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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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:
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
Please help this is due tomorrow and I have no idea what to do
Step-by-step explanation:
#1Yes
If you connect the points plotted, they will form a line and will pass through the origin.
This is indication of the proportional relationship.
The equation of circumference is:
C = 2πrSince 2π is a constant value, the equation above represents a proportional relationship.
#2AC is the dimeter#3DB is the radius#4Circumference is the perimeter of the circle.What is three times a number is increased by 11 ,the result is 32
Answer:
7
Step-by-step explanation:
let x be the number
3x + 11 = 32
3x = 21............subtract both sides by 11
x = 7................divide both sides by 3
Answer:
Expression-
3×r+11=32
r=7
Step-by-step explanation:
I have run this answer the calculator a million times so trust me on this one
geomtry plzzzz help me
Step-by-step explanation:
it is an isoceles triangle (equally long legs).
there is a right angle at W, so YW is the height of the isoceles triangle XYZ.
that means W splits XZ in half.
therefore,
ZW = XZ/2 = 38/2 = 19
What is: 17/21 + 1/3 - 5/7 as a fraction in simplest form?
(Giving brainliest, 5 stars and a thanks)
Answer:
3/7
Step-by-step explanation:
How do you multiply 47.5 by 28
Answer: uhhhh
Step-by-step explanation:
Answer:
Step-by-step explanation:
1330 is the answer
Solve T in the following formula P=nRT/V
Answer:
T = PV/nR
..............................................
find the amount accumulated in an account after $9000 is invested for 8 years at a 4% coumpounded monthly
Step-by-step explanation:
9000(1+0.04/12)^(8*12)
9000(1.0033333)^96
9000(1.3763)
A=12,387.56
An experiment is conducted examining the effects of a new type of toothpaste on reducing cavities. Individuals in the treatment condition are given the new toothpaste; individuals in the control condition are given the standard toothpaste, but are told that they're receiving the new toothpaste. At the end of the experiment, the control group participants demonstrate a slightly higher decline in cavities. This is an example of a(n):____.
a. Wording bias.
b. Voluntary response bias.
c. Over-sampling effect.
d. Placebo effect.
d. Hawthorne effect.
The experimental effect highlighted by the scenario described would most likely be an example of placebo effect.
An observed change in the control group which are being given the placebo would have been triggered due to psychological expectation based on the information given. Hence, this is called the placebo effect. The standard toothpaste was not suppose to cause decline in cavities, however, since the group have been told that they we given the new toothpaste which is said to reduce cavities, this could trigger a psychological change hence causing them to have higher cavity decline.Learn more : https://brainly.com/question/25704508
What is the value of y in the following system of equation3x-4y=-20 -x+2y=10
For males in a certain town, the systolic blood pressure is normally distributed with a
mean of 125 and a standard deviation of 5. What percentage of males in the town that
have a systolic blood pressure higher than 131, to the nearest tenth?
Answer:
11.5 %
Step-by-step explanation:
mean- 125 | sd: 5
z-score: 131-125/5= 6/5= 1.2
for z= 1.2, percent: 88.49 %
100-88.49= 11.51 -> 11.5
mega movies hotel a fil premiere on Friday night. they charged $7 for adults and $5 for children. One hundred twenty-three adults and children attended, and $829 was made in ticket sales. How many children and how many adults went to the film premiere?
Answer:
107 adults 16 children
Step-by-step explanation:
can i get brainlest
Let p=x^2+6. Which equation is equivalent to (x^2 + 6)^2 - 21 = 4x^2 + 24 in terms of p?
Answer:
p^2-4p-21=0
Step-by-step explanation:
Where you see (x^2 + 6) you put in p.
p 2 - 21 = 4 ( x 2 + 6 )
p 2 - 21 = 4p
p 2 - 4p - 21 = 0
:)
Which two triangles are congruent by the SAS Theorem?
Answer:
triangle ABC and triangle HFG, I know it is filled out as DCE, but I don't see any triangle DCE
Step-by-step explanation:
check the sides and the angles
A forest covers 48,000 acres. A survey finds that 0.6% of the forest is old-growth trees. How many acres of old-growth trees are there?
Answer:
288
Step-by-step explanation:
48000*0.6/100=288
Answer:
[tex]0.06 * 48 000 = 2,880 acres[/tex]
Cheers :D
A bullet train can travel at 170 miles per hour. Will a graph representing distance in miles compared to time in hours show a proportional relationship? Explain
Answer:
yes
Step-by-step explanation:
the relationship between the hours and miles traveled is a direct relationship therefor would be able to be graphed as a linear function.
Tell whether the fractions are equivalent. Write = or [tex]\neq[/tex]
3/4 ____ 8/12
A solid right square prism is cut into 4 equal pieces parallel to its bases. The
volume of each piece is V = 1/4s2h.Solve the formula for s
Answer:
Step-by-step explanation:
If the volume of each piece is V = 1/4s²h then formula for s is 2√V/h
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that a solid right square prism is cut into 4 equal pieces parallel to its bases
The volume of each piece is V = 1/4s²h.
We have to solve for s
4V/h=s²
Take square root on both sides
√4V/h = s
2√V/h = s
Hence, if the volume of each piece is V = 1/4s²h then formula for s is 2√V/h
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
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For each value of U determine whether it is a solution to 35>24+u
julieta drew the triangle that is shown below. julieta rotated the triangle 180 degrees clockwise about the origin. what is the new triangle?
Step-by-step explanation:
The coordinates of the rotated triangle is A' ( -1, -1 ) , B' ( -3 , -2 ) , C' ( -2 , 2 )
What is Rotation?The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.
90° clockwise rotation: (x,y) becomes (y,-x)
90° counterclockwise rotation: (x,y) becomes (-y,x)
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
Given data ,
Let the triangle be represented as ABC
Now , the coordinates of the triangle ABC is
The coordinate of A = A ( 1 , 1 )
The coordinate of B = B ( 3 , 2 )
The coordinate of C = C ( 2 , -2 )
Now , on rotating the triangle ABC by 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
Substituting the values in the equation , we get
The rotated triangle will have the coordinates A'B'C'
The coordinate of A' = A' ( -1 , -1 )
The coordinate of B' = B' ( -3 , -2 )
The coordinate of C' = C' ( -2 , 2 )
Hence , the coordinates of the triangle is A' ( -1, -1 ) , B' ( -3 , -2 ) , C' ( -2 , 2 )
To learn more about rotation click :
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Find the volume of a square based pyramid with a base length of 8 m and a height of 14 m.
[tex]V = \frac{1}{3} \times base \: area \: \times height \\ [/tex]
[tex]V = \frac{1}{3} \times {8}^{2} \times 14 \\ [/tex]
[tex]V = \frac{1}{3} \times 64 \times 14 \\ [/tex]
[tex]V = \frac{896}{3} \: \: \: {m}^{3} \\ [/tex]
Which statement is true ?
Answer:
d
Step-by-step explanation:
plan 2 grows exponentially so it grows at a faster rate than plan 1, even though plan 1 starts with 100 members
Please do this step by step!
Answer:
Step-by-step explanation:
Let the amount creating equality = x
10% x + 625 = 20%x Convert The percentages to a decimal
10/100 x + 625 = 20/100 x Multiply both sides by 100
10x + 62500 = 20 x Subtract 10x from both sides
62500 = 20x - 10x Combine
62500 = 10x Divide by 10 on both sides
62500/10 =10 x/10
6250 = x
The equality is reached when 6250 sales is made.
HELP PLS ASAP!!!!!!! I WILL GIVE BRAINLIEST, 5 STARS, AND A THANKS PLS HELP
Eloise bought 2 boxes of crackers to share with her friends. Her friends ate 1/2 of the first box and 2/3 of the second box. How many boxes were left over?
A. 1/2 box
B. 3/5 box
C. 5/6 box
D. 1 2/5 box
Answer:
c
brainlest
Step-by-step explanation:
Robert earns $498.00 for 40 hours of work. How much does he earn if works 30 hours at the same pay rate? Do not round your answer.
Answer:$373.50
Step-by-step explanation:
$498.00 divided by 40 is 12.45
12.45 times 30 is $373.50
❗❗CORRECT ANSWER+EXPLANATION=BRAINLIEST❗❗
Simplify: (question in the pic)
The simplified form of the function is [tex]f(x) = \frac{x+3}{x}[/tex]
Functions and equationGiven the following function as shown:
[tex]f(x)=\frac{x^2-9}{x^2-3x}[/tex]
This can be factorized as:
[tex]f(x)=\frac{x^2-3^2}{x(x-3)}\\f(x)= \frac{(x+3)(x-3)}{x(x-3)} \\[/tex]
Cancel out the common terms:
[tex]f(x) = \frac{x+3}{x}[/tex]
Hence the simplified form of the function is [tex]f(x) = \frac{x+3}{x}[/tex]\
Learn more on functions here: https://brainly.com/question/10439235
Hi Phoenix! :)
I'm much late lol.
Answer:
[tex]\boxed{ \cfrac{x + 3}{x}} [/tex]
Step-by-step explanation:
Given:
[tex] \cfrac{x {}^{2} - 9}{x {}^{2} - 3x } [/tex]
Solution:
[Here the best option is to factorise the expression.]
Rewrite the numerator of the expression as
[tex] \cfrac{x {}^{2} - 3 {}^{2} }{x {}^{2} - 3x} [/tex]
It can be seen that the numerator is like an algebraic identity:
> a² - b² = (a+b)(a-b)
ATP, numerator : a = x² and b = 3²
[tex] \cfrac{(x + 3)(x - 3)}{ {x}^{2} - 3x} [/tex]Now in the denominator take x common:
[tex] \cfrac{(x + 3)(x - 3)}{x(x - 3)} [/tex](x-3) in the denominator and (x-3) in the numerator gets canceled.
[tex] \cfrac{(x + 3) \cancel{(x - 3)}}{x \cancel{(x - 3)}} [/tex][tex] \boxed{\cfrac{x + 3}{x} }[/tex]Welp,Done, that's it! :D
Addition and subtraction of fractions! find the missing number of 5/6= -/12
The ratio of 70 minutes to 2 hours is
Hey there!
70 minutes
= 1 hour 10 minutes
2 hours
= 60 minutes * 2 minutes
= 60 minutes + 60 minutes
= 120 minutes
70/120
= 70 ÷ 10 / 120 ÷ 10
= 7 / 12
Therefore, your answer is: 7:12 OR 7/12
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
i really need help on my question
Answer:
D
Step-by-step explanation:
-1.25 is less than -1.02 and 1.4.
> -1.25 + 1.02 = -0.23
1.4 is a greater amount because it is a positive number
So, if you put it this way, -1.25 is lesser, -1.02 is the 2nd least, & 1.4 is the greatest.
Which means your overall answer should be -1.25 < -1.02 < 1.4
3) The recipe calls for 6 cups of flour for every 2 1/3 cups of sugar. How many cups of flour
are needed per cup of sugar?
Answer:
Im pretty sure its 3 cups
Step-by-step explanation:
