State the solution of the system of linear equation using its grap 6. SOLUTION: ( -2

Mathematics

1 answer:

IRINA_888 [86]2 years ago

3 0

Answer:

Solution is (2, -1)

Step-by-step explanation:

The lines cross at the point where x = 2 and y = -1.

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The function f(x)=(x-5)^2 +2 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the in

Anon25 [30]

We have been given a quadratic function $f(x)=(x-5)^{2} +2$ and we need to restrict the domain such that it becomes a one to one function.

We know that vertex of this quadratic function occurs at (5,2).

Further, we know that range of this function is $[2,\infty)$ .

If we restrict the domain of this function to either $(-\infty,5]$ or $[5,\infty)$ , it will become one to one function.

Let us know find its inverse.

$y=(x-5)^{2}+2$

Upon interchanging x and y, we get:

$x=(y-5)^{2}+2$

Let us now solve this function for y.

$(y-5)^{2}=x-2\\
y-5=\pm \sqrt{x-2}\\
y=5\pm \sqrt{x-2}\\$

Hence, the inverse function would be $f^{-1}(x)=5+\sqrt{x-2}$ if we restrict the domain of original function to $[5,\infty)$ and the inverse function would be $f^{-1}(x)=5-\sqrt{x-2}$ if we restrict the domain to $(-\infty,5]$ .

8 0

2 years ago

Which Postulate/Theorem below would prove that the triangles shown below are congruent?

velikii [3]

Answer:

Correct answer is D. ASA

Step-by-step explanation:

Let us first define ASA congruence rule:

2 triangles are called congruent according to ASA congruence rule if 2 angles of the triangle and the corresponding side between these two angles are equal to each other.

In the question figure, we can figure out following conclusions from Triangles $\triangle SRT\text{ and }\triangle WXY$ respectively: