Answer:
Amy: 8, Ben: 3
Step-by-step explanation:
No explanation here
(6x-18)(x+4)/(3x-9)=6(x-3)(x+4)/3(x-3)=2(x+4)=2x+8
Answer:
Hopefully, this is your desired setup. (I noticed the formula you have to fill in there.)
Have a good day.
Step-by-step explanation:
Hi.
You could use the percent change formula.
Since we know it is a percent increase then we will do new-old instead of old-new:
x is the new amount of shampoo.
16.5 is the original amount (old) of shampoo.
The percent increase is 30%=0.30 .
So we have the following equation:
We could have found the equation like this:
Subtract 16.5 on both sides:
Divide both sides by 16.5:
By us of symmetric property of equality:
Answer:
A: This polynomial has a degree of 2 , so the equation 12x2+5x−2=0 has two or fewer roots.
B: The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots.
Step-by-step explanation:
f(x) = 12x^2 + 5x - 2.
Since this is a quadratic equation, or a polynomial of second degree, one can easily conclude that this equation will have at most 2 roots. At most 2 roots mean that the function can have either 2 roots at maximum or less than 2 roots. Therefore, in the A category, 2nd option is the correct answer (This polynomial has a degree of 2 , so the equation 12x^2 + 5x − 2 = 0 has two or fewer roots).
To find the roots of f(x), set f(x) = 0. Therefore:
12x^2 + 5x - 2 = 0. Solving the question using the mid term breaking method shows that 12*2=24. The factors of 24 whose difference is 5 are 8 and 3. Therefore:
12x^2 + 8x - 3x - 2 = 0.
4x(3x + 2) -1(3x+2) = 0.
(4x-1)(3x+2) = 0.
4x-1 = 0 or 3x+2 = 0.
x = 1/4 or x = -2/3.
It can be seen that f(x) has two distinct real roots. Therefore, in the B category, 1st Option is the correct answer (The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots)!!!
The answer in slope intercept form is y = 6x-11
If you want the answer in standard form, then it would be 6x-y =11
notes:
* Slope intercept form is y = mx+b
* Standard form is Ax+By = C
=====================================
Explanation:
The given slope is m = 6
The line goes through (x,y) = (3,7)
Plug those three values into the equation below. Isolate b
y = mx+b
7 = 6*3+b
7 = 18+b
7-18 = 18+b-18 ... subtract 18 from both sides
-11 = b
b = -11
So because m = 6 and b = -11, this means y = mx+b turns into y = 6x-11
The answer in slope intercept form is y = 6x-11
To convert to standard form Ax+By = C, we just have to get all the x and y terms together on the same side. I'm going to move the y term to the right side and move the 11 to the left side
y = 6x-11
y+11 = 6x-11+11
y+11 = 6x
y+11-y = 6x-y
11 = 6x-y
6x-y = 11
The answer in standard form is
6x-y = 11
which is a different way to write the same line
