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The values of x in f(x) = 3|x - 2| + 6 when f(x) = 18 are 6 and -2

The function is given as:

f(x) = 3|x - 2| + 6

The value of f(x) is

f(x) = 18

So, we have:

3|x - 2| + 6 = 18

Subtract 6 from both sides

3|x - 2| = 12

Divide both sides by 3

|x - 2| = 4

Remove the absolute bracket

x - 2 = 4 or x - 2 = -4

Add 2 to both sides

x = 6 or x = -2

Hence, the values of x are 6 and -2

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The measurement is closest to height of tree is 8.7

The correct option is (B).

The branch of mathematics concerned with specific functions of angles and their application to calculations.

As the distance between base and tip of tree's shadow is 24 feet

Angle of Elevation is  20 degrees

[tex]tan \theta \; = \frac{P}{B}[/tex]

tan 20 = [tex]\frac{P}{24}[/tex]

0.3639 = [tex]\frac{P}{24}[/tex]

P= 0.3639 *24

P = 8.7336

The measurement is closest to height of tree is 8.7

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Answer:

A. B and D are functions

Step-by-step explanation:

Functions are either one-to-one or many-to one    (x-value --> y value)

C is not a function because   -3  (x) maps to 1 and also to 0 (y).

Answer:

Probability of an event must be from 0 to 1.

Here,6/5 is more than 1 i.e. 1.2.

Hence,the answer is incorrect.

Answer:

The axis of Symmetry divides a line into two equal halves.

Step-by-step explanation

An easy relation to get this value without plotting a graph is x = –b/2a

Where

a = coefficient of x²

b = coefficient of x

From the Question, We need a symmetry of value –½

The only Option that'll give this value is OPTION D

2x – y = 5 – 2x²

Since its a line, Don't forget to make "y" subject before doing any operation.

y = 2x² + 2x – 5

a = 2

b= 2

x = –(2)/2(2)

= –2/4

= –½

Answer:

Step-by-step explanation:

let S₁ be the set of factors of 45 that are less or equal to 6:

S₁ : {1 , 3 , 5}

let S₂ be the set of the even numbers that are less or equal to 6:

S₂ : {2 , 4 , 6}

S₁ ∪ S₂ = {1 ,2 , 3 , 4 , 5 , 6}

⇒ card(S₁ ∪ S₂) = 6

Then

p(even or factor of 45) = p(S₁ ∪ S₂) = 6/6 = 1

Therefore

p(even or factor of 45) = 100%

Part A

I'm assuming you want the area of a circle with radius 17 yards.

We'll use the formula below

A = pi*r^2

A = (22/7)*17^2

A = (22*17^2)/7

A = 6358/7

A = 908  2/7

The sprinkler covers an area of about 908  2/7 square yards.

You'll type 908 in the left-most box

Then for the other two boxes, you'll have 2 up top and 7 down below to represent the fraction 2/7

The number 908  2/7 is a mixed number.

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

Part B

You mentioned that the radius reduces to 11 yards here. We'll use the same formula as above and pi = 22/7 approximately

A = pi*r^2

A = (22/7)*11^2

A = (22*11^2)/7

A = 2662/7

A = 380  2/7

The sprinklers can water an area of about  380  2/7  square yards.

This value is also a mixed number

380 is the value in the left most box (it's the whole part)

The other two boxes are filled out the same exact way as the previous part above.

Answer:

The 6 is in the ten-thousands place

Step-by-step explanation:

6 written as a ten-thousand is 60,000

Answer:

y = 8x + 9

Step-by-step explanation:

Slope-intercept form of an equation is a fill-in-the-blank formula for writing an equation of a line. It is in the form:

y = mx + b

where m is the slope and b is the y-intercept (hence the name) In the problem slope is given, fill it in for m, next to the x. Y-intercept is given in the question also, fill it in in place of b.

y = 8x + 9

Answer:

it's 1 L

Step-by-step explanation:

it's pretty easy just do some multiplication

Answer:

105 units²

Step-by-step explanation:

Area of triangle = ½bh

b = 11 + 4

b = 15

A = 2(½15(7))

2 and ½ cancel

A = 15(7)

A = 105 units²

Answer:

A

Step-by-step explanation:

The answer is A because the point intercepts at (2,7), and answer A has the points (2,7) in it's answer.

Answer:

As a fraction it would be 4.5

Step-by-step explanation:

3/4 × 6 = 92 = 4 12 = 4.5

By finding the roots of the polynomial, we conclude that the correct graph is the second one.

Here we have the polynomial:

[tex]f(x) = x^3 + x^2 - 2x[/tex]

To identify it, we need to find the roots, we can rewrite the equation as:

[tex]f(x) = x*(x^2 + x - 2)[/tex]

And we can rewrite the last part by using the Bhaskara's formula:

[tex]x = \frac{-1 \pm \sqrt{1^2 + 4*2} }{2} \\\\x = (-1 \pm 3)/2[/tex]

Then the roots are:

x = -2

x = 1

Then we rewrite:

[tex]f(x) = x*(x + 2)*(x - 1)[/tex]

So the roots are at x = 0, x = -2, and x = 1.

The graph with these roots is the second graph (top right).

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Answer:

72

Step-by-step explanation:

If he reads 24 pages in 1/3 of an hour, he reads 3 times as many pages in 1 hour.

3 × 24 pages = 72 pages

Answer: 72

Answer:

Step-by-step explanation:

16, 18, 23, 25, 26, 34, 37, 37, 40, 41, 46

( 16 + 18 + 23 + 25 + 26 + 34 + 37 + 37 + 40 + 41 + 46 ) ÷ 11 = 31.181818...

mean ≈ 31

median = 34

mode = 37

Answer:

12 units

Step-by-step explanation:

(4, 7) and (4, -5)

7-(-5)=12

4-4=0

Answer:

the answer would b B solid

Step-by-step explanation:

because the figure appears to have depth as you look at it so it is solid.

Answer:

The new function is

[tex]g(x) = {2}^{x + 3} - 2[/tex]

The supplement of each interior angle has measure

180° - 165° = 15°

and so

n = 360°/15° = 24

since the exterior angles add up to 360° and are all congruent.

Answer:

no

Step-by-step explanation:

using the converse of Pythagoras' identity

If the square on the longest side is equal to the sum of the squares of the other 2 sides, then the triangle is right.

longest side = 50 ⇒ 50² = 2500

16² + 14² = 256 + 196 = 452

since 452 ≠ 2500 then the triangle is not right

A triangle has sides of lengths 16,14 and 50. Is the triangle right angle triangle?

We will solve this question using Pythagoras theorem.

We know,

[tex] \small \boxed{\rm{ c² = a² + b²}}[/tex]

[tex] \small\rm{Where,} [/tex] [tex]\small\sf{ c > a \: and \: c > b}[/tex]

[tex] \small\sf{ 50² = 16² + 14²}[/tex]

[tex]2500 = 256+ 196[/tex]

[tex]2500≠452[/tex]

[tex] \small\bf{ c² ≠ a² + b²}[/tex]

Hence, the triangle is not a right-angled triangle.

Answer:

  3° < x < 32.538°

Step-by-step explanation:

The possible values of the angle marked with an x-expression may not be as obvious as they first seem. There is a somewhat complicated interaction between the angle value and the length of the side(s) marked 'a'.

__

We can label the vertices of the figure A through D, clockwise from the bottom.

The minimum value of angle ACB (marked 3x-9°) is 0°. That will be its measure when AB +BC = AC, or B lies on line AC. In this case, the value of x is ...

  3x -9° = 0°

  3x = 9° . . . . add 9°

  x = 3° . . . . . divide by 3

value of 'a'

The maximum value of angle ACB will be found where both triangles are isosceles: AC ≅ BC ≅ DC. The length of 'a' can be found for that case using the Law of Sines:

  27/sin(93°) = a/sin(43.5°) . . . where (180° -93°)/2 = 43.5° is the base angle

  a = 27×sin(43.5°)/sin(93°) ≈ 18.611

value of 3x -9°

Angle ACB will obey the same Law of Sines requirement. If z represents the base angle in isosceles triangle ABC, then we have ...

  sin(z)/18.611 = sin(180-2z)/26

Recognizing that sin(180-2z) = sin(2z) and using the double-angle formula, we find ...

  sin(z)/18.611 = 2sin(z)cos(z)/26

  sin(z)(1/18.611 -cos(z)/13) = 0 . . . . . subtract the right side, factor

This has solutions that make the factors zero:

  sin(z) = 0   ⇒   z = 0 . . . . . . an extraneous solution in this case

  cos(z) = 13/18.611 ≈ 45.6925°

Then the value of x can be found from ...

  3x -9° = 180° -2z ≈ 88.615°

  x ≈ 3° +(88.615°/3) = 32.538°

_____

Additional comment

In the above, we have shown numerical values for the side lengths and angles in the maximum-x case. The various expressions can be combined to give ...

  3(x -3°) = 180° -2(arccos(13/27×sin(93°)/sin(43.5°)))

  x = 63° -2/3·arccos(13/27·sin(93°)/sin(43.5°))

Answer:

[tex]8(156 \times 1.1) + 12(156 \times 1.2) [/tex]

Answer:

Equation: 4x = 128

[tex]m\angle 1 = 84\degree[/tex]

[tex]m\angle 2 = 96\degree[/tex]

Step-by-step explanation:

Answer:

Parent function:
[tex]x^2+y^2=r^2[/tex]
General equation:
[tex](x-h)^2+(x-k)^2=r^2[/tex]
Transformations:
Its a circle with a center of (100,60) and a radius of 15

Answer:

about 2/5 of the question probability lol