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Dima020 [189]
2 years ago
15

A 340 m wire is cut into three pieces. The second piece is 4 times as long as the first. The third piece is 3 times as long as t

he second. How long is each piece
Mathematics
1 answer:
USPshnik [31]2 years ago
3 0

Answer: total length 5780

Step-by-step explanation:

1st wire. 340m

2nd wire. 1360m

3rd wire. 4080

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A portrait has dimensions of 30“ x 60“ and is surrounded by a frame of uniform width. If the total area (Portrait plus frame) is
Law Incorporation [45]

Answer:

The width of the is 4 inches

Step-by-step explanation:

Assume that the width of the frame is x

∵ The width of the fame is x inches

→ That means each dimension will increase by 2x ⇒ x from each side

∵ The portrait has dimensions of 30“ x 60“

∴ Its dimensions including the frame = (30 + 2x) × (60 + 2x)

∴ The total area of the portrait plus frame = (30 + 2x)(60 + 2x)

→ Multiply the brackets

∵ (30 + 2x)(60 + 2x) = 30(60) + 30(2x) + 2x(60) + (2x)(2x)

∴ (30 + 2x)(60 + 2x) = 1800 + 60x + 120x + 4x²

→ Add the like terms

∴ (30 + 2x)(60 + 2x) = 1800 + 180x + 4x²

∴ The total area of the portrait plus frame = 4x² + 180x + 1800

∵ The total area of the portrait plus frame = 2584 square inches

→ Equate the two right sides of the area

∴ 4x² + 180x + 1800 = 2584

→ Subtract 2584 from both sides

∴ 4x² + 180x + 1800 - 2584 = 0

→ Add the like terms in the left side

∴ 4x² + 180x - 784 = 0

→ Divide all terms by 4 to simplify

∴ x² + 45x - 196 = 0

→ Factorize it to find the value of x

∵ x² + 45x - 196 = (x - 4)(x + 49)

→ Equate the right side by 0

∴ (x - 4)(x + 49) = 0

→ Equate each factor by 0

∵ x - 4 = 0  

→ Add 4 to both sides to find x

∴ x = 4

∵ x + 49 = 0

→ Subtract 49 from both sides to find x

∴ x = -49 ⇒ refused it x can not be -ve (no negative dimensions)

∴ The width of the is 4 inches

7 0
2 years ago
on a piece of paper, graph y&lt;-3/4x+2. Then determine which answer choice matches the graph you drew.
exis [7]

Answer:

  D.  Graph D

Step-by-step explanation:

The  "y <" tells you two things: (1) shading will be below the line, where y-values are less than those on the line, and (2) the line will be dashed, because the "equal to" case is not included.

Only one graph has a dashed line with shading below: Graph D.

7 0
2 years ago
I need help with this ​
jeka94

Answer:

a15 = 50

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Step-by-step explanation:

<em>Insert/Substitute the number given in for n.</em>

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~

t25 = 2^25 - 5     <em>2 times itself 25 times. 25 is the exponent in this equation</em>

t25 = 33554432 - 5

t25 = 33554427

8 0
3 years ago
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