For each set of angle measurements, determine if they would form a triangle (Answer YES or NO for
1 answer:
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Answer:
The cost of the 1 muffin is $1.5 and 1 quart of milk cost is $3 .
Step-by-step explanation:
Let us assume that the cost of one muffins be x.
Let us assume that the cost of one 1 quarts of milk be y.
As given
The cost of 8 muffins and 2 quarts of mil is $18.
Than the equation becomes
8x + 2y = 18
As given
The cost of 3 muffins and 1 quart of milk is $7.50.
Than the equation becomes
3x + 1y = 7.50
Two equations are
8x + 2y = 18 and 3x + 1y = 7.50
Multiply 3x + 1y = 7.50 by 2 and subtracted from 8x + 2y = 18 .
Thus
8x - 6x + 2y - 2y = 18 - 15
2x = 3
x = 1.5
Put x = 1.5 in 3x + 1y = 7.50
3 × 1.5 + y = 7.50
y = 7.50 - 4.5
y = 3
Therefore the cost of the 1 muffin is $1.5 and 1 quart of milk cost is $3 .
A rectangle with dimensions and
has perimeter 20 if
and we can deduce
So, the dimensions of the rectangle must be and
, where x ranges from 0 to 10 (both extremes are excluded, otherwise you'd have a degenerate rectangle, which is actually a segment).
So, all the possible areas are given by the product of the dimensions, i.e.
The function represents a parabola, facing downwards, and thus it admits a maximum, which is its vertex.
In particular, the vertex of this parabola is given by
And it yields an area of
(a) So, she can frame a maximum area of 25 squared yards.
(b)The dimensions of the rectangle with greatest area are and
, so it's actually a square.
This is a well known theorem: if you fix the perimeter, the rectangle with the largest area is the square yielding that perimeter.
(c) If we increase both dimensions by 2 yards, our 5x5 square would become a 7x7 square...
(d) ...and the new area would be squared yards. So, the new area is
squared yeards more than the old one.
Opposite angles have the same measures. This allows you to set and solve the following equations:
To solve both equations, let's move all the terms involving the variables on the left hand side, and all constant terms on the right hand side:
Sum like terms:
Divide the first equation by 2 and the second by -4: