One of the legs of the obtuse isosceles △ABC and △DBE lie on the same line sharing vertex B without overlapping. The sides DE and AC intersect at point F, DC = 12 in, m∠BDF=m∠BCF=30°. Find AE and CE.
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PLZ HELP ILL GIVE 100 POINTS

One Of The Legs Of The Obtuse Isosceles ABC And DBE Lie On The Same Line Sharing Vertex B Without Overlapping.

Answers

Answer 1

9514 1404 393

Answer:

  AE = CE = 12 in

Step-by-step explanation:

Angles BDF and BCF are base angles of their respective isosceles triangles. That means the a.pex angle of each, DBF and ABC respectively is ...

  180° -2×30° = 120°

In your diagram, BC is 120° from the -x axis, so is 60° from the +x axis. It bisects the angle DBE. Similarly, BE is 120° from the +x axis, so is 60° from the -x axis. It bisects angle ABC. In an isosceles triangle, the a.pex angle bisector is an altitude and is the perpendicular bisector of the base segment. Any point on that line is equidistant from the base vertices.

Point C lies on the perpendicular bisector of DE, so CD ≅ CE = 12 in.

Point E lies on the perpendicular bisector of AC, so EC ≅ EA = 12 in.

The measurements of interest are ...

  AE = CE = 12 in.

_____

Additional comment

Point F serves no purpose except to confuse the issue. Each of the angles that reference point F could be described equally well using a different point:

  ∠BDF = ∠BDE

  ∠BCF = ∠BCA

This makes it more obvious that the triangles of interest are similar.

Answer 2

Answer:

12

12

Step-by-step explanation:

see the below figure

i got that both triangles are similar

we get that in triangle ABC angle BCF is 30

so angle A is also 30 (isosceles)

so the remaining angle ABC is 120

and angle CBD becomes 180 - 120 = 60

now in triangle BDE angle BDF is 30

so angle BED is also 30

now angle EBC becomes 120 - angle CBD = 120 - 60

and got angles ABE EBC CBD as 60 each

so three 60 degree angles are formed at vertex B as shown in the figure

 tw0 30 30 120 degree triangles are similar

BC becomes perpendicular angular bisector of ED

C is a point on that line which is at equal distance from the base vertices

so CD = CE = 12

here BE is perpendicular bisector of AC

so AE = EC = 12    

One Of The Legs Of The Obtuse Isosceles ABC And DBE Lie On The Same Line Sharing Vertex B Without Overlapping.

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Step-by-step explanation:

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Find the argument of the complex number 2 = 4+ 3i to the nearest whole degree.​

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Using it's formula, it is found that the argument of the complex number z = 4+ 3i is of 37º.

The standard format of a complex number is:

[tex]z = a + bi[/tex]

In which:

a is the real part.b is the imaginary part.

The argument is given by:

[tex]\theta = \tan^{-1}\left(\frac{b}{a}\right)[/tex]

In this problem, the number is:

[tex]z = 4 + 3i[/tex]

Hence, [tex]a = 4, b = 3[/tex], and:

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What is 2x-3 when x=6

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Answer:

0

Step-by-step explanation:

Write a function in any form that would match the graph shown below

Answers

Answers:

Vertex form:  y = -2(x-1)^2 + 8Standard form: y = -2x^2 + 4x + 6

Pick whichever form you prefer.

=============================================================

Explanation:

The vertex is the highest point in this case, which is located at (1,8).

In general, the vertex is (h,k). So we have h = 1 and k = 8.

One root of this parabola is (-1,0). So we'll plug x = -1 and y = 0 in as well. As an alternative, you can go for (x,y) = (3,0) instead.

Plug those four values mentioned into the equation below. Solve for 'a'.

y = a(x-h)^2 + k

0 = a(-1-1)^2+8

0 = a(-2)^2+8

0 = 4a+8

4a+8 = 0

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a = -2

The vertex form of this parabola is   y = -2(x-1)^2+8

Expanding that out gets us the following

y = -2(x-1)^2+8

y = -2(x^2-2x+1)+8

y = -2x^2+4x-2+8

y = -2x^2+4x+6 .... equation in standard form

Find the point on the line y=x that is closest to the point (-4,8)

Answers

Answer:

(2,2)

Step-by-step explanation:

Interest and fees
the total cost of a credit purchase.
A. maintain
O B. decrease
C. do not affect
D. increase

Answers

Answer:

D. increase

Step-by-step explanation

Intrest and fees are used to make process, and It increases the cost. You have to pay it back in the end.

Answer:

B

Step-by-step explanation:

Normally a normal card purchase won't affect the credit but since your using your credit's to purchase I think it will decrease it, it also depends how many times you use your card, cuz banks sure do be checking. So I hope I helped!

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Answer:

Lemons ( 27 ) = Cups ( 9 )

Cups ( 50) = Lemons (30)

What is the equation in slope-intercept form of the line that passes through the points (-4, 6) and (-2,5) ?
y=20 - 8
y=-30+4
y=-22 +4
y = -x + 8

Answers

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{(-4)}}}\implies \cfrac{-1}{-2+4}\implies \cfrac{-1}{2}\implies -\cfrac{1}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{-\cfrac{1}{2}}[x-\stackrel{x_1}{(-4)}] \\\\\\ y-6=-\cfrac{1}{2}(x+4)\implies y-6=-\cfrac{1}{2}x-2\implies \underset{\textit{slope-intercept form}}{y=-\cfrac{1}{2}x+4}[/tex]

Silvia is planning to use a 4-year loan to purchase a car.
• The price of the car is $8,575.
• The amount of interest she will have to pay on the loan is $1,036
Silvia will combine the price of the car and the amount of interest to determine how much she must repay. She will make 48 equal monthly
payments.
Which of the following is the best estimate of each monthly payment Silvia will make?
A. $175
B. $200
C. $225
D. $250

Answers

Answer:

B

Step-by-step explanation:

8575 + 1036 = 9611

9611 is the full payment

9611 / 48 months = 200.229

About $200 every month

The best estimate of each monthly payment that Silvia will make is given by: Option B: $200

What to calculate net payable amount after interest is applied?

The net payable amount is the sum of main amount to be paid + the amount of interest.

For this case, it is specified that:

The price of the car is $8,575.The amount of interest she will have to pay on the loan is $1,036

Thus, we get:
Total payable amount by Silvia for car purchasing = $8575 + $1036 = $9,611

This payable amount is divided in 48 equal parts. The value of each part (the monthly payment amount by Silvia) is:

[tex]\dfrac{9611}{48} \approx 200 \: \rm dollars[/tex]

Thus, the best estimate of each monthly payment that Silvia will make is given by: Option B: $200

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Answer:

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Step-by-step explanation:

Answer:

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Answer:

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Answer:

24.489%, but most of the time they only go to 2 decimal places so 24.49%

Step-by-step explanation:

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Answers

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Answer:

Length=12mi

Step-by-step explanation:

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Width=10.3mi

Length=u

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Area÷W=u

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Answers

Answer:

1052 is MLII, 450 is CDL, 952 is CMLII, and 942 is CMXLII.

Step-by-step explanation:

For 1052, M=1000 L=50 and II= 2 and if you add all those you get 1052. For 450, CD=400 and L=50 and if you add all those up then you get 450. For 952, CM=900 L=50 and II=2 and if you add all those up then you get 952. For 942, CM=900 XL=40 and II=2, and if you add all those up then you get 942.

A new hotel was built with r rooms. The first weekend it was open, 3/5 of them were reserved. Which of the following expressions represents the number of rooms which were reserved?

A r-3/5
B r x 3/5
C r+3/5
D ÷3/5

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Answers

Answer:

c r/ 3/5

Step-by-step explanation:

i think

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Answers

Answer:

Your GPA would be 1.5 If you have 6 periods.

Step-by-step explanation:

A = 4 GPA Points

B = 3 GPA points

C = 2 GPA Points

D = 1 GPA Points

F = 0 GPA Points

With that knowledge you calculate 2 (C) + 4 (A) + 3 (B) + 0 (F) + 0 (F)  + 0 (F) assuming you have 6 periods which adds up to 9. You divide  by the number of periods (6) totaling to 1.5 GPA Points.

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Answers

Answer:

6

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Answer:

4

Step-by-step explanation:

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Answers

Step-by-step explanation:

sqrt(5x)×(sqrt(8x²) - 2×sqrt(x)) =

sqrt(5x × 8x²) - 2×sqrt(5x × x) =

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The ratio of ronnys tern, dougs rent and ronalds rent is 4:5:8. Their total rent if $3723. What is the cost of each persons rent

Answers

Answer:

The cost of Ronny is $876, Dough is $1095 and Ronald is $1752.

Step-by-step explanation:

Firstly, make all ratios into units:

Let Ronny = 4 units, Doug = 5 units,

Ronald = 8 units, Total = $3723

4 units + 5 units + 8 units = 17 units

17 units = $3723

1 unit = $3723 ÷ 17

1 unit = $219

Given that 1 unit is equals to $219. Let find the amounts:

Ronny = 4 × 219 = $876

Doug = 5 × 219 = $1095

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Which set of side lengths will form a triangle
A: 16ft, 4ft, 21ft
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Answers

Answer:

the set of side lengths will be d

HELPPP LAST ATTEMPT!!

Answers

Answer:

B' (-1,-5)

Step-by-step explanation:

When it is reflected over the y-axis, the y coordinate stays the same but the x coordinate inverses. In this situation since the x in point B is a positive, the x in point B' will be a negative.

(-1,5)

since it’s being translated over the y axis the only coordinate that’s changing would be the x coordinate. when it’s translated over it would be the opposite to the original point. (positive original point would become a negative point after translated)
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The graph of y=⅔ x - 12 intersects the y-axis at Q (0, -12) and is perpendicular to a line joining Q to the point P ( x , 0). Find x

Answers

They will go over point 3,0 and /4,9 then

If right you get brainiest!
A little mermaid can swim 12 miles downstream in the same amount
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Answers

Answer:

20 mph

Step-by-step explanation:

time = distance / speed

speed up stream = s - 4

speed down stream = s + 4

time up = time down

8 / (s - 4) = 12 / (s + 4)

cross multiply

8s + 32 = 12s - 48

subtract 8v from both sides

32 = 4s - 48

add 48 to both sides

80 = 4s

Divide both sides by 4

20 = s

20mph

In which quadrant does the angle t lie if tan(t)>0 and cos(t)<0?

A) II
B) IV
C) Cannot be determined
D) III
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Answers

Quadrant is a quarter of a coordinate plane

The location of angle t is in quadrant 3

The trigonometry equations are given as:

tan(t)>0 and cos(t)<0

The cosine of an angle is negative in the following quadrants

Quadrant 2Quadrant 3

The cosine of an angle is positive in the following quadrants

Quadrant 3

The intersection of the above points is quadrant 3

This means that the angle is in quadrant 3

Hence, the true option is (D) III

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The ratio of the number of cupcakes to the number of pastries in a box is 7:2. Which table shows the possible amounts of cupcakes and pastries in a box, given the ratio? (2 points)

Question 1 options:

1)

Cupcakes Pastries
7 2
21 6
42 8
84 10

2)

Cupcakes Pastries
7 2
21 6
28 12
35 24

3)

Cupcakes Pastries
7 2
21 17
42 38
84 80

4)

Cupcakes Pastries
7 2
14 4
28 8
56 16

Answers

Answer:

I wish I could help but I don't know

Answer:

D is correct

Step-by-step explanation:

19 /5 as a mixed number

Answers

Answer:

[tex]\frac{19}{5}= 3\frac{4}{5}[/tex]

Step-by-step explanation:

5 can go into 19 three times. This will leave a remainder of 4. Therefore, 19/5 as a mixed number is 3 4/5.


The graphs show information about the different journeys of 4 people.

a)
Which graph shows a person running then walking?
b)
Which graph shows a person who forgot something
and had to return home?

Answers

Answer:

A) b

B) c

Step-by-step explanation:

A) a large distance is covered in a short period of time but then the speed decreases

B) the person travels some distance but then returns to their starting point for a while(their home) and then starts on their journey again

Write a function in any form that would match the graph shown below

Answers

9514 1404 393

Answer:

  f(x) = 2(x +2)^2(x -5)

Step-by-step explanation:

The root at x=-2 has even multiplicity. The curve is not flat there, so the multiplicity is 2, not higher. The root at x=5 has multiplicity 1. Then the factored form of this cubic is ...

  f(x) = a(x +2)^2·(x -5)

The local minimum when a=1 is about -50, so we judge the leading coefficient to be 2. The desired function is ...

  f(x) = 2(x +2)^2(x -5)

Hi. can you help me?

Answers

Answer:

Sure

Step-by-step explanation:

First you need to ____

Next you need to ____

Last, put nothing

That's what you did, so I helped you out.

Is dis good

i- I think you forgot to put the picture.

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