8 cups of salsa. 5.2 is 65 percent of 8.
Answer: Negative
If the same negative number is multiplied to each side of a true inequality, then the inequality sign flips to make the new inequality true as well
Example:
Take 1 < 5 and multiply both sides by -2 and we get -2 > -10. The "less than" sign flips to "greater than" since -2 < -10 is false. The value of -10 is further to the left of -2 so -10 is smaller in value. The negative basically takes the complete opposite which is why the flip must happen.
This sign flip rule does not happen if you multiply both sides by a positive number.
Answer:
<em>y=mx+b</em>
y = 4/3x + 2
Step-by-step explanation:
You get the mx number by doing rise over run and you get b by looking at where the number on the y axis is
I hope this helps you! :)
<em><u>-KeairaDickson</u></em>
Answer:
![PQ=22\\\\QR=7\\\\PR=29](https://tex.z-dn.net/?f=PQ%3D22%5C%5C%5C%5CQR%3D7%5C%5C%5C%5CPR%3D29)
Step-by-step explanation:
To find the value of y, you can create an equation where two parts of the line are equal to the whole line:
![PQ+QR=PR](https://tex.z-dn.net/?f=PQ%2BQR%3DPR)
Substitute given values:
![(8y+6)+(y+5)=(19y-9)](https://tex.z-dn.net/?f=%288y%2B6%29%2B%28y%2B5%29%3D%2819y-9%29)
Solve for y. Simplify parentheses:
![8y+6+y+5=19y-9](https://tex.z-dn.net/?f=8y%2B6%2By%2B5%3D19y-9)
Combine like terms to simplify the equation:
![8y+y+6+5=19y-9\\\\9y+11=19y-9](https://tex.z-dn.net/?f=8y%2By%2B6%2B5%3D19y-9%5C%5C%5C%5C9y%2B11%3D19y-9)
Get the variable on one side of the equation and the constants on the other. Add 9 to both sides:
![9y+11+9=19y-9+9\\\\9y+20=19y](https://tex.z-dn.net/?f=9y%2B11%2B9%3D19y-9%2B9%5C%5C%5C%5C9y%2B20%3D19y)
Subtract 9y from both sides:
![9y-9y+20=19y-9y\\\\20=10y](https://tex.z-dn.net/?f=9y-9y%2B20%3D19y-9y%5C%5C%5C%5C20%3D10y)
Isolate the variable. Divide both sides by 10:
![\frac{20}{10} =\frac{10y}{10} \\\\y=2](https://tex.z-dn.net/?f=%5Cfrac%7B20%7D%7B10%7D%20%3D%5Cfrac%7B10y%7D%7B10%7D%20%5C%5C%5C%5Cy%3D2)
The value of y is 2. Insert this value into each line segment value and solve:
![PQ=8(2)+6\\\\PQ=16+6\\\\PQ=22](https://tex.z-dn.net/?f=PQ%3D8%282%29%2B6%5C%5C%5C%5CPQ%3D16%2B6%5C%5C%5C%5CPQ%3D22)
![QR=(2)+5\\\\QR=7](https://tex.z-dn.net/?f=QR%3D%282%29%2B5%5C%5C%5C%5CQR%3D7)
![PR=19(2)-9\\\\PR=38-9\\\\PR=29](https://tex.z-dn.net/?f=PR%3D19%282%29-9%5C%5C%5C%5CPR%3D38-9%5C%5C%5C%5CPR%3D29)
:Done
You can check by using:
![PQ+QR=PR\\\\22+7=29](https://tex.z-dn.net/?f=PQ%2BQR%3DPR%5C%5C%5C%5C22%2B7%3D29)
This statement is true, so the values are correct.
Decoding the LaTeX that didn't render, we seek sum of the angles of the seventh roots of
![- \frac 1 {\sqrt 2} - \frac i {\sqrt{2}}](https://tex.z-dn.net/?f=%20-%20%5Cfrac%201%20%7B%5Csqrt%202%7D%20-%20%5Cfrac%20i%20%7B%5Csqrt%7B2%7D%7D%20)
That's on the unit circle, 45 degrees into the third quadrant, aka 225 degrees.
The seventh roots will all be separated by 360/7, around 51 degrees. The first seventh root has
![\theta_1 = 225^\circ / 7](https://tex.z-dn.net/?f=%20%5Ctheta_1%20%3D%20225%5E%5Ccirc%20%2F%207)
That's around 32 degrees.
The next angle is
![\theta_2 = \frac{1}{7}( 225^\circ + 360^\circ)](https://tex.z-dn.net/?f=%20%5Ctheta_2%20%3D%20%5Cfrac%7B1%7D%7B7%7D%28%20225%5E%5Ccirc%20%2B%20%20360%5E%5Ccirc%29)
The next one is
![\theta_3 = \frac{1}{7}( 225^\circ + 720^\circ)](https://tex.z-dn.net/?f=%20%5Ctheta_3%20%3D%20%5Cfrac%7B1%7D%7B7%7D%28%20225%5E%5Ccirc%20%2B%20%20720%5E%5Ccirc%29)
and in general
![\theta_n = \frac{1}{7}( 225^\circ + (n-1)360^\circ) = \frac 1 7(-135^\circ + 360^\circ n)](https://tex.z-dn.net/?f=%20%5Ctheta_n%20%3D%20%5Cfrac%7B1%7D%7B7%7D%28%20225%5E%5Ccirc%20%2B%20%20%28n-1%29360%5E%5Ccirc%29%20%3D%20%5Cfrac%201%207%28-135%5E%5Ccirc%20%2B%20360%5E%5Ccirc%20n%29)
![S = \displaystyle \sum_{n=1}^7 \theta_n = \frac{1}{7} \sum_{n=1}^7 -135^\circ + \frac{360}{7} \sum_{n=1}^7 n](https://tex.z-dn.net/?f=S%20%3D%20%5Cdisplaystyle%20%5Csum_%7Bn%3D1%7D%5E7%20%5Ctheta_n%20%3D%20%5Cfrac%7B1%7D%7B7%7D%20%5Csum_%7Bn%3D1%7D%5E7%20-135%5E%5Ccirc%20%2B%20%20%5Cfrac%7B360%7D%7B7%7D%20%5Csum_%7Bn%3D1%7D%5E7%20n)
The first sum is just -135° since it's one seventh of the sum of seven -135s.
We have 1+2+3+4+5+6+7 = (1+7)+(2+6)+(3+5) + 4 = 28 so
![S = -135^\circ + 360^\circ (\frac{28} 7) = 4(360)-135 = 1305^\circ](https://tex.z-dn.net/?f=%20S%20%3D%20-135%5E%5Ccirc%20%2B%20360%5E%5Ccirc%20%28%5Cfrac%7B28%7D%207%29%20%3D%204%28360%29-135%20%3D%201305%5E%5Ccirc)
If I didn't screw it up, that means the answer is
Answer: 1305°