1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
andre [41]
3 years ago
13

In isosceles triangle ∆ABC,

Mathematics
1 answer:
Hitman42 [59]3 years ago
3 0
Check the picture below.

the triangle is an isosceles, meaning it has two twin sides, that make two twin angles, namely AB = BC, and the angles at A and C are twins as well.

now, the AD segment, is an angle bisector, meaning it cuts the angle at A in two equal halves, so if say the angles are x° each, then the bisectors cuts it in (x/2)°.

now, we know ∡ADB is 110°, therefore its supplementary angle, in green, is 70°.

recall that the sum of all interior angles in a triangle is 180°, thus

\bf 70~+~\cfrac{x}{2}+x=180\impliedby \textit{let's multiply both sides by the LCD 2}
\\\\\\
2\left( 70~+~\cfrac{x}{2}+x \right)=2(180)\implies 140+x+2x=360
\\\\\\
3x=220\implies x=\cfrac{220}{3}\implies x=73\frac{1}{3}\\\\
-------------------------------\\\\
\measuredangle B+x+x=180\implies \measuredangle B+\cfrac{220}{3}+\cfrac{220}{3}=180
\\\\\\
\measuredangle B=180-\cfrac{440}{3}
\implies 
\measuredangle B=\cfrac{540-440}{3}\implies \measuredangle B=\cfrac{100}{3}
\\\\\\
\measuredangle B=33\frac{1}{3}

You might be interested in
Suppose you toss a 6-sided die 40 times, with 14 tosses landing on the five. What percentage of the tosses would be fives?
Alex777 [14]
\dfrac{14}{40}\cdot100\%=35\%
3 0
3 years ago
Read 2 more answers
The exponential distribution applies to lifetimes of a certain component. Its failure rate is unknown. Find the probability that
wlad13 [49]

Answer:

a) 0.0821

b) 0.0111

c) 0.0041

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

f(x) = \lambda e^{-\lambda x}

In which \lambda is the decay parameter.

The probability that x is lower or equal to a is given by:

P(X \leq x) = \int\limits^a_0 {f(x)} \, dx

Which has the following solution:

P(X \leq x) = 1 - e^{-\lambda x}

Either it lasts more 5 years or less, or it survives more than 5 years. The sum of the probabilities of these events is decimal 1. So

P(X \leq 5) + P(X > 5) = 1

In all 3 cases, we want P(X > 5). So

P(X > 5) = 1 - P(X \leq 5)

In which

P(X \leq 5) = 1 - e^{-5\lambda}

(a) lambda=.5

P(X \leq 5) = 1 - e^{-5*0.5} = 0.9179

P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9179 = 0.0821

(b) lambda=0.9

P(X \leq 5) = 1 - e^{-5*0.9} = 0.9889

P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9889 = 0.0111

(c) lambda=1.1

P(X \leq 5) = 1 - e^{-5*1.1} = 0.9959

P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9959 = 0.0041

7 0
3 years ago
You just bought a dog and need to put a fence around your yard. If your yard is 22.5 ft by 28.5 how many feet of fencing will yo
Diano4ka-milaya [45]

Answer:

102 feet of fencing.

Step-by-step explanation:

Since this is asking to <u> enclose </u> the yard, it is a perimeter question.

22.5 x 2 = 45

28.5 x 2 = 57

45 + 57 = 102

102 is your answer.

Hope this helps.

4 0
3 years ago
Read 2 more answers
When we slice a three-dimensional object, we expose new faces that are two dimensional. The two-dimensional face is called _____
zlopas [31]

Answer:

Cross section

Step-by-step explanation:

Cross section refers to the new two dimensional face exposed when we slice through a three dimensional objects.

It can also be the surface or shape exposed by making a straight cut through something, especially at right angles to an axis.

Cross section is the plane surface(two-dimensional objects) formed by cutting across a solid shape (three-dimensional shape) especially perpendicular to its longest axis.

8 0
3 years ago
Help me find the scale factor​
atroni [7]
The scale factor for the first one is 2.25
And for the second one it’s 7
I hope this helps :)
3 0
3 years ago
Other questions:
  • Juan cuts a piece of paper in half. he then cuts each half into thirds and each of those pieces into eights. finally, he cuts ea
    11·1 answer
  • Jane arranges m chairs in each of n rows to seat x people.
    13·1 answer
  • String a is 35 centimeters long. String b is 5 times long as string a. Both are necessary to create a decorative bottle. Find th
    14·2 answers
  • Mr. Eaton bought 15 bags of topsoil for his garden. Each bag weighs 45 pounds. What is the total weight of the topsoil Mr. Eaton
    15·1 answer
  • Find the length of each leg. Leave answer in simplest radical form.
    15·1 answer
  • The bakers made 25 each of lemon, apple, and
    14·2 answers
  • The coordinations of A are (1,-6) and the coordinations of C is (-4,2). What are the coordinates of B on AC such that the ratio
    12·1 answer
  • Graph the linear equation x=4.
    6·1 answer
  • Find the equations of the line that:
    15·1 answer
  • The side lengths in yards of a triangle and a square are shown in the diagram. The perimeter of the triangle is equal to the per
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!