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3 years ago

Will award Brainliest and extra points to whoever can get me the correct answer the fastest:

1 answer:

5 0

Y is less than or equal to 4, y is less than or equal to 14, x is less than or equal to 10, x is less than or equal to 20

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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

3 years ago

What is the common ratio of 2, 10/3, 50/9

mojhsa [17]

The common ratio of 2, 10/3, 50/9 is $\frac{10}{6}$

Solution:

Given, series of elements are $2, \frac{10}{3}, \frac{50}{9}$

We have to find the common ratio of the above given series.

We know that, common ratio of an G.P is division of any number in that series with the previous number of the series.

So, now take $\frac{10}{3}$ and 2

$\text { Then, common ratio }=\frac{\frac{10}{3}}{2}$

$\begin{array}{l}{\text { Common ratio }=\frac{10}{3} \times \frac{1}{2}} \\\\ {\text { Common ratio }=\frac{10}{3 \times 2}=\frac{10}{6}}\end{array}$

Hence, the common ratio of the given series is $\frac{10}{6}$

6 0

3 years ago

On a number line 6.64 would be located

Dominik [7]

Answer:

yes

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

The circles are identical. What is the circumference of each circle? Circle 1: radius of 2x; Circle 2: diameter of 2x+3. A. 3/2

Delicious77 [7]

Answer:

C=6π

Step-by-step explanation:

It is given that, two circles are identical. The radius of first circle is 2x and the diameter of other circle is 2x+3.

If identical, it means that the radius of both circles are same i.e.

$2x=\dfrac{2x+3}{2}\ \ (\because\ r=\dfrac{D}{2}, d=\text{diameter})\\\\4x=2x+3\\\\2x=3\\\\x=1.5$

Radius of both circles is 2(1.5)=3

The circumference of a circle is given by :

$C=2\pi r\\\\C=2\pi (3)\\\\C=6\pi$

So, the circumference of each circle is 6π.

7 0

3 years ago

Please explain how to do this, I'm using all my points A. 40 L B. 80 L C. 4 L D. 8L

exis [7]

Answer: choice A. 40 liters

====================================

Explanation:

x = number of liters of the 50% alcohol solution

If we have x liters of 50% alcohol, then we have 0.50*x liters of pure alcohol. This is added to 0.90*40 = 36 liters of pure alcohol (from the 90% solution).

So far we have 0.50*x + 36. This expression represents the total amount of pure alcohol. We want a 70% solution, so we want 70% of the total 40+x meaning 0.50*x + 36 is to be set equal to 0.70*(40+x) and we solve for x as shown below

0.50*x + 36 = 0.70*(40+x)

0.50*x + 36 = 0.70*(40)+0.70*(x)

0.50*x + 36 = 28+0.70*x

36 - 28 = 0.70*x - 0.50x

8 = 0.20x

0.20x = 8

x = 8/0.20

x = 40

So that is why the answer is choice A. 40 liters

6 0

3 years ago