Answer:
60 Units
Step-by-step explanation:
The length of AC does not change. Since the translation is a rotation, nothing about the size of the triangle should change. Meaning A'B'C' is still 60 units in length.
The longest straight line that can be drawn between any two points of a square is the one that includes the points on the opposite corners of the squares. To determine the length of this straight line, we must first determine the length of the square's side. Since the area of the square can be calculated by taking the square of the side, then
s^2 = 72
s = 6 sqrt(2)
Then, using the Pythagorean theorem, we will find c (the longest side of straight line of the square)
c^2 = a^2 + b^2
Upon substitution of the length of the square's side, we have
c^2 = (6 sqrt(2))^2 + (6 sqrt(2))^2
c^2 = 72+72
c = 72
The length of the longest line is 72.
Solving problems means making choices. Typically, effective problem-solving skills result in “happier, more confident, and more independent” individuals. When children tackle problems on their own, or in a group, they become resilient
5x = 10/7
x = (10/7) / 5
x = 10/7 * 1/5
x = 10/35 which reduces to 2/7 <==
Answer:
Length = 8 inches
Width = 4 inches
Height = 6 inches
Step-by-step explanation:
Volume of the box = 192 cubic inches
Volume of a box = length × width × height
Let
Width = x
Length = 2x
Height = x + 2
Volume of a box = length × width × height
192 = 2x * x * (x + 2)
192 = 2x^2 (x + 2)
192 = 2x^3 + 4x^2
Divide through by 2
96 = x^3 + 2x^2
Subtract 96 from both sides
x ^3 + 2x^2 - 96 = 0
Factorise
(x - 4) (x^2 + 6x + 24) = 0
x^2 + 6x + 24 has no real x-value
So,
Divide both sides by (x^2 + 6x + 24).
0 ÷ (x^2 + 6x + 24) = 0
So,
(x - 4) = 0
x = 4
Width = x = 4 inches
Length = 2x
= 2(4)
= 8 inches
Height = x + 2
= 4 + 2
= 6 inches
Check:
Volume of a box = length × width × height
= (8 * 4 * 6) inches
= 192 inches
