Dennis mowed his next door neighbor's lawn for a handful of dimes and nickles, 80 coins in all. Upon completing the job he count
1 answer:
Answer:
28 nickels and 58 dimes
Step-by-step explanation:
This situation has two unknowns - the total number of dimes and the total number of nickels. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.
• is an equation representing the total number of coins
• is an equation representing the total value in money based on the number of coin. 0.10 and 0.05 come from the value of a dime and nickel individually.
We write the first equation in terms of n by subtracting it across the equal sign to get . We now substitute this for d in the second equation.
After simplifying, we subtract 8 across and divide by the coefficient of n.
We now know of the 80 coins that 28 are nickels. To find the total number of dimes, we subtract 28 from 80 to get 52 dimes.
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Three important properties of the diagonals of a rhombus that we need for this problem are:
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus
First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°.
Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.
For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.
Similarly, we have
Now, to find the lengths of the diagonals,
So, the lengths of the diagonals are 10 and 10√3.
Answer: 10 and 10√3 units
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus
First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°.
Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.
For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.
Similarly, we have
Now, to find the lengths of the diagonals,
So, the lengths of the diagonals are 10 and 10√3.
Answer: 10 and 10√3 units