Rachel newton scored 31 points in a recent basketball game. she scored 21 times, making several free throws worth 1 point each and several field goals worth two points each. how many 2-point field goals did she make?

10

Step-by-step explanation:

This problem can be solved with a system of equations...

Lets say that x is the number of free throws worth one point that Rachel made and that y is the number of two-point field goals that Rachel made.

We know that Rachel scored 21 times, so

x + y = 21.

We also know that Rachel scored 31 points, and each field goal made(y) is worth two points, so

x + 2y = 31

Now, to find the number of 2-point field goals she made, we need to solve the following system,

1)x + y = 21

2)x + 2y = 31

Our value of interest is y, so we can write x as function of y, from equation 1) and replacing it in equation 2)

So

x = 21 - y

Replacing in 2)

21 - y + 2y = 31

y = 31-21

y = 10

So, Rachel Newton made 10 2-point field goals.

la parábola es el lugar

geométrico en el cual los puntos tienen una distancia idéntica, equidistantes,

de un punto denominado foco, f, y una recta denominada directriz

el radio vector de una

parábola es el segmento que existe entre un punto cualquiera y el foco.

por la ecuación se observa

que la parábola abre hacia la derecha, por lo cual podemos usar las siguientes fórmulas

la ecuación ordinaria de la

parábola es y^2 = 4px, donde p es la longitud desde el vértice de la parábola al

foco.

la fórmula de la directriz

es x + p = 0

resolviendo:

y^2-9x = 0

y^2 = 9x

4p = 9, entonces p = 9/4

entonces el foco tendrá la

coordenada f(9/4,0)

la directriz vendrá

expresada por

x + p = 0

x = -p

x = -9/4

el problema indica que la

ordenada es igual a 6, entonces

(6)^2=9x

x = 36/9

x = 4

entonces el punto al cual

hay que obtener la distancia será p(4,6)

calculando se tendrá: pf = 

pf = 6,25 u

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step-by-step explanation: