Complete the factor tree for 1,575.
Press each hotspot
Label the corresponding number below with the requested factor.

in order to find the shorter side of a golden rectangle we need to divide 13

by 1.6180.

A golden rectangle is a rectangle in geometry whose side lengths are in the golden ratio, or display style 1:tfrac 1+sqrt 5 2 which is display style 1:varphi 1:varphi (the Greek letter phi), where display style var phi var phi is roughly 1.618.

All rectangles made by including or excluding a square from one end are also golden rectangle, which is a unique example of self-similarity.

Length of longer side a = 13

let the length of shorter side is b.

them by the property of golden rectangle,

a : b = 1: (1+sqrt 5)/2

by substitution method

13 : b = 1 : (1+sqrt 5)/2

b = 8.034

so to get the length of shorter side we need to divide by 1.6180

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Answer:

46.2%

Step-by-step explanation:

6 divided by 13 multiplied by 100. rounded up

Answer: You draw the shape on the coordinate plan and then you can count the number of unit squares

Step-by-step explanation:

The change in the price from Monday to Friday is $0.75

The graph that completes the question is added as an attachment

From the attachment, we have:

Monday = $0.75

Friday = $1.50

There are 5 days between Monday and Friday

So, we have the change in the price from Monday to Friday to be

Change = Friday - Monday

This gives

Change = $1.50 - $0.75

Evaluate

Change = $0.75

Hence, the change in the price from Monday to Friday is $0.75

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y = -8.

An ordered pair is a composition of the x coordinate and the y coordinate, having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane for better visual comprehension.

Ordered pairs are often used to represent two variables. When we write (x, y) = (7, - 2), we mean x = 7 and y = - 2. The number which corresponds to the value of x is called the x-coordinate and the number which corresponds to the value of y is called the y-coordinate.

see attachment for the table

we observe from the given table that

As x increases by 2, y decreases by 4

As x decreases by 2, y increases by 4

for example x = 10, y = -12

when x decreases by 2 (to 8), the value of y will increase by 4 (to -8).

Hence, the value of y when x = 8 is -8

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Answer:

Given y = 0,

[tex]\sf 4(6y+1)\\4(6* 0+1)\\(6 * 0 + 1)\\(6 * 0)\\= 0\\= 0 + 1\\= 1\\= 1 * 4\\= 4[/tex]

Thus, the answer is 4.

Hence , the graph of the equation is y = 1.5 sin(x - 2π/3) + 3 is given below .

The general form of a sine function is of the form:

y = a×sin(bx − c) + d,

here the amplitude is a,

the period is 2π/|b|,

the phase shift is c/b, and

the vertical shift is d.

From the given equation we have,

The amplitude, a = 1.5

The period, = 2π/|1| = 2π

The phase shift = (2π/3)/1 = 2π/3

And the vertical shift is d = 2

The given equation can be graphed using the amplitude, period, phase shift, vertical shift, and points.

Refer to the attached image(table) for the points to plot the graph.

Refer to the attached image(sine_graph) for the graph of this equation.

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Disclaimer:

The question is not complete.

Assume the following to answer this question.

Graph of the equation: y = 1.5 sin(x - 2π/3) + 3

Answer:

Step-by-step explanation:

Given two points on the linear toll function T(d) are (20, 119) and (33, 184), you want the equation for the function T(d), and the value of T(96).

It is usually convenient to write the equation of a line in slope-intercept form when you want to find the value at a particular point. To use that form, we need to know the slope of the line. It is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

Using the given points, we have ...

  m = (184 -119)/(33 -20) = 65/13 = 5

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

Using the first point and the slope we found, the equation is ...

  y -119 = 5(x -20)

Solving the above equation for y, we get ...

  y = 5x -100 +119 . . . . . . . simplify, add 119

  y = 5x +19 . . . . . . . . . . combine terms

Using variables d and T instead of x and y, the function is ...

  T(d) = 5d +19

The value T(96) is ...

  T(96) = 5(96) +19 = 480 +19 = 499

The toll for 96 miles is 499 cents.

Answer:

249798.8

Hope this helps! <3

Answer:

Step-by-step explanation:

639÷0.3=

2130

the answer is

639÷0.3=

2130

Answer:

5/6*5/3

25/18

so the answer is 25/18

Number of households only own one or more DVD players = 219

Total number of households considered for the survey = 400

Let n(A) represent the number of households only own one or more HDTVs.

Then n(A) = 315

Let n(B) denotes the number of households only own one or more DVD players. We need to find n(B).

Number of households own one or more HDTVs and one or more DVD players, n(A∩B) = 150

Number of households do not own an HDTV or a DVD player = 16

So the number of households which own an HDTV or a DVD player, n(A∪B) = 400 - 16 = 384

Then we have the formula relating n(A∪B), n(A), n(B) and n(A∩B).

n(A∪B) = n(A) + n(B) - n(A∩B)

⇒ n(B) = n(A∪B) - n(A) + n(A∩B)

           = 384 - 315 + 150

           = 219

The number of households only own one or more DVD players = 219

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Answer:

  (d)  519

Step-by-step explanation:

You want the ratio of (7.785×10^10) to (1.5×10^8) expressed in standard form.

Since you want the result in standard form, it can work well to make the numerator and denominator powers of ten be the same.

  [tex]\dfrac{7.785\times10^{10}}{1.5\times10^8}=\dfrac{7785\times10^7}{15\times10^7}=\dfrac{7785}{15}=\boxed{519}[/tex]

The linear equation with  the given information is

2y+2 = 3x+18

Given :

The slope of Parallel Lines:

Slopes of parallel lines are equal. The parallel lines are equally inclined with the positive x-axis and hence the slope of parallel lines is equal. If the slopes of two parallel lines are represented as m1, m2 then we have

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.

The net change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx.

Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,

m = change in y/change in x = Δy/Δx

Where “m” is the slope of a line.

The slope of the line can also be represented by

tan θ = Δy/Δx

So, tan θ to be the slope of a line.

Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ‘m’

m1 = m2.

y 2/3 = x + 1 ...1

2y = 3x+3

y = 3/2x +3/2

m1= 3/2

x,y = -6,-1

y = mx +b

(y-y1 ) =m (x-x1) +b

m1=m2

m2= 3/2

(y +1) = 3/2 (x+6)

2(y+1 )= 3x+18

the equation of the line that is parallel to y 2/3 = x + 1 and passes through the point (–6, –1) = 2y+2 = 3x+18

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Answer:

100,000

Step-by-step explanation:

Multiply 10 by 10 by 10 by 10 by 10 to get 100000

The solution of the given equation  y ==2x² - 24r – 56​ :

(6 , -128)

Graph technology aids in the discovery of unknown links in data that cannot be detected or examined using traditional methods. When the broad term graph is introduced as both a topic, it frequently blurs three distinct topics: graph theory, graph analytics, and graph data management.

Graphs and charts are useful visual tools because they deliver information quickly and readily. It is hardly surprising, then, that graphs are widely utilized in print and electronic media. Data can be easier understood when displayed as a graph rather than a table since the graph can illustrate a pattern or comparison.

y =2x² - 24x – 56​

Solving for :

Parabola equation in polynomial form

ax² + bx + c  for x = -b/(2a)

a = 2

b = -24

c = -56.

on solving we get

= -(- 24)/2* 2

= 6

The value of x = 6

putting the value of x to get y:

2x² - 24x – 56​

2(6)² - 24(6) – 56​

-128

the value of y = -128.

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Answer:

  x = 11°

Step-by-step explanation:

You want to know the value of x given a triangle with exterior angles 147°, 4x, and an interior angle of x at the third vertex.

The exterior angle of the triangle at B is the supplement of x: 180°-x. The sum of the exterior angles of a polygon is 360°, so we have ...

  147° +4x +180° -x = 360°

Collecting terms, we have ...

  327° +3x = 360°

  3x = 33° . . . . . . . . . subtract 327°

  x = 11° . . . . . . . . . . divide by x

Mean = 20; standard deviation = 4;

Let x be the success of receiving the right response.

The total number of trials in this case is 100.

The likelihood of receiving the right response is p = 1/5.

In light of the average number of correct answer;

μₓ = np

μₓ = 100 * (1/5);

μₓ = 20;

The standard deviation is now; σ = √(n)(p)(1 - p)

                                                    σ = √(100)(1/5)(4/5)

                                                   σ  = 4

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Answer:

To set up an equation, you must first see what the question is looking for.

Hope this helps :)

Answer:

Determine what the question is asking. Write down the relevant information in simple statements. Assign symbols to unknown values that need to be found. Determine how the statements relate to each other mathematically.

Step-by-step explanation:

Answer:

go get smart and stop cheating on online websites

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the difference between 8.72 and 0.872. This just means to subtract 0.872 from 8.72. [tex]8.72-0.872=7.848[/tex]

Answer:

98

Step-by-step explanation:

For every 1 true or false question, there are 2 answers

so that means, it would mean you could do

7 x 7 = 49

then do 49 x 2 =

98

the reason you would do this is that you want to find all the possible answers chances.

Answer:

D [tex]y = - \frac{1}{4} x - \frac{1}{4} [/tex]

Step-by-step explanation:

a. The weight of a particular crate such that the probability of randomly selecting a heavier crate is 0.05 is 16.30kg.

b. The probability that a randomly selected crate will weigh more than 16kg is 0.0764.

c. The probability that.at least 2 of them will weigh more than 16kg is 0.4584.

a. From the information, there is a mean of 14 kg and a standard deviation of 1.4 kg. The weight will be:

Let the weight = x

X = (Z × mean × standard deviation)

= (1.645 × 1.4 ×14)

= 16.30kg

b. The probability that a randomly selected crate will weigh more than 16kg will be:

P(z > 16)

= P(Z > 16-14/1.40)

= P(Z > 1.43)

Looking under the normal distribution table, the value is 0.0764.

c. The probability that at least 2 of them will weigh more than 16kg when 20 crates are randomly and independently selected will be through binomial distribution where n = 20 and p = 0.0764.

This will give a value of:

= 1 - 0.5416

= 0.4584

Therefore, the probability that.at least 2 of them will weigh more than 16kg is 0.4584.

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Answer:

-7+5 >2

-7+5=2

collect like terms

-7 =2-5

-7 = -3

Answer:30

Step-by-step explanation:

30+30+30+30 just do 120/4

Answer:

1-13 and 2-13 and 4-13 because if you add them that is the answer

The area of the regular pentagon is 60 square units

The given parameters are

Radius, r = 5 units

Side length, l = 6 units

The area of the pentagon is calculated as

A = 1/4√[25 + 10√5] * l^2

Substitute 6 for l in the above equation

So, we have

A = 1/4√[25 + 10√5] * 6^2

Evaluate the product

A = 60 (approximated)

Hence, the area of the regular pentagon is 60 square units

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