Answer:
a = -3 b = -5 c = 9
Step-by-step explanation:
A quadratic function is written in the form
ax^2 +bx +c =0
-3x^2-5x+9=0
a = -3 b = -5 c = 9
The given equation
x/2 = y/3 = z/4
can be broken into three separate equations which I'll call equations (A), (B) and (C)
- x/2 = y/3 ..... equation (A)
- y/3 = z/4 .... equation (B)
- x/2 = z/4 .... equation (C)
We'll start off solving for z in equation (C)
x/2 = z/4
4x = 2z ... cross multiply
2z = 4x
z = 4x/2 ... divide both sides by 2
z = 2x
Now let's solve for y in equation (A)
x/2 = y/3
3x = 2y
2y = 3x
y = 3x/2
y = (3/2)x
y = 1.5x
The results of z = 2x and y = 1.5x both have the right hand sides in terms of x. This will allow us to replace the variables y and z with something in terms of x, which means we'll have some overall expression with x only. The idea is that expression should simplify to 3 if we played our cards right.
We won't be using equation (B) at all.
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The key takeaway from the last section is that
Let's plug those items into the expression (2x-y+5z)/(3y-x) to get the following:
(2x-y+5z)/(3y-x)
(2x-y+5(2x))/(3y-x) ..... plug in z = 2x
(2x-y+10x)/(3y-x)
(12x-y)/(3y-x)
(12x-1.5x)/(3(1.5x)-x) .... plug in y = 1.5x
(12x-1.5x)/(4.5x-x)
(10.5x)/(3.5x)
(10.5)/(3.5)
3
We've shown that plugging z = 2x and y = 1.5x into the expression above simplifies to 3. Therefore, the equation (2x-y+5z)/(3y-x) = 3 is true when x/2 = y/3 = z/4. This concludes the proof.
Answer:
-4 = x
Step-by-step explanation:
g(x) = -X – 1
g(x) = 3
3 = -x-1
Add 1 to each side
3+1 = -x-1+1
4 = -x
Multiply by -1
-4 = x
9514 1404 393
Answer:
5/6
Step-by-step explanation:
If q is the quantity of cereal in the box before Heba ate some, the problem tells us ...
q - 1/12 = 3/4
q = 3/4 + 1/12 = 9/12 + 1/12 = 10/12
q = 5/6
There was 5/6 of a box before Heba ate.
