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Ber [7]
3 years ago
11

Which inequality is represented by this graph? 0 - 345> x O 0 -34.5 0 -355 cx​

Mathematics
1 answer:
julia-pushkina [17]3 years ago
8 0

Answer:

Step-by-step explanation:

If x is the white dot on the graph:

From what it looks like, x is right between -35 and -34 x (which is -35.5).

If that is the case then none of the answers are correct since -35.5 is <u>equal or less</u> than x. (the sign looks like this:  "\leq" )

But if you have to choose one of the answers then number 4 (-35.5 < x) would be closest.

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Consider the function h(x) =x2 – 12x + 58.
alekssr [168]

Answer:

The correct option is;

x ≥ 6; h⁻¹(x) = 6 +√(x - 22)

Step-by-step explanation:

Given the function, h(x) = x² - 12·x + 58

We can write, for simplification;

y = x² - 12·x + 58

Therefore;

When we put x as y to find the inverse in terms of x, we get;

x = y² - 12·y + 58

Which gives;

x - x = y² - 12·y + 58 - x

0 = y² - 12·y + (58 - x)

Solving the above equation with the quadratic formula, we get;

0 = y² - 12·y + (58 - x)

x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}

a = 1, b = -12, c = 58 - x

Therefore;

x = \dfrac{-(-12)\pm \sqrt{(-12)^{2}-4\times (1)\times (58 - x)}}{2\times (1)}= \dfrac{12\pm \sqrt{144-232 + 4 \times x)}}{2}

x =  \dfrac{12\pm \sqrt{4 \times x - 88}}{2} =  \dfrac{12\pm \sqrt{4 \times (x - 22)}}{2}  = \dfrac{12\pm 2 \times \sqrt{ (x - 22)}}{2}

x = \dfrac{12\pm 2 \times \sqrt{ (x - 22)}}{2} = {6 \pm  \sqrt{ (x - 22)}}

We note that for the function, h(x) = x² - 12·x + 58, has no real roots and the real minimum value of y is at x = 6, where y = 22 by differentiation as follows;

At minimum, h'(x) = 0 = 2·x - 12

x = 12/2 = 6

Therefore;

h(6) = 6² - 12×6 + 58 = 22

Which gives the coordinate of the minimum point as (6, 22) whereby the minimum value of y = 22 which gives √(x - 22) is always increasing

Therefore, for x ≥ 6, y or h⁻¹(x) = 6 +√(x - 22)  and not 6 -√(x - 22) because 6 -√(x - 22) is less than 6

The correct option is  x ≥ 6; h⁻¹(x) = 6 +√(x - 22).

7 0
2 years ago
Question 7
Colt1911 [192]

Answer:

Step-by-step explanation:

xxcSD1EA

7 0
2 years ago
I need it ASAP! Melanie had bags of sand for a sandbox. The sandbox needs bags of sand to fill it.
Orlov [11]
 <span>Melanie had 2 1/2 bags of sand for a sandbox. The sandbox needs 3 1/4 bags of sand to fill it. Melanie said she still needs 3/4 of a bag to fill it. Is that answer reasonable?
</span><span>
3.25 or 3 and 1/4 - 2.25 or 2 and 1/2= .75 or 3/4</span> so the answer is C.
7 0
3 years ago
Which is the best definition of a counterexample?
Leni [432]

Answer:

D. An example that shows a statement is not true.

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Your business partner describes this as a high positive correlation. Is your partner correct? Why or why not? (2 points)
zaharov [31]

Answer:

if the points are in a straight line going upward then they are corect

but if the points are scattered they are wrong its hard to answer this question he graph to look at

4 0
3 years ago
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