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3 years ago

Solve the compound inequality. graph the solution set. 4x-4>-4 and -3x+2<11

Mathematics

1 answer:

Illusion [34]3 years ago

3 0

Answer:

Step-by-step explanation:

4x - 4 > -4 add 4 to both sides

4x > 0 divide both sides by 4

x > 0

-3x + 2 < 11 subtract 2 from both sides

-3x < 9 change the signs

3x > -9 divide both sides by 3

x > -3

x > 0 and x > -3 → x > 0

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(a) How is the number e defined? e is the number such that lim h → 0 e−h − 1 h = 1. e is the number such that lim h → 0 eh − 1 h

Fed [463]

Answer:

is the number such that lim h → [infinity] eh + 1 h = 1.

Step-by-step explanation:

The number e is known as the Euler's constant or Euler's number. The number basically is a mathematical expression that is equal to the rational number 2.71828. In addition, it is also the base of the natural logarithm or the Naperian logarithms. It is the number that the natural logarithm is equal to one. In addition, it is the limit of :

$\lim_{n \to \infty} (1 + \frac{1}{n })^{n}$

as n approaches infinity.

The expression is calculated as a sum of the infinite series

e = $\frac{1}{1!} = \frac{1}{1} + \frac{1}{1} + \frac{1}{1*2} + \frac{1}{1*2*3}+ ...$

7 0

3 years ago

Read 2 more answers

Please help quick!!

Nataly [62]

Hi !

$∫ \frac{t}{t + 1}dt$

We need to prove that it is equal to

$∫ \frac{u - 1}{u}du$

As per given options, Substitute u by t+1 

$= > ∫ \frac{u - 1}{t + 1} du$

Then given t = u-1

$= > ∫ \frac{t}{t + 1} du$

Then substitue the third given value also

$= > ∫ \frac{t}{t + 1} dt$

Therefore, it's proved

~Hope it helps

7 0

2 years ago

john is twice as old as mary. the sum of their ages is 21. how old is mary? let j = john's age and m = mary's age. select the sy

Verdich [7]

Hello,

let's assume j the john's age, m the mary's age.

"John is twice as old as mary"==>j=2*m

"the sum of their ages is 21" ==>j+m=21

==>2*m+m=21
==>3m=21
==>m=7
and j=21-7=14

3 0

4 years ago

So, I undestood slope right. But, I get confused with the other points that intersect there is multiple of them. How do i look f

ivanzaharov [21]

Answer:

slope = 2

Step-by-step explanation:

Find 2 points on the line that land perfectly on the grid. I'll choose these 2 here:

(-2, -1) and (0, 3)

Rise is the change in the y value from one point to the other, and run is the change in the x. Looking at these 2 points, y went from -1 to 3. That is a rise of 4. The x went from -2 to 0, so that is a run of 2. "rise over run" means rise literally over run in a fraction like this:

$m=\frac{rise}{run}$

The more proper way to calculate slope looks like this, but it's really the same thing in the end:

$m=\frac{y2-y1}{x2-x1}$

where (x1, y1) and (x2, y2) are your 2 points.

Finally, the slope of this line is:

$m=\frac{3--1}{0--2}\\\\m=\frac{4}{2}\\\\m=2$

That's a rise of 4 over a run of 2, and that simplifies to just a slope of 2.

8 0

3 years ago

Consider the paragraph proof.

podryga [215]

Applying the distance formula, DE = a. Therefore, the missing information is: A. a.

<h3>What is the Distance Formula?</h3>

Distance Formula for determining the distance between two points on a coordinate plane is given as: $d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}$ .