Answer: x ( y + 1) + y ( y + 3) + 2
Step-by-step explanation:
( x + y + 2) ( y + 1)
x ( y + 1) + y ( y + 1) + 2 ( y + 1)
expanding the bracket
( xy + x) + ( y2 + y) + ( 2y + 2)
removing the bracket
xy + x + y2 +y + 2y + 2
collecting like terms
xy + x + y2 + 3y + 2
given as: x(y + 1) + y ( y + 3) + 2
A number that can add up to 10 and multiplies to 11 is 1 since 11 is a prime number
To determine the number of cubes he needs to fill the box (this is assuming the cubes are 1 in cubes, he would need to calculate the volume of the box. To find the volume he would multiply the length by the width by the height. This would be 5 in x 6 in x 7 in. The volume is 210 cubic inches, so he could fill it with 210 one inch cubes.
Your answer would be the last option, (6x² - 5)(x² + 2).
This is because when you expand it, you get:
6x² × x² = 6x⁴
6x² × 2 = 12x²
-5 × x² = -5x²
-5 × 2 = -10
Which are all the correct terms.
I hope this helps!
First, we define variables:
x: small hat
y: medium hat
z: large hat
We now write the system of equations:
x + y + z = 47
5.50x + 6y + 7z = 302
-3x + y = 0
We can write the system in matrix form as:
Ax = b
Where,
A = [1 1 1; 5.50 6 7; -3 1 0]
b = [47; 302; 0]
x = [x; y ; z]
Solving the system we have:
x = 6
y = 18
z = 23
Answer:
the coach did purchase 23 large hats
d. 23