answer and step by step in the attachment
Answer:
the answer would be 6x^2(x+6)(x-2)
Step-by-step explanation:
6x^4 + 24x^3-72x^2
= 6x^2(x^2+4x-12)
= 6x^2(x+6)(x-2)
Slope = (0-2)/(-2-4)=(-2)/(-6)=1/3
y-0=(1/3)(x+2)
y=(1/3)x+2/3
A line crossing the circle at point A and passing through its center O is perpendicular to a line tangent to the circle at point A.
Therefore, segment AB is perpendicular to OA. And segment BC is perpendicular to OC:
Answer:
3 dogs and 5 cats were adopted out on Christmas eve.
Step-by-step explanation:
Let the number of dogs adopted out on Christmas eve be x and the number of cats be y.
From the question,
On Christmas Eve, the animal adopted out 8 total animals
That is, x + y = 8 ...... (1)
and brought in $400 in total adoption fees.
Also from the question,
Each dog adoption fee was $75 and each cat adoption fee was $35.
∴ On Christmas Eve,
75x + 35y = 400 ...... (2)
Now, to determine how many dogs and how many cats were adopted out on Christmas Eve, we will solve the two equations simultaneously.
From equation (1)
x + y = 8
Make x the subject of the relation.
∴ x = 8 - y ...... (3)
Substitute the value of x into equation (2)
75(8 - y) + 35y = 400
600 - 75y + 35y = 400
600 -40y = 400
600 - 400 = 40y
200 = 40y
∴ 40y = 200
y = 200/40
y = 5
Substitute the value of y into equation (3)
x = 8 - y
x = 8 - 5
x = 3
∴ x = 3 and y = 5
Hence, 3 dogs and 5 cats were adopted out on Christmas eve.
