I believe you need to solve this using the quadratic formula!
To begin, this is what it is:
x= -b ± <span>√ b^2 - 4ac / 2a
Just plug in what you have in your problem...
2 being a, 13 being b, and -24 being c.
So we get:
x= -13 </span>± <span>√13^2 - 4(2)(-24) / 2(2)
x= -13 </span><span>± √169 - 8 (-24) / 4</span>
<span>x= -13 <span>± √169 + 192 / 4</span>
x= -13 </span>± √<span>361 / 4
The square root of 361 is 19.
So you have: -13 </span><span>± 19 / 4.
Here's where you take the equation </span>-13 <span>± 19 and put the addition and subtraction sign to use.
-13 - 19 = -32
and
-13 + 19 = 6
Now all is left to do is divide the two numbers by 4.
-32/4 = -8
and
6/4 = 3/2
x = -8, 3/2</span>
Lcm stands for Least common multiple
The lcm of these numbers is 48
6 - 6, 12, 18, 24, 30, 36, 42, [ 48]
16 - 16, 32, [48 ]
Therefore 48 is the lcm because it is the lowest number 6 and 16 have in common
Answer:
These points aren't a function
Step-by-step explanation:
The two points on the y-values are stacked, therefore, the function is not a function.
Let x represent the gallons of water that is 10% salt.
Let y represent the gallons of water that is 25% salt.
Now, write the system of equations:
x + y = 10
.10x +.25y = 0.20 • 10
1) To make the system easier to solve, multiply all the terms in .10x +.25y = 0.20(10) by 100 to make them integers.
10x + 25y = 20 • 10
10x + 25y = 200
2) Solve for x.
x + y = 10
x = 10 - y
3) Substitute x with 10 - y in the other equation.
10(10 - y) + 25y = 200
100 - 10y + 25y = 200
Combine like terms.
100 + 15y = 200
Subtract 100 from both sides.
15y = 100
y = 20/3 or 6 2/3
4) Now that we have the numerical value of y, solve for the value of x by substituting once more.
a) x + y = 10
x + 20/3 = 10 or x + 6 2/3 = 10 (either equation is fine)
x = 10/3 or x = 3 1/3
The manager should combine 3 1/3 (3.33) gallons of 10% salt water and 6 2/3 (6.67) gallons of 25% salt water.
5) Always check the answers to make sure.
a) x + y = 10
3 1/3 + 6 2/3 = 10
9 3/3 = 10
10 = 10
b) .10x +.25y = 0.20 • 10
.10(3 1/3) +.25(6 2/3) = 0.20 • 10
1/3 + 5/3 = 2
6/3 = 2
2 = 2
now, the (x-3) is there 5 times, namely (x-3)(x-3)(x-3) and (x-3)(x-3), that simply means, the root of 3 has a multiplicity of 5, is all
to get the y-intercepts, simple, when the graph touches the y-axis, "x" is zero, thus
