Find the area of the complex figureSaA.37B.32C.28D.51

Answer:

( a - 6 )² = b

Step-by-step explanation:

a = √b + 6

Take 6 to the left side.

a - 6 = √b

Square both sides to remove the root of b.

( a - 6 )² = b

The correct answer is Graph 1: y = cos(x/4)Graph 2: y = cos(x/2)

Based on the given descriptions of the graphs and the patterns they follow, the correct pairs are:

Graph 1: y = cos(x/4) ⟶ This graph has a period of 8 units and matches the pattern described.Graph 2: y = cos(x/2) ⟶ This graph has a period of 4 units and matches the pattern described.

Graph 3: y = cos(x) ⟶ This graph has a period of 2π (or approximately 6.28 units) and matches the pattern described.

Graph 4: (Not used)

Graph 5: (Not used)

Please note that without visual representation, it's difficult to provide a definitive answer. The pairs are based on the descriptions provided and may vary depending on the actual shapes of the graphs.

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Let the set of all Odd multiples of 9 between 2 and 82 be denoted by D, then, using set-builder notation,

\(D=\{ 18n+9 \mid n \in \mathbb{N}, 0\le n\le 4 \}\)

The odd multiples of 9, \(m\), in the range \(2\le m \le 82\) form the set

\(\{9,27,45,63,81\}\)

Each member of the set is a term of the arithmetic progression

\(U_n=18n+9\)

where the values of \(n\) range from 0 to 4, or \(0\le n\le 4\)

Putting these facts together, we get the result

\(D=\{ 18n+9 \mid n \in \mathbb{N}, 0\le n\le 4 \}\)

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The probability that a person will wait for more than 9 minutes is approximately 0.0912 or 9.12%. This means that out of 100 people, about 9 of them will wait for more than 9 minutes in the line.

We know that,

To solve this problem, we need to use the normal distribution and standardize the variable of interest. We know that the mean waiting time is 5 minutes and the standard deviation is 3 minutes, so we can write: Z = (X - μ) / σ

where X is the waiting time, μ is the mean waiting time (5 minutes), σ is the standard deviation (3 minutes), and Z is the standardized variable.

To find the probability that a person will wait for more than 9 minutes, we need to find the area under the normal curve to the right of 9. We can do this by standardizing 9 using the formula above: Z = (9 - 5) / 3 = 1.33 .

We can use a standard normal table or a calculator to find the probability that Z is greater than 1.33. Using a calculator, we find that this probability is approximately 0.0912.

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Yes, Timothy is correct because triangle AKLM was dilated by using a scale factor of 1.5 centered at the origin.

In Mathematics, dilation can be defined as a type of transformation that is typically used for enlarging or reducing the size of a geometric object but not its shape, based on the scale factor.

For the given coordinates of the preimage triangle KLM, the dilation with a scale factor of 1.5 from the origin (0, 0) would be calculated as follows:

Coordinate K (-1, 3) → Coordinate K' (-1 × 1.5, 3 × 1.5) = Coordinate K' (-1.5, 4.5).

Coordinate L (8, 4) → Coordinate L' (8 × 1.5, 4 × 1.5) = Coordinate L' (12, 6).

Coordinate M (10, -3) → Coordinate M' (10 × 1.5, -3 × 1.5) = Coordinate M' (15, -4.5).

In conclusion, the coordinates of the image triangle K'L'M after a dilation with a scale factor of 1.5 from the origin are (-1.5, 4.5), (12, 6), and (15, -4.5) as shown in the graph above, therefore, Timothy is correct.

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Answer:

$120

Step-by-step explanation:

\(x - x * 0,6 = 48\\0,4x = 48 \\x = 120\)

The exact value of x (in ft) so that the greatest possible amount of light is admitted is 8.96 ft

According to the question,

A norman window has the shape of a rectangle surmounted by a semicircle.

Let The width of rectangle be x and height be y

It is given that  the diameter of the semicircle is equal to the width of the rectangle

Therefore , Diameter of circle = x

Radius = x/2

Perimeter of window  = 32 = Perimeter of rectangle + Perimeter of semi-circle

=> 32 = Width + 2height + πr

=> x + 2y + πx/2 = 32

=> 2x + 4y +  πx = 64

Solving for y,

=> 4y = 64 - 2x - πx

=> y = 64  - 2x - πx/ 4 ----------(1)

Area of the window = Area of rectangle + area of semi-circle

=> A = Width × hiegth +  πx²/8

=> A = xy + πx²/8

Substituting the value of y from equation (1)

=> A =  x (  64  - 2x - πx/ 4  ) + πx²/8

\(A = x ( \frac{64 - 2x -\pi x}{ 4} ) + \frac{\pi x^2}{8}\\A = ( \frac{ 64x - x^2 ( 2 + \pi)}{4 } ) + \frac{\pi x^2}{8}\)

Differentiating A w.r.t x

=> \(\frac{dA}{dx} = (\frac{64 - 2x(2 + \pi)}{4} ) + \frac{\pi x}{4}\)

Now , To find a maximum area

dA/dx = 0

=> \(\frac{dA}{dx} = (\frac{64 - 2x(2 + \pi)}{4} ) + \frac{\pi x}{4} = 0\)

Solving for x ,

64 - 4x - 2π + πx = 0

=> x = 64 / 4 + π ------(2)

Differentiating A again w.r.t x

=> d²A / dx² = -2(2 + π)/4 + π/4

=> -π+4 / 4 which is less than zero

Therefore,

Area is maximum when x = 64 / 4 + π

The exact value of x (in ft) so that the greatest possible amount of light is admitted is  8.96 ft

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Find line of aproximation to data

the regression data line gives as result

y = ax + b

a= 11.73

b= 193.85

The second and third are the transformation of the quadratic functions.

Given that,

In the picture there are 3 questions,

We have to identify the transformation of the quadratic function.

Transformation is nothing f(x) = x² is the quadratic family's parent function. The function g(x) = a(x - h)² + k, where a 0, is a modification of the parent function's graph.

The first quadratic function is f(x)=-(x+)³.

Here the quadratic function is not there the function is in cubic function.

So, the it is not a transformation.

The second quadratic function is g(x)=2/3x²+5

g(x)=2/3(x-0)²+5

This is in the form of function g(x) = a(x - h)² + k.

The quadratic function is a transformation.

The third is a graph.

The transformation is quadratic function when quadratic function shifts are represented graphically in both directions.

Therefore, the second and third are the transformation of the quadratic functions.

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Answer:

\(x^2 - 3x -10 = 0\)

Step-by-step explanation:

Given

Roots = -2 and 5

Required

Write the equation

We have that:

x = -2 and x = 5

Simplify further

x + 2 = 0 or x - 5 = 0

Multiply the results of the above

\((x + 2)(x - 5) = 0\)

Open brackets

\(x^2 + 2x - 5x -10 = 0\)

\(x^2 - 3x -10 = 0\)

Answer:

a) When y = -33,

=> -33 + (-14)

=> -33 - 14

=> -47

b) When y = 30,

=> 30 + (-14)

=> 30 - 14

=> 16

Answer:

1140 ways.

Step-by-step explanation:

The applicable formula is: (n +r - 1)C(r-1), where n is the number of identical items (the candies), and r is the possible number of recipients (the kids).

The 17 identical candies, can be distributed among the 4 children in :  

=(17 + 4 - 1)C(4–1) = 20C3 ways.

= 20!/((20–3)!*3!) ways.

= 20*19*18*17!/(17!*(3*2*1)) = 20*19*18/6 ways

= 20*19*3 ways.  

=1140 ways.

Step-by-step explanation:

length 'l' 2m=(2*100)cm

=200 cm

breadth 'b' =70cm

Area of rectangle =l*b

=200*70

=14000cm^2

Answer:

The warranty the company should use is of 57,520 mile.

Step-by-step explanation:

Let X denote the tread life of a particular brand of tire.

It is provided that,  \(X\sim N(60,000, 1600^{2})\).

Also provided that the company wants 94% of the tires to outlast the warranty.

Let x denote the warranty .

That is, P (X > x) = 0.94.

⇒ P (X < x) = 0.06

⇒ P (Z < z) = 0.06

The corresponding value of z is -1.55.

*Use a z-table.

Compute the value of x as follows:

\(z=\frac{X-\mu}{\sigma}\\\\-1.55=\frac{x-60000}{1600}\\\\x=60000-(1.55\times 1600)\\\\x=57520\)

Thus, the warranty the company should use is of 57,520 mile.

Answer: 90 degrees

Step-by-step explanation: A circle is 360 degrees so since that is 1/4 you can divide

360/4 = 90 (: hope this helps

Answer:

90* x 4 = 360*

360* / 4 = 90*

Step-by-step explanation:

A circle has 360* all around.

In the angle that was drawn, it is 90*

The degrees for the space outside of 90* is x

x = ?                360* - 90* = 280*                 x = 280*

hope this helped

Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

Answer:

To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:

r = (a/2) * cot(π/n)

where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.

In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:

6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)

36 = 50 - 50cos(x)

cos(x) = (50 - 36)/50

cos(x) = 0.28

x = cos^-1(0.28) ≈ 73.7°

Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:

(5/2)^2 + h^2 = 5^2

25/4 + h^2 = 25

h^2 = 75/4

h = sqrt(75)/2 = (5/2)sqrt(3)

Now we can find the radius of the inscribed circle using the formula:

r = (a/2) * cot(π/n)

where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:

r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm

Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.

So, the graph of f(x - 2) is just the graph of f(x) translated 2 units to the right.

Sadly we don't have the original function f(x), but we can answer in a general form.

Remember that for a general function f(x), a horizontal translation of N units can be written as:

g(x) = f(x + N).

So, the graph of f(x - 2) is just the graph of f(x) translated 2 units to the right.

So you need to resketch f(x), but just move it 2 units to the right side (positive x-axis side).

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the answer is 659 because if x = 5 that means 25x25 = 625

and if y = 2 then 625 + 52 = 677

and then 677-18 = 659

Problem solved

Cesar initially had $2,500 in savings.

Let's solve the problem step by step.

Let's assume that the initial amount of money Cesar had is represented by "x" dollars.

According to the problem, Cesar spent 15% of his savings on a cellphone, which means he has 85% of his initial savings left. We can represent this mathematically as:

0.85x = 2,125

To find the initial amount of money Cesar had, we need to solve for x. We can do this by dividing both sides of the equation by 0.85:

x = 2,125 / 0.85

Calculating this value:

x = 2,500

Cesar initially had $2,500 in savings.

Please note that the calculations are done assuming a straightforward interpretation of the problem. If there are additional factors or context that could affect the interpretation, it's important to consider them in order to arrive at an accurate answer.

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Answer:

Regular triangles or squares

Answer:

d

Step-by-step explanation:

Answer:

(3, 2)

Step-by-step explanation:

I will solve using the elimination method

 x + y = 5

- (x - y = 1)

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

       2y = 4

          y = 2

plug y = 2 into any equation and solve for x

x + 2 = 5

x = 3

(3, 2)

Answer:

For the x-axis:Time(minutes).

For the y-axis:Distance(m)

Step-by-step explanation:

Answer:

Nope-

Step-by-step explanation:

24x + 18 = 138

6 (4x + 2) = 132

Answer:

\(\huge\boxed{\overrightarrow{u}-\overrightarrow{v}=\left<-10;\ -3\right>}\)

Step-by-step explanation:

\(\overrightarrow{u}=\left<-8;\ 4\right>;\ \overrightarrow{v}=\left<2;\ 7\right>\\\\\overrightarrow{u}-\overrightarrow{v}=\left<-8;\ 4\right>-\left<2;\ 7\right>=\left<-8-2;\ 4-7\right>=\left<-10;\ -3\right>\)

Answer:

Step-by-step explanation:

-u-v = 6,-11

u-v = -10,-3

v-u = 10,3