someone please solve this

Drop a perpendicular from [tex]\overline{AK}[/tex] to $\overline {DE}$.

Let $l(AK)=h$ and $l(AB)=l(DC)=L$

$h$ is the height of the parallelogram and the triangle.

$L$ is the length of the base of the triangle and one of the sides of parallelogram.

We have area of parallelogram $=A_{para}=hL$

And the area of triangle is:

$A_{tria}=\frac{1}{2} h\times (L+L)=hL$

Thus we can see that they are equal.

Answer:

See below

Step-by-step explanation:

Given:

ABCD is a parallelogram

DC = CE

To Prove:

area of the ADE triangle is equal to the area of the parallelogram​.

Proof:

Let The Point between B and C be F

To prove that area of the ADE triangle is equal to the area of the parallelogram​, we'll first prove that ΔADF ≅ ΔECF

Statements                             |               Reason

DC ≅ CE                                  |                Given

But,  CD ≅ AB                         |    Opposite sides of a ║gm

So,  CE ≅ AB                           |   Transitive Property of Equality

∵  ΔABF ↔ ΔECF                    |

 CE ≅ AB                                |       Already Proved

  ∠CFE ≅ ∠ BFE                     |       Vertical Angles

  ∠ECF ≅ ∠ABF                      |      Alternate Angles

So, ΔABF ≅ ΔECF                   |    S.A.A.  Postulate

Now,                                         |

Area of ║gm = Area of            |

quad ADCF + ΔABF                |

But,    ΔABF ≅ ΔECF               |        Already Proved

So,                                            |

Area of ║gm = Area of            |

quad ABCF + ΔECF                 |

But Area of ΔADE = Area of   |

quad ABCF + ΔECF                 |

So,                                            |

Area of ║gm = Area of ΔADE |     Hence Proved

Answer:

The total number of trout in the lake is 760.

Step-by-step explanation:

We are given that Raglan's Trout Sanctuary catch a sample of 95 trout and tag them. They then release these trout.

The next day they catch another sample of 64 trout and find 8 of these trout had been tagged the previous day.

Let the total number of trout in the lake be 'N'.

Number of trout caught and tagged = 95

Number of trout caught on next day = 64

Number of trout that were tagged the previous day = 8

This situation can be represented through the following ratio;

[tex]\frac{\text{Total number of trout}}{\text{Trout that were tagged}}= \frac{\text{ Number of trout caught }}{\text{Trout that were tagged}}[/tex]

[tex]\frac{\text{N}}{95} = \frac{64}{8}[/tex]

[tex]\frac{\text{N}}{95} = 8[/tex]

[tex]\text{N} = 8 \times 95[/tex] = 760

Hence, the total number of trout in the lake is 760.

Answer:

Step-by-step explanation:

7 + 3i / 2 - 5i would be clearer if written as (7 + 3i) / (2 - 5i).  We must remove the symbol i from the denominator, and that can be accomplished by multiplying both 7 + 3i and 2 - 5i by the conjugate 2 + 5i:

(2 + 5i)(7 + 3i)

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

     4 + 29

which simplifies to     14 + 6i + 35i - 15 over 33, or

-1 + 41i

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

    33

Answer:

Step-by-step explanation:

The relation describe in the table Continuous .

The domain of the relation is X- values greater than or equal to 0 .

The range of the. Relation is Y- values greater than or equal to 0

Answer:

The relation described in the table is  continuous

The domain of the relation is   x-values greater than or equal to 0

The range of the relation is  y-values greater than or equal to 0

Step-by-step explanation:

Any number of pounds of almonds can be purchased, including partial amounts, so the relation described in the table is continuous.

Because x can be any positive number of pounds, the domain of the relation is x ≥ 0, or x-values greater than or equal to 0.

Because y can be any positive dollar amount, the range of the relation is y ≥ 0, or y-values greater than or equal to 0.

The number of possible outcomes there could be at the end of their game is 6 outcomes

This is a permutation problem since it required arrangement

If Alex, Toby, and Samuel are playing a game together and at the end, they will make a classification with one of them in first  place, one of them in Second place and one of them in Third place, this can be done in 3! ways

Since n! = n(n-1)(n-2)!

Hence 3! = 3(3-1)(3-2)

3! = 3 * 2 * 1

3! = 6 ways

Hence the number of possible outcomes there could be at the end of their game is 6 outcomes

Learn more here: https://brainly.com/question/24115376

Answer:

C

Step-by-step explanation:

It is an iscoceles triangle because there are 180 degrees in a triangle and the right angle plus the 45 degree equals 135 and 180 minus 135 is 45.

Since it is an iscoceles triangle that means that n = 3 and the pythagorean theorom says that a^2 + b^2 = c^2 which means that m = 3^2 plus 3^2 with a root.

3^2 is 9 so you get 18

the root of 18 is infinite, however can be simplified to 3 root to 2 because 3 times 3 equals 9 times 2 equals a root of 18

Hope this helps!

Answer:

Greater than the original = 2, 4

Less than the original = 5

Same as the original = 1, 3

Step-by-step explanation:

Let the original value be x.

1. A $30 increase followed by a $30 decrease.

New value [tex]=x+30-30=x[/tex], it is same as original value.

2. A 20% decrease followed by a 40% increase.

Afer 20% decrease.

New value [tex]=x-\dfrac{20}{100}x=x-0.2x=0.8x[/tex]

Afer 40% increase.

New value [tex]=0.8x+\dfrac{40}{100}(0.8x)=0.8x+0.32x=1.12x[/tex], it is greater than original value.

Similarly check the other values.

3. A 100% increase followed by a 50% decrease.

New value [tex]=x+\dfrac{100}{100}x-\dfrac{50}{100}(x+x)=x[/tex], it is same as original value.

4. A 75% increase followed by a 33% decrease

New value [tex]=x+\dfrac{75}{100}x-\dfrac{33}{100}(x+0.75x)=1.1725x[/tex], it is greater than the original value.

5. 55% decrease followed by a 25% increase

New value [tex]=x-\dfrac{55}{100}x+\dfrac{25}{100}(x-0.55x)=0.5625x[/tex], it is less than the original value.

Therefore, Greater than the original = 2, 4, Less than the original = 5, Same as the original = 1, 3 .

A 100% increase followed by a 50% decrease

A $30 increase followed by a $30 decrease

55% decrease followed by a 25% increase

A 20% decrease followed by a 40% increase

A 75% increase followed by a 33 1/3% decrease

Answer:

The correct statements are:

1: mEFD = mEGD

3: mED = mFD

5: mFD = 120°

Step-by-step explanation:

Let's analyse each statement:

1: mEFD = mEGD

Let's find the value of the angle ECD, using the sum of the internal angles of a quadrilateral:

[tex]60 + 90 + 90 + mECD = 360[/tex]

[tex]mECD = 120\°[/tex]

The angle ECD is a central angle, related to the arc ED, so the arc ED also has 120°.

The angle EFD inscribes the arc ED, so we have:

[tex]mEFD = mED/2[/tex]

[tex]mEFD = 120/2 = 60\°[/tex]

So the angles mEFD and mEGD are equal. The statement is TRUE.

2. mEGD = mECD

This statement is FALSE, because mEGD = 60° and mECD = 120°

3. mED = mFD

If mED is 120° and mEF = mFD, we have:

[tex]mED + mEF + mFD = 360[/tex]

[tex]2*mFD = 360 - 120[/tex]

[tex]mFD = 120\°[/tex]

So the statement is TRUE, both arcs have 120°.

4. mEF = 60°

This statement is FALSE, because we calculated before that mEF = mFD = 120°

5. mFD = 120°

This statemente is TRUE, because we calculated before that mFD = 120°.

So the correct statements are 1, 3 and 5

The true statements are: [tex]\angle EFD =\angle EGD[/tex], [tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex]

Start by calculating the measure of angle ECD.

We have:

[tex]\angle ECD = 2 * \angle EGD[/tex]

So, we have:

[tex]\angle ECD = 2 * 60[/tex]

[tex]\angle ECD = 120[/tex]

The above means that:

[tex]\overset{\huge\frown}{ED} = 120[/tex]

So, the measure of angle EFD is:

[tex]\angle EFD = 0.5 * \overset{\huge\frown}{ED}[/tex]

[tex]\angle EFD = 0.5 * 120[/tex]

[tex]\angle EFD = 60[/tex]

From the question, we have:

[tex]\angle EGD = 60[/tex]

So, it is true that:

[tex]\angle EFD =\angle EGD[/tex]

To calculate the measure of arc FD, we have:

[tex]\overset{\huge\frown}{FD} + \overset{\huge\frown}{DE} + \overset{\huge\frown}{EF} =360[/tex]

Lengths EF and DE are congruent.

So, we have:

[tex]2\overset{\huge\frown}{FD} + \overset{\huge\frown}{DE} =360[/tex]

[tex]\overset{\huge\frown}{DE} = \overset{\huge\frown}{ED} = 120[/tex]

So, we have:

[tex]2\overset{\huge\frown}{FD} + 120 =360[/tex]

Divide through by 2

[tex]\overset{\huge\frown}{FD} + 60 =180[/tex]

Subtract 60 from both sides

[tex]\overset{\huge\frown}{FD} =120[/tex]

This means that:

[tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex] are true

Hence, the true statements are: [tex]\angle EFD =\angle EGD[/tex], [tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex]

Read more about cyclic theorems at:

https://brainly.com/question/26168678

Answer:

Reflect the points across the y-axis and then translate them 7 units down.

Step-by-step explanation:

Let's look at Points A and A''. We notice that to transform A into A'', we need to reflect the point across the y-axis and then translate it down 7 units. We know this because 3 and -3 are opposite numbers are 8 - 7 = 1.

Answer:

D

Step-by-step explanation:

The points The points

A (3, 8),

B (6, 8),

C (6, 3),

D (5, 3)

need to be transformed to points

A'' (–3, 1),

B'' (–6, 1),

C'' (–6, –4),

D'' (–5, –4).

What transformations are made to make Building 4?

Answer:

here, 1m= 39.37 inches

or, 39.37 inches =1m

or, 3000 inches = 3000÷39.37 m

therefore, the measurement in m is 76.20015 m

hope it will help uh..

Answer: draw a straight line trough point B, same thing with the second one,for the third you must draw a straight line from the angle across to the segment. (make sure all of the intersections are 90 degrees

Answer:

25 and 1/6

Step-by-step explanation:

Area of the figure= Area of larger figure-Area of smaller figure

Area of larger figure: 7.25x6=43.5

Area of smaller figure: 55/3

43.5 can be written as 87/2

87/2-55/3

151/6, or 25 and 1/6

Answer:

A . -25 1/6 yd^2

Step-by-step explanation:

[tex]Area -of-a-rectangle = Length\times Breadth\\Area -of-bigger-rectangle :\\L = 7\frac{1}{4} \\B = 6\\A = 7\frac{1}{4} \times 6\\A = 43\frac{1}{2} \\\\Area-of-white-rectangle\\A = L\times B\\A = 5 \times 3\frac{2}{3} \\A = 18\frac{1}{3} \\Area of Figure = \\\\43\frac{1}{2} - 18\frac{1}{3} \\Area = 25\frac{1}{6}[/tex]

Answer:

$0.56/lb

Step-by-step explanation:

Given

Cost of a chicken = $2.15 per pound

26 pound of a chicken = $41.34

Required

Calculate how much saved.

The first step is to calculate the unit price of a chicken when 26 pound of chicken was bought.

Unit Price = Price ÷ Weight

Unit Price = $41.34 ÷ 26lb

Unit Price = $1.59/lb

The next step is to calculate the difference between these two prices

Difference = |$1.59/lb - $2.15/lb|

Difference = |-$0.56/lb|

Difference = $0.56/lb

The calculated difference is the amount saved per pound of chicken when I bought 26 pound of chicken.

Answer:

-3a+30

Step-by-step explanation:

-5a+30+2a.

-5a+2a=-3a

-3a+30

Answer:

Step-by-step explanation:

-5(a - 6) + 2a = -5*a -6 * (-5)  + 2a  

                     = -5a + 30 + 2a   {Add/ subtract like terms}

                    = -5a + 2a + 30

                     = -3a + 30

Answer:

a) x = 128 degrees

b) Angle APD is the arc angle, which is equal to the central angle x subtended by the arc.  Therefore angle APD = 128 degrees (and not 116 degrees)

Step-by-step explanation:

Given:

attached diagram

ABC is a straight line

Solution:

a) Find x

ABC is a straight line

angle ABD = supplement of CBD = 180-CBD = 180-116 = 64 degrees.

x is the central angle of the arc APD

so angle ABD is the inscribed angle which equals half of the arc angle =>

angle ABD = x/2 = 64 degrees

Solve for x

x/2 = 64

x = 2*64

x = 128 degrees

b.

Angle APD is the arc angle, which is equal to the central angle x subtended by the arc.  Therefore angle APD = 128 degrees (and not 116 degrees)

Answer:

A) 7%

Step-by-step explanation:

There are 360 degrees in a circle.  Thus, a 25 degree sector would make up 25/360 of the circle.  25/360 can be simplified to .06944444.  This rounds to .07, which is 7%.

Answer:

A. 7%

Step-by-step explanation:

A percent can be found by dividing the part by the whole and multiplying by 100.

(part/whole) *100

There are a total of 360 degrees in a circle. This is the whole.

We want to find what percent a 25 degree angle will take up. This is the part.

(25/360) * 100

First, divide 25 by 360.

0.0694444444 * 100

Now, multiply the numbers together  

6.94444444 %

Round to the nearest whole number. The 9 in the tenth place tells us to round the 6 to a 7.

7 %

Therefore, the answer is A. 7%

Answer:

Step-by-step explanation:

x=✓64*36=✓8^2*6^2

x=8*6

x=48

Answer:

Here,

Two points given: (3,1) and (7,-7)

[tex]slope(m) = \frac{y2 - y1}{x2 - x1} \\ \: \: \: \: \: \: \: \: \: \: \: = \frac{ - 7 - 1}{7 - 3} \\ \: \: \: \: \: \: \: \: \: = \frac{ - 8}{4} \\ \: \: \: \: \: \: \: \: \: \: = - 2 \\ [/tex]

Equation of line is y= Mx+b

y= -2x +b

It passes through (3,1)

[tex]1 = - 2(3) + b \\ 1 = - 6 + b \\ - b = - 6 - 1 \\ - b = - 7 \\ b = 7[/tex]

Equation of line:

Hope this helps..

Good luck on your assignment..

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Quadrilaterals.

Basically we know that, the sum of opposite angles of a quadrilateral inscribed in a circle is always 180°.

so applying this law here, we get as,

2X + (3X-10) = 180°

=> 5X - 10° = 180°

=> 5X = 190°

=> X = 190°/5

=> X = 38°

thus the angle X= 38°.

Answer:

the amount of fuel consumed every 100 kilometers is 62.5 litres.

Step-by-step explanation:

To determine the amount of fuel consumed every 100 kilometers.

Note: since the graph is a straight line graph (linear graph) the amount of fuel consumed every 100 kilometers is constant (i.e the same for every 100 kilometers). So, we only need to derive the amount of fuel consumed any 100 kilometers on the graph.

From the graph, the amount of fuel consumed for the first 100 kilometers is;

[tex]F = F_0 - F_{100} .........................1[/tex]

[tex]F_0 = 500\\F_{100} \simeq 437.5\\[/tex]

substituting into equation 1.

[tex]F = F_0 - F_{100} \\F = 500 - 437.5\\ F = 62.5 litres\\[/tex]

Therefore, the amount of fuel consumed every 100 kilometers is 62.5 litres.

Answer:500

Step-by-step explanation:got it on Kahn

Answer:

Option A) Speed = 1/20 of an inch per minute

Step-by-step explanation:

Given:

Distance = 6 inches

Time = 120 mins

Required:

Average Speed = ?

Formula:

Average Speed = Total Distance Covered / Total Time Taken

Solution:

Speed = 6/120

Speed = 1/20 of an inch per minute

Answer:

[tex]\frac{1}{20}[/tex] of an Inch per minute

Step-by-step explanation:

Speed = Distance ÷ Time

So....

6 ÷ 120 = 0.05 or [tex]\frac{1}{20}[/tex]

Also by process of elimination

[tex]\frac{1}{2}[/tex] of an inch per min would complete 6 inches in 12 min.

2 inches per min would complete 6 inches in 3 min

20 inches per minute would complete 6 inches in a few seconds.

Answer:

Total cost of the car including tax=$4,066

Step-by-step explanation:

Sales tax rate=7%

Price of the car=$3800

Sales tax=7% of 3800

=7/100×3800

=$266

Total cost of the car=price of the car+ sales tax

=$3800+$266

=$4,066

Answer:

[tex]m = 5 \sqrt{3}[/tex]

[tex]n = 5[/tex]

Step-by-step explanation:

Given

The triangle above

Required

Find the missing lengths

The missing lengths can be calculated by applying trigonometry ratios

From the triangle above,

the Hypotenuse is 10

Angle = 60

Calculating m

The relationship between m, the Hypotenuse and angle 60 is defined as follows;

[tex]sin \theta = \frac{Opp}{Hyp}[/tex]

Where [tex]\theta = 60[/tex]

[tex]Opp = m[/tex]

[tex]Hyp = 10[/tex]

The above formula becomes

[tex]sin60= \frac{m}{10}[/tex]

Multiply both sides by 10

[tex]10 * sin60= \frac{m}{10} * 10[/tex]

[tex]10 * sin60= m[/tex]

In radical from, [tex]sin60 = \frac{\sqrt{3}}{2}[/tex]

[tex]10 * sin60= m[/tex] becomes

[tex]10 * \frac{\sqrt{3}}{2}= m[/tex]

[tex]\frac{10* \sqrt{3}}{2}= m[/tex]

[tex]5 \sqrt{3}= m[/tex]

[tex]m = 5 \sqrt{3}[/tex]

Calculating n

The relationship between n, the Hypotenuse and angle 60 is defined as follows;

[tex]cos\theta = \frac{Adj}{Hyp}[/tex]

Where [tex]\theta = 60[/tex]

[tex]Adj = n[/tex]

[tex]Hyp = 10[/tex]

The above formula becomes

[tex]cos60= \frac{n}{10}[/tex]

Multiply both sides by 10

[tex]10 * cos60= \frac{n}{10} * 10[/tex]

[tex]10 * cos60= n[/tex]

In radical from, [tex]cos60= \frac{1}{2}[/tex]

[tex]10 * cos60= n[/tex] becomes

[tex]10 * \frac{1}{2}= n[/tex]

[tex]\frac{10*1}{2}= n[/tex]

[tex]5 = n[/tex]

[tex]n = 5[/tex]

Answer:

Step-by-step explanation:

5. cut the five fruits into 3 equal parts....

5x3=15 pieces

15/3(bowls)=5 pieces in each bowl

cut the fruits in multiples of 5 divisible by 3....that many ways possible

(similarly 4th qstion can be done)!!

Answer:

0.60715731075

I hope this helps.

Answer:

First question = 800 cm^3

Second question =120π

Step-by-step explanation:

The formula for volume is base x height x width.

The formula for area of cylinder is 2πrh+2πr^2 but it has no lid so

2πrh+πr^2.

Answer:

ACG and EGC

Step-by-step explanation:

Same side interior angles are on the inside of the parallel lines

The same side interior angles are ACG and EGC

Answer:either HGC or maybe ECG

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

The function is indeed a polynomial. We have the single variable [tex]x[/tex] plus a constant [tex]\pi[/tex] (it's irrational, but it's still simply just a constant number). This fits the definition of polynomials.

Answer:

a) 8

b) 2 1/4 hours

c) 4 7/8 hours

d) 4 1/8 hours

Step-by-step explanation:

a) LCD to be used to solve this problem is calculated as the Lowest common denominator of the above mixed fractions.

We have 1 1/2 hours and 1 1/8 hours

The lowest common denominator is the denominator calculated by

Multiplying the two denominators together and dividing by the common factor of the two denominators

Hence , we have

2 × 8 = 16

The common factor of 2 and 8 = 2

LCD = 16/2 = 8

b) How long did Matt drive?

We are told that Matt drove twice as long as John

John drove for 1 1/8 hours

Hence, the number of hours that Matt drove for =2 × 1 1/8

= 2 × 9/8 = 9/4 hours = 2 1/4 hours

c) How long the Sam, John and Matt drive ?

We are told in the question that

Sam drove for 1 1/2 hours

John drove for 1 1/8 hours

Matt drove for 2 1/4 hours

We would sum up the number of hours that each of them drove.

1 1/2 + 1 1/8 + 2 1/4

The Lowest common multiple of denominators is 8

= (1 + 1 + 2)( 4 + 1 +2/8)

= 4(7/8)

= 4 7/8 hours

d) How many hours is left for Bob to drive

We are told that the entire journey = 9 hours

The number of hours Sam, John and Matt drove for has been calculated in question c as 4 7/8 hours

The number of hours Bob will drive for is calculated as

9 hours - 4 7/8 hours

= 4 1/8 hours