Given:
In triangle ABC, AB = AC, AD is angle bisector and measure of angle C is 49 degrees.
To find:
The value of x and y.
Solution:
In triangle ABC,
[tex]AB=AC[/tex] (Given)
So, triangle ABC is an isosceles triangle and by the definition of base angles the base angles of isosceles triangle are congruent.
In isosceles triangle ABC,
[tex]\angle B\cong \angle C[/tex]
[tex]m\angle B\cong m\angle C[/tex]
[tex]m\angle B\cong 49^\circ[/tex]
The angle bisector of an isosceles triangle is the median and altitude of the triangle. So, the angle bisector is perpendicular to the base.
[tex]m\angle ADB=90^\circ[/tex]
[tex]x^\circ=90^\circ[/tex]
In triangle ABD,
[tex]m\angle DAB+m\angle ABD+m\angle ADB=180^\circ[/tex] [Angle sum property]
[tex]y^\circ+49^\circ+x^\circ=180^\circ[/tex]
[tex]y^\circ+49^\circ+90^\circ=180^\circ[/tex]
[tex]y^\circ=180^\circ-49^\circ-90^\circ[/tex]
[tex]y^\circ=41^\circ[/tex]
Therefore, the correct option is B.
what is a an expression that contains at least one variable
Answer:
An algebraic expression is a type of expression that contains a variable or variables.
What is the value of x? Enter your answer in the box. pe X=
Answer:
x = 26
Step-by-step explanation:
x+64 is a right angle
x+64 = 90
Subtract 64 from each side
x = 90-64
x = 26
Answer:
x = 26°.
Step-by-step explanation:
This is a complementary angle. Complementary angles are two angles that have a sum of 90°.
[tex]90-64=26.[/tex]
[tex]26+64=90.[/tex]
[tex]x=26.[/tex]
If mAD = (17x + 2)°, mAC = (7x - 10°), and m∠ABC = (4x + 15)°, find m∠ABC
Please help
Answer:
m<ABC = 51degrees
Step-by-step explanation:
The angle at the vertex is half the difference of the angles at the intercepted arcs. Hence;
m<B = 1/2 (arcAD - arcAC)
<ABC = 1/2(17x + 2 -(7x - 10°))
4x + 15 = 1/2(17x-7x+2+10)
2(4x+15) = 10x+12
8x + 30 = 10x+12
8x-10x = 12-30
-2x = -18
x = 18/2
x = 9
Get m<ABC
m<ABC = 4x + 15
m<ABC = 4(9) + 15
m<ABC = 36 + 15
m<ABC = 51degrees
The measure of angle ∠ABC = 51 degree.
Since we know that,
For a circle,
The angle at the vertex is half the difference of the angles at the intercepted arcs.
Therefore,
m∠ABD = 1/2 (arcAD - arcAC)
⇒ ∠ABC = (1/2)(17x + 2 -(7x - 10°))
⇒ 4x + 15 = (1/2)(17x-7x+2+10)
⇒2(4x+15) = 10x+12
⇒ 8x + 30 = 10x+12
⇒ 8x-10x = 12-30
⇒ -2x = -18
⇒ x = 18/2
⇒ x = 9
Get m∠ABC
⇒ m∠ABC = 4x + 15
⇒ m∠ABC = 4(9) + 15
⇒ m∠ABC = 36 + 15
⇒ m∠ABC = 51 degree
Learn more about the angle visit:
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At Mathville Middle School, there were 50 students and 50 lockers. Each year for Pi Day (March 14), the students lined up in alphabetical order and performed the following strange ritual. The first student opened every locker. The second student went to every second locker and closed it. The third student went to every third locker and changed it (i.e. if the locker was open, the student closed it; if the locker was closed, the student opened it). In a similar manner, the fourth, fifth, sixth, . . . student changed every fourth, fifth, sixth, . . . locker. After all 50 students had passed by the lockers, which lockers were left open?
PLZZZZ help me T^T
Step-by-step explanation:
This problem is a bit tedious to work out all at once. The first student opens every locker so lockers 1 to 50 are open.
The second student closes every two lockers so every even locker is closed while every odd locker is open. This will repeat over and over and will take too long.
An alternative for this would be checking the factors of each number. For example, 4 has three unique factors, which are 1, 2 and 4. The number of unique factors determine whether the locker is open or closed. In this case, locker 4 will be open after all 50 students finished. Student 1 opens locker 4, student 2 closes locker 4, student 3 doesn't change locker 4 and student 4 opens locker 4. However, students 5 to 50 will never change the locker.
I can't help put all of the answers at once but this should help.
Find the distance between each pair points
Solve for P.
-1 + 14 p = -435
Answer:
P = -31
Step-by-step explanation:
-1 + 14p = -435
Remove the -1 by adding it from both sides.
14p = -434
Remove the 14 by dividing it from both sides.
p = -434/14
p = -31
Answer:
-31
Step-by-step explanation:
-1+14p=-435
14p=-435-(-1)
14p=-435+1
14p=-434
p=-434/14
p=-31
Hey there! Can someone tell me the answer please? Will give brainliest.
Answer:
24 edges, 24 vertices, 8 faces - For that weird Cylender thing.
Step-by-step explanation:
There are six faces on sides (and two on both tops, these don´t have vertices or edges of their own), 4 edges on each one, 4 vertices on each one.
Answer:
There are 6 faces
One up one down one front one backs one right one left
12 edges and 8 ventricles
HELP/ solve for x. Write your answer as "x=__"
Answer:
Hello! answer: x = 50
Step-by-step explanation:
This is a supplementary angle meaning it will add up to 180 degrees! so...
50 × 3 = 150 150 - 20 = 130
130 + 50 = 190 therefore x = 50 hope that helps!
How much heat will be necessary to supply 0.25 kg of a substance with specific heat 0.2 cal / g · ºC, so that its temperature goes from 5ºC to 59ºc? Q = Q = Q = Q =
I have no idea but maybe if you would pay attention in class you would know how to do it. I just need my points so I can keep getting answers. good luck tho
In a specific arithmetic sequence, if -4 is the first term and 10 is the third term, which term is 157?
Step-by-step explanation:
everything can be found in the picture
The nth term of an arithmetic sequence is expressed as Tn = a +(n - 1)d. The 157th term of the sequence is 2180
Arithmetic sequenceThe nth term of an arithmetic sequence is expressed as:
Tn = a +(n - 1)d
where
a is the first termd is the common differencen is the number of termsIf -4 is the first term and 10 is the third term, then;
a = -4
a + d = 10
d = 10 - (-4)
d = 14
Determine the 157th term
T157 = -4 + (157 - 1)(14)
T157 = -4 + (156*14)
T157 = 2180
Hence the 157th term of the sequence is 2180
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Question on image. (5)
will report answers out of question. Thank you
Answer:
AD = 6
Step-by-step explanation:
If a radius is perpendicular to a chord, then it bisects the chord.
Here XB is the radius, AC is the chord. Given XB and AC are perpendicular to each other. Therefore, XB bisects AC at D.
So,
[tex]AD = \frac{1}{2} \times AC = \frac{1}{2} \times 12 = 6[/tex]
Is
−
379
in the sequence below?
−
5
,
−
7
,
−
9
,
−
11
,
−
13
Answer:
no 379s not in the sequence below
6. What is the 10th term of the geometric sequence -20, -10,-5, ... ?
Answer:
-0.0390625
Step-by-step explanation:
each is cut in half
so we do this
20, 10, 5, 2.5, 1.25, .625, .3125, .15625, 0.078125, 0.0390625
Q. Find the missing side
Answer:
What missing side? You're missing a picture.
which of the following inequalities is graphed on the coordinates plane ?
Answer:
It Should Be A
Step-by-step explanation:
Answer:
option D.
[tex]y \geqslant 2x + 2[/tex]
Step-by-step explanation:
we have two points on the line
(0, 2)(-1, 0)using these points to find the equation of the line (shown as red in the figure)
[tex]y - y_{1} = \frac{y _{2} - y _{1} }{x _{2} - x _{1}} (x - x_{1})[/tex]
let,
x₁ = -1 , y₁ = 0x₂ = 0 , y₂ = 2[tex]y - 0 = \frac{2 - 0}{ 0 + 1} (x + 1) \\ y = 2(x + 1) \\ y = 2x + 2[/tex]
so the equation of the required line (boundary line) is y = 2x+ 2
the shaded portion is represented by inequality :-
[tex]y \geqslant 2x + 2[/tex]so, option D is the answer
(-3) x (+5)
What’s the answer to that? Someone help me please
Answer:
[tex] - 15[/tex]
Step-by-step explanation:
We know that,
[tex]( - ) \times ( + ) = (- )[/tex]
So,
[tex] (- 3) \times ( + 5) = - 15[/tex]
hope this helps you.
Have a nice day!
Answer:
-15
Step-by-step explanation:
(-3)*(+5) = -15
which shape has 74 sides
Answer:
Heptacontakaitetragon
I'm not sure though 'cause it ain't a shape, but that's the term for a shape that has 74 sides.
PLS HELP!! WILL GIVE BRAINLIEST!!
Answer:
Step-by-step explanation:
take lcm of (2x-1)(x+2)
lcm=(2x-1)(x+2)
=2(x+2)-1(2x-1)/(2x-1)(x+2)
=(2x+4)-(2x-1)/(2x(x+2)-1(x+2)
=2x+4-2x+1/2x^2+4x-x+2
=4+1/2x^2+3x+3
=5/2x^2+3x+3
What fraction is at point A on the number line below? А ++ 0 + 1 Use the number pad to enter your answers in the boxes.
Answer:
1/2 .Step-by-step explanation: on the number line, draw the number line and mark a point A to represent 1. Now, divide the gap between O and A into two equal parts
If two angles are both vertical and supplementary, can we determine the angles? Is it possible to be both vertical and complementary? If so, can you determine the angles? Explain how you know ASAP
Answer:
Two angles can be vertical and supplementary only if they add up to 90 degrees because there perpendicular.
Step-by-step explanation:
Answer:
90 + 90 = 180, 45 + 45 = 90
Step-by-step explanation:
Supplementary angles add up to 180 and to be vertical angles they need to be equal to each other so 2x = 180
x = 90
Hence both angles will be equal to 90
Complementary angles add up to 90 and as previously stated, to be vertical angles they need to be equal to each other so 2x = 90
x = 45
Hence both angles equal to 45
Hope this helped!
In the United States, only Hawaii has a tropical wet climate. In some parts of Hawaii, rainfall is very heavy- over 400 inches per year on the windward side of the Hawaiian island of Kauai. The table shows the monthly rainfall for one year at a reporting station in Hawaii.
Answer:
Mean = 14.33333333
Median = 11
Mode= 9 and 11
Range = 42
Step-by-step explanation:
To find the mean, add all the numbers
(5+1+15+43+9+9+11+11+14+12+36+6) = 172
Divide by the number of numbers
172/12 = 14.33333333
Median is the middle number when listed from smallest to largest
1,5,6,9,9,11,11,12,14,15,36,43
Split into 2 even groups
1,5,6,9,9,11, 11,12,14,15,36,43
The middle is between 11 and 11
(11+11)/2 = 11
Mode is the number that appears mode often
This has 2 modes, 9 and 11
Range is largest number minus smallest number
43-1 = 42
Find the value of x. please help
Answer:
x= 15
Step-by-step explanation:
Since this is an isosceles triangle, the other angle is also 5x-6
The sum of the angles of a triangle is 180
42+ 5x-6 + 5x-6 = 180
Combine like terms
10x+30 =180
Subtract 30 from each side
10x+30-30 = 180-30
10x = 150
Divide by 10
10x/10 = 150/10
x= 15
Need answer asapppp I have 10 min only!!!
Help me PLZ! I’ll give u brainliest!
Answer:
Step-by-step explanation:
area of card board=(6+4+6+4)×10+2×6×4
=200+48
=248 in²
Describe the behavior of the function h around its vertical asymptote at x=-6.
Answer:
B
Step-by-step explanation:
One good way to look at this is to graph both polynomials, as shown in the picture. A tip to help graph is to factor it out and work from there. For example, in x²+14x+48, we can gather that (x+6)(x+8) is the same thing, and it is easier to then graph it. Similarly, for x²+12x+36, we can factor it out as (x+6)² .
When x²+12x+36 approaches 6, it is getting really close to 0, but it stays positive. When x²+14x+48 approaches 6 from the negative side, it is also getting close to 0, but it's negative. When x²+14x+48 approaches 6 from the positive side, it is positive.
Therefore, on the negative side, there is one positive and one negative (dividing a negative by a positive is negative, and a positive by a negative is also negative) , and on the positive side, there are two positives, forming one answer.The answer is therefore B
the diameter of a circle is 18 miles. What is the area? Give the exact answer in simplest form
Answer:
254.47
Step-by-step explanation:
Raidus of the circle is 9
Formula to find the area is pi r^2
Given that f(x) = 9 − x and g(x) = x^2
Calculate
a) f(3)
b) g(−4)
Answer:
a) f(3) =6
b) g(-4) =16
Step-by-step explanation:
answer to a, substitute X with 3. which will be f(3)=9-3
=6
answer to b, substitute X with -4, which will be g(-4)=(-4)^2
=16
The bakery owner will use both machines to glaze a total of 375 dozen
doughnuts. She plans to start both machines at the same time.
Based on the rates fromwhat is the total number of hours it
will take both machines working together to glaze 375 dozen doughnuts?
Answer:
2250 i think
Step-by-step explanation:
Let’s say you don’t invest at all, and just put $6000 under your mattress every year. How much money will you have in 40 years?
how many solutions -(3 - 6b) = 6b + 5
Answer:
There are no solutions
Steps :
First we expand it
[tex]-3+6b=6b+5[/tex]
Then we add 3 to both sides
[tex]-3+6b+3=6b+5+3[/tex]
Then we simplify
[tex]6b=6b+8[/tex]
Then we subtract 6b from both sides
[tex]6b-6b=6b+8-6b[/tex]
Simplify
[tex]0=8[/tex]
No solutions !
