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.
A right triangle can be considered as a special type
because the relationship of its sides can be described using the hypotenuse
formula:
c^2 = a^2 + b^2
or
c^2 = x^2 + y^2
where,
c is the hypotenuse of the triangle and is the side
opposite to the 90° angle
while a and b are the sides adjacent to the 90° angle
In the problem statement, we are given that one of the
side has a measure of 2 = x, while the hypotenuse is 5 = c, therefore calculating
for y:
y^2 = c^2 – x^2
y^2 = 5^2 – 2^2
y^2 = 21
y = 4.58
The natural number is the number before the decimal.
Therefore the answer is:
y = 4
Answer:
56.5 in
Step-by-step explanation:
Explicación paso a paso:
Debemos buscar el costo de cada boleto y la cantidad de personas que deben ir.
Dada la función que da forma al comportamiento expresado como;
f (x) = (-2x) ^ 2 + 80x + 300 donde;
x es el costo de cada boleto
f (x) es el número de personas que deben ir
Para obtener x, usaremos la expresión;
x = -b / 2a
De la ecuación cuadrática dada, a = -2, b = 80 yc = 300
Sustituir;
x = -80/2 (-2)
x = -80 / -4
x = 80/4
x = 20
Por lo tanto, el boleto cuesta $ 20.
Lo siguiente es obtener la cantidad de personas que deben ir. Para conseguirlo, sustituiremos x = 20 en la expresión modelada como se muestra;
f (x) = (-2x) ^ 2 + 80x + 300
f (20) = (-2 (20)) ^ 2 + 80 (20) +300
f (20) = (-40) ^ 2 + 1600 + 300
f (20) = 1600 + 1600 + 300
f (20) = 3500
Por lo tanto, 3500 personas tienen que ir
Answer:
b = 58
Step-by-step explanation:
Complementary angles add to 90 degrees.
a+b = 90
32+b = 90
Subtract 32 from each side
32+b-32 = 90-32
b = 58
