The Synthetic Division form of Given Division Problem is :
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Option C is the Answer
Two angles are supplementary if they add up to 180 degrees.
We have then:
m ∠ DAB + m ∠ ABC = 180
Substituting:
(85 - 2x) + (90 + x) = 180
From here, we clear the value of x:
-x + 175 = 180
x = 175 - 180
x = - 5
Let's try now that it is a parallelogram.
The opposite angles of a parallelogram are equal in measure:
m ∠ DAB = m ∠ BCD
85 - 2x = 80 - 3x
85 - 2 (-5) = 80 - 3 (-5)
85 + 10 = 80 +15
95 = 95
Answer:
x = -5
m ∠ DAB = m ∠ BCD (It is shown to be a parallelogram)
9514 1404 393
Answer:
Step-by-step explanation:
If all of Brent's coins were pennies, their value would be 1.63. The value is actually 4.42 -1.63 = 2.79 more than that. Replacing a penny by a dime increases the value by .09. Hence there must be 2.79/.09 = 31 replacements.
Brent has 31 dimes and 132 pennies.
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<em>Solution using an equation</em>
You can write an equation that solve the problem in basically the same way. Let the variable represent the number of coins of highest value: d = dimes. Then the value (in cents) of the collection is ...
1(163-d) +10d = 442
9d +163 = 442 . . . . . . . . . . simplify (note 9 is the difference in value; 163 is the value of all pennies)
9d = 442 -163 = 279 . . . . . . subtract 163
d = 279/9 = 31 . . . . . . . . . . divide by 9
Brent has 31 dimes and 163-31 = 132 pennies.
Estimate:
2.3 rounds down to 2
So after multiplying by 2, the area is estimated to be 4 cm squared.
Actual Area:
2.3 x 2 = 4.6
The actual area of the shape is 4.6 cm squared.
Hope this helped!