1. Let A(a,b) be a point in the coordinate axis. The reflection of A with respect to the x-axis is the point A'(a, -b).
2. So the reflection of C(6, 4) is C'(6, -4)
3. Remark, a picture is always helpful when dealing with reflections.
Here you go
Let me know if it is right
Answer:
614656h²⁸k⁸
Step-by-step explanation:
Exponent Power Rule:
Step 1: Write expression
[4h⁷7k²]⁴
Step 2: Distribute power 4 to each term
4⁴h⁷⁽⁴⁾7⁴k²⁽⁴⁾
Step 3: Simplify
256h⁷⁽⁴⁾2401k²⁽⁴⁾
614656h⁷⁽⁴⁾k²⁽⁴⁾
Step 4: Use Exponent Rule
614656h²⁸k⁸
Answer:
A translation by the rule (x,y) - (x,y-9) and then a 180° clockwise rotation about the origin
Step-by-step explanation:
In order to solve this, you have to remember the rules of rotation about the origin, they state that under a 90º clockwise rotation about the origin the the coordinates would switch positions and one of them will change its sign, ( x, y ) becomes ( y, - x ), so if you check out the image you will notice that point A (2,3) becomes A' (-2,6) so since the coordinates changed not only switched you can figure out that this is not only rotation about the origin, but also a translation beforehand, since a 180º rotation about the origin will keep the values of the coordinates on each of them just changing both signs, this means that that is what we are looking for, since point A (2,3) becomes A' (-2,6), you can see the value of "x" remained the same but changed signs, now you just have to use the rule (x,y)-(x,y-9)
(2,3)=(2,3-9)
A' will be translated to (2,-6) if you do a 180º rotation about the origin on that point you will get (-2,6) cause you'd only need to change signs, that's why that is your answer.
Answer:
66.67 ml of 5% solution and 133.33 ml of 6.5% solution are mixed.
Step-by-step explanation:
Let 200 ml of 6% solution is formed by mixing x ml of 5% solution and y ml of 6.5% solution.
We can write the equation x + y = 200 ........ (1)
Now, x ml of 5% solution will contain ml of acid
Again, y ml of 6.5% solution will contain ml of acid.
So, mixing them together will give (0.05x + 0.065y) ml of acid in 200 ml of solution.
So, from the condition given we can write
⇒ 0.05x + 0.065y = 12
⇒ x + 1.3 y = 240 ........... (2) {Dividing both sides by 0.05}
Now, solving equations (1) and (2), we get
0.3y = (240 - 200) = 40
⇒ y = 133.33 ml
From equation (1) we get, x = 200 - 133.33 = 66.67 ml
Therefore, 66.67 ml of 5% solution and 133.33 ml of 6.5% solution are mixed. (Answer)