Different examples above! hope this helps c:
First one
remember that all triangles internal angles (the 3 at the vertices) add to 180
we want BCD
we know BAD already
and ABC is a right angle
the measure of BDA is just there to throw us off
so
all adds to 180
BAD+ABC+BCD=180
59+90+BCD=180
149+BCD=180
minus 149 both sides
BCD=31
BCD=31 degrees
2nd problem
all angles add to 180 degrees
so
CAB+ABC+BCA=180
6x+147+2x+78+126+x=180
6x+2x+x+147+78+126=180
9x+351=180
minus 251 both sides
9x=-171
divide both sides by 9
x=-19
x=-19 degrees
Answer:
2.8+.55x=5 x=4
Step-by-step explanation:
5-2.8=2.2
2.2/.55=4
The total if all 236 coins were nickels would be $11.80, which is $3.95 short of the actual amount.
Replacing a nickel with a dime adds $0.05 to the total value, so there must have been $3.95/$0.05 = 79 such replacements.
There are 79 dimes.
There are 236 -79 = 157 nickels.
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Using the given variables, the problem statement gives rise to two equations. One is the based on the number of coins. The other is based on their value.
- n + d = 236
- .05n +.10d = 15.75
Solving the first for n, we get
... n = 236 - d
Substituting that into the second equation, we have
... .05(236 -d) +.10d = 15.75
... .05d = 15.75 -236·.05 . . . . . collect terms, subtract .05·236
... d = 3.95/.05 . . . . . . . . . . . . . divide by .05
... d = 79
... n = 236-79 = 157
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The solution should look familiar, as it matches the verbal description at the beginning.
