Find the area of the rhombus.
answer options: 48, 12, 24, 36

Option 3. 24 is the area of the rhombus.

Step-by-step explanation:

Since we know the area of a rhombus = 1/2(multiplication of the diagonals of rhombus)

Here the vertices of rhombus are (-4, 1), (0, 5),(6, 5), and (2,1)

Now distance between (-4, 1) and (6, 5) is

d = √(-4-6)²+(1-5)² = √10²+4² = √100+16 = √116 = 2√29

Now distance between (0, 5), (2, 1) is

d' = √(0-2)²+(5-1)² = √4+16 = √20 = 2√5

So the area = 1/2×2√29×2√5 = 2√29×5 = 2√145 = 24

Therefore the correct option 3 is the correct answer.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

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

ver más en -

step-by-step explanation: