Answer:
(x, y) = (0, 1/2) or (1, 3)
Step-by-step explanation:
The first equation factors as ...
x(3x -y) = 0
This has solutions x=0 and y=3x.
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<u>x = 0</u>
Using this in the second equation gives ...
2y -0 = 1
y = 1/2
(x, y) = (0, 1/2) is a solution
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<u>y = 3x</u>
Using the expression for y in the second equation, we get ...
2(3x) -5x = 1
x = 1 . . . . . . . . . simplify
y = 3x = 3 . . . . using x=1 in the first equation
(x, y) = (1, 3) is a solution
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Interestingly, the (red line) graph of 3x^2 -xy = 0 produced by this graphing calculator has a "hole" at x=0, It says that point is (0, undefined). In a sense, y is undefined, in that it can be <em>anything</em>. A more appropriate graph would graph that equation as the two lines x=0 and y=3x.
Step-by-step explanation:
Since we have given that
Number of muffins Diana sold at the bake sale = 336
Number of muffins Bob sold at the bake sale = 287
Now, here we are using the method of estimation i.e. rounding the integers to nearest ones.
By estimation, we get
Number of muffins Diana sold at the bake sale = 340
Number of muffins Bob sold at the bake sale = 290
So,
Difference between them is given by
Hence, Bob sold 50 fewer muffins than Diana.
The answer is -500, hope this helped
Answer:
a = 5 and b = 12
Step-by-step explanation:
<u>Step 1: Find angle B</u>
<em>Angle C = 90°</em>
<em>Angle A = 22.6°</em>
<em>Angle B = B</em>
<em>All angles in a triangle are equal to 180°.</em>
Angle A + Angle B + Angle C = 180°
22.6 + 90 + B = 180°
B = 180 - 112.6
B = 67.4°
<u>Step 2: Find the value of side AC 'b'</u>
<em>Hypotenuse = 13</em>
<em>Adjacent = b</em>
<em>Angle A = 22.6°</em>
Cos (Angle) = Adjacent/Hypotenuse
Cos (22.6) = b/13
b = 12
<u>Step 3: Find the value of side CB 'a'</u>
<em>Hypotenuse = 13</em>
<em>Opposite = a</em>
<em>Angle A = 22.6°</em>
Sin (angle) = Opposite/Hypotenuse
Sin (22.6°) = a/13
a = 4.99 rounded off to 5
Therefore, the value of a=5 and b=12.
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