Given that the following two triangles are similar find x

Answer:

4 : 25

Step-by-step explanation:

given 2 similar figures with linear ratio a : b , then

ratio of areas = a² : b²

here the linear ratio = 2 : 5 , then

area ratio = 2² : 5² = 4 : 25

By 15% percent does the population of weeds decrease each day given that the function representing the number of weeds is W(d)=1650(0.85)^d. This can be obtained by using the function representing the exponential decay.

Number of weeds is represented by the function,

W(d)=1650(0.85)^d

⇒ W(d)=1650(1 - 0.15)^d

Here, d = number of days since application

Function representing the exponential decay is,

⇒ A(r) = A(1 - r)^t

where,

A = Initial value

r = Percentage decay

t = duration

By comparing the given function and function representing the exponential decay,

r = 0.15 ≈ 15/100

Or r = 15%    

Therefore, population of weeds will decrease 15% each day.

Hence by 15% percent does the population of weeds decrease each day given that the function representing the number of weeds is W(d)=1650(0.85)^d.

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If the data is symmetrical, then the mean is the best measure of central tendency to use, and the standard deviation is the best spread to use.

If the data is asymmetrical, the median is the best measure of central tendency to use, and the inter-quarterly range is the best spread to use.

A histogram for symmetrical data will give a symmetrical shape, and the mean, median and mode will all be the same value. Therefore, the best measure of the central tendency to use is the mean. The standard deviation shows how far away the values in a given data set are from the mean, and since the mean is used as the measure of central tendency in this case, the standard deviation should be used as the spread.

A histogram for a an asymmetric data set will give an asymmetric shape, and the mean is not always equal to the median. Therefore, the best measure of central tendency to use is the median. The inter-quarterly range shows the range of the middle 50% of a certain data, which is considered from the median value. Since the median is used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.

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Answer:

(0, -5/2).

Step-by-step explanation:

The coordinates of the mid point of (x1, y1) and (x2, y2) are

(x 1 + x2)/2 , (y1 + y2)/ 2

So here we have:

(-3 + 3)/ 2, (-4 + -1)/2

= 0/2, -5/2

= (0, -5/2).

Answer:

Step-by-step explanation:

Comment

The semicircle comes out towards we the viewer, then it goes upwards, and what one gets is 1/2 a sphere. If one keeps on rotating in the direction of the arrow eventually winding up where one started, the result is a full sphere.

Answer: Sphere

Inverse variation is the relationship that occurs between two quantities in which one decreases as the other increases.

The types of variation which exists are;

For instance;

The relationship between John's speed and distance is inversely proportional. If John's speed is 5km/h, his distance is 6km. Find John's distance when his speed increases to 6km/h.

s = k / d

where,

k = constant of proportionality

s = k / d

5 = k/6

30 = k

s = k / d

6 = 30/d

6d = 30

d = 30/6

d = 5 km

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Answer:

11/24 ths each

Step-by-step explanation:

Add the portions left...then divide by the five of them

3/4 + 5/8 + 11/12  = ?      must find common denominator (24) and convert

(18 + 15+22) / 24 = 55/24  now divide by 5 (which is the same as mult by 1/5)

55/24 * 1/5 = 55/120     now simplify to 11/24

Answer:

$279.25

Step-by-step explanation:

Multiply 6.50x43

[tex]w = 279.50 + (0.5 \times 6.50) \times (43 - 40)[/tex]

Multiply 0.5x6.50

[tex]w = 279.50 + 3.250 \times (43 - 40)[/tex]

Add 43-40

[tex]w = 279.50 + 3.250 \times 3[/tex]

Multiply 3.250x3

[tex]w = 279.50+ 9.750[/tex]

Solution

Answer: Reagan's pay was increased by 62%

Step-by-step explanation:

First, lets find the difference between the two pays:

$347,247 - $214,350 = $132,897

Let 214350 = 100%

Dividing 132,897 by 214350 to find the percent increase

[tex]\bold{\frac{132,897}{214,350} }=0.62\times100=62[/tex]

Therefore, Reagan's pay was increased by 62%

The given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.

In the question, we are asked to show that x.cosec²x = cot x - d/dx x.cot x.

To prove, we go by the right-hand side of the equation:

cot x - d/dx x.cot x.

We solve the differential d/dx using the product rule, according to which, d/dx uv = u. d/dx(v) + v. d/dx(u), where u and v are functions of x.

cot x - {x. d/dx(cot x) + cot x. d/dx(x)}

= cot x - {x. (-cosec²x) + cot x} {Since, d/dx(cot x) = -cosec²x, and d/dx(x) = 1}

= cot x + x. cosec²x - cot x

= x. cosec²x

= The left-hand side of the equation.

Thus, the given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.

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Answer:

12.8 km

Step-by-step explanation:

each mile has 1.6 km in it so in order to find the total distance in km we need to multiply the miles by 1.6= 8 miles x 1.6 =12.8 km

Answer:

see explanation

Step-by-step explanation:

(a)

let the two consecutive odd integers ne n and n + 2 , then

n + 2(n + 2) = 85

n + 2n + 4 = 85

3n + 4 = 85 ( subtract 4 from both sides )

3n = 81 ( divide both sides by 3 )

n = 27

n + 2 = 27 + 2 = 29

the 2 consecutive odd integers are 27 and 29

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

(b)

let the first integer be n , then 2nd integer is 3n and 3rd is 3n + 5 , so

n + 3n + 3n + 5 = 40

7n + 5 = 40 ( subtract 5 from both sides )

7n = 35 ( divide both sides by 7 )

n = 5

3n = 3 × 5 = 15

3n + 5 = 15 + 5 = 20

the 3 integers are 5, 15, 20

Answer:

4 is correct answer.

Step-by-step explanation:

That because it contains property of communicative. That is a×b=b×a.

The distributive Property States that when a factor exists multiplied by the sum/addition of two terms, it exists critical to multiply each of the two numbers by the factor, and eventually complete the addition operation.

Let the expression be 4+(6+8u)

4 + (6 + 8u) = (4 + 6) + 8u

The distributive Property States that when a factor exists multiplied by the sum/addition of two terms, it exists critical to multiply each of the two numbers by the factor, and eventually complete the addition operation.

Adding (distributing) the first numbers of each set, outer numbers of each set, inner numbers of each set, and the last numbers of each set. Combine like terms. Solve the equation and simplify, if needed.

The expression be 4+(6+8u)

4+(6+8u) = (4 + 6)+8u

Therefore, the correct answer is distributive property.

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Answer:

Step-by-step explanation:

The answer is 114.5%.

Let the original population be denoted by x.

Now, let's go through the percentage increase per year.

Year 1

Year 2

Year 3

Year 4

Overall increase : 214.5% - 100% = 114.5%

Hence, the overall percentage increase in these 4 years is 114.5%.

she should use 2 by 6

Step-by-step explanation:

2 divided by 6 will give 0.3 in 1d.p

Answer: А=480.

Step-by-step explanation:

Using proportions, it is found that the work required to compress the spring an additional one-half inch is of 1.0625 ft-lb.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

For 4 inches, 8.5 ft-lb of work is needed, hence for a single inch the amount needed is:

8.5/4  = 2.125.

Hence for half an inch, the amount if:

0.5 x 2.125 = 1.0625 ft-lb.

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Answer:

$63.36

Step-by-step explanation:

The home audio system costs $264 wholesale.

The system's price had been increased by 60 percent at the electronics retailer.

Consequently, the increased cost is 60/100x264=$158.40.

The audio system's total cost is now $422.40 (264 + 158.40).

Given that Lori received a commission of = 15% on $422.40, her commission is now (15/100) x 422.40

= $63.36

Answer:

You can count how many boxes that are not shaded to find how many eggs were not used, but that's to find out the fraction

Step-by-step explanation:

Count the boxes total in the grid. then count the number of boxes were not shaded. the number of total boxes is your denominator, and the number of boxes thar aren't shaded is your numerator.

I think...

The value of angle x of the given cyclic segment is; 49.5°

We are given the measure of the angle of  arc QS as (4x – 18)°

Now, to find the measure of arc QS, this angle is to be equal to 180° and as such;

Thus;

(4x – 18)° = 180°

4x - 18 = 180

4x = 180 + 18

4x = 198

x = 198/4

x = 49.5°

The angle subtended by the arc at the center of a circle with center C is the angle of the arc. It is denoted by. m AB, where A and B are the endpoints of the arc. With the help of the arc length formula, we can find the measure of arc angle.

The formula to measure the length of the arc is;

Arc Length Formula (if angle θ is in degrees); s = 2πr (θ/360°)

Arc Length Formula (if θ is in radians) s = ϴ × r.

Thus, the value of x of the given cyclic segment is; 49.5°

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The equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)

Herein we have a representation of an ellipse in the image attached aside, ellipses are characterized by the following standard formula:

(x - h)² / a² + (y - k)² / b² = 1     (1)

Where:

Please notice that ellipse will be vertical if b > a, otherwise it will be horizontal. The graph exhibits a vertical ellipse centered at the origin and therefore we conclude that (h, k) = (0, 0) and b > a (b = 10, a = 2). Finally, the equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)

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The value of output, h, when the input, x, is -18 for the given equation is 14

From the given question, we are to determine the value of the output, h, when the input x is -18

The given equation written properly is

h = 17 + x/6

Now, to determine the value of output, h, we will put in the value of x into the equation

h= 17 + x/6

The given value of x is -18

Thus, putting the given value of x into the equation, we get

h= 17 + x/6

h= 17 + -18/6

h = 17 + -3

h = 17 - 3

NOTE: + × - = -

h = 14

∴ h is 14 when x is -18

Hence, the value of output, h, when the input, x, is -18 for the given equation is 14

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Answer: A: y= 3x + 3

Step-by-step explanation:

The y intercept has to be 3 which is found when x = 0 that eliminates B and C. Then just plug in -1 or 1 into A or D and you will find that plugging in either with get you the y value provided on A.

(a) The velocity when the particle reaches B is 8 m/s.

(b) The distance between point A and B is 5.33 m.

(c) The value of t when the particle reaches C is 1.63 seconds.

(d) The distance AC​ is 8.7 m.

The velocity when the particle reaches B is calculated as follows;

v = ∫a. dt

where;

v =  ∫(4t . dt)

v = 4t²/2

v = 2t²

v(2) = 2(2)²

v(2) = 8 m/s

Thus, the velocity when the particle reaches B is 8 m/s.

x = ∫v

where;

x = ∫2t². dx

x = ²/₃t³

x(2) = ²/₃(2)³

x(2) = 5.33 m

Thus, the distance between point A and B is 5.33 m.

when the particle reaches point C, final velocity, vf = 0

vf = v + at

where;

0 = 8 - 3t(t)

0 = 8 - 3t²

3t² = 8

t² = 8/3

t² = 2.67

t = √(2.67)

t = 1.63 seconds

x = ∫vf

x = ∫(8 - 3t²)

x = 8t  - t³

x(1.63) = 8(1.63) - (1.63)³

x(1.63) = 8.7 m

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