inequality Form:

y<−1/2

Interval Notation:

(−∞,−1/2)

Step-by-step explanation:

6 0
3 years ago
A 120° sector of a circle has an area of 67 cm². To the nearest centimeter what is the diameter of the circle?
qaws [65]

Answer:

degree = 120°

A =67 cm²

d=?

note : diameter= 2×radius

area of a circle = πr²

67=22/7 ×r²

67×7=22r²

469=22r²

r²=469/22

r²=21.32

r=4.62

diameter=2 × radius

d= 2× 4.62

d=9.24

d=9

I hope it helps :)

3 0
3 years ago
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