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larisa [96]
3 years ago
10

A bag contains two steel balls and five brass balls. The total weight of the bag is 13 pounds. If two steel balls are added and

two brass balls are removed, the bag’s weight decreases to 12 pounds. If s is the weight of a steel ball and b is the weight of a brass ball, the system of linear equations representing this situation is . Solving the system of linear equations, the weight of a steel ball is , and the weight of a brass ball is . NextReset
Mathematics
1 answer:
nlexa [21]3 years ago
5 0

x = the weight of one steel ball y = the weight of one brass ball 2x + 5y = 13 (2 + 2)x + (5 - 2)y = 12 by solving the above system of equations we find:

x = 1.5 lbs y =2 lbs one steel ball weighs 1.5 lbs.one brass ball weighs 2 lbs.

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3. Given ABCD ≅ FGHJ and mC = 9x - 7, mH = 5x + 13, find the value of x and the measures of angle C and angle H. Show all work
kondor19780726 [428]

Answers:

x = 5

m∠C = m∠H = 38 degrees

 

 

WORKINGS

 

Given that ABCD ≅ FGHJ

We know that corresponding angles of two congruent quadrilaterals are equal

Therefore,

m∠A = m∠F

m∠B = m∠G

m∠C = m∠H

m∠D = m∠I

 

Given,

m∠C = 9x – 7

m∠H = 5x + 13

 

Since m∠C = m∠H

9x – 7 = 5x + 13

 

Add 7 to both sides of the equation

9x – 7 + 7 = 5x + 13 + 7

9x = 5x + 20

 

Subtract 5x from both sides of the equation

9x – 5x = 5x – 5x + 20

4x = 20

 

Divide both sides of the equation by 4

4x/4 = 20/4

x = 5

 

 

To determine the measures of angle C and angle H

m∠C = m∠H

 

We know that m∠C = 9x – 7

Since x = 5

m∠C = 9(5) – 7

m∠C = 45 – 7

m∠C = 38

 

Therefore, m∠C = m∠H = 38 degrees
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