Arrange the cards into three pairs of the same total. -7,-5,-3,3,1,-1
1 answer:
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Answer: 2±√3 and 1/(2±√3)
This might seem wrong, but you'll understand when you read the explanation.
Step-by-step explanation:
For this problem, you can write 2 equations to find the two numbers. Let's establish x for the first number and y for the second number.
Equation 1:
x+y=4
This equation comes from the problem that says the 2 numbers add up to 4.
Equation 2:
x*y=1
This equation comes from the part that says multiplies to 1.
Even if the problem states that the numbers can be negative, it is tricking us. We know in order for the product of 2 numbers to be positive, it has to be +*+ or -*-. Since the added numbers have to be +4, we know we cannot use -1 and 1 as our answer. What we can do is to use substitution to solve for x and y.
x+y=4 becomes y=4-x
We can substitute this into equation 2.
x(4-x)=1
4x-x²=1
4x-x²-1=0
-x²+4x-1=0
Since this equation is not factorable, we use the quadratic equation, (<em>Please ignore the weird looking A that's in front of the ± sign. I don't know what's wrong with the system, but it's not supposed to be there)</em>
We plug our a, b, c into the equation and get x=2±√3.
Now that we know our x, we can plug it into any of the above equations.
(2±√3)(y)=1
y=1/(2±√3)
Our final 2 numbers are 2±√3 and 1/(2±√3)
Answer:
a 90° clockwise rotation about the origin
a 180° rotation about the origin
a 90° counterclockwise rotation about the origin
Step-by-step explanation:
Transformations are done on a Cartesian Plane, which is the grid with four quadrants. (See picture) Each quadrant is 90°, so two quadrants is 180°.
When you rotate counterclockwise it is like in the picture. When you want to rotate clockwise, it's the other way.
When we rotate 180°, it does not matter if it is counterclockwise or clockwise because the result is the same (both move two quadrants).
We can imagine an example to help us solve the problem. Let's say we are rotating an object <u>starting in </u><u>first quadrant</u><u>.</u> (Upper right quadrant).
<u>Find out which quadrant the object ends up with each instruction:</u>
FROM THE PICTURE:
"a 90° counterclockwise rotation about the origin (Q2) and then a 180° rotation about the origin"
End: Quadrant 4
"a reflection across the x-axis (Q4) and then a reflection across the y-axis"
End: Quadrant 3
"a 90° clockwise rotation about the origin (Q4) and then a rotation 180° about the origin"
End: Quadrant 2
FROM YOUR LIST:
"a 90° counterclockwise rotation about the origin " Quadrant 2
"a 180° rotation about the origin " Quadrant 3
"a 90° clockwise rotation about the origin" Quadrant 4
Match each ending quadrant from your list with the same ending quadrant from the picture.
The order that you should put your list into the boxes is:
a 90° clockwise rotation about the origin
a 180° rotation about the origin
a 90° counterclockwise rotation about the origin
Answer:
Linear
Step-by-step explanation:
The definition of linear is "the property of a mathematical relationship that can be graphically represented as a straight line." If the robot arm moved 1/4 inch every time the controller is moved 1/4 inch. That means the relation is linear. This is because if the controller was moved 1 inch, the robot would move 1 inch. This relation is shown in the graph below, the equation is y = x.
