Given the function f(x) = 3|x – 2| 6, for what values of x is f(x) = 18?

Answer:

Step-by-step explanation:

For three side lengths to form a triangle, the sum of the shorter two must exceed the longest.

__

  7 + 11 = 18 > 14 . . . . Will make a triangle.

__

  2 + 8 = 10 . . . not greater than 10. Will not make a triangle.

__

This is a direct consequence of the triangle inequality, which requires for sides a, b, c that ...

  a +b > c  and  b +c > a  and  c +a > b

_____

Additional comment

There is a version of the triangle inequality that uses the ≥ comparison, rather than >. If that is the version of the inequality you are using, then both these sets of lengths will form a triangle. The second "triangle" will look like a line segment and have zero area.

Answer:

4.7

Step-by-step explanation:

Answer:

4.7

Step-by-step explanation:

Check the picture below.

to check where the functions intersect, we can simply set them equal to each other so (x-2)² = 2x - 1, anyhow, not to bore you to death with that, it's as the picture shows it, at x = 1 and x = 5, so those are our bounds.

to get the R² part of the washer, what I do is using the "area under the curve" method of f(x) - g(x), where g(x) is the axis of rotation and f(x) is the farthest radius, so to get R² I'd process (x-2)² - (-1), that'd give me R and then I'd square that.

to get r², I do pretty much the same thing, f(x) - g(x) where g(x) is the axis of rotation and f(x) is the closest radius, in this namely (2x - 1) - (-1), and that'd give "r" and then we can square that to get r².

[tex]\begin{cases} R = 2x\\ r = x^2-4x+5 \end{cases}\hspace{5em} \begin{array}{llll} \stackrel{R^2}{4x^2}~~ - ~~\stackrel{r^2}{(x^4-8x^3+26x^2-40x+25)} \\\\\\ -x^4+8x^3-22x^2+40x-25 \end{array} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \pi \int\limits_{1}^{5}(-x^4+8x^3-22x^2+40x-25)dx \\\\\\ \pi \left[ -\cfrac{x^5}{5}+2x^4-\cfrac{22x^3}{3} +20x^2-25x\right]_{1}^{5}\implies \cfrac{1408\pi }{15}[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

By squaring the sum of two variables identity ~

[tex]\qquad \sf  \dashrightarrow \:(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab[/tex]

Now, plug in the given values ~

[tex]\qquad \sf  \dashrightarrow \:( - 6) {}^{2} = 20 + 2ab[/tex]

[tex]\qquad \sf  \dashrightarrow \:36 = 2(10 + ab)[/tex]

[tex]\qquad \sf  \dashrightarrow \:10 + ab = 36 \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \:10 + ab = 18[/tex]

[tex]\qquad \sf  \dashrightarrow \:ab = 18 - 10[/tex]

[tex]\qquad \sf  \dashrightarrow \:ab = 8[/tex]

I hope it was clear through my steps ~

Answer:

8

Step-by-step explanation:

(a+b)^2 = (-6)^2

a^2 + 2ab + b^2 = 36

a^2 + b^2 = 36 - 2ab

Equating 36 - 2ab with 20

36 - 2ab = 20

2ab = 16

ab = 8

Hope this helps out, feel free to mark this answer as brainliest :)

From the information given, the towline must be completely released to enable it to get to the maximum height. This problem is a trigonometry problem because it involves a solution that looks like a right-angled triangle.

In order to determine the maximum height of the parasailer, the length of the rope or towline must be established.

If the length and the height are known, the angle of elevation can be determined using the SOHCAHTOA rule.

SOH - Sine is Opposite over Hypotenuse

CAH - Cosine is Adjacent Over Hypotenus; while

TOA - Tangent is Opposite over Adjacent.

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Answer:

49

Step-by-step explanation:

Simplify the expression such that the variable has a positive exponent.

Substitute x = 7.

Answer:

I don't even have to look at it It's 17 final answer

Answer:

7 < 3 is false.

Explanation:

a) -3 > -5 is a true statement

b) 7 < 3 is a false statement

c) -5 < -3 is a true statement

d) 3 < 7 is a true statement

The original air present after 8 breaths will be equal to 179.81 ml.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

It is given in the question that:-

During normal breathing, about 12% of the air in the lungs is replaced after one breath

If the initial amount of air in the lungs is 500 mL

how much of the original air is present after 8 breaths?

The calculation for the eduction of the air will be done by the following equation:-

[tex]\rm =Volume \ present\times (0.88)^n\\\\\\= 500\times (0.88)^8[/tex]

=179.88 ml

Hence original air present after 8 breaths will be equal to 179.81 ml.

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Answer:

Step-by-step explanation:

In the two highlighted rows show that for the same amount of yellow, Green #1 uses more blue than Green #2 and green #1 is bluer shade of green than Green # 2.

The ratio of two number is the fraction part, which represent that how a number is more or less compare to the other.

There are two tables which give the number of pints of blue and yellow that are used to make different amounts of two shades of green dye. The table is given below;

The first one has 2 parts of blue at 3 parts of yellow. In the two highlighted rows show that for the same amount of yellow, Green #1 uses more blue than Green #2.

In grade two the blue part is half of the yellow part. This means that green #1 is bluer shade of green than Green # 2.

Hence, in the two highlighted rows show that for the same amount of yellow, Green #1 uses more blue than Green #2 and green #1 is bluer shade of green than Green # 2.

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Based on the excerpt given on Paco's evaluation of Dan DeLuca's argument, the correct order is 3 - 4 - 1 - 2.

3 is the best sentence to start because it introduces the direction that DeLuca is taking in his argument. 4 is next because it then says what DeLuca's claims are.

1 is the third sentence because it expands on DeLuca's arguments and then 2 is the last sentence as it contains Paco's evaluation of the argument.

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Answer:

its C: 3 – 4 – 1 – 2

Answer:

Option c, G(x) = 12x

Step-by-step explanation:

Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1

In the equation f(x) = mx, the m is acting as the vertical stretch or compression of the identity function.

- f(x) = x by m vertically stretches the graph of f by a factor of m units if

m > 1

- vertically compresses the graph of f by a factor of m units if

0 < m < 1.

This means the larger the absolute value of m, the steeper the slope.

Answer:

Here, the parent should pass through the origin, which is through the coordinate (0,0).

The only function that passes through this (0,0) point and is vertically stretched is only valid is:

y = 12x

The number of views snapgram, bookface and giggle have are 8, 32.3, 17.7 views respectively.

let

= x + 24.3 - 14.6

= x + 9.7

Total = snapgram + bookface + giggle

58 = x + (x + 24.3) + (x + 9.7)

58 = x + x + 24.3 + x + 9.7

58 = 3x + 33

3x = 58 - 34

3x = 24

x = 24/3

x = 8 views

Therefore,

snapgram views = x

= 8 views

Bookface views = x + 24.3

= 8 + 24.3

= 32.3 views

Giggle views = x + 9.7

= 8 + 9.7

= 17.7 views

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Answer: [tex]\displaystyle d=\sqrt{53}[/tex]

Step-by-step explanation:

   We will use the distance formula to solve. See attached and view the work below.

[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]

[tex]\displaystyle d=\sqrt{(5-3)^2 +(11-4)^2}[/tex]

[tex]\displaystyle d=\sqrt{(2)^2 +(7)^2}[/tex]

[tex]\displaystyle d=\sqrt{4+49}[/tex]

[tex]\displaystyle d=\sqrt{53}[/tex]

   Since 53 is prime, this is the simplest form. Since it asks for an exact answer, we are done.

Answer:

A

Step-by-step explanation:

First lets take not of the given coordinations.

Based on these cordinates you can conclude the correct places on the map.

Answer:

either C or D

Step-by-step explanation:

The amount of bottles that Dylan needs each week to bottle all the milk is; 64 bottles

We are given;

Amount of Milk produced by Dylan's cow per day = 21 ¹/₃ liters

Thus, amount of liters of milk produced in a week = 21 ¹/₃ liters * 7 = 448/3 liters.

Then, number of bottles required in a week = 448/3 ÷ 2¹/₃ = 448/7

Number of bottles required in a week = 64 bottles

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Answer:

36 students.

Step-by-step explanation:

5 + 7 = 12.

So the number of students must be a multiple of 12.

So as the number is  between 25 and 43 it must be 36.

Answer:

I think none are solutions

Answer:

image below

Step-by-step explanation:

Answer:

6.75$

Step-by-step explanation:

because 15% of 45$ is 6.75$

Answer: y = -13

Step-by-step explanation:

Given:

[tex]\displaystyle \frac{y-8}{3} =-7[/tex]

Multiply both sides by 3:

[tex]\displaystyle y-8 = -21[/tex]

Add 8 to both sides:

[tex]\displaystyle y= -13[/tex]

Given equation,

Aim :

Cross multiplying them,

>> y - 8 = -7 × 3

>> y - 8 = -21

Transposing -8 from L.H.S. to R.H.S.,

>> y = -21 + 8

>> y = -13

Therefore :

Answer

[tex]x = \frac{\pi }{6} + 2\pi n, \frac{5\pi }{6} + 2\pi n, \frac{3\pi }{2} + 2\pi n[/tex], for any integer n

Answer:

D or 270°

Step-by-step explanation:

2sin^2x+sinx-1

2sin^2(270°)+sin(270°)-1=0

Answer:

7.04, 7.134 ,7.2, 7.413

Step-by-step explanation:

Answer:

cosΘ = [tex]\frac{\sqrt{3} }{2}[/tex]

Step-by-step explanation:

sin²Θ + cos²Θ = 1 ( subtract sin²Θ from both sides )

cos²Θ = 1 - sin²Θ ( take square root of both sides )

cosΘ = ± [tex]\sqrt{1-sin^20}[/tex]

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

       = ± [tex]\sqrt{1-\frac{1}{4} }[/tex]

      = ± [tex]\sqrt{\frac{3}{4} }[/tex]

     = ± [tex]\frac{\sqrt{3} }{2}[/tex]

since 0° < Θ < 90° , then

cosΘ = [tex]\frac{\sqrt{3} }{2}[/tex]

width= area /length

width= 192/60

Width= 3.2 inches

Answer:

36 is the width.

Step-by-step explanation:

A rectangle has four sides.

So the equation should be:

60+60+?+?= 192.

In order to cancel out the two 60s, you subtract it from 192.

So,

?+?=72.

The sides opposite of a rectangle is congruent, thus,

72/2=36.

The width of the rectangular banner is 36, and to check the answer you just plug all the digits in.

60+60+36+36=192.

Hopefully this helped!

Answer:

240 points game 3

Step-by-step explanation:

use what is given and put everything in variable terms since this asks for the average, you have to divide by the number of games in the end

Answer:

90 degree counter clockwise rotation about the origin
reflect across the x-axis

Step-by-step explanation:

Answer:

Lesser x = -14

Greater x = 0

Step-by-step explanation:

Given equation:

[tex]\sf (x+7)^2-49=0[/tex]

Add 49 to both sides:

[tex]\implies \sf (x+7)^2-49+49=0+49[/tex]

[tex]\implies \sf (x+7)^2=49[/tex]

Square root both sides:

[tex]\implies \sf \sqrt{(x+7)^2}=\sqrt{49}[/tex]

[tex]\implies \sf x+7=\pm7[/tex]

Solve for x:

[tex]\implies \sf x+7=7 \implies x=0[/tex]

[tex]\implies \sf x+7=-7 \implies x=-14[/tex]

As -14 < 0

Answer:

the answer is c=34

Step-by-step explanation:

use the pythogoras therom since there is a right angle triangle c2=a2+b2

hope this helped:)

Answer:

34

Step-by-step explanation:

[tex]Formula: a^2+B^2=C^2[/tex]

[tex]30^2= 900 \\\\16^2= 256\\\\900+256= 1156\\\\[/tex]

[tex]c^2=1156[/tex]

to find the answer we have to figure out what times itself = 1156

30x30=900 greater than 30 35x35=1225 less than 35

7x - 35 < 2(x -5)

Use distributive property on the right side:

7x -35 < 2x - 10

Add 35 to both sides:

7x < 2x + 25

Subtract 2x from both sides

5x < 25

Divide both sides by 5

X < 5

[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

Solve the inequality 7x-35<2(x-5)

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]

First, use the distributive property on the right-hand side:-

     7x-35<2x-10

Remember, we need to ensure that variables are on one side of the inequality and numbers are on the other.

Since we have variables on both sides, we need to move all of them to the other side (usually the left-hand side), using the opposite operation.

Therefore

7x-35-2x<-10

Combine like terms:-

5x-35<-10

Now add 35 on both sides:-

5x<-10+35

On simplification,

5x<25

Divide by 5 on both sides:-

x<5

So the values of x less than 5 will satisfy this inequality.

[tex]\rule{300}{1}[/tex]