Find 4 consecutive odd integers whose sum is 456.
2 answers:
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9514 1404 393
Answer:
(x, y) = (-3, -13) or (-8, -23)
Step-by-step explanation:
The values for y can be equated and the resulting quadratic solved by factoring.
2x -7 = x^2 +13x +17
0 = x^2 +11x +24 . . . . . . subtract 2x-7
0 = (x +8)(x +3) . . . . . . . .factor*
The values of x that make these factors zero are x=-8 and x=-3. The corresponding values of y are ...
y = 2(-8) -7 = -23
y = 2(-3) -7 = -13
The solutions are ...
(x, y) = (-8, -23) and (-3, -13)
_____
* The constants in the binomial factors are factors of 24 that total 11. You know that ...
24 = 1×24 = 2×12 = 3×8 = 4×6
The sums of these factors are 25, 14, 11, 10. The factors 3 and 8 are the constants in the binomial factors of the quadratic.
"24" is the constant in the quadratic. "11" is the coefficient of the x term.
Answer:
J'(2,-3), K'(4, -3) and L'(5,-2)
Step-by-step explanation:
The given triangle has vertices at J(2,3), K(4, 3) and L(5,2).
The transformation rule for a reflection in the x-axis is:
We substitute the points to obtain the coordinates of the image triangle J'K'L'
In other words, we negate the y-coordinates of triangle JKL to obtain the coordinates of J'K'L'
See attachment for graph.
