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arlik [135]
2 years ago
10

What is the solution to the inequality 1 2/3 > r - 7/12

Mathematics
1 answer:
lukranit [14]2 years ago
3 0

Answer:

r ≤ 2 1/4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Rewriting Fractions

Step-by-step explanation:

Step 1: Define

1 2/3 ≥ r - 7/12

Step 2: Solve for r

Rewrite:                    5/3 ≥ r - 7/12

Isolate r:                    9/4 ≥ r

Rewrite:                    r ≤ 9/4

Reduce:                    r ≤ 2 1/4

Here we see that any number r less than or equal to 2 1/4 will work as a solution to the inequality.

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F is a twice differentiable function that is defined for all reals. The value of f "(x) is given for several values of x in the
nadezda [96]

The correct answer is actually the last one.

The second derivative f''(x) gives us information about the concavity of a function: if f''(x) then the function is concave downwards in that point, whereas if f''(x)>0 then the function is concave upwards in that point.

This already shows why the first option is wrong - if the function was concave downwards for all x, then the second derivate would have been negative for all x, which isn't the case, because we have, for example, f''(8)=5

Also, the second derivative gives no information about specific points of the function. Suppose, in fact, that f(x) passes through the origin, so f(0)=0. Now translate the function upwards, for example. we have that f(x)+k doesn't pass through the origin, but the second derivative is always f''(x). So, the second option is wrong as well.

Now, about the last two. The answer you chose would be correct if the exercise was about the first derivative f'(x). In fact, the first derivative gives information about the increasing or decreasing behaviour of the function - positive and negative derivative, respectively. So, if the first derivative is negative before a certain point and positive after that point. It means that the function is decreasing before that point, and increasing after. So, that point is a relative minimum.

But in this exercise we're dealing with second derivative, so we don't have information about the increasing/decreasing behaviour. Instead, we know that the second derivative is negative before zero - which means that the function is concave downwards before zero - and positive after zero - which means that the function is concave upwards after zero.

A point where the function changes its concavity is called a point of inflection, which is the correct answer.

7 0
3 years ago
What am I doing wrong
stiv31 [10]
For this answer it is:

12 inches = 36 feet
7 0
3 years ago
I need help asap!!!
gizmo_the_mogwai [7]

Answer:

x = 9

Step-by-step explanation:

-5(1 + 1x) = -50

-5 + -5x = -50

-5 + -5x + 5 = -5x

-50 + 5 = -45

-5x = -45

-5x / -5 = x

-45 / -5 = 9

x = 9

5 0
3 years ago
A shirt is regularly priced at 42$. It is on sale for 15% off of the regular price. What is the sale price of the shirt ?
gulaghasi [49]

Answer:

$35.7

Step-by-step explanation:

you can convert 15% to a decimal by dividing by 100.

15/100 = .15

if you multiply the decimal by the cost of the shirt you get how much the discount is.

0.15 * $42 = 6.30

so a 15% discount on a $42 shirt is $6.30 off. So you subtract the discount from the total cost.

$42 - $6.30 = $35.70 that is the sale price of the shirt.

4 0
2 years ago
Read 2 more answers
Q10. Consider the following algorithm:
maw [93]

Answer:

  61,940

Step-by-step explanation:

For a recursive sequence of reasonable length, it is convenient to use a suitable calculator for figuring the terms of it. Since each term not only depends on previous terms, but also depends on the term number, it works well to use a spreadsheet for doing the calculations. The formula is easily entered and replicated for as many terms as may be required.

__

The result of executing the given algorithm is shown in the attachment. (We have assumed that g_1 means g[-1], and that g_2 means g[-2]. These are the starting values required to compute g[0] when k=0.

That calculation looks like ...

  g[0] = (0 -1)×g[-1] +g[-2} = (-1)(9) +5 = -4

The attachment shows the last term (for k=8) is 61,940.

8 0
2 years ago
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