Solve the following inequality: |x + 1| <_3

<_ = greater than or equal to

QUESTION-:

The inequalities x < -5 and -X > -5 are the same.

True

False

ANSWER-:

FALSE

!! HOPE ITS HELP U !!

Answer:

x = 1, x = 2

Step-by-step explanation:

Given

3x(x - 2) = x² - 4 ← distribute parenthesis on left side

3x² - 6x = x² - 4 ( subtract x² - 4 from both sides )

2x² - 6x + 4 = 0 ( divide through by 2

x² - 3x + 2 = 0 ← in standard form

Consider the factors of the constant term (+ 2) which sum to give the coefficient of the x- term (- 3)

The factors are - 1 and - 2 , since

- 1 × - 2 = + 2 and - 1 - 2 = - 3 , then

(x - 1)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

Use main properties of powers

(a^m)^n=a^{m\cdot n};(am)n=am⋅n;

\dfrac{1}{a^n}=a^{-n}an1=a−n

to simplify given equation.

1.

4^x=(2^2)^x=2^{2x}.4x=(22)x=22x.

2.

\left(\dfrac{1}{8}\right)^{x+5}=\left(\dfrac{1}{2^3}\right)^{x+5}=(2^{-3})^{x+5}=2^{-3x-15}.(81)x+5=(231)x+5=(2−3)x+5=2−3x−15.

3. Then the equation is

2^{2x}=2^{-3x-15}.22x=2−3x−15.

The bases are the same, so equate the powers:

2x=-3x-15,

2x+3x=-15,

5x=-15,

x=-3.

Answer: for x=-3.

Answer:

i) where the digits can repeat

1. 30

2. 50

3. 33

4. 55

5. 35

6. 53

ii) where the digits cannot be repeated

1. 30

2. 50

3. 35

4. 53

Answers:

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

Explanation:

The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that [tex]-4 < x \le 3[/tex]. It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).

The interval [tex]-4 < x \le 3[/tex] then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.

It says: x is between -4 and 3. It can't equal -4 but it can equal 3.

So the use of parenthesis versus square brackets tells the reader which endpoint is included or not.

--------------------------------------------------

The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.

The range as a compound inequality is [tex]-5 < y \le 5[/tex]. This condenses into the shorthand of (-5, 5] which is the range in interval notation.

Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.

Answer:

Hello,

Step-by-step explanation:

Domain(f)= ]-4;3]={x€R | -4<x≤3}

Rang(f)=]-5;5]={y€R | -5< y ≤5}

9514 1404 393

Answer:

  after 89 years

Step-by-step explanation:

For principal p, interest rate r, and number of years t, the two account balances are ...

  a = p·e^(rt) . . . . continuous compounding

  a = p(1+r)^t . . . . annual compounding

Using the given values, we have

  3000·e^(0.07t) . . . . . compounded continuously

  20000·1.05^t . . . . . . compounded annually

We want to find t so these are equal.

  3000·e^(0.07t) = 20000·1.05^t

  0.15e^(0.07t) = 1.05^t . . . . divide by 20,000

  ln(0.15) +0.07t = t·ln(1.05) . . . . take natural logarithms

  ln(0.15) = t·(ln(1.05) -0.07) . . . . subtract 0.07t

  t = ln(0.15)/(ln(1.05) -0.07) ≈ -1.8971/-0.02121 . . . . . divide by the coefficient of t

  t ≈ 89.4 ≈ 89

The two accounts will have the same balance after 89 years.

Answer:

916.11 ft³

Step-by-step explanation:

(9×6)×7.83/2×13/3

= 211.41×13/3

= 916.11 ft³

Answered by GAUTHMATH

Answer:

916.11 ft³

Step-by-step explanation:

Answer:

x = 100

Step-by-step explanation:

(100-40)/2

= 60/2

= 30

So it's 100

Answered by GAUTHMATH

Answer:

The answer is "C" f(x)= x+ 4 and g(x)= x^3 - 1

Step-by-step explanation:

all you have to do is replace the x in "G" with the "F" function

F(x) = x+4  and  G(x) = x^3-1

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

Explanation:

Let's try choice A to see if it works or not

G(x) = (x+4)^3

G( F(x) ) = ( F(x)+4 ) ^3 .... replace every x with F(x)

G( F(x) ) = ( x-1+4 ) ^3 .... plug in F(x) = x-1

G( F(x) ) = (x+3)^3

This isn't the same as (x+4)^3 - 1. You can confirm this with a graph or a table of values. We cross choice A off the list.

------------

Let's try choice B

G(x) = x+4

G( F(x) ) = F(x)+4

G( F(x) ) = x^3-1 + 4

G( F(x) ) = x^3 + 3

Similar to choice A, this isn't the same as (x+4)^3-1. We can cross this off the list as well.

--------------

Now choice C

G(x) = x^3 - 1

G( F(x) ) = ( F(x) )^3 - 1

G( F(x) ) = (x+4)^3 - 1

We found the final answer.

Answer:

enlarge it

Step-by-step explanation:

I ft = 12 inches

Thus 8 in → 12 in makes the transformation larger.

Thus going from 8 in to 12 in is an enlargement

Answer:

A

Step-by-step explanation:

The inscribed angle IJK is half the measure of its intercepted arc, so

arc IK = 2 × 75° = 150°

The 3 arcs sum to  360° , then

arc IJ = 360° - (150 + 110)° = 360° - 260° = 100° → A

Answer:

Both Ava and Finn are correct

Step-by-step explanation:

There are 4 tables and 9 pencils at each table

4 ( 9) = 36

9 * 4 = 36

Both Ava and Finn are correct

Answer:

2

Step-by-step explanation:

slope = rise/run

rise = difference in y

run = difference in x

slope = (8 - 2)/(3 - 0)

slope = 6/3

slope = 2

Answer:

Step-by-step explanation:

The most obvious answer is the line y = 1.

Answer: 133,827 lb/ft^3

Step-by-step explanation:

V = (4/3) (3.14)(8^3) = 133,827

Answer:

y: 1, -3, -7, -11, -15

Step-by-step explanation:

Substitute the value of x in the chart for the formula given:

y = -4x + 1

For the first column in the x-row, do the following

y = -4(0) + 1

y = 1

And...

y = -4(1) + 1

y = -3

And so on.

Answer:

Step-by-step explanation:

[tex]\frac{\sqrt{x}+1 }{x-\sqrt{x}+1 }=\frac{\sqrt{x}+1}{(x+1)-\sqrt{x}}\\\\=\frac{(\sqrt{x}+1)([x+1]+\sqrt{x})}{([x+1]-\sqrt{x})+([x+1)+\sqrt{x}])}\\\\=\frac{\sqrt{x}*x+\sqrt{x}*1+\sqrt{x}*\sqrt{x}+1*x+1*1+1*\sqrt{x}}{(x+1)^{2}-(\sqrt{x})^{2}}\\\\\\=\frac{x\sqrt{x}+\sqrt{x}+x+1+x+\sqrt{x}}{x^{2}+2x+1-x}\\\\=\frac{x\sqrt{x}+2\sqrt{x}+2x+1}{x^{2}+x+1}\\\\[/tex]

Answer:

195.06

Step-by-step explanation:

area of circle = πr^2 = π8^2 = 64π

area of triangle = 1/2 x 4 x 3 = 6

area of shape = 64π-6 = 195.061929 = 195.06

Answer:

C. II only

Step-by-step explanation:

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Answer:

B. SAS

Step-by-step explanation:

Ratio of sides equal:

• 4/2= 6/3

So the 2 sides are congruent and also share same angle between.

• B. SAS is the similarity reason

Answer:

kslskd बोडलालामसूनिविवल

30^∘ Another boy is standing on the roof of a 10 second string be x mIn Δ ABC sin 30^∘ = AC/AB 1/2 = AC/100 AC =

Answer: hope this helps ♡

The kite was 16.9 feet high.

Step-by-step explanation:

Pythagorean theorem

b = [tex]\sqrt{c^{2} - a^{2} }[/tex]

b = [tex]\sqrt{22^{2} - 14^{2} }[/tex]

b = [tex]\sqrt{484 - 196}[/tex]

b = [tex]\sqrt{288}[/tex]

b = 16.9

The required inequality that expresses the given condition is 36 + 29x ≤ 210.

Given that,
A rental car company charges $29 per day to rent a car and $0.09 for every mile driven. Claire wants to rent a car, knowing that she plans to drive 400 miles. she has at most $210 to spend.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Let the number of days be x,
Total cost to drive 400 miles = 400(0.09) = $36.
According to the question,
36 + 29x ≤ 210

Thus, the required inequality that expresses the given condition is 36 + 29x ≤ 210.

Learn more about inequality here:

brainly.com/question/14098842

#SPJ5

Answer:

108 squared centimeters

Step-by-step explanation:

Let's exchange π for 3:

area = πr^2

        = 3r^2

Now, as you can see, the radius of this circle is 6. Let's plug in the value of r:

area = 3r^2

        = 3 · 6^2

Simplify 6^2:

area = 3 · 6^2

        = 3 · 36

Multiply 3 by 36:

area = 3 · 36

area = 108

108 squared centimeters

Answer:

- 5i

Step-by-step explanation:

sqrt(-100) / -sqrt(4)

We know that  sqrt(a) / sqrt(b) = sqrt(a/b)

- sqrt(-100/4)

- sqrt(-25)

We know that sqrt(ab) = sqrt(a) sqrt(b)

- sqrt(25) sqrt(-1)

We know sqrt(-1) = i

Taking the principle value of sqrt(25)

- 5i

Answer:

You ordered 5 tickets for a show on line...

The cost was $5 a ticket Plus a one time ordering fee of $15.

you total cost was $45 ....

Solving for x will determine the cost of one ticket

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

a taxi charges $5 a mile plus $15 "pull fee" ...

you ride cost a total of $45 ... x is the number of miles that you got driven

Step-by-step explanation:

You rent a car for a down payment of $15 and $5 is charged per mile driven. The total charge is therefore, $45. In essence, x is the no. of miles driven.

According to the question;

In essence, x is the no. of miles driven in this scenario.

By solving for x in 5x + 15 = 45, we may determine the no. of miles driven.

Read more:

https://brainly.com/question/2319353

7(5 + t) - 4(t + 4) =

= 35 + 7t - 4t - 16 =

= 7t - 4t + 35 - 16 = 3t + 19

Answer:

Domain is all real numbers, and range is all numbers greater than or equal to -2.  If thee was anything you didn't understand let me know.  

Step-by-step explanation:

The domain is what x values work, or it may be better to say the horizontal axis.  is there any number you cannot use?  if you cannot tell, this is a parabola, like x^2.  Is there any number you cannot plug into x^2.  The answer is no, the domain for all parabolic functions is all real numbers.

The range you really want to look at visually here.  Range is y values you can get, or values on the vertical axis.  I would also compare it to x^2 again.  You should know you can make it as high as you want, here is the same.  but at -2, there is no point below that.  so the range is -2 and up

The other options are just specific numbers.  you can disprove those by choosing a number not on their lists.  For the domain literally any other number.  For range any number not on the list greater than -2