Answer:
2 2/3
Step-by-step explanation:
hope this helps :)
don't be afraid to ask questions
There are two equation:
1) From Kim
2) From Daniel
Let:
x be the cost of rolls of plain wrapping paper
y be the cost of rolls of shiny wrapping paper
Kim:
7x + 8y = 140
Daniel:
14x + 7y = 154
<u>Using elimination method:</u>
(7x + 8y = 140) * -2 (Multiplying the equation by -2)
-14x - 16y = -280
-14x -16y = -280
14x + 7y = 154
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0x - 9y = -126
9y = 126 (Negative sign cancels from both sides)
y = 126 /9
y = 14
The cost of each shiny wrapping paper is $14.
Now solve x, you pick any two equation to solve for x.
7x + 8y = 140
7x + 8(14) = 140 (You know from above y =14)
7x + 112 = 140
7x = 28
x = 28/7
x = 4
The cost of each plain wrapping paper is $4.
Solution: (4,14)
Problem 1) The triangles are similar because of the AA (angle angle) Similarity Theorem. The first A is the pair of congruent 39 degree angles. The second pair is unmarked, but look at where the triangles meet. They form a pair of vertical angles which are congruent. So we have two pairs of congruent angles allowing us to use the AA Similarity Theorem.
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Problem 2) We can use the SAS (Side Angle Side) Similarity Theorem to prove that these two triangles are similar. The angles are congruent. They are both 29 degrees. So that checks off the "A" portion of SAS. Then notice how the bottom sides are 32 and 64 for the small and large triangle respectively. They form the ratio 32/64 = 1/2, ie the smaller triangle's side is 1/2 as long as the longer counter part. Similarly, 8/16 = 1/2 as well. The ratio is constant at 1/2. This allows us to use the other "S" portions of SAS.
Answer:
4(x - 1) = 4x - 4
3x + 6 = 3(x + 2)
Step-by-step explanation:
The first equation is
We simplify to get;
This is not true, therefore this equation has no solution.
The second equation is
Combine like terms:
This has a unique solution.
The 3rd equation is
Group similar terms:
The 4th equation is :
This is always true. The equation has infinite solution.
The 5th equation is:
This also has infinite solution
The 6th equation is
It has a unique solution.
