Answer:
![y \geqslant - 2x - 5](https://tex.z-dn.net/?f=y%20%5Cgeqslant%20%20-%202x%20-%205)
Step-by-step explanation:
Since the shaded area is above the line and the line is solid, you will use the greater-than-or-equal-to sign.
Not to mention inequalities still have a slope and y-intercept. (In this case, the y-intercept will be -5, since the line crosses the y-axis at that point, and the slope will be -2 because the line is going down 2 units and to the right 1 unit.)
Hope this helps :)
Answer: 8
<u>Step-by-step explanation:</u>
log₃ (x² - 32) = log₃ (4x) restrictions: x² - 32 > 0 and 4x > 0 ⇒ x > 4√2
x² - 32 = 4x
x² - 4x - 32 = 0
(x - 8)(x + 4) = 0
x - 8 = 0 or x + 4 = 0
x = 8 or x = -4
<em> -4 does not meet the restriction so not valid</em>
********************************************************************************************
Answer: y = 7x - 6
<u>Step-by-step explanation:</u>
<u> 7x -6 </u>
x² + 0x + 4 ) 7x³ - 6x² + 0x + 7
<u>-7x³ + 0x² - 28x</u>
-6x² - 28x + 7
<u> 6x² + 0x + 24</u>
-28x + 31
********************************************************************************************
Answer: x = ![\frac{6}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B5%7D)
<u>Step-by-step explanation:</u>
ln 3 + ln x = ln 6 + ln (3x - 3) restrictions: x > 0 and 3x - 3 > 0 ⇒ x > 1
ln (3 * x) = ln (6*(3x - 3))
ln (3x) = ln (18x - 18)
3x = 18x - 18
<u>-18x </u> <u>-18x </u>
-15x = -18
![\frac{-15x}{-15} = \frac{-18}{-15}](https://tex.z-dn.net/?f=%5Cfrac%7B-15x%7D%7B-15%7D%20%3D%20%5Cfrac%7B-18%7D%7B-15%7D)
x = ![\frac{6}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B5%7D)
> 1 so answer is valid
********************************************************************************************
Answer: -5.9761
<u>Step-by-step explanation:</u>
log ₁₎₂ 63
= ![\frac{log (63)}{log(\frac{1}{2})}](https://tex.z-dn.net/?f=%5Cfrac%7Blog%20%2863%29%7D%7Blog%28%5Cfrac%7B1%7D%7B2%7D%29%7D)
= ![\frac{1.7993}{-0.3010}](https://tex.z-dn.net/?f=%5Cfrac%7B1.7993%7D%7B-0.3010%7D)
= -5.9761
Answer:
Subtract the maximum and minimum values.
Step-by-step explanation:
The range of a data set is the interval that contains all values in the set and is determined as the difference between the maximum and the minimum values within the data set. Therefore, in order to find the range of a set of data, simply subtract the maximum and minimum values.
1/4 times 16x is 4x
1/4 times 4 is 1
4x minus 9x is -5x
So, 1/4 (16x+4)-9x is -5x+1
-5 times x is -5x
-5 times 1 is -5
So,-5 (x+1) is -5x-5
Therefore they are not equivalent