Polygon LMNOP was transformed to create polygon L'M'N'O'P'.2 pentagons have identical side lengths and angle measures. The points are labeled with the same letters.

Which angle corresponds to AngleN?
Angle
Angle
Angle
Angle

The height of the trapezoid is 6 cm

The given parameters are:

Bases = 5cm and 9cm

Area = 42 square cm

The height is calculated using

Area = 0.5 * (Sum of bases) * Height

So, we have:

42 = 0.5 * (5 + 9)* Height

This gives

42 = 7* Height

Divide through by 7

Height= 6

Hence, the height of the trapezoid is 6 cm

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Using translation concepts, the transformations are given as follows:

a) The function is horizontally compressed by a factor of 3 and shifted down one unit.

b) The function is shifted right 3 units and vertically stretched by a factor of 2.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Item a:

The transformations are:

Item b:

The transformations are:

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Answer:

30π in

Step-by-step explanation:

Circumference of a circle = 2πr

Where r is the radius

In the given diagram, the radius is 15 in

2×π×15 in = 30π in

Answer:

The correct answer is 6

Step-by-step explanation:

x/10=3/5

then cross multiply

it will now give

5x=30

x=6

If [tex]251_x\equiv100_{10}[/tex], then this translates to the equation

[tex]251_x = 2x^2 + 5x + 1 = 100[/tex]

Solve for [tex]x[/tex].

[tex]2x^2 + 5x = 99[/tex]

[tex]2\left(x^2 + \dfrac52 x\right) = 99[/tex]

[tex]2 \left(x^2 + \dfrac52 x + \dfrac{25}{16}\right) - \dfrac{25}8 = 99[/tex]

[tex]2 \left(x + \dfrac54\right)^2 = \dfrac{817}8[/tex]

[tex]\left(x + \dfrac54\right)^2 = \dfrac{817}{16}[/tex]

[tex]x + \dfrac54 = \pm \dfrac{\sqrt{817}}4[/tex]

[tex]x = \dfrac{-5\pm\sqrt{817}}4[/tex]

though it is a bit unusual (but not entirely out of the question) to have an irrational base number system.

In case you meant [tex]100_2[/tex] on the right side, then [tex]100_2 = 2^2 = 4_{10}[/tex], so that

[tex]2x^2 + 5x + 1 = 4 \\\\ 2x^2 + 5x - 3 = 0 \\\\ (x+3) (2x-1) = 0 \\\\ x=-3 \text{ or } x = \dfrac12[/tex]

which at first glance seem like more reasonable choices of base.

Answer:

x=1

Step-by-step explanation:

It's pretty obvious to see that x equals 1 after you subtract 3 from both sides, but this question specifies using change base, so:

log(b)a means log base b with a as the contents
1.
4^x+3-3=7-3

4^x=4

log(4)4^x=log(4)4    (both logs are base 4 in this case to free the x)

x=log(4)4

x=log(10)4/log(10)4   (both logs are base 10 in this case)

x=1

Change base is definitely unnecessary in this problem

Answer:

[tex]\huge\boxed{\sf 46.2\%}[/tex]

Step-by-step explanation:

Prediction = 19 throws

Actual = 13 throws

[tex]\displaystyle =\frac{Predication -Actual}{Actual} \times 100 \%\\\\= \frac{19-13}{13} \times 100 \%\\\\= \frac{6}{13} \times 100 \%\\\\= 0.462 \times 100 \%\\\\= 46.2\%\\\\\rule[225]{225}{2}[/tex]

Answer:

B: 75

Step-by-step explanation:

5^2 is 5 times itself twice, so 5 times 5 = 25

3 times 25 is 75

Answer:

Hello! The answer to your question is B. 75.

Step-by-step explanation:

To solve this question, you have to first convert the exponents:

[tex]5^2 = 25[/tex]

Now that you have converted the exponents, you can multiply:

3 × 25 = 75

Answer:

The first answer is correct:

[tex]\{\frac{1}{3},-3.45,\sqrt{9}\}[/tex]

Step-by-step explanation:

Since [tex]\frac{1}{3}, -3.45, \sqrt{9}=3[/tex] are all rational numbers, the set that contains those numbers is the set of rational numbers.

In the second set, number [tex]\sqrt{37}[/tex] is irrational number since it can not be written as quotient.

Also in the third and fourth set, numbers [tex]\sqrt{44}[/tex] and [tex]\sqrt{2}[/tex] are irrational numbers.

Therefore, the first answer is correct.

Answer:

6

Step-by-step explanation:

the sequence increases by 1,2,3,4,5,6 each time, thus it is 6

Answer:

22.6

Step-by-step explanation:

a^2 + b^2 = c^2  We know one of the legs and the hypotenuse.  The hypotenuse must be c.  The leg that we do know can be a or b.  It is our choice.  I am going to let it be a

8^2 + b^2 = 24^2  Plug in the numbers that I know

64 + b^2 = 576   Square the numbers that I know

b^2 = 512   Subtract 64 from both sides

b = 22.6  Put this in your calculator to find the square root and round.

Answer:

24 Inches

Step-by-step explanation:

Its 24 Inches away from the centre lol

Answer:

Step-by-step explanation:

Directions

Givens

AC = 13 inches                   Given

CB = 24 inches                  Given

CE = 12 inches                    Construction and property of a midpoint.

So what we have now is a right triangle (ACE) with the right angle at E.

What we seek is AE

Formula

AC^2 = CE^2 + AE^2

13^2 = 12^2 + AE^2

169 = 144 + AE^2                     Subtract 144 from both sides.

169 - 144 = 144-144 + AE^2     Combine

25 = AE^2                                Take the square root of both sides

√25 = √AE^2

5 = AE

Answer

The 24 inch chord is 5 inches from the center of the circle.

The initial population at time t = 0 was 0.39 while the size of the bacteria population after 4 hours was 6553600

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the bacteria population at time t. a represent the initial population at t = 0. Since the doubling period of a bacteria population is 10 minutes, hence:

[tex]y=a(2)^\frac{t}{10}[/tex]

At time t = 110 minutes, the bacterial population was 800. Hence:

[tex]800=a(2)^\frac{110}{10} \\\\a = 0.39[/tex]

At 4 hours (240 minutes):

[tex]y=0.39(2)^\frac{240}{10} =6553600[/tex]

The initial population at time t = 0 was 0.39 while the size of the bacteria population after 4 hours was 6553600

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Answer:

f (4,0)

Step-by-step explanation:

Hope it helps!!!

y=4

x=0

⊱_______________________________________________________⊰

Answer:

Step-by-step explanation:

[tex]\large\displaystyle\begin{gathered} \sf{The \ y-intercept \ is \ the \ point \ where \ the \ graph \ intercepts \ the \ y \ axis. \\ \sf{Thus, \ assuming \ that \ each \ little \ square \ represents \ one \ unit, \ the \ y-intercept} \\ \sf{is \ 4} \end{gathered}[/tex]

done !!

⊱_______________________________________________________⊰

Answer:

Step-by-step explanation:

Define two ways of painting to be in the same class  if one can be rotated to form the other.We can count the number of ways of painting for each specific class .

Case 1: Black-white color distribution is 0-6 (out of 6 total faces)

Trivially [tex]1^{2}[/tex]=1 way to paint the cubes.

Case 2: Black-white color distribution is 1-5

Trivially all [tex]\frac{6}{5}[/tex] =6 ways belong to the same class , so [tex]6^{2}[/tex] ways to paint the cubes.

Case 3: Black-white color distribution is 2-4

There are two classes for this case: the class  where the two red faces are touching and the other class where the two red faces are on opposite faces. There are 3 members of the latter class  since there are  3 unordered pairs of  2 opposite faces of a cube. Thus, there are [tex]\frac{6}{4}[/tex]-3=12  members of the former class . Thus, [tex]12^{2} + 3^{2}[/tex] ways to paint the cubes for this case.

Case 4: Black-white color distribution is 3-3

By simple intuition, there are also two classes  for this case, the  class where the three red faces meet at a single vertex, and the other class where the three red faces are in a "straight line" along the edges of the cube. Note that since there are 8 vertices in a cube, there are 8  members of the former class and [tex]\frac{6}{3} -8=12[/tex] members of the latter class. Thus, [tex]12^{2} - 8^{2}[/tex]  ways to paint the cubes for this case.

Note that by symmetry (since we are only switching the colors), the number of ways to paint the cubes for black-white color distributions 4-2, 5-1, and 6-0 is 2-4, 1-5, and 0-6 (respectively).

Thus, our total answer is[tex]\frac{2*(6^{2} + 1^{2}+ 12^{2}+ 3^{2})+12^{2}+8^{2}}{2^{12} } =\frac{588}{4096} = \frac{147}{1024}[/tex]

Answer:

12.0 to 3 dig digs You must include the 0 to get 3 significant figures.

Step-by-step explanation:

Comment

This is a Pythagorean Problem. Use the formula

c ^2 = a^2 + b^2

Givens

a = 8 - 7 = 1 cm

b = 12 cm

c = ?

solution

c^2 = 1^2 + 12^2  

c^2 = 1 + 144

c^2 = 145                 Take the square root of both sides

√c^2 = √145  

c = 12.04

c = 12.0 to 3 sig digs.

The x- and y-intercepts of the graphs of the function described are; (2,0) and (4,0) respectively.

It follows from the task content that the function given is; f(x) = −2| x +1 | + 6.

Since the x- and y-intercepts corresponds to x and y values for which y and x are zero respectively, it follows that;

x -intercept is;

0 = -2(x+1) + 6

2x = -2 +6

2x = 4

x = 4/2 = 2

y-intercept is;

y = -2(0+1) +6

y = 4.

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Step-by-step explanation:

Type the correct answer in the box. Use numerals instead of words.

The graphs of functions f and g are shown.

Graph shows 2 functions. First curve f begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 2), (8, 3) in quadrant 1. Second curve g begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 4), and (8, 6) in quadrant 1.

Function g is defined as . What is the value of k?

The value of k is

(1,0)

The perimeter of polygon JKLM = 85 units

The perimeter of polygon EFGH = 34 units.

The perimeter of polygon JKLM = JK + KL + LM + JM

The perimeter of polygon EFGH = EF + FG + GH + EH

Find the missing lengths using the similarity theorem:

JK/EF = KL/FG = LM/GH = JM/EH

Plug in the values

20/8 = KL/11 = LM/3 = 30/EH

20/8 = KL/11

KL = (20 × 11)/8 = 27.5

20/8 = LM/3

LM = (20 × 3)/8

LM = 7.5

20/8 = 30/EH

EH = (30 × 8)/20

EH = 12

The perimeter of polygon JKLM = 20 + 27.5 + 7.5 + 30 = 85 units

The perimeter of polygon EFGH = 8 + 11 + 3 + 12 = 34 units.

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The required polar equation of a conic is given be: [tex]r = \frac{6}{1-2sin\Theta }[/tex]. option b is correct.

For a conic we have directrix = 3 and eccentricity = 2

Polar equation can be identified as of the form of x= a+b.sinФ.
Which contain simple variable along with trigonometric operators.

Here,

Standard polar equation for the conic is given as,

    [tex]r=\frac{ep}{1-esin\theta}[/tex]  
By putting given values
[tex]r = \frac{6}{1-2sin\Theta }[/tex].
Thus, the required polar equation for the conic is  [tex]r = \frac{6}{1-2sin\Theta }[/tex].

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The question was incomplete. Below you will find the missing content.

In the figure below, BL, AM, and CK are medians of △ABC. If KC = 108 and OC = 2n + 10, then n=

The picture is attached below.

The value of n is 31.

The median is the line connecting the vertex and its midpoint on the opposite side of the triangle.

The intersection of all 3 medians of the triangle is called the centroid.

As we know centroid divides the median in the ratio of 2:1.

In the given picture,

Medians of triangle △ABC are AM, BL, and CK.

So the centroid of the triangle is O.

Given that KC= 108

As the centroid O divides the line KC in 2:1.

Let OC=2x

KO= X

As KC= KO+OC

⇒ 108= x+2x

⇒ 3x=108

⇒ x=108/3

⇒ x=36

Then OC= 2x= 2*36= 72

As given in the question OC= 2n+10

putting the value of OC in above equation

⇒ 72= 2n+10

⇒ 2n= 72-10

⇒ 2n=62

⇒ n=62/2

⇒n=31

Therefore the value of n is 31.

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2. Converse of corresponding angles theorem.

3. Given

4. Perpendicular transverse theorem

According to the converse of corresponding angles theorem, if two corresponding angles are congruent, then the lines cut by the transversal that both angles line on are parallel to each other.

Thus, given that ∠1 ≅ ∠2, lines p and q will be parallel based on the converse of corresponding angles theorem.

We are given that lines p and r are perpendicular to each other, therefore, we can conclude that, based on the perpendicular transverse theorem, q⊥r.

The missing reasons in the proof are:

2. Converse of corresponding angles theorem.

3. Given

4. Perpendicular transverse theorem

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Adam's weekly money deposit is a linear relation with a slope of $6 per week.

A) Money deposited by Adam each week is $6.

B) The answer can be determined by observing the graph provided to us, in which the point representing 1 week on the x-axis is intersected by the point representing $6 on the y-axis. This helps us determine that Adam's weekly deposit is $6.

C) An alternative strategy of calculating the slope can be used.

The slope can be calculated in the following way:

m = (y₂ - y₁)/(x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two points on the line.

Thus slope of this line can be calculated as,

m = (12 - 6)/(2 - 1) = 6/1 = 6 {Since, the line passes through the points (2, 12) and (1, 6)}.

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The appropriate values are; [tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex], [tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex], [tex]cot\theta= -\frac{1}{3}[/tex], [tex]sec\theta=-\sqrt{10}[/tex] and [tex]csc\theta= \frac{\sqrt{10} }{3}[/tex].

Given the equation and interval.

tanθ = -3, [ π/2 < θ < π ]

First, we use the definition of tangent to determine the known sides of the unit circle right triangle.

Note that; the quadrant determines the sign of each values.

tanθ = opposite / hypotenuse

We can use Pythagoras theorem to find the hypotenuse of the unit circle right triangle as the opposite and adjacent sides are known.

Hypotenuse = √( opposite² + adjacent² )

Hence, we have;

Hypotenuse = √( [3]² + [-1]² )

Hypotenuse = √( 9 + 1 )

Hypotenuse = √10

1) To find sinθ

sinθ = opposite / hypotenuse

sinθ = 3/√10

We simplify

sinθ = 3/√10 × √10/√10

sinθ = 3√10 / 10

[tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex]

2) cosθ

cosθ = adjacent / hypotenuse

cosθ = -1 / √10

Simplify

cosθ = -1 / √10 × √10/√10

cosθ = -√10 / 10

[tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex]

3) cotθ

cotθ = adjacent / opposite

cotθ = -1 / 3

[tex]cot\theta= -\frac{1}{3}[/tex]

4) secθ

secθ = hypotenuse / adjacent

secθ = √10 / -1

[tex]sec\theta=-\sqrt{10}[/tex]

5) cscθ

cscθ = hypotenuse / opposite

cscθ = √10 / 3

[tex]csc\theta= \frac{\sqrt{10} }{3}[/tex]

Therefore, the appropriate values are; [tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex], [tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex], [tex]cot\theta= -\frac{1}{3}[/tex], [tex]sec\theta=-\sqrt{10}[/tex] and [tex]csc\theta= \frac{\sqrt{10} }{3}[/tex].

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Answer:

a line that is perpendicular to the line l

The factorized expression of -x - 10 is -(x + 10)

The expression is given as:

-x - 10

Factor out -1 from the expression

-1(x + 10)

Rewrite as:

-(x + 10)

Hence, the factorized expression of -x - 10 is -(x + 10)

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The Parabola is a locus of points equidistant from a single point called focus and a line called Directrix. The correct option is C.

A parabola is a U-shaped figure, all the point on the parabola is equidistant from the focus, and a line called Directrix.

The Parabola is a locus of points equidistant from a single point called focus and a line called Directrix.

Therefore, The correct option is C.

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Answer: 390 m².

Step-by-step explanation:

[tex]Surface \ area = 11*13+11*12+11*5+2*\frac{12*5}{2}=11*(13+12)+11*5+12*5=\\ =11*25+5*(11+12)=275+5*23=275+115=390\ (m^2).[/tex]

Minerva's account balance will be about $100 ,  it is True and Option A is the correct answer.

Compounded Annually means when the interest is given even on the interest accrued from the principal amount . This is done once a year.

It is given that

Principal Amount = $50

From the graph attached in the answer which was missing in the question ,

It can be confirmed that after 12 years

Minerva's account balance should be about $100.

Therefore it is True and Option A is the correct answer.

The graph missing is attached

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