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A turning point is a point at which the derivative changes sign. A turning point may be either a relative maximum or a relative minimum (also known as local minimum and maximum). 

It looks like the inequality is

[tex]\bigg|x + 6 - |3x + 6|\bigg| + |x + 2| - x - 4 \le 0[/tex]

or equivalently,

[tex]\bigg|x + 6 - 3 |x + 2|\bigg| + |x + 2| - x - 4 \le 0[/tex]

Recall the definition of absolute value:

[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]

By this definition, we have

[tex]|x + 2| = \begin{cases} x + 2 & \text{if } x + 2 \ge 0 \\ -(x + 2) & \text{if } x + 2 < 0 \end{cases} = \begin{cases} x + 2 & \text{if } x \ge -2 \\ -x - 2 & \text{if } x < -2 \end{cases}[/tex]

Suppose [tex]x < -2[/tex]. Then

[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |x + 6 - 3 (-x - 2)| + (-x - 2) - x - 4 \\\\ = |4x + 12| - 2x - 6[/tex]

By definition of absolute value,

[tex]|4x + 12| = 4 |x + 3| = \begin{cases} 4x + 12 & \text{if } x \ge -3 \\ -4x - 12 & \text{if } x < -3 \end{cases}[/tex]

so we further suppose that [tex]x < -3[/tex]. Then

[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |4x + 12| - 2x - 6 \\\\ = (-4x - 12) - 2x - 6 \\\\ = -6x - 18 \le 0 \\\\ \implies x \ge -3[/tex]

but this is a contradiction, so this case gives no solution.

If instead we have [tex]-3 \le x < -2[/tex], then

[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |4x + 12| - 2x - 6 \\\\ = (4x + 12) - 2x - 6 \\\\ = 2x + 6 \le 0 \\\\ \implies x \le -3[/tex]

and [tex]-3 \le x[/tex] and [tex]x \le -3[/tex] means that [tex]\boxed{x = -3}[/tex].

Now suppose [tex]x \ge -2[/tex]. Then

[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |x + 6 - 3 (x + 2)| + (x + 2) - x - 4 \\\\ = |-2x| - 2 \\\\ = 2 |x| - 2[/tex]

If we further suppose that [tex]-2 \le x < 0[/tex], then

[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = 2 |x| - 2 \\\\ = -2x - 2 \le 0 \\\\ \implies x \ge -1[/tex]

Otherwise, if [tex]x \ge 0[/tex], then

[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = 2 |x| - 2 \\\\ = 2x - 2 \le 0 \\\\ \implies x \le 1[/tex]

Taken together, this case gives the solution [tex]\boxed{-1 \le x \le 1}[/tex]

So, the overall solution to the inequality is the set

[tex]\boxed{\left\{ x \in \mathbb R : x = -3 \text{ or } -1 \le x \le -1 \right\}}[/tex]

4

1-

6

Step-by-step explanation:

its because i cant understand

Answer:

[tex]\Large \displaystyle \frac{7}{8}[/tex]

Step-by-step explanation:

Volume = area of cross-section × height

Mixed to improper fraction

7/4 × 1/2 = 7/8

Answer:

$70.88

Step-by-step explanation:

He bought the boots for $80*75% = $80*0.75 = $60

Let x = the original price of the belt

He spent x * 85% = 0.85x for the belt

total cost = 60 + 0.85x = 120.25

0.85x = 120.25 - 60 = 60.25

x = 60.25/0.85 = $70.88

Using the graph, it is found that:

a) The local minimum value of the function is of y = 0.

b) The values are x = -3, x = 3.

The local minimum of a function in a graph is the point at which the function changes from decreasing to increasing. In this problem, they are given by y = 0.

The values at which this happen is the values of x, that is, the horizontal axis. In this problem, they are at x = -3 and x = 3.

More can be learned about functions at https://brainly.com/question/25537936

❑ Twσ triαnglєѕ αrє cσnѕidєr cσngruєnt if єαch αnd єvєrч ѕidє αѕ wєll αѕ αnglєѕ σf σnє triαnglє iѕ єquαl tσ thє cσrrσѕpσnding ѕidєѕ αnd αnglєѕ σf tht σthєr triαnglє.

❑ cσngruєnt ѕhαpєѕ cαn cσíncídє wíth єαch σthєr pєrfєctlч íf σvєrlαppєd.

[tex]\rule{7cm}{1 mm}[/tex]

Answer:

2.55

Step-by-step explanation:

First take 11 and subtract it by 3 to get 8.

Then divide it by 3.14 and get 2.547770701...

After that round it to 2.55

Answer:

18

Step-by-step explanation:

I2=h2+r2

25(2)=h2+7(2)

50=h2+14

-14 -14

36=h2

÷2 ÷2

18=h

Answer:

Arachnid is my guess.

Answer:

C = 25.1

Step-by-step explanation:

Use the formulas:

Solving for C:

Round to the nearest tenth:

Answer:

NE = 8 cm

Step-by-step explanation:

Radius OA = OE = 5 cm

In right triangle OAN, OA² + AN² = ON²

5² + 12² = ON²

ON² = 25 + 144 = 169

so ON = 13 cm

NE = ON - OE = 13 - 5 = 8 cm

Answer:

7.48

Step-by-step explanation:

C=2πr

Solving for

r=C

2π=47

2·π≈7.48028

Answer:

Step-by-step explanation:

Circumference = 47 inches

[tex]2\pi r = 47\\\\2*3.14*r = 47\\\\6.28*r = 47\\\\r = \dfrac{47}{6.28}\\\\[/tex]

r = 7.48 in

Hey there!

10^2 + (3 + 5)^2 - 5

= 10 * 10 + (3 + 5)^2 - 5

= 100 + (8)^2 - 5

= 100 + (8 * 8) - 5

= 100 + 64 - 5

= 164 - 5

= 159

Therefore, your answer is: 159

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

10² + (3 + 5)² - 5 = 159

Step-by-step explanation:

Given expression,

→ 10² + (3 + 5)² - 5

Evaluating the expression,

→ 10² + (3 + 5)² - 5

→ 10² + 8² - 5

→ 100 + 64 - 5

→ 100 + 59

→ 159

Hence, the answer is 159.

Answer:

26.6

Step-by-step explanation:

because you are multiplying a couple of numbers

Answer:

  x = {-9/4, 15/4}

Step-by-step explanation:

To use the square root property to solve the quadratic, you need to get it to a form where the square root function can be usefully applied. That will mean having a square of a binomial on one side of the equal sign, and a constant on the other side of the equal sign.

We can get that from the given equation by adding 5 to both sides.

  (x -3/4)^2 -5 = 4 . . . . . . given

  (x -3/4)^2 = 9 . . . . . . . add 5 to get the square by itself

  x -3/4 = ±3 . . . . . . . . . take the square root

  x = ±3 +3/4 = {-9/4, 15/4} . . . . add 3/4 and expand the result

Answer:

$13,020

Step-by-step explanation:

65,100 * 20% = 65,100 * 0.20 = 13,020

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$16000\\ r=rate\to 3.6\%\to \frac{3.6}{100}\dotfill &0.036\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &20 \end{cases} \\\\\\ A=16000\left(1+\frac{0.036}{4}\right)^{4\cdot 20}\implies A=16000(1.009)^{20}\implies A\approx 19100[/tex]

Answer:

3

Step-by-step explanation:

Numbers include 3,4,5

smallest is 3

Answer:

I counted 24.

Step-by-step explanation:

Its probably a trick question though

Answer: I counted 36.

(edit) But the answer is 40.

Step-by-step explanation:

Count all the "normal" squares. 16.

Then all the 2x2 normal squares. 9.

Then count all the tiny squares. 8.

Then the 2 big squares the tiny squares make. 2.

Then the giant square, which is all the squares. 1.

And I agree this probably is a trick question.

16 + 9 + 8 + 2 + 1 = 36 squares in total

*EDIT*

Apparently 3x3 squares exist so...

3x3 squares . 4

so 36 + 4 = 40 squares in total

(thanks to the person who asked the question in the first place for telling me about those 3x3 squares)

Answer:

2) X = 14 and y = 19.8

3) X = 25.45

5) X = 5.66

6) X = 7.07

Step-by-step explanation:

2) tan45° = 14/x

x(tan45) = 14

x = 14 / tan45

x = 14

[tex] y = \sqrt{14 ^{2} + 14 ^{2} } [/tex]

y = 19.79

3) cos45 = 18/x

x(cos45) = 18

x = 18/cos45

x = 22.45

5) cos45 = x/8

8(cos45) = x

x = 5.66

6) cos45 = x/10

10(cos45) = x

x = 7.07

Step-by-step explanation:

what did we learn in the other question ?

there are 8 equal sub-segments of 1/8 length between neighboring whole numbers.

so, each little line is 1/8.

the marker goes first to 1, and then one little line towards 2.

therefore, that number is 1 1/8.

Answer:

I would say 2 ft

Step-by-step explanation:

Have amazing day!

Please rate!

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Work Shown:

A = P(consonant)

A = 3/4 since there are 3 consonants out of 4 letters in the word "SKIP".

B = P(even number)

B = 3/6

B = 1/2

P(consonant, even number) = A*B

P(consonant, even number) = (3/4)*(1/2)

P(consonant, even number) = 3/8

P(consonant, even number) = 0.375

Answer:

(a) 105

(b) 105

(c)105

Step-by-step explanation:

(a) You can subtract 75 from 180 to find your answer

(b) This angle is corresponding with (a)

(c) This is a consecutive exterior angle with the 75 degree one in 4th street and King Ave, therefore it will be 105

Answer:

x = 5 ± i√11 / 2

Step-by-step explanation:

At the y-intercept the value of y is equal to 0.

=> 0 = x² + 5x + 9

=> x = -5 ± √25 - 4(9) / 2

=> x = 5 ± √-11 / 2

=> x = 5 ± i√11 / 2

Answer:314 in squared

Step-by-step explanation:

99+44+99+72

Answer:

taena mo bobo mo sa math hindi ka mag kakajowa sa February 14 hahahhahahah