Answer:
length=53 in
width= 23 in
Step-by-step explanation:
First, we know that each corner has now a square of 6 in long, so the heigth of the box will be of this size (as you can see in the picture attached). Then, the length and the width of the box would be the same as the piece, but with 12 in less. Therefore the equations to solve the problem are:
We factorize the 6 and we get:
Finally we solve for x, and we get the initial dimensions of the piece of metal:
You can perform the horizontal line test on the original to see if the inverse will be a function. You will not perform the horizontal line test on the inverse.
Remember that the equation of a circle is:
Where (h, k) is the center and r is the radius.
We need to get the equation into that form, and find k.
Complete the square. We must do this for x² - 6x and y² - 10y separately.
x² - 6x
Divide -6 by 2 to get -3.
Square -3 to get 9. Add 9,
x² - 6x + 9
Because we've added 9 on one side of the equation, we have to remember to do the same on the other side.
Now factor x² - 6x + 9 to get (x - 3)² and do the same thing with y² - 10y.
y² - 10y
Divide -10 by 2 to get -5.
Square -5 to get 25.
Add 25 on both sides.
Factor y² - 10y + 25 to get (y - 5)²
Now our equation is in the correct form. We can easily see that h is 3 and k is 5. (not negative because the original equation has -h and -k so you must multiply -1 to it)
Since (h, k) represents the center, (3, 5) is the center and 5 is the y-coordinate of the center.
Answer:
n+3=5m
Step-by-step explanation:
Tenemos que
la capacidad del frasco es igual a 3/8 de litro
cuatro litros y medio es igual a decir 4 1/2 litros----> (4*2+1)/2----> 9/2 litros
realizamos una regla de tres
si un frasco tiene capacidad para--------------> 3/8 litros
X frascos-----------------------------------------> para 9/2 litros
X=(9/2)/(3/8)--------> 72/6-----> 12 frascos
la respuesta es
12 frascos
