Answer:
11x-8
Step-by-step explanation:
![3(x - 2) + 2(4x - 1) \\ multiply \: inside \: the \: bracket \\ 3x - 6 + 8x - 2 \\ 11x - 8](https://tex.z-dn.net/?f=3%28x%20-%202%29%20%2B%202%284x%20-%201%29%20%5C%5C%20multiply%20%5C%3A%20inside%20%5C%3A%20the%20%5C%3A%20bracket%20%5C%5C%203x%20-%206%20%2B%208x%20-%202%20%5C%5C%2011x%20-%208%20)
Answer: FIrst option, Fourth option and Fifth option.
Step-by-step explanation:
First it is important to know the definition of "Dilation".
A Dilation is defined as a transformation in which the Image (which is the figure obtained after the transformation) and the Pre-Image (this is the original figure, before the transformations) have the same shape, but their sizes are different.
If the length of CD is dilated with a scale factor of "n" and it is centered at the origin, the length C'D' will be:
![C'D'=nCD=(n)(12\ units)](https://tex.z-dn.net/?f=C%27D%27%3DnCD%3D%28n%29%2812%5C%20units%29)
Therefore, knowing this, you can determine that:
1. If
, you get:
![C'D'=(\frac{3}{2})(12\ units)=18\ units](https://tex.z-dn.net/?f=C%27D%27%3D%28%5Cfrac%7B3%7D%7B2%7D%29%2812%5C%20units%29%3D18%5C%20units)
2. If
, then the length of C'D' is:
![C'D'=(4)(12\ units)=48\ units](https://tex.z-dn.net/?f=C%27D%27%3D%284%29%2812%5C%20units%29%3D48%5C%20units)
3. If
, then:
![C'D'=(8)(12\ units)=96\ units](https://tex.z-dn.net/?f=C%27D%27%3D%288%29%2812%5C%20units%29%3D96%5C%20units)
4. If
, then, you get that the lenght of C'D' is:
![C'D'=(2)(12\ units)=24\ units](https://tex.z-dn.net/?f=C%27D%27%3D%282%29%2812%5C%20units%29%3D24%5C%20units)
5. If
, the length of C'D' is the following:
![C'D'=(\frac{3}{4})(12\ units)=9\ units](https://tex.z-dn.net/?f=C%27D%27%3D%28%5Cfrac%7B3%7D%7B4%7D%29%2812%5C%20units%29%3D9%5C%20units)
Answer:
The slope is -5/6
Step-by-step explanation:
To find the slope of a line given two points, we use the formula
m= (y2-y1)/(x2-x1)
= (-1-4)/(4--2)
=-5/(4+2)
=-5/6
Answer:
False
Step-by-step explanation:
The measure of an acute angle is less than 90°
Answer: Amber use 30 feet of basic tiles and 6 feet of decorative tiles.
Step-by-step explanation:
Let x be the foot of basic tiles and y be the foot of decorative tiles.
Now, according to the question, we have the following equations
![x+y=36\\y=36-x\ .......(1)\\\\8x+20y=36\times10\\2x+5y=90.......(2)\ \ \ [\text{divide equation by 4}]](https://tex.z-dn.net/?f=x%2By%3D36%5C%5Cy%3D36-x%5C%20.......%281%29%5C%5C%5C%5C8x%2B20y%3D36%5Ctimes10%5C%5C2x%2B5y%3D90.......%282%29%5C%20%5C%20%5C%20%5B%5Ctext%7Bdivide%20equation%20by%204%7D%5D)
Put y=36-x in (2), we get
![2x+5(36-x)=90\\\Rightarrow2x+180-5x=90\\\Rightarrow-3x=-90\\\Rightarrow\ x=30\\\\\Rightarrow\ y=36-30=6](https://tex.z-dn.net/?f=2x%2B5%2836-x%29%3D90%5C%5C%5CRightarrow2x%2B180-5x%3D90%5C%5C%5CRightarrow-3x%3D-90%5C%5C%5CRightarrow%5C%20x%3D30%5C%5C%5C%5C%5CRightarrow%5C%20y%3D36-30%3D6)
Hence, Amber use 30 feet of basic tiles and 6 feet of decorative tiles.