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
pls help i’ll mark brainliest!!
Interpret the slope of the function in the terms of the problem.
25 ml of water are lost every hour
5 ml of water are lost every hour
10 ml wat are lost every hour
2mL of water are lost
if 4/3divided by 1/6 then the value of p is between which of the following pairs of numbers
3 and 4
5 and 6
6 and 7
7 and 9
Answer:
7 and 9
Step-by-step explanation:
4/3÷1/6 = 4/3 × 6/1
= 8
So the value of p falls between the range of 7 and 9
PAGE 77/215 #1A-C
What percentage of a dollar is the value of each coin combination?
a. 4 dimes
b. 1 nickel and 3 pennies
c. 5 quarters and 1 dime
?
Answer:4 dimes = 40 cents
1 nickel 3 pennies =8 cents
5 quarters and 1 dime = $1 and 35 cents
step explanation:
What's the answer to this question?
[tex]3\dfrac 23 -1 \dfrac 45 = 3 \dfrac{10}{15} - 1 \dfrac{12}{15}[/tex]
Rest of the options
Yep, it's C. The answer is C
Which expression is NOT equal to 729?
3 × 3 × 3 × 3 × 3 × 3
63
9 × 9 × 9
36
Answer:
6^3
Step-by-step explanation:
3 × 3 × 3 × 3 × 3 × 3=729
6^3=216
3 × 3 × 3 × 3 × 3 × 3=729
3^6=729
Hope this helps :)
3 × 3 × 3 × 3 × 3 × 3
63
9 × 9 × 9
36
6 A local theater charges $26 for each adult ticket and
$17 for each student ticket. For one show, the theater
took in $988 from adults and $731 from students. How
many people attended the performance?
Answer:
81 people
Step-by-step explanation:
Simplify the expression: (5.2 + 6.8)x - (25 ÷ 5)x
Answer:
7x
Step-by-step explanation:
(5.2 + 6.8)x - (25 ÷ 5)x
12x-(25divied by 5)x
12x-5x
7x
I need help on the "the slopes are" part on these 2 plz help
Answer:
Negative reciprocals
tammy has soccer practice every 12 days, basketball 18 days, band practice 20 days, and music class every 24 days. If she has all these practices on the same day today, then how many days will it be until she has all four practices.
Answer:
360 days
Step-by-step explanation:
It would be a whole year until the classes line up on the same day again, because it would only be the exact same date of the next year that they line up.
Hope this helps!
The quotient of a number p and 3 is 24
Answer:
p= 8
Step-by-step explanation:
because 8 x 3 is 24
hope this helps!❄︎
A vendor sells burgers and cookies. A customer buys 2 burgersand 2 cookies for $7.50. Another customer buys 4 burgers and 3 cookies for $13.75. Find the cost of each item.
Answer:
The burgers cost $2.50 and the cookies cost $1.25.
Step-by-step explanation:
Let b represent burgers and c represent cookies.
2b + 2c = 7.50
4b + 3c = 13.75
Step 1: Use one of the two equations and isolate one of the variables.
2b + 2c = 7.50
- 2c -2c
[tex]\frac{2}{2}[/tex]b = [tex]\frac{7.50}{2}[/tex] - [tex]\frac{2}{2}[/tex]c
b = 3.75 - c
Step 2: Plug what you get for b into the second equation.
4(3.75 - c) + 3c = 13.75
15 - 4c + 3c = 13.75
15 - 1c = 13.75
Step 3: Isolate the variable and solve for c.
15 - 1c = 13.75
-15 -15
[tex]-\frac{1}{1}[/tex]c = [tex]\frac{-1.25}{-1}[/tex]
c = 1.25 ← price for cookies
Step 4: Plug in what you have for c into one of the previous equations and solve for b.
2b + 2(1.25) = 7.50
2b + 2.50 = 7.50
- 2.50 -2.50
[tex]\frac{2}{2}[/tex]b = [tex]\frac{5}{2}[/tex]
b = 2.50 ← price for burgers
Now you know the cost of each item:
The burgers cost $2.50 and the cookies cost $1.25.
PLS HELP ASAP
x^2 - 4x-1=0
Solve using formula
Answer:
Your answer would be x=2±√5
Step-by-step explanation:
Albert is 5 years 6 months. How old is Albert in months
Answer:
5x12=60,+6=66
Step-by-step explanation:
Answer:
66 months
Step-by-step explanation:
12months x 5= 60
60 + 6= 66
L shcool W clash royale
Answer:
THEY ARE CONGRUENT BY ASA TEST OF CONGRUENCEIn year one the population of rabbits is 100. In year three the population is 300. Assuming the population is to go unchecked and is linear what will be the population in year 10? Construct a formula for this.
Answer:
the rabbits ran away
Step-by-step explanation:
now its 300 rabbits
How many pounds are in 1 1/2 pounds and 8 ounces?
Answer:
2 pounds
Step-by-step explanation:
Because 8 ounces = 0.5 pounds
1.5+0.5=2
At the movies, tickets cost $16.50 for adults and $5.50 for kids under 12. How many total tickets would someone get if they purchased 11 adult tickets and 16 kids tickets? How many total tickets would someone get if they purchased aa adult tickets and kk kids tickets?
Answer: 27 tickets a+k
Step-by-step explanation:
11+16
There is a 0.9968 probability that a randomly selected 50 year old female lives through the year (based on data from the US department of Health and Human Services). A Fidelity life insurance company charges $226 for insuring that the female will live through the year. If she does not survive the year, the policy pays out $50,000 as a death benefit.
There is a 0.9968 probability that a randomly selected 50-year-old female lives through the year (based on data from the U.S. Department of Health and Human Services).
-------------------
A Fidelity life insurance company charges $226 for insuring that the female will live through the year. If she does not survive the year, the policy pays out $50,000 as a death benefit.
From the perspective of the 50-year-old female, what are the values corresponding to the two events of surviving the year and not surviving?
----
Ans: -226 ; 50,000-226 = 49774
-------------------------
If a 50-year-old female purchases the policy, what is her expected value?
WORK TRIED:
In the event she lives, the value is -$226. In the event she dies, the value is $49,774.
----
E(x) = 0.9968*(-226) + 0.0032(49774) = -$66
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Cheers,
ROR
can someone help with this problem
Check the picture below.
(PHOTO) Please help need this done by tomorrow thank you.
Solve for x. k 2x + 4 4x - 88 x = [?]
Answer:
2x + 4 = 4x - 88
x = 46
Answer:
x = 46
Step-by-step explanation:
These angles are known as corresponding angles. This means they are equal to one another.
[tex]4x-88=2x+4\\2x-88=4\\2x=92\\x=46[/tex]
A researcher estimates that a fossil is 3200 years old. Using carbon-14 dating a procedure used to determine the age of an object the researcher discovers that the fossil is 3600. Find the percent error
Answer:
11.1
Step-by-step explanation:
The percentage error for the given data will be 12.5%
What is the percentage?According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.
The percentage error will be calculated as:-
percent error = (|experimental value - theoretical value| / theoretical value) x 100
In this case, the experimental value is 3600 years (from carbon-14 dating) and the theoretical value is 3200 years (from the researcher's estimate). Plugging these values into the formula:
percent error = (|3600- 3200| / 3200) x 100 = (400/ 3200) x 100 = 12.5%
Learn more about percentage error on:
brainly.com/question/5493941
#SPJ2
Can someone help me please
Answer:
15 - 17 = 0.013333 (1.3333%)
latte drop = 8.3%
gasoline = 9%
Find the slope of the line passing through the points (7.6) and (7.-2).
Is y=1/2x+7 a function
a 25 -ft ladder rests against the side of a house. the distance between the top of the lader and the ground is 17 ft more than the distance between the base od the ladder and the bottom of the house. find both distances.
Answer:
Step-by-step explanation:
x² + (x + 17)² = 25²
x² + x² + 34x + 289 = 625
2x² + 34x - 336 = 0
x² + 17x - 168 = 0
x = (-17 ±√(17² - 4(1)(-168))) / (2(1))
x = 7 or - 24 the negative distance makes no sense, but if we plug our good answer of 7 ft in for the base length, the height comes out to be + 24 ft
base = 7 ft
height = 24 ft
Lin's family has completed 30% of a trip, they have travelled 45 miles. How far is the trip?
Answer:
2 hours
Step-by-step explanation:
Answer:
150 miles
Step-by-step explanation:
45/3=15
15*7=105 15*3=45
105+45=150
15*10=150
:)
Solve the inequality -3p + 7 < -2p+8
p > − 1
............................................................................................
The length of a rectangular garden is 7 feet longer than its width. The garden's perimeter is 178 feet. Find the length of the garden.
Answer: 48
Step-by-step explanation:
l = w + 7
2w + 2l = 178
2w + 2(w + 7) = 178
2w + 2w + 14 = 178
4w = 164
w = 41
l = w + 7
l = 41 + 7
l = 48