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Bumek [7]
3 years ago
10

What is the value of x?

Mathematics
1 answer:
Lerok [7]3 years ago
4 0
The value of x is about 4.7
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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
A track star runs two races on a certain day. The probability thathe wins the first race is 0.7, the probability that he wins th
NARA [144]

Answer:

a) 80% probability that he wins at least one race.

b) 30% probability that he wins exactly one race.

c) 20% probability that he wins neither race.

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that he wins the first race.

B is the probability that he wins the second race.

C is the probability that he does not win any of these races.

We have that:

A = a + (A \cap B)

In which a is the probability that he wins the first race but not the second and A \cap B is the probability that he wins both these races.

By the same logic, we have that:

B = b + (A \cap B)

The probability that he wins both races is 0.5.

This means that A \cap B = 0.5

The probability that he wins the second race is 0.6

This means that B = 0.6

B = b + (A \cap B)

0.6 = b + 0.5

b = 0.1

The probability that he wins the first race is 0.7.

This means that A = 0.6

A = a + (A \cap B)

0.7 = a + 0.5

a = 0.2

A) he wins at least one race.

This is

P = a + b + (A \cap B) = 0.2 + 0.1 + 0.5 = 0.8

There is an 80% probability that he wins at least one race.

B) he wins exactly one race.

This is

P = a + b = 0.2 + 0.1 = 0.3

There is a 30% probability that he wins exactly one race.

C) he wins neither race

Either he wins at least one race, or he wins neither. The sum of these probabilities is 100%.

From a), we have that there is an 80% probability that he wins at least one race.

So there is a 100-80 = 20% probability that he wins neither race.

6 0
2 years ago
What is the inequality for the statement Johnny can work no more than 25 hours each week?
Greeley [361]
J less than or equal to 25(w) ? Idk if that’s right but that’s what I would do
8 0
2 years ago
What is the square root of 175
ankoles [38]

the square root of a number is: one number times itself equals that number. Confusing '-' An example is the square of 4 is 2 because 2 times 2 = 4, or the square root of 56 is 8 because 8 times 8 is 64. The square root of 175 is about 13.22875 because 13.22875 times 13.22875 = about 175
5 0
2 years ago
Prove that x=2 if 4^x=8x...where ^ stands for "to the power of".
Romashka [77]
In order to prove this, you simply plug in the number 2 everywhere you see X:

4^(2) = 8(2). 

Simplify

16 = 16 √

Since this checks out, x is proven to be 2.
4 0
3 years ago
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