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Answer:
The volume is 343 times as large.
The length is 7 times as large.
Step-by-step explanation:
If the original cube has side length s, its volume is given by ...
V = s³
When the side length is changed by a factor of 7, the new volume is ...
V = (7s)³ = 7³×s³ = 343s³
The volume of the cube changes by a factor of 7³ = 343.
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The problem statement tells you the length is 7 times as large.
Answer:
No, A''C''B'' is located at A''(1, 1), C''(4, 3), and B''(1, 5)
Step-by-step explanation:
In general, such a pair of transformations <em>cannot</em> map a figure to itself unless all of the points are on the line y=x. Only point A is located on that line, so ...
- any answer choice with "yes" must be rejected
- any answer choice with original point coordinates must be rejected
That only leaves the last answer choice, as shown above.
Complementary angles - the sum of two angles equals 90 degrees
Exterior angle theorem- the sum of the remote interior angles of a triangle equals the outside angle
Isosceles triangle- has two equal sides and two equal angles
Supplementary angle- the sum of two angles equals 180 degrees
Triangle sum theorem- the sum of of interior angles equal 180
Vertical angles- congruent angles that are opposite of each other.
First write the equations in the slope-intercept form:
![y=mx+b \\ \\ m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=y%3Dmx%2Bb%20%5C%5C%20%5C%5C%0Am%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Line 1 passes through the points (-6,-6) and (-4,-3).
![m=\frac{-3-(-6)}{-4-(-6)}=\frac{-3+6}{-4+6}=\frac{3}{2} \\ \\ (-6,-6) \to x=-6, \ y=-6 \\ -6=\frac{3}{2} \times (-6) + b \\ -6=-9+b \\ b=3 \\ \\ y=\frac{3}{2}x+3](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-3-%28-6%29%7D%7B-4-%28-6%29%7D%3D%5Cfrac%7B-3%2B6%7D%7B-4%2B6%7D%3D%5Cfrac%7B3%7D%7B2%7D%20%5C%5C%20%5C%5C%0A%28-6%2C-6%29%20%5Cto%20x%3D-6%2C%20%5C%20y%3D-6%20%5C%5C%0A-6%3D%5Cfrac%7B3%7D%7B2%7D%20%5Ctimes%20%28-6%29%20%2B%20b%20%5C%5C%0A-6%3D-9%2Bb%20%5C%5C%0Ab%3D3%20%5C%5C%20%5C%5C%20y%3D%5Cfrac%7B3%7D%7B2%7Dx%2B3)
Line 2 passes through the points (0,3) and (2,6).
![m=\frac{6-3}{2-0}=\frac{3}{2} \\ \\ (0,3) \to x=0, \ y=3 \\ 3=\frac{3}{2} \times 0 + b \\ b=3 \\ \\ y=\frac{3}{2}x+3](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B6-3%7D%7B2-0%7D%3D%5Cfrac%7B3%7D%7B2%7D%20%5C%5C%20%5C%5C%0A%280%2C3%29%20%5Cto%20x%3D0%2C%20%5C%20y%3D3%20%5C%5C%0A3%3D%5Cfrac%7B3%7D%7B2%7D%20%5Ctimes%200%20%2B%20b%20%5C%5C%0Ab%3D3%20%5C%5C%20%5C%5C%0Ay%3D%5Cfrac%7B3%7D%7B2%7Dx%2B3)
These are two identical lines so the system of equations has infinitely many solutions. The answer is D.
Alex definitely had the most work done between all of them