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3 years ago

Which expression is equivalent to |b| >2?

Mathematics

2 answers:

Alex3 years ago

8 0

Answer:

|b| > 2 is equivalent to -2 > b > 2.

Step-by-step explanation:

Definition of absolute value is:

The set of all points that satisfy the inequality |x| < c is the set of all points between c and -c except of -c and c.

In question statement , we observe that

x = b and c = 2.

Hence, the given inequality means the set of set of all points that is between 2 and -2 except 2 and -2.

hence, |b| > 2 is equivalent to -2 > b > 2.

vovangra [49]3 years ago

6 0

Answer:

The equivalent expression for |b| > 2 is {b : b < -2} ∪ {b : b > 2}.

Step-by-step explanation:

The expression |x| < a is equivalent to -a < x < a and the expression |x| > a is equivalent to {x : x < -a} ∪ {x : x > a}.

This means, the set of all points that satisfy the inequality |x| < a is the set of all points between -a and a exclusive of -a and a.

The set of all points that satisfy the inequality |x| > a is the set of all points that are less than -a and the set of all points that are greater than a.

Hence, the equivalent expression for |b| > 2 is {b : b < -2} ∪ {b : b > 2}.

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Which type of transformation preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd functi

Alexus [3.1K]

The type of transformation that preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x) is vertical translation.

<h3>What is vertical translation?</h3>

Vertical translation of a graph is done by moving the base graph up or down in the y-axis direction. Each point on a graph is moved k units vertically to translate the graph by that many units.

The vertical translation is the movement of the curve along the y-axis by a certain number of units without altering the function's shape or domain.

The function's form is preserved in the case of vertical translation.

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2 years ago

The opposite process rule says to solve for ________. a known variable by replicating the process used to form the original equa

ioda

Answer:

An unknown variable by reversing the process used to form the original equation.

Step-by-step explanation:

The opposite process rule says to solve for - an unknown variable by reversing the process used to form the original equation.

If an equation indicates an operation such as addition, subtraction, multiplication, or division, solve for the unknown variable by using the opposite process.

For example:

Lets say we have to find $x+25=35$

Here 25 is subtracted from both sides of the equation to isolate x.

$x+25-25=35-25$

we get x = 10

Check this : $10+25=35$

4 0

3 years ago

Write the algebraic expression representing the length and width of Marliens house. Someone please tell me the process of how to

Katarina [22]

This is telling you to find out the dimensions of her house.
I suggest using mathpapa for each equation. It will show you how to solve it and then the answer.
So for the top dimensions, put the following into mathpapa: (2x-10)+(x-2)+(.5x-4)+(x-2)

3 0

3 years ago

Read 2 more answers

Write 2.2 as a mixed number.

Anna35 [415]

Answer:

I believe the answer is 2⅕

8 0

3 years ago

A report by the US Geological Survey indicates that glaciers in Glacier National Park, Montana, are shrinking. Recent estimates

postnew [5]

Answer

a) C

b) B

c) C, E

d) 15.5

e) 0.7

f) 67.7

Step-by-step explanation

a) A linear equation can be written as $y=mx+c$ where $m$ is the slope and $c$ is the intercept on the $y$ -axis. The slope describes how $y$ changes when $x$ changes. A negative value means the it is a decreasing change. In our case, $y$ is $A$ and $x$ is $t$ . Thus, the slope of the equation is $m=-0.062$ . This means that the area of glacier is decreasing by $0.062 \text{km}{}^2 = 62000 \text{m}{}^2$ every year since 2000.

b) The $A$ -intercept (= 16.2 $\text{km}{}^2$ ) represents the area covered when $t=0$ . But $t=0$ starting from year 2000. This intercept then represents the area covered by glacier in the year 2000. Therefore, the area covered by glacier in 2000 was 16.2 $\text{km}{}^2$ .

c) $A=f(t)$ means the area covered after year 2000. Setting it to 12 means the area covered after $t$ years is 12 $\text{km}{}^2$ ). $t$ is therefore the number of years since 2000 that the total area covered will be 12 $\text{km}{}^2$ ).

d) $f(12)=16.2−0.062\times12 =16.2-0.744 = =15.456 15.5 \text{km}{}^2$ to 1 decimal place.

e) The term involving $t$ represents the disappearing area. In 12 years, the disappeared area is $0.062\times12=0.744 =0.7 \text{km}{}^2$ to 1 decimal place.

f) $f(t)=16.2−0.062t =12$

$0.062t = 16.2-12 = 4.2$

$t = \dfrac{4.2}{0.062}=67.7419\ldots =67.7$ years to 1 decimal place.

8 0

3 years ago