You can substitute what y is into the second equation, so:
3x + 4(2x + 1) = 26
3x + 8x + 4 = 26
11x + 4 = 26
- 4
11x = 22
÷ 11
x = 2
y = (2 × 2) + 1
y = 5 + 1
y = 5
So you get x as 2 and y as 5, I hope this helps!
Answer:
A. If the side lengths are the same, then a triangle is not scalene.
Step-by-step explanation:
A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.
Simply stated, any polygon with three (3) lengths of sides is a triangle.
In Geometry, a triangle is considered to be the most important shape.
Generally, there are three (3) main types of triangle based on the length of their sides and these include;
I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.
II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.
III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.
First Chart: Perimeter
Square Portion:
Original Side Lengths: P = 4 (1 + 1 + 1 + 1 ) =4
Double Side Lengths: P = 8 (2 x 4 = 8)
Triple Side Lengths: P = 12 (4 x 3 = 12)
Quadruple Side Lengths: P = 16 (4 x 4 = 16)
Rectangle Portion:
Original Side Lengths: P = 6 (1 x 2 + 2 x 2 = 6)
Double Side Lengths: P = 12 (2 x 2 + 4 x 2 = 12)
Triple Side Lengths: P = 24 (4 x 2 + 8 x 2 = 24)
Quadruple Side Lengths: P = 48 (8 x 2 + 16 x 2 = 48)
Second Chart: Area
Square Portion:
Original Side Lengths: A = 1 (1 x 1 = 1)
Double Side Lengths: A = 4 (2 x 2 = 4)
Triple Side Lengths: A = 9 (3 x 3 = 9
Quadruple Side Lengths: A = 16 ( 4 x 4 = 16)
Rectangle Portion:
Original Side Lengths: A = 2 ( 1 x 2 = 2 )
Double Side Lengths: A = 8 ( 2 x 4 = 8)
Triple Side Lengths: A = 18 ( 3 x 6 = 18)
Quadruple Side Lengths: A = 32 (4 x 8 = 32)
Answer:
{1, (-1±√17)/2}
Step-by-step explanation:
There are formulas for the real and/or complex roots of a cubic, but they are so complicated that they are rarely used. Instead, various other strategies are employed. My favorite is the simplest--let a graphing calculator show you the zeros.
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Descartes observed that the sign changes in the coefficients can tell you the number of real roots. This expression has two sign changes (+-+), so has 0 or 2 positive real roots. If the odd-degree terms have their signs changed, there is only one sign change (-++), so one negative real root.
It can also be informative to add the coefficients in both cases--as is, and with the odd-degree term signs changed. Here, the sum is zero in the first case, so we know immediately that x=1 is a zero of the expression. That is sufficient to help us reduce the problem to finding the zeros of the remaining quadratic factor.
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Using synthetic division (or polynomial long division) to factor out x-1 (after removing the common factor of 4), we find the remaining quadratic factor to be x²+x-4.
The zeros of this quadratic factor can be found using the quadratic formula:
a=1, b=1, c=-4
x = (-b±√(b²-4ac))/(2a) = (-1±√1+16)/2
x = (-1 ±√17)2
The zeros are 1 and (-1±√17)/2.
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The graph shows the zeros of the expression. It also shows the quadratic after dividing out the factor (x-1). The vertex of that quadratic can be used to find the remaining solutions exactly: -0.5 ± √4.25.
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The given expression factors as ...
4(x -1)(x² +x -4)
