the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
and to get it, we simply need two points off of the straight line, hmm let's use the ones in the picture below.
![(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}}\implies \cfrac{2}{4}\implies \cfrac{1}{2}](https://tex.z-dn.net/?f=%28%5Cstackrel%7Bx_1%7D%7B2%7D~%2C~%5Cstackrel%7By_1%7D%7B4%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B6%7D~%2C~%5Cstackrel%7By_2%7D%7B6%7D%29%20~%5Chfill%20%5Cstackrel%7Bslope%7D%7Bm%7D%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%20%7B%5Cstackrel%7By_2%7D%7B6%7D-%5Cstackrel%7By1%7D%7B4%7D%7D%7D%7B%5Cunderset%7Brun%7D%20%7B%5Cunderset%7Bx_2%7D%7B6%7D-%5Cunderset%7Bx_1%7D%7B2%7D%7D%7D%5Cimplies%20%5Ccfrac%7B2%7D%7B4%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B2%7D)
Remember, the exact value cannot involve any rounding or estimates. Now, let's solve this problem. First, we have to translate it into an expression:
√72 - √8 + √128 separate the terms into square roots
√36·2 - √4·2 + √64·2 square root the terms that you can
6√2 - 2√2 + 8√2 they have like radical terms, so combine the terms
6 - 2 + 8 = 12 the coefficients are 12 when combined
12√2 this is the EXACT VALUE of the expression
Hope this helps!
Google translation
2/3 of a basket of apples rot. We eat 4/5 of the rest and use the remaining 25 to make jam. How many apples were in the basket
Answer:
375
Step-by-step explanation:
Since the basket was full, ⅔ rot so the remaining for any use will be 1-⅔=⅓
Since we only eat 4/5 of this remaining quantity, we use the 1-4/5=1/5 of ⅓ for making jam
1/5 of ⅓=1/5*⅓=1/15
If 1/15 equals 25 pieces then the full basket had
25*15/1=375 pieces
The answer is <em>X</em>= 15/19