y < –12
Solution:
Step 1: Given inequality is y + 15 < 3.
To find the solution to the inequality.
Step 2: Subtract –15 on both sides to equal the expression.
⇒ y + 15 –15 < 3 –15
Step 2: Using addition identity property, any number adding with zero gives the number itself.
⇒ y + 0 < –12
⇒ y < –12
Hence the solution to the inequality is y < –12.
Answer:
66 cups
Step-by-step explanation:
16 cups in 1 gallon
16*6 = 96 cups in 6 gallons
96 - 30 = 66
Answer: x = 8
(the correct answer was not provided as an option)
<u>Step-by-step explanation:</u>
![log_2(x-6)+log_2(x-4)=log_2(x)\\\\log_2[(x-6)(x-4)]=log_2(x)\\\\(x-6)(x-4)=x\\\\x^2-10x+24=x\\\\x^2-11x+24=0\\\\(x-3)(x-8)=0\\\\x=3\qquad x=8\\\\\\\text{The term after the log symbol (inside the parenthesis) must be greater than 0!}\\\\Check:\\3-6>0\ \text{FALSE --- so 3 is not a valid solution}\\\\8-6>0\ \text{TRUE}\\8-4>0\ \text{TRUE}\\8>0\ \text{TRUE --- 8 is a valid solution because it is true for all}](https://tex.z-dn.net/?f=log_2%28x-6%29%2Blog_2%28x-4%29%3Dlog_2%28x%29%5C%5C%5C%5Clog_2%5B%28x-6%29%28x-4%29%5D%3Dlog_2%28x%29%5C%5C%5C%5C%28x-6%29%28x-4%29%3Dx%5C%5C%5C%5Cx%5E2-10x%2B24%3Dx%5C%5C%5C%5Cx%5E2-11x%2B24%3D0%5C%5C%5C%5C%28x-3%29%28x-8%29%3D0%5C%5C%5C%5Cx%3D3%5Cqquad%20x%3D8%5C%5C%5C%5C%5C%5C%5Ctext%7BThe%20term%20after%20the%20log%20symbol%20%20%28inside%20the%20parenthesis%29%20must%20be%20greater%20than%200%21%7D%5C%5C%5C%5CCheck%3A%5C%5C3-6%3E0%5C%20%5Ctext%7BFALSE%20---%20so%203%20is%20not%20a%20valid%20solution%7D%5C%5C%5C%5C8-6%3E0%5C%20%5Ctext%7BTRUE%7D%5C%5C8-4%3E0%5C%20%5Ctext%7BTRUE%7D%5C%5C8%3E0%5C%20%5Ctext%7BTRUE%20---%208%20is%20a%20valid%20solution%20because%20it%20is%20true%20for%20all%7D)
Answer: option a
Step-by-step explanation:
You must apply the formula for calculate the distance between the two points. which is shown below:

Therefore, keeping on mind that the points given in the problem are (6, 11), (0, 3), when you substitute values into the formula shown above, you obtain that the distance between these two points is the following:
