In the above quadrilateral ABCD,
AD || EF || BC and
|AE| = 2 EB, BM = 4, |AD = 6, BC| =
, 9
Then DO​

In The Above Quadrilateral ABCD,AD || EF || BC And|AE| = 2 EB, BM = 4, |AD = 6, BC| =, 9Then DO

Answers

Answer 1

Answer:

The length of segment [tex]\overline{DO}[/tex] is [tex]\displaystyle \frac{24}{5}[/tex].

Step-by-step explanation:

Start by verifying that [tex]\triangle DAB \sim \triangle MEB[/tex], and that [tex]\triangle DOA \sim \triangle BOC[/tex].

Both [tex]\triangle DAB[/tex] and [tex]\triangle MEB[/tex] contain the angle [tex]\angle DBA[/tex]. Hence, another pair of equal angles will be sufficient to prove [tex]\triangle DAB \sim \triangle MEB[/tex] by the angle-angle similarity postulate.

Notice that because [tex]\overline{AD} \; \| \; \overline{EF}[/tex], the corresponding angles next to those two lines would be equal: [tex]\angle MEB = \angle DAB[/tex]. Both [tex]\angle MEB[/tex] is in [tex]\rm \triangle MEB[/tex] whereas [tex]\angle DAB[/tex] is in [tex]\triangle DAB[/tex].

Hence, [tex]\triangle DAB \sim \triangle MEB[/tex] by the angle-angle similarity postulate.

Notice how [tex]\angle DOA[/tex] in [tex]\triangle DOA[/tex] and [tex]\angle BOC[/tex] in [tex]\triangle BOC[/tex] are two vertically opposite angles (and are thus equal to one another.) That is: [tex]\angle DOA = \angle BOC[/tex].

Because [tex]\overline{AD} \| \overline{BC}[/tex], the alternate interior angles [tex]\angle DAO[/tex] and [tex]\angle BCO[/tex] are also equal to one another. That is: [tex]\angle DAO = \angle BCO[/tex]

Hence, [tex]\triangle DOA \sim \triangle BOC[/tex], also by the angle-angle similarity postulate.

Notice that [tex]\triangle DAB \sim \triangle MEB[/tex] implies that:[tex]\begin{aligned} & \frac{\left| \overline{BM} \right|}{\left| \overline{BD} \right|} \\ &= \frac{\left|\overline{EB}\right|}{\left|\overline{AB}\right|} && (\triangle MEB \sim \triangle DAB) \\ &= \frac{\left|\overline{EB}\right|}{\left|\overline{AE}\right| + \left|\overline{EB}\right|} \\ &= \frac{\left|\overline{EB}\right|}{2\, \left|\overline{EB}\right| + \left|\overline{EB}\right|} && (\text{given that $\left|\overline{AB}\right| = 2\,\left|\overline{EB}\right|$})\\ &= \frac{1}{3}\end{aligned}[/tex].

Therefore:

[tex]\begin{aligned}&\left|\overline{BD}\right|\\ &= 3\, \left|\overline{BM}\right| \\ &= 12\end{aligned}[/tex].

Similarly, [tex]\triangle DOA \sim \triangle BOC[/tex] implies that:

[tex]\begin{aligned} \frac{\left| \overline{DO} \right|}{\left| \overline{BO} \right|} &= \frac{\left|\overline{AD}\right|}{\left|\overline{BC}\right|} && (\triangle DOA \sim \triangle BOC) \\ &= \frac{6}{9} = \frac{2}{3}\end{aligned}[/tex].

Therefore, [tex]\displaystyle \left|\overline{BO}\right|= \frac{3}{2}\, \left|\overline{DO}\right|[/tex].

[tex]\begin{aligned} \frac{\left| \overline{DO} \right|}{\left| \overline{BD} \right|} &= \frac{\left| \overline{DO} \right|}{\left| \overline{BO} \right| + \left| \overline{DO} \right|} \\ &= \frac{\left| \overline{DO} \right|}{(3/2)\, \left| \overline{DO} \right| + \left| \overline{DO} \right|} = \frac{2}{5}\end{aligned}[/tex].

It was already found that [tex]\left|\overline{BD}\right| = 12[/tex]. Therefore:

[tex]\displaystyle \left|\overline{DO}\right| = \frac{2}{5}\, \left|\overline{BD}\right| = \frac{24}{5} = 4.8[/tex].


Related Questions

Kim uses decals to decorate 5 cars and 2 motorbikes. She uses 2/3 of the decals on the cars and 2/5 of the remaining on the motorbikes. She has 6 decals left. How many decals does Kim use on each car?​

Answers

Answer:

I decal per car and motor bike

Step-by-step explanation:

The larger of two numbers is 10 less than twice the smaller number. If the sum of the two
numbers is 38, find the two numbers.

Answers

Answer:

Let the larger number = y and the smaller number = x.

The largest number is 10 less than twice the smaller number. Remember that less than means subtract the 10 from the other amount while twice means multiply by two. Therefore,

y = 2x - 10

The sum of the two numbers is 38. Remember sum means add the two numbers to get their result. Therefore,

x + y = 38

Since y = 2x - 10, we rewrite the lower equation as:

x + (2x - 10) = 38

Solving:

3x - 10 = 38

3x = 48

x = 16

The lesser number is 16 and the greater number is 2(16) - 10 or 22.

PLZ I NEED ANSWERS. THIS IS MIDDLE SCHOOL LEVEL NOT COLLEGE
Select ALL the expressions that are greater than one

A: 4 Divided by 3/4
B: 1/3 Divided by 10
C: 5/6 Divided by 2/5
D: 3 1/8 Divided by 2 7/8
E: 9/7 divided by 8/7

Answers

All are greater than 1 except for letter B.

Answer: The answers are all of the options except for B.

Step-by-step explanation:

Option A. 4/1 x 4/3 is 16/3. 16/3 > 1

Option B. 1/3 x 1/10 is 1/30. 1/30 < 1

Option C. 5/6 x 5/2 is 25/12. 25/12 > 1

Option D. 25/8 x 8/23 is 200/184. 200/184 > 1

Option E. 9/7 x 7/8 is 63/56. 63/56 > 1

Hence, the correct answer is option A, C, D, and E.

(4x+3)(3x)-25 graph

Answers

Answer:

12x^2+9x^2-25    (quadratic equation)

a=12, b=9, c=-25

put this in quadratic formula

Step-by-step explanation:

Answer:

Plz brainliest

Step-by-step explanation:

2) How can 4(3 + 8) be rewritten using the distributive property?
O 12 + 8
O 3 +32
O 12 +32
O 43 + 48

Answers

1. 4(3 + 8)
= (4 * 3) + (4 * 8)
= 12 + 32
= 44
So, the answer to this question is the third option.
Glad I could help and have a fantastic day!
Also, can you please mark my answer as the brainliest answer?
Thanks.

can u pls help me with this question asap ​

Answers

Answer:

bro this is easy search it up online u dont have to use brainly for these type of questions but the answer is 402.39 but if u want it rounded it is 402.40

Step-by-step explanation:

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78.9 x 510/ 100 = 402.39

402.4 (to the nearest tenth)

MATH WORK PLEASE HELP GIVING MANY POINTS ONLY DO THE ONES IN PURPLE!!

Answers

Answer:

Step-by-step explanation:

8,3,4,6,7,2,5,

Quick IM timed!!
A researcher is comparing three new formulas for grass killer. To conduct the experiment, the researcher purchases 30 pieces of sod from various vendors to use in the study. The 30 pieces of sod are laid out in three different areas. The researcher places three slips of paper in a bowl labeled formula 1, formula 2, and formula 3 and randomly picks a piece of paper to apply that formula to the sod in the first area. Then the researcher picks again and applies that formula to the second area. Finally, the last formula is used on the last area.

Which component is missing from the researcher’s process?

A The researcher should not have laid out the pieces of sod in different areas.
B The researcher did not randomly assign the pieces of sod to the treatment groups.
C The researcher did not randomly pick the vendors when purchasing the pieces of sod.
D The researcher did not use randomization when selecting the pieces of sod from the vendors.

Answers

Answer:

The researcher did not randomly assign the pieces of sod to the treatment groups.

Step-by-step explanation:

Edge 2020/2021

Answer:

The researcher did not assign the chosen pieces of sod to treatment groups.

Step-by-step explanation:

The researcher needs to create three treatment groups, each containing 10 pieces of sod, and assign the chosen pieces of sod to these groups. Without this step, it is not clear how the three formulas will be applied to the pieces of sod.

If x = 7 and y = 4, then x + 2y =

Answers

15!

x + 2y = ?
(7) + 2(4) = ?
7 + 8 = 15

Given that if x = 7 and y = 4, the value of x + 2y = 15

Given the following:

x = 7

y = 4

Required:

Find the value of x + 2y.

Therefore, substitute x = 7 and y = 4 into the algebraic expression, x + 2y.

Thus, plug in the values into the expression:

(7) + 2(4) = 7 + 8

x + 2y = 15

Therefore, given that if x = 7 and y = 4, the value of x + 2y = 15

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He had to wait 1 hour and 45 minutes at the airport in San Francisco. Then Frank
father had to wait another 35 minutes while the plane was in Portland.
How long did Frank's father spend waiting?

Answers

Answer:

Step-by-step explanation:

Find the measure of one interior angle in each regular polygon.

Answers

Answer:

108°

Step-by-step explanation:

Polygon has n sides.

Each interior angle = 180° - (360/n)°

n = 5 ⇒ interior angle = 180° - (360/5)° = 108°

ML is equal to 342 L 645 ML

Answers

Answer:

1 L = 1000 ml

Step-by-step explanation:

342L = 342 ml

645 ml = 645 ml

The given quantity 342 l 645 ml can be written as 342645 ml.

Given that, 342 l 645 ml.

What is metric conversion?

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

We know that, 1 l = 1000 ml

Now, 342 l = 342000 ml

So, 342 l 645 ml = 342000+645 = 342645 ml

Therefore, the given quantity 342 l 645 ml can be written as 342645 ml.

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The amount of time it takes for a student to complete a statistics quiz is uniformly distributed (or, given by a random variable that is uniformly distributed) between 26 and 63 minutes. One student is selected at random. Find the probability of the following events.

A. The student requires more than 58 minutes to complete the quiz.
Probability =
B. The student completes the quiz in a time between 32 and 36 minutes.
Probability =
C. The student completes the quiz in exactly 40.85 minutes.
Probability =

Answers

Answer:

A.  This is possible but less likely

B.  This is very possible

C.  This is highly unlikely

B. is the most possible   A. is the second most possible   C. is least possible

Hope this helps <33

How do I solve 300x300=

Answers

Answer:

its 90,000

Step-by-step explanation:

just put the zeros together then multiply 3x3

GUYS PLS HELP 25 POINTS PLUS BRAINLIEST IF CORRECT

Answers

Answer:

I looked it up and it says in a hierarchy based on similarities and physical traits as well as binomial nomenclature but you don't have that answer and it also says it describes the linnean taxonomy

Step-by-step explanation: but I think it's animals and species

sorry but hope this helps

Convert to degrees −31π/36

Answers

Answer:

−31π/36 = -15.5°

Step-by-step explanation:

We need to convert −31π/36 to degrees.

The conversion from radian to degrees is calculated as follows :

[tex]\text{Degrees}=\dfrac{180}{\pi }\times \text{radian}\\\\=\dfrac{180}{\pi}\times \dfrac{-31\pi }{360}\\\\=-15.5^{\circ}[/tex]

So, −31π/36 is equal to -15.5 degrees.

really need the answer to​ this thanks !

Answers

Answer: 2662.25 (now u just need to round it to the whole)

Step-by-step explanation: Ok we know that it can last 5750 years, and we know 53.7 percent of those years is gone, meaning it only got 46.3 percent of it years left. until it gone. So 46.3 percent of 5750 is 2662.25. Now go round it if u need to.

Helppppp!! Pleaseeeee

Answers

you need to subtract your interest paid by your principal paid. which would be $352.15 so the answer is A.

The table represents a linear function.
What is the slope of the function?
0-6
O 4
х
-2
-1
0
1
2
у
8
2
-4
-10
-16
04
O 6
Mark this and retum
Save and Exit
Next
Submit

Answers

The ratio of the change in the y and x values, in the table gives the slope

graph of the linear function.

Correct response:

The slope of the linear function is -6

Method used for finding the slope

From the given table, we have;

The first difference of the y-values = 2 - 8 = -6 = Constant

The rate of change of the x-values = 1 = Constant

Therefore;

The function is a linear function;

The slope, m, is given by the formula;

[tex]Slope, \ m = \mathbf{ \dfrac{y_2 - y_1}{x_2 - x_1}}[/tex]

Taking a pair of points as follows;

(0, -4) = (x₁, y₁)

(2, -16) = (x₂, y₂)

We have;

[tex]m = \dfrac{-16 - (-4)}{2 - 0} = \dfrac{-16 + 4}{2} = \dfrac{-12}{2} = \mathbf{ -6}[/tex]

The slope of the linear function, m = -6

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If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h =
-161 +62 + 4. Round your answer to the nearest hundredth.

Answers

Answer: 100 ft

Step-by-step explanation:

please help me please please

Answers

Answer:

I am pretty sure the answer is A

Step-by-step explanation:

Answer:

I think but l sure answer is A

Find the distance between the points (4,-8) and (7-10).

Answers

Answer:

[tex]\displaystyle d = \sqrt{13}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (x, y)

Algebra II

Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Step-by-step explanation:

Step 1: Define

Point (4, -8)

Point (7, -10)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Substitute in points [DF]:                     [tex]\displaystyle d = \sqrt{(7-4)^2+(-10+8)^2}[/tex](Parenthesis) Subtract/Add:                [tex]\displaystyle d = \sqrt{(3)^2+(-2)^2}[/tex][√Radical] Exponents:                         [tex]\displaystyle d = \sqrt{9+4}[/tex][√Radical] Add:                                    [tex]\displaystyle d = \sqrt{13}[/tex]

Answer:

The distance between the points (4,-8) and (7-10)

[tex] = \sqrt{ {(7 - 4)}^{2} + {( - 10 - ( - 8))}^{2} } \\ = \sqrt{ {(7 - 4)}^{2} + {( - 10 + 8)}^{2} } \\ = \sqrt{ {3}^{2} + { (- 2)}^{2} } \\ = \sqrt{9 + 4} \\ = \sqrt{13} \: units [/tex]

√13 is the right answer.

Classifg each angle as acute , right , obtuse , or straight

1) 10°

2) 98°

3) 180°

4) 90°

Answers

Answer:

1) acute

2) obtuse

3) straight

4) right

Step-by-step explanation:

acute angle=less than 90

right angle=90 exactly

obtuse=greater than 90

straight=exactly 180

hope this helps

If a truck weighs 1200 kg and is traveling at 30 m/s, how much kinetic energy does it have?

Answers

KE = 540,000 or J = 540 kJ

Factor 7x3y4−7x2y5 completely.

A) 7xy(x^2y^3−xy^4)
B) 7x^2y^4(x−y)
C) 7(x^3y^4−x^2y^5)
D) x^2y^4(7x−7y)

Answers

Answer:

B

Step-by-step explanation:

when we factor completely, we take a look at what is the biggest common factor of 7x³y⁴ and 7x²y⁵. In this case it is 7x²y⁴.

7x³y⁴-7x²y⁵ = 7x²y⁴(x-y) which is B.

A car uses a litre of petrol to travel 4km. How many litres will it use to travel 32 kilometres.

Answers

Given that,

A car uses a litre of petrol to travel 4 km.

To find,

How many litres will it use to travel 32 kilometres.

Solution,

We have,

1 litre = 4 km

or

1 km = (1/4) litre

Let it will use x litres to travel 32 km.

32 km = (32/4) litres

= 8 litres

Hence, 8 litres it will use to travel 32 km.

The Blue Streak Taxi Company charges each customer $3.00 plus $0.22 a mile, Which equation could be used to find the number of miles m the cab traveled if the fare was $8.75?​

Answers

Answer:

3.00+0.22m=8.75

Step-by-step explanation:

In a survey of school students, 64 had taken mathematics course, 94 had taken chemistry course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and chemistry, 22 had taken chemistry and physics course, and 14 had taken all the three courses. Find how many had taken one course only by using Venn diagram.

Answers

Answer:

ask again

Step-by-step explanation:

The number of students taken only one course is 106

What is Venn diagram?

A Venn diagram exists as an illustration that utilizes circles to illustrate the relationships among things or finite groups of things. Circles that overlap include a commonality while circles that do not overlap do not share those traits. Venn diagrams permit visually illustrating the similarities and contrasts between two concepts.

Let M =sets of students who had taken mathematics

     C= sets of students who had taken chemistry

     P= represent sets of students who had taken physics

From the given information, we have

n(M) = 64 , n(C) = 94, n(P) = 58,

n(MnP) = 28, n(MnC) = 26, n(CnP) = 22

n(MnCnP) = 14​​​​​​​

No. of students who had taken only Math :

= n(M) - [n(MnP) + n(MnC) - n(MnCnP)]

= 64 - [28+26-14]

= 64 - 40

= 24​​​​​​​

No. of students who had taken only Chemistry

= n(C) - [n(MnC) + n(CnP) - n(MnCnP)]

= 94 - [26+22-14]

= 94 - 34

= 60

No. of students who had taken only Physics

= n(P) - [n(MnP) + n(CnP) - n(MnCnP)]

= 58 - [28+22-14]

= 58 - 36

= 22

Total no. of students who had taken only one course

= 24 + 60 + 22

= 106

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Please helpppp me pleaseee

Answers

The answer is square

Which equation represents the linear function that is shown on the graph below?
10.14
9
8
00
7 6 5
4 +
3
2
1
1 2 3 4 5 6 7 8 9
Х

Answers

Answer:

[tex]y = \frac{1}{2}x - 2[/tex]

Step-by-step explanation:

Given

The attached graph

Required

Determine the linear equation

First, we need to calculate the slope

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

From the graph, the following relationships exist:

[tex](x_1,y_1) = (4,0)[/tex]

[tex](x_2,y_2) = (10,3)[/tex]

So, the expression for calculating slope becomes:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \frac{3-0}{10-4}[/tex]

[tex]m = \frac{3}{6}[/tex]

[tex]m = \frac{1}{2}[/tex]

Next, we calculate the equation using:

[tex]y - y_2 = m(x - x_2)[/tex]

This gives:

[tex]y - 3 = \frac{1}{2}(x - 10)[/tex]

Open bracket

[tex]y - 3 = \frac{1}{2}x - 5[/tex]

Make y the subject:

[tex]y = \frac{1}{2}x - 5+3[/tex]

[tex]y = \frac{1}{2}x - 2[/tex]

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