Answer:
The answer to your question is 732 in³
Step-by-step explanation:
Data
Rectangular prism layers
Base layer = 12 in x 10 in x 4 in
Second layer = 3 in smaller x 4 in
Volume = ?
Formula
Total volume = Volume of the base layer + Volume of the second layer
Total volume = length 1 x width 1 x height + length 2 x width 2 x height
Substitution
Total volume = 12 x 10 x 4 + (12 - 3)(10 - 3)(4)
Simplification
Total volume = 480 + (9)(7)(4)
Total volume = 480 + 252
Result
Total volume = 732 in³
Answer:
n=-6
Step-by-step explanation:
-3n-4n-17=25
-7n-17=25
-7n=42
n=-6
This question is worded slightly strangely but I believe I understand it.
To eliminate x, multiply the second equation by 8, so that it becomes 4x + .8y= 96
<span>Then you can subtract 4x on the top by 4x on the bottom to eliminate it. </span>
Just for reference, here's the vertex form of a parabola equation:
f(x) = a(x - h)^2 + k
because this is in vertex form, finding the vertex is a little easier -- it's just (2, -1), bc the vertex is found as (h, k)
the domain is all real numbers, (-∞, ∞), because there aren't any constraints on the domain in this case
to determine the range, you have to figure out whether or not this parabola curves upwards or down, and in this case it curves up!! you know this because your A value (the implied coefficient of 1) is positive, so the range will be from the y value of your vertex to POSITIVE infinity, so [-1, ∞)
then your x and y intercepts are found by plugging in zeros for the values:
x-intercept: (plug in 0 for y)
0 = (x - 2)^2 - 1
1 = (x - 2)^2
1 = x - 2
x = 3
y-intercept: (plug in 0 for x)
y = (0 - 2)^2 - 1
y = 4 - 1
y = 3