Answer:
See below
Step-by-step explanation:
This is a system of equations. That means you are trying to find the point that makes both lines true at the same time.
To do this you have to solve for one variable at a time. Luckily, these equations already have one variable that will cancel. If you add 2x and -2x, you get 0. I'm going to line these up like a vertical math problem to show you how it works.
-2x + 3y = 12
2x +3y = 0 Add together
-------------------
0x + 6y = 12 Simplify by removing the 0x
6y =12 Divide both sides by 6 to solve for y
y = 2
Plug 2 in for y in one of the original equations.
2x + 3(2) = 0
2x + 6 = 0 Subtract 6 from both sides
2x = -6 Divide by 2 to solve for x
x = -3
The point that makes both lines true is (-3,2). This is where the lines intersect.
Answer:
1) The solve by graphing will the preferred choice when the equation is complex to be easily solved by the other means
Example;
y = x⁵ + 4·x⁴ + 3·x³ + 2·x² + x + 3
2) Solving by substitution is suitable where we have two or more variables in two or more (equal number) of equations
2x + 6y = 16
x + y = 6
We can substitute the value of x = 6 - y, into the first equation and solve from there
3) Solving an equation be Elimination, is suitable when there are two or more equations with coefficients of the form, 2·x + 6·y = 23 and x + y = 16
Multiplying the second equation by 2 and subtracting it from the first equation as follows
2·x + 6·y - 2×(x + y) = 23 - 2 × 16
2·x - 2·x + 6·y - 2·y = 23 - 32
0 + 4·y = -9
4) An example of a linear system that can be solved by all three methods is given as follows;
2·x + 6·y = 23
x + y = 16
Step-by-step explanation:
Answer:
The answer is <em>1</em>.
Step-by-step explanation:
Given the expression:
To find:
The expression without absolute value.
Solution:
First of all, let us learn about the absolute value function:
i.e. value is x if x is positive
value is -x if x is negative
Here the given expression contains two absolute value functions:
and
Using the definition of absolute value function as per above definition.
Now, it is given that z < 5 that means z will also be lesser than 6 i.e. z < 6
So, given expression will be equivalent to :
So, the expression is equivalent to <em>1</em>.
Use our brains and what we know
f(x)=a(x-h)²+k
vetex is (h,k)
and a is te leading coefient
if directix is below the focus, then it opens up and a is positive
if directix is above focus, then it opens down and a is negaitve
vertex is in between directix and focus
so
(3,-1) and y=1
-1<1
so directix is above
a is negative
directly in between
distance from -1 to 1 is 2
2/2=1
1 above (3,-1) is (3,0)
vertex is (3,0)
y=a(x-3)²+0
y=a(x-3)²
the only option with a negative 'a' value is B
answer is B
That's a pretty confusing one. I think it's 10 minutes.