Answer: Option b.
Step-by-step explanation:
1. You have the following parent function given in the problem above:
f(x)=x³ (This is the simplest form. We need to translate it 3 units left and 2 units down)
2. If you take the parent function and make y=f(x+3), then you have:
(The function is shifted 3 units left on the x-axis).
3. Then you if you make y=f(x+3)-2, as following, you obtain:
(The function is shifted 2 units down on the y-axis).
4. Therefore, that is how you obtain the final function.
The answer is the graph shown in the option b.
Step-by-step explanation:
option number of b is write
The answer to the system of equations is x = 3, y = -2 and z = 5.
In order to find this you can use elimination to create two equations with only x and y. First we will add equation one with equation 2 multiplied by 2.
-x + 2y + 2z = 3
6x + 2y - 2z = 4
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5x + 4y = 7
Then we can add equation 2 with equation 3.
3x + y - z = 2
2x + y + z = 9
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5x + 2y = 11
Now we can use these two equations together to solve for y. It will be easiest if we multiply the second one by -1.
5x + 4y = 7
-5x - 2y = -11
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2y = -4
And then we can solve for y.
2y = -4
y = -2
With that answer we can go back to any equation with just y and x and solve for x.
5x + 4y = 7
5x + 4(-2) = 7
5x - 8 = 7
5x = 15
x = 3
Now we can use x and y in any equation to find z.
2x + y + z = 9
2(3) + (-2) + z = 9
6 - 2 + z = 9
4 + z = 9
z = 5
Answer:
Irrational Number
Step-by-step explanation:
So, since it's a right triangle, you can use Pythagorean Theorem to calculate the measure of the hypotenuse.
Pythagorean Theorem says the hypotenuse squared = the sum of the sides squared.
5² + 6² = 25 + 36 = 61
And the square root of 61 is 7.8102496.... and the decimal continues in no distinguishable pattern. Therefore, the length of the hypotenuse is an irrational number.
