<span>Label the place value 12 354.897
=> the given numbers are mixed number. We have the whole number which is 12
354 and the decimals which id 897.
Now, Let us label each digit’s place values:
1 – ten thousands = equals to 10 000
2 – thousands = equals to 2 000
3 – hundreds = equals to 300
5 – tens = equals to 50
4 – ones = equals to 4
.8 – tenths = equals to 8/10
.09 – hundreds = equals to 9/100
.007 – thousands = equals to 7/1 000</span>
A)
The slope-intercept form:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
m - slope
b - y-intercept
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We have the points (2, 5.1) and (-1, -0.5). Substitute:
![m=\dfrac{-0.5-5.1}{-1-2}=\dfrac{-5.6}{-3}=\dfrac{5.6}{3}=\dfrac{56}{30}=\dfrac{28}{15}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B-0.5-5.1%7D%7B-1-2%7D%3D%5Cdfrac%7B-5.6%7D%7B-3%7D%3D%5Cdfrac%7B5.6%7D%7B3%7D%3D%5Cdfrac%7B56%7D%7B30%7D%3D%5Cdfrac%7B28%7D%7B15%7D)
Therefore we have:
![y=\dfrac{28}{15}x+b](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B28%7D%7B15%7Dx%2Bb)
Put the coordinates of the point (-1, -0.5) ot the equation:
![-0.5=\dfrac{28}{15}(-1)+b](https://tex.z-dn.net/?f=-0.5%3D%5Cdfrac%7B28%7D%7B15%7D%28-1%29%2Bb)
<em>multiply both sides by 2</em>
<em>add
to both sides</em>
<em>divide both sides by 2</em>
![b=\dfrac{41}{30}](https://tex.z-dn.net/?f=b%3D%5Cdfrac%7B41%7D%7B30%7D)
Answer: ![\boxed{y=\dfrac{28}{15}x+\dfrac{41}{30}}](https://tex.z-dn.net/?f=%5Cboxed%7By%3D%5Cdfrac%7B28%7D%7B15%7Dx%2B%5Cdfrac%7B41%7D%7B30%7D%7D)
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B)
We have the points (-2, 3) and (3, -4).
Calculate the slope:
![m=\dfrac{-4-3}{3-(-2)}=\dfrac{-7}{5}=-\dfrac{7}{5}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B-4-3%7D%7B3-%28-2%29%7D%3D%5Cdfrac%7B-7%7D%7B5%7D%3D-%5Cdfrac%7B7%7D%7B5%7D)
Therefore we have:
![y=-\dfrac{7}{5}x+b](https://tex.z-dn.net/?f=y%3D-%5Cdfrac%7B7%7D%7B5%7Dx%2Bb)
Put the coordinates of the point (-2, 3) to the equation of a line:
![3=-\dfrac{7}{5}(-2)+b](https://tex.z-dn.net/?f=3%3D-%5Cdfrac%7B7%7D%7B5%7D%28-2%29%2Bb)
<em>subtract
from both sides</em>
![\dfrac{1}{5}=b\to b=\dfrac{1}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B5%7D%3Db%5Cto%20b%3D%5Cdfrac%7B1%7D%7B5%7D)
Answer: ![\boxed{y=-\dfrac{7}{5}x+\dfrac{1}{5}}](https://tex.z-dn.net/?f=%5Cboxed%7By%3D-%5Cdfrac%7B7%7D%7B5%7Dx%2B%5Cdfrac%7B1%7D%7B5%7D%7D)
Answer:
The answer should be 16 because they gained 14 yards, then they lost 7 yards, and finally they gained 9 yards.
14 -7 + 9 = 16
Answer:
firt thing i would do is take out things that are alike but if these are the options then i would a) multiply the first equation by -1
Vertex = (1/2,5/2) x= 1 + or - square root of 5-2y all over 2