Answer:
x = 0, x = 4
Step-by-step explanation:
12x - 21 = 5x + 7(x - 3)
First, foil out the right side --> 5x² - 15x + 7x - 21, which simplifies down to 5x² - 8x - 21.
Move the 12x - 21 to the right side by subtracting --> 0 = 5x² - 20x.
Factor out a 5x --> 0 = 5x(x - 4)
If you want to solve for x, set 5x = 0 and x - 4 = 0.
For 5x = 0, divide both sides by 5 to isolate the x --> x = 0/5, which simplifies down to x = 0.
For x - 4 = 0, add 4 to both sides to isolate the x --> x = 0 + 4, which simplifies down to x = 4.
Plug the values back into the original equation to check if it works
12(0) -21 = 5(0) + 7((0) - 3) --> -21 = -21
12(4) - 21 = 5(4) + 7((4) -3) --> 27 = 27
Hope this helps!
<h3>
Answer: Both angles are equal to 45 degrees</h3>
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Explanation:
When using the SSS congruence rule, we can prove that triangle DCA is congruent to triangle BCA.
Since the triangles are congruent, the corresponding pieces angle DCA and angle BCA are equal in measure (if they weren't, then the triangles wouldn't be congruent).
Recall that any square has four right angles, ie all angles are 90 degrees each. Angle DCB is cut in half to get 90/2 = 45.
The angles DCA and DCB are 45 degrees each.
*see attachment for the possible choice answers showing the boxes and dimensions
Answer:
Box D = 27 ft³
Step-by-step explanation:
To find out which has the greatest volume, we need to calculate the volume of each box given in the option using the formula of the volume of a rectangular prism = w × h × l.
Where w = width; h = height; and l = length.
Thus, the volume for the boxes are as follows:
=>Box A:
V = w × h × l
V = 3 × 1 × 5
V = 15 ft³
=>Box B:
V = w × h × l
V = 2 × 3 × 4
V = 24 ft³
=>Box C:
V = w × h × l
V = 1 × 2 × 7
V = 14 ft³
=>Box D:
V = w × h × l
V = 3 × 3× 3
V = 27 ft³
The shipping box with the largest volume is box D with a volume of 27 ft³