ABCD is parallelogram. AED, CED and BCF are straight lines Find AED , DEF and CFE

Answer: 31, 33, 35

Step-by-step explanation:

The length of the shortest ladder is 16.64 ft.

In triangle ABC, using Pythagoras theorem

[tex]AC^{2} = AB^{2} + BC^{2}[/tex]  OR

[tex]L^{2} = h^{2} + (x+4)^{2}[/tex]       .....(1)

We also have similar triangles if we consider:

△ABC and △DEC

Which gives us the proportional relationship:

AB:DE = BC:EC

or    h/8 = (4+x) / x

h = 8( 4+x) /x      

Substituting this last expression for h into Eq [1] we get:

[tex]L^{2} = \frac{(8(x+4))^{2} }{x^{2} } + (x+4)^{2}[/tex]

Our aim is to now minimize L wrt x, and this involves looking for critical points of the derivative, so differentiation wrt x we get:

[tex]2L\frac{dL}{dx} = 2( 8 + \frac{32}{x} ) (-\frac{32}{x^{2} } ) + 2(x+4)[/tex]

At a critical point the derivative is zero and so we have the equation:

         =  [tex]2 (x + 4) ( 1 - \frac{256}{x^{3} } ) = 0[/tex]

From here we can find the value x :

x + 4 = 0                                                            1 - [tex]\frac{256}{x^{3} }[/tex]  = 0

x = -4                                                                 x  = [tex]\sqrt[3]{256}[/tex]

We require x > 0 so we neglect the -ve solution and only take +ve solution

therefore the minimum height of the ladder can be given by putting the value of x in eqn 1.

[tex]L^{2} = ( 8 + \frac{32}{\sqrt[3]{256} } )^{2} + ( \sqrt[3]{256} +4) ^{2}[/tex]

L² = 277.14

L = 16.64 ft

learn more about lagrange method here :

https://brainly.com/question/24208980

#SPJ4

In 286 ways are there to distribute seven identical apples and six identical pears to three distinct people.

There are 7 identical apples and 6 identical pears.

So total number of fruits here = 7+6 = 13 identical fruits

The number of ways to distribute 13 fruits in three distinct people is given by [tex]=^{13}C_3=286[/tex] ways.

Hence the number of ways is 286.

To know more about Combination refer to:

https://brainly.com/question/11732255

#SPJ4

Answer:

Step-by-step explanation:

You have two revenue relations and want the price of each adult and child ticket. 150 adult and 100 child tickets sold for $3087.50; 200 adult and 150 child tickets sold for $4287.50.

Each of the revenue relations can be formulated as an equation. If x and y represent the price of each adult and child ticket, respectively, then ...

  150x +100y = 3087.50

  200x +150y = 4287.50

The solution can be found many ways. A graphing calculator (first attachment) shows the solution to be ...

The calculator function that reduces a matrix to row-echelon form can be used on the augmented matrix of coefficients. That, too, gives the solution about as quickly as you can enter the coefficients. This is shown in the second attachment.

Subtracting twice the second equation from 3 times the first will eliminate the y-variable:

  3(150x +100y) -2(200x +150y) = 3(3087.50) -2(4287.50)

  50x = 687.50

  x = 13.75 . . . . . . divide by 50

From the second equation, ...

  y = (4287.50 -200(13.75))/150 = 1537.50/150

  y = 10.25

If a country's public debt in 2009 was $11,982,000,000,000 and its budget for 2010 was $101,347,000,000 in deficit, the public debt in 2010 is $12083347000000.

As given

if the public debt of a country in 2009 was $11,982,000,000,000 and the budget for 2010 was in deficit by $101,347,000,000 .

Total public debt in 2010 = Public debt in 2009 + Amount by which 2010 budget deficit .

= $ 11982000000000 + 101347000000

= $ 12083347000000

Therefore the public debt in 2010 is $12083347000000.

To learn more about public debt, refer to:

https://brainly.com/question/19572686

#SPJ13

Answer:

11.725

Step-by-step explanation:

Add all the numbers together and divide it by how many numbers are in the set

Answer:

64822

Step-by-step explanation:

Half-life model:

            [tex]P=P_o* \left(\frac{1}{2}\right)^{\frac{t}{D}}[/tex]

[tex]P_o[/tex] is the initial value, D is the time taken for the quantity to reduce half-life and t is the given time period.

       [tex]\sf P_o = 259,288 \ grams\\\\D = 1 \ hour\\\\t = 2 \ hours[/tex]

            [tex]P = 259,288*(\frac{1}{2})^\frac{2}{1}\\\\P = 259,288*(\frac{1}{2})^2\\\\P = 259,288*\frac{1}{4}\\\\P = 64822[/tex]

Answer:

       7 [tex]\frac{7}{8}[/tex]

Step-by-step explanation:

Multiply 3 1/2 by 2 1/4

Convert to improper fraction to make it simpler:

7/2 times 9/4 = 7 7/8 square millimeters.

Hope this helps :)

Answer:

Step-by-step explanation:

3.5 x 2.25 = 7.875 or 7 and 7/8

It can take 3 years that a physics major to spend doing post-graduate research

Given that,

A physics professor is curious about the proportion of physics majors who will pursue post-graduate study during the coming years. He has the probability distribution shown below. x P(x) x*P (x) 1 0.35 2 0.20 3 0.15 4 5 0.10 6 0.05

To find P(X<=3)

P(X<=3)=P(X=0,1,2,3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)

            = 0.35+0.20+0.15

            = 0.7

P(X<=3)=0.7

Hence, A physics major may need to spend three years conducting post-graduate research. and the probability that a physics major will spend no more than three years conducting post-graduate research is 70% or 0.7

Learn more about probability distribution :

brainly.com/question/14210034

#SPJ4

The ratio of c and 10 is c:10.

According to the question,

We have the following information:

We have one variable and one number which are c and 10 respectively.

Now, we already know that ratio can be simply understood as division. So, to find the ratio of c and 10 we will divide c by 10. We also know that a variable can not be divided by a number.

(For example, x can not be divided by 20.)

So, we will replace the sign of division by that of the ratio.

c/10

c:10

Hence, the ratio of c and 10 is c:10.

To know more about ratio here

https://brainly.com/question/13419413

#SPJ1

The value of the equation y(t) at y(25) is 150

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Equations can be linear, quadratic or polynomials.

if y(t) = -14t + 500

The y(25)  means substitute t = 25 into the equation

y(25) = -14(25) + 500

y(25) = -350 + 500

y(25) = 150

In conclusion, the value of y(25) is 150

Learn more about linear equations: https://brainly.com/question/14323743

#SPJ1

Answer: D

Step-by-step explanation:

Answer:

It would take them 13.5 days to raise enough money.

Step-by-step explanation:

In order to find the answer, you just have to take the amount of money they want to raise, which is $162, and divide it by the amount of money they save each day, or $12. In this case that would be dividing 162/12 giving you an answer of 13.5 days.

Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.

As given in the question,

Given equation is :

Original equation (1/2) + (1/2x) = (x² -7x +10)/4x

Simplify the original equation to get the equivalent equation

Least common multiple is 2 and 2x is equal to 2x

Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is Equivalent to the proportion is given by:

( x + 1) / 2x = (x² -7x +10)/4x

Therefore, original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.

Learn more about equivalent here

brainly.com/question/14672772

#SPJ1

The total number of students at library using part part whole model is 13.

What is part part whole model ?

  The idea that numbers may be divided into parts, often known as the part-whole model or part-part-whole reasoning, is one that can be used to the study of mathematics. The relationship between the entire number and its component components will be clear to children utilising this model, which will aid learners in connecting addition and subtraction.

Here Number of student who leave library = 6

Number of students who stay at library = 7

Here we have to take  Number of student who leave library as one part and Number of students who stay at library as another part . Then

Total number of students at library at start = 6+7 = 13.

The part part whole model like,

=>        Total = 13

Part=6              Part=7

Hence the Total number of students is 13.

To learn more about part part whole model

https://brainly.com/question/19786525

#SPJ13

Ana and Bonita were born nn year apart and its value of nn is 12.

Here we have to find nn which difference in the year in which Ana and Bonita were born.

Let x be the age of Ana and y be the age of Bonita.

It is given that last year Ana was 5 times as old as Bonita so from this statement we get the first equation:

x - 1 = 5(y -1)

x -1 = 5y - 5

5y -x = 4--------(1)

The second statement is Ana is square of Bonita's age. From this we get another equation:

x = y²-----------(2)

Putting equation 2 in equation 1 we get:

5y - y² = 4

y² - 5y +4 = 0

y² - 4y - y + 4 = 0

y(y-4) -1(y -4) = 0

(y - 4)(y -1) = 0

y = 4,1

As x = y²

x = 4² = 16 or x = 1² =1

We cannot take 1 as there is a difference in their age

So we get x = 16 and y =4

So the difference in their age = 16-4= 12

Therefore we get the value of nn as 12.

To know more about the age refer to the link given below:

https://brainly.com/question/1581212

#SPJ4

a) 90° counterclockwise about the origin

How can a rectangle be rotated?

A shape with rotational symmetry is a rectangle, for instance. When a rectangle is rotated around its center, the shape and placement remain unchanged. The placement of the specified points is the only distinction. Rectangles are of order 2 because they have half-turn symmetry.

When rectangle ABCD is rotated 90° counterclockwise about the origin , the vertex of 'A' in rectangle ABCD is (2,1) becomes (-1,2) in rectangle A'B'C'D'.

Therefore when rectangle ABCD is rotated we get rectangle A'B'C'D'.

To learn more about  a rectangle be rotated from the given link

https://brainly.com/question/9604569

#SPJ13

Answer:

1. 10

Step-by-step explanation:

1. 20% of 50

[tex] \frac{20}{100} \: \: \: \times \: \: \: 50 \\[/tex]

=

[tex] \frac{1000}{100} [/tex]

= 10

Answer:

23%

Step-by-step explanation:

We can create two equations:

\[m = \frac{1}{5}(A - s)\]\[s  = \frac{1}{20}(A - m)\]

Substituting we get:

\[m = \frac{1}{5}(A - \frac{1}{20}(A - m))\]which yields:

\[m = \frac{19}{99}A\]

Now we can find s and we get:

\[s = \frac{4}{99}A\]

Since we want to find what fraction of $A$ did Roger pay for his movie ticket and soda, we add $m$ and $s$ to get:

\[\frac{19}{99}A + \frac{4}{99}A \implies \boxed{\text{(D)}\ 23\%}\]

Assume the account pays a nominal annual interest of r% compounded quarterly, the value of the interest rate (r) is equal to 7.87%.

Mathematically, compound interest can be calculated by using this formula:

A(t) = P(1 + r/n)^{nt}

Where:

Substituting the given parameters into the formula, we have;

1.6(3,818) = 3,818(1 + r/8)^{8 × 6}

1.6 = (1 + r/8)^{48}

Taking the 48th root of both sides of the equation, we have:

[tex]\sqrt[48]{1.6} = \sqrt[48]{(1 + \frac{r}{8} )^{48} }[/tex]

1.00983983823726 = 1 + 0.125r

0.125r = 1.00983983823726 - 1

0.125r = 0.00983983823726

Interest rate, r = 0.00983983823726/0.125

Interest rate, r = 0.0787

Interest rate, r = 7.87%

Read more on interest rate here: https://brainly.com/question/26343258

#SPJ1

The converse statement is:

"If next month ends in the letter r, then this month is September."

And a counterexample of this is the month of September.

A conditional statement is of the form:

If P, then Q.

And a converse statement of the above one will be:

if Q, then P.

Here our conditional statement is:

"If this month is September, then next month ends in the letter r."

So we have:

P = this month is September.

Q = The next month ends in the letter r.

Replacing that in the converse statement formula we get:

"If next month ends in the letter r, then this month is September."

A counterexample is September, it ends with an r, and the month after it is not September.

Learn more about conditional statements:

https://brainly.com/question/11073037

#SPJ1

Answer:

If next month ends in the letter r, then this month is September. The converse is invalid; a counterexample is December.

The percentage increase in the area of the building from its initial space is 35% of the increase. Hence, option A is correct.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

As per the data provided in the question,

The initial area of the building = 12,500

Increase in area of building = 16875

The percentage increase in the area will be,

% increase = (16875 - 12500)/12500 ×100

⇒  4375/12500 × 100

% increase = 35%

To know more about Percentage:

https://brainly.com/question/29306119

#SPJ1

Answer:

1. 1

2. 1

Step-by-step explanation:

Step 1

recall the eqn of a line y = mx + c

where m is the slope

step 2

compare you eqn given with the eqn y = mx + c

y = mx + c

y = 1 x + 17

then m = 1 which is slope.

both qns follows the same procedure

The value of function is positive so the function have maximum value 30 at x=3.

In the given question we have to find the maximum or the minimum value of a function.

The given function is

f(x) = -3x^2+18x+3

To find the maximum or minimum value we firstly find the value of f'(x).

f'(x) = -6x+18

Now put f'(x)=0

-6x+18=0

Subtract 18 on both side we get

-6x=-18

Divide by -6 on both side we get

x = 3

Now finding the value of function at x=3

f(3)= -3*(3)^2+18*3+3

f(3)= -3*9+54+3

f(3)= -27+54+3

f(3)= 30

Since the value of function is positive so the function have maximum value 30 at x=3.

To learn more about maximim and minimum value of quadratic equation link is here

brainly.com/question/28769828

#SPJ1

The transformation of g(x) = 3(2)⁻ˣ+2   from the parent function f(x) = 2ˣ    will be carried out by reflecting f(x) across the y-axis, then stretching the graph of f(x) vertically by a factor of 3 and then shifting 2 units up,

What is a transformation function?

A function that transforms one function or graph into another, typically a related function or graph, is called a transformation function.

How to convert the parent function into the transformation function?

The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.

Here, we have

Transformation Function - g(x) = 3(2)⁻ˣ+2

Parent Function - f(x) = 2ˣ

To convert the parent function into the transformation function, we will follow some steps:

Hence, the transformation of g(x) = 3(2)⁻ˣ+2   from the parent function f(x) = 2ˣ   will be carried out by reflecting f(x) across the y-axis, then stretching the graph of f(x) vertically by a factor of 3 and then shifting 2 units up.

To learn more about the transformations from the given link

https://brainly.com/question/18433394

#SPJ1

Answer:

it is d

Step-by-step explanation:

Answer: Down Below ↓

Step-by-step explanation: Here's an easy tip for measuring the angles of triangles. Every triangle has a sum (total) of 180 degrees. Take the two angles that are already shown, add them together, then subtract them from 180.

I cannot read the numbers on the paper, so I hope this answer somewhat helps.

Edit: Oh my lord, it's a coloring page too? I remember those, they suck. :')

The equations that are  quadratic in form are:

x4 – 6x2 – 27 = 0

6(2x + 4)2 = (2x + 4) + 2

6x4 = -x2 + 5

The concept that is been used here is quadratic functions which can be written in three ways  :

Where  vertical line x = h and a not equal to zero, Hence we can see that the three selected options above followed the concept that is decribed as the quadratic function.

Therefore, the first, fourth and fifth options are correct.

Read more about  quadratic at:

https://brainly.com/question/1560261

#SPJ1

Answer:

A, D, E

Step-by-step explanation:

125° is the  angle of CBD

An angle pair that forms a straight line is referred to as a straight angle pair. This pair's sum of any two or more angles is always equal to 180°.

A straight angle has a 180° angle.

The two angles are from a straight line, and they sum to 180 degrees.

A + B + C = 180

8x -41+ 9x+17 = 180

Conjoin similar terms

17x -24 = 180

24 more on each side

17x -24+24 = 180 +24

17x = 204

multiply by 17

17x/17 = 204/17

x =12

We desire CBD angled.

CBD = 9x+17

= 9*12+17=108+17

= 125

To learn more about Straight angle refer to:

brainly.com/question/24024505

#SPJ1