Answer:
x= 0, and x=4
Step-by-step explanation:
x² -x = 3x, we can subtract 3x from both sides
x² -x -3x = 0, combine like terms
x² -4x = 0 , factor x
x *( x-4) = 0, if the product of 2 numbers equals 0 at least one is 0
x=0 and
x-4 = 0, add 4 to both sides
x= 4
A = {a, l, o, w, n, c, e}
Answer:
- $12,000 at 4%
- $9,000 at 2%
Step-by-step explanation:
If x represents the amount invested at 4%, then the total interest earned is ...
0.04x + 0.02(21000 -x) = 660
0.02x = 240 . . . . . . . . . . . simplify, subtract 420
x= 240/0.02 = 12,000 . . . . amount invested at 4%
21,000 -x = 9,000 . . . . . . . . amount invested at 2%
The amount invested at 2% is $9,000.
The amount invested at 4% is $12,000.
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<em>Comment on method of solution</em>
These problems can usually be solved using one variable for the amount associated with the highest contribution to the mix. Here, that is the amount getting 4% interest. This keeps the numbers in the solution positive, helping to minimize errors. As you can see, the solution develops in about 2 or 3 steps. Other methods can take longer.
The rule for a rotation of 180 degrees is (x,y)—>(-x,-y) so when you have two negative points both of them will be positive. The answer would be (5,2) after this transformation.
Answer:
Step-by-step explanation:
Use <u> law of cosine</u> to calculate the other side.
c² = a² + b² -2ab Cos C
Here, c is the length of the side which is opposite side to ∠E
a = 29 ; b = 25 and C = 109
c² = 29² + 25² - 2*29*25*Cos 107
= 841 + 625 - 1450* (-0.2923)
= 1466 + 423.835
= 1889.835
c =√1889.835
c = 43.47 ≈ 43
No, find ∠D using again use <u>law of cosine</u>
<u></u>
β = ∠C = 34°
α = 180 - (34 +107)
α = ∠D = 39
Other angles are
∠C = 34° and ∠D°39