In circle B, given isosceles triangle BTX, BA ⟂ WX, and WX = 10, what is the radius of circle B rounded to the nearest whole number?
Answers
Solution :
We observe that :
[tex]$\overline {BA} \perp \overline {WX}$[/tex]
But BA is the perpendicular.
From the center B and WX is a chord.
Therefore, TW = TX (perpendicular from the centre of a circle to a chord bisects it)
Consider Δ BTX,
∠BTX = 90° (BA ⊥ WX)
BT = XT (Δ BTX is isosceles)
Since the angles opposite to equal sides are equal of a triangle arc are equal.
∠BTX = ∠BXT
But in the triangle,
∠TBX + ∠TXB + ∠BTX = 180°
∠TBX + ∠TBX + 90° = 180°
2 ∠TBX = 90°
∠TBX = 45°
From trigonometry, we get
[tex]$\sin \theta =\frac{TX}{BX}$[/tex] ...............(1)
WX = 10
i.e., TX + TW = 10
But TX = TW
2 TX = 10
Tx = 5
BX = radius of circle.
∴ [tex]$\sin 45^\circ = \frac{5}{BX}$[/tex]
[tex]$\frac{1}{\sqrt2} = \frac{5}{BX}$[/tex]
[tex]$BX = 5\sqrt2$[/tex]
[tex]$=5 \times 1.41$[/tex]
= 7
Therefore, the radius of the circle is 7 units.
Related Questions
Solve : 3X + 3x + 1 + 3x + 2 = 39
Answers
Step-by-step explanation:
[tex]3x + 3x + 1 + 3x + 2 = 39 \\ 9x + 3 = 39 \\ 9x = 39 - 3 \\ 9x = 36 \\ x = \frac{36}{9} \\ x = 4[/tex]
Answer:
x = 4
Step-by-step explanation:
combine all of the 3x first to get:
9x + 1 + 2 = 39
9x + 3 = 39
subtract 3 from both sides:
9x = 36
divide by 9
x = 4
Which points are possible approximations for this system? Select two options.
Answers
Step-by-step explanation:
second: (2.2,-1.4)
third: (2.2,-1.35)
Step-by-step explanation:
hope it helps✨
PLEASE HELP IT IS DUE IN TWO HOURS AND I CANT UNDERSTAND IT PLSSSSSS
Answers
The distance from Tre’s house to Owen’s house is 10 miles.
The distance from Owen’s house to Alejandro’s house is 14 miles.
The distance from Alejandro’s house to the beach is about 10.77 miles.
The total distance of the trip to the beach is about 33.53 miles
Step-by-step explanation:
What does media literacy mean?
A. The practice of reading things that are on a screen
B. The practice of being able to identify the different types of media
C. The practice of being able to access, analyze, and evaluate media
D. The practice of using multiple media at one time
Answers
Answer:
C.
Step-by-step explanation:
Media literacy encompasses the practices that allow people to access, critically evaluate, and create or manipulate media.
A picture is 46 cm by 32 cm. A scale diagram of the picture must fit in a space that is 3 m by 2 m. Which scale would be the most reasonable one to use for the scale diagram?
Answers
Answer:
A picture that is 46cm by 32 cm must fit in a space that is 3m by 2m
First, let's rewrite both of these dimensions in the same units.
Knowing that:
1m = 100cm
Then the dimensions of the space can be rewritten from:
3m by 2m
to:
300cm by 200cm
So, if we enlarge our original picture by a scale factor K, the new dimensions of the picture will be:
K*46cm by K*32cm
Now we just need to find a value of K such that:
K*46cm is something near to 300cm
K*32cm is something near to 200cm
First, we can solve the equation:
K*46cm = 300cm
solving this for K we get:
K = 300cm/46cm = 6.5
While if we solve the equation:
K*32cm = 200cm
we get:
K = 200cm/32cm = 6.25
So we got two possible scale factors.
Which one we should take?
Notice that if we wanted to use the larger one (K = 6.5) for the 32cm side. the new length would be:
32cm*6.5 = 208cm
This is larger than the 200cm of space that we have
Then we can not select the larger option, we can only take the other value:
K = 6.25
Then we can conclude that a reasonable scale factor to use is K = 6.25
Which of the following statements is false?
Answers
Answer:
option D is false it's not parallelogram
In ΔABC, m∠A=a, m∠B=β, m∠C=y. AB = c, AC = b, BC = a. Find the remaining parts of each triangle if the following parts are given.
a=5, b=7, y=31°
Answers
Answer:
9.013 square units
Step-by-step explanation:
Need answer asap the topic is inverses and cxompositions in algebra 2
Answers
Answer:
2nd option
Step-by-step explanation:
To find g(f(x)) , substitute x = f(x) into g(x)
g(x + 3) = [tex]\sqrt{x+3}[/tex] + 7
Answer:
To find g(f(x)) , substitute x = f(x) into g(x)
g(x + 3) = \sqrt{x+3}
x+3
HELPHELPHELPHELPHELP
Answers
Answer:
2¼ mph
Step-by-step explanation:
It takes ⅓hour to walk to the library.
⅓ •3 = 1 hour
¾ • 3 = 9/4 = 2¼ miles/hour
Find angle CBA
pls help
Answers
Answer:
40
Step-by-step explanation:
u can draw a line at point c parallel to line ab
angle at d and lower part of c is interior angle so u can find the value at lower part of c that is 180-145=35
so point c 75-35=40 is upper part of point c
upper part of c and angle b is alternate angle so both angle are the same
angle cba is 40
Answer:
<CBA = 40°
Step-by-step explanation:
If AB is parallel to DE, you can make an irregular pentagon by continuing AB and drawing a line perpendicular to DE. The sum of the interior angles of a pentagon is 540. You can use this to solve for the supplement of <CBA, then subtract that from 180. (I’m sure there’s an easier way, but I cant think of one right now).
540-90-90-145-75=x
140=x
<CBA=180-140= 40°
Please someone explain
Triangles and angles
X=______ degrees
X 48
96
Answers
Exterior Angle property = sum of interior opposite angle is equal to the exterior Angle
x= 48+96
x= 144°
Answer:
144°
Step-by-step explanation:
x is an exterior angle of the triangle.
Angles 96° and 48° are interior angles of the triangle that are not adjacent to angle x. Angles 96° and 48° are called the "remote interior angles" of exterior angle x.
Theorem:
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
x = 48 + 96
x = 144
Answer: 144°
2, Nine people fit comfortably in a 3 ft. by 3 ft. area. Use this value to
estimate the size of a crowd that is 8 yards deep and 1 mile long.
Determine the Ratio? A
Ratio = 9 x (3x3). B
O Ratio = 9/3
C
Ratio = 9/(3x3)
D Ratio = 8/5280
Answers
The ratio for Nine people fit comfortably in a 3ft by 3ft area is [tex]\frac{9}{3X3}[/tex]
Option C [tex]Ratio =\frac{9}{3X3}[/tex]
Size of crowd: [tex]\frac{9}{3 \cdot 3} \cdot 24 \cdot 5280[/tex]
Given :
Nine people fit comfortably in a 3 ft. by 3 ft. area
To find : we need to estimate the size of a crowd that is 8 feet deep and 1 mile long. we need to determine the ratio as well
Ratio = number of people / total area
[tex]Raio=\frac{9}{3X3}[/tex]
To find the size of the crowd , convert yards into feet and mile into feet
1 yard = 3 miles
8 yards= 3 times 8 = 24 feet
1 mile = 5280 feet
Now we find the area in feet
[tex]24 \cdot 5280[/tex]
size of the crowd=ratio times the area in feet
[tex]\frac{9}{3 \cdot 3} \cdot 24 \cdot 5280[/tex]
Learn more : brainly.com/question/24367786
Use the interactive to solve. What is the difference between –5 and 3?
Answers
difference is another way to say subtract so it could be shown as (-5) - 3
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{When you hear the word \underline{\underline{difference}} in math it means subtract/}\\\large\text{subtraction}[/tex][tex]\large\text{When you hear the word \underline{\underline{sum}} in math it means add/addition}[/tex][tex]\large\text{When you hear the word \underline{\underline{product}} in math it means multiply/}\\\large\text{multiplication}[/tex][tex]\large\text{When you hear the word \underline{\underline{quotient}} it means divide/division}[/tex][tex]\large\text{Question reads \underline{\underline{What is the \boxed{\large\text{DIFFERENCE}} between -5 \& 3}} ?}[/tex]
[tex]\large\text{Fun fact: you can use a number line to find your result as well.}\\\large\text{For example in this equation you START at -5 and move down 3}\\\large\text{spaces to your left}[/tex]
[tex]\large\text{REMEMBER: we said difference means \boxed{\large\text{subtract}}, so we have to}\\\large\text{\underline{subtract} both numbers from each other to find their differences.}[/tex]
[tex]\large\text{-5 - 3}\\\large\text{= \bf -8}[/tex]
[tex]\large\text{So, the DIFFERENCE between -5 \& 3 is \boxed{\bf -8}}[/tex]
[tex]\boxed{\boxed{\huge\text{The difference is: \boxed{\bf -8}}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find the surface area of the composite figure,
2 cm
6 cm
14 cm
8 cm
8 cm
4 cm
6 cm
2 cm
SA = [?] cm²
Answers
A class of 245 students went on a field trip. They took 9 vehicles, some cars and some buses. Find the number of cars and the number of buses they took if each car holds 5 students and each bus hold 45 students.
Answers
Answer:
4 cars and 5 buses
Step-by-step explanation:
245÷ 45=5.4
45×5=225
245-225=20
20÷5=4
Pls help and fast! 17 points!
Answers
Answer:
54 square units
Step-by-step explanation:
144 - 18 - 4(18) = 54 square units
how can i learn math well?
Answers
Answer:
you can use brainly because the ppl on here are smarter than all of us and they also explain how to solve answer so you can focus really hard to understand heh
what is the one solution for the linear equations y=3x-5 and y=-3x+7
Answers
Answer:
y=1 and x=2
Step-by-step explanation:
Add the two linear equation and you will have 2y=2, y=1. Plugging this in any equation, we have x=2
Answer:
The solution is (2,1)
Step-by-step explanation:
Set the two equations equal
y=3x-5 and y=-3x+7
3x-5 = -3x+7
Add 3x to each side
3x-5+3x = -3x+7+3x
6x-5 = 7
Add 5 to each side
6x-5+5 = 7+5
6x = 12
Divide by 6
6x/6 = 12/6
x=2
Now find y
y =3x-5
y=3(2)-5
y = 6-5
y=1
The solution is (2,1)
85°
4x + 21°
what do I am suppose
Answers
Answer:
x= 16
4x+21 = 85 degrees
Step-by-step explanation:
The angles shown are vertical angles and vertical angles are equal
85 = 4x+21
Subtract 21 from each side
85 -21 = 4x+21-21
64 = 4x
Divide by 4
64/4 = 4x/4
16 = x
Answer:
16degrees
Step-by-step explanation:
As these angle are (vertically opposite angles)
So,85=4x+21,
85-21=4x
x=64/4
x=16degrees
G is a transformation of f. The graph below shows f as a solid blue line and g as a dotted red line. What is the formula of g in terms of f?
Answers
Answer: f(x-2) which is choice A.
The blue f(x) curve is shifted 2 units to the right to get the red g(x) dashed curve.
============================================================
Explanation:
For now, ignore the red dashed curve g(x). Imagine that the blue curve f(x) is fixed in place. If we shifted the xy axis to the left 2 units, then this gives the illusion the blue curve is moving even though the curve is fixed in place.
The operation "shift xy axis 2 units to the left" means each x input is 2 units smaller. So each x input is now x-2.
Therefore, going from f(x) to f(x-2) will shift the blue curve 2 units to the right to land perfectly on the red dashed g(x) curve.
What is the range & domain of the set
R: {(−4, 23), (25, 17), (-15, -29), (32, 21), (3, −10)}
Answers
This question is solved using range and domain concepts. Doing this, it is found that:
The domain is: {-15, -4, 3, 25, 32}The range is: {-29, -10, 17, 21, 23}--------------------------------------
Domain: In a data-set, the domain is composed by the input values.Range: In a data-set, the range is composed by the output values.--------------------------------------
In a set of ordered pairs, the first term in a pair represents the input and the second represents the output.In this set, the inputs are: -4, 25, -15, 32, 3The outputs are: 23, 17, -29, 21, -10Thus:
The domain is: {-15, -4, 3, 25, 32}The range is: {-29, -10, 17, 21, 23}A similar question is given at https://brainly.com/question/18141895
a kitchen floor is 9 feet long and 6 feet wide. the number of yards of molding needed to old the linoleum around the outside edge is
Answers
Answer:
30 feet
Step-by-step explanation:
The molding needed would be equal to the perimeter of the kitchen floor. The perimeter of the kitchen floor is 2*(9+6)=30 feet
A kitchen floor is 9 feet long and 6 feet wide of rectangle, then the perimeter of the kitchen floor is 30 feet.
How to find the perimeter of a rectangle?For a rectangle with length and width L and W units, we get:
Perimeter of the rectangle = 2(L + W) \: \rm unit
A kitchen floor is 9 feet long and 6 feet wide is given.
The molding needed would be equal to the perimeter of the kitchen floor.
The perimeter of the kitchen floor = 2 (9+6)
The perimeter of the kitchen floor = 30 feet
Therefore, A kitchen floor is 9 feet long and 6 feet wide of rectangle, then the perimeter of the kitchen floor is 30 feet.
Learn more about the perimeter;
https://brainly.com/question/4762047
#SPJ2
please help with question 6.
A,b,c and d
Answers
9514 1404 393
Answer:
a) 6.4 m
b) 5.7 m
c) 6.3 m
d) 6.0 m
Step-by-step explanation:
The benefit of using a spreadsheet for repetitive calculations such as these is that it can also help with the addition/subtraction necessary to find the length not given directly.
In the attached, the "a" length is the one requiring arithmetic; the "b" length is given directly on the diagram, and the "c" length is the hypotenuse of the right triangle with legs "a" and "b". "c" is the direct distance from A to B.
For example, consider figure (a). The horizontal distance from A to B is 10 m-6 m = 4 m. In the attached spreadsheet that difference is entered in row 'a', column 'a' as "=10-6". The length "c" is computed using the Pythagorean theorem:
c² = a² +b²
c = √(a² +b²)
For figure (a), this is ...
c = √(4² +5²) = √41 ≈ 6.4 . . . meters
solve for θ:
sin(θ-70)=cos(θ)
pls help and explain step by step
thank you
Answers
Answer:
Use this rule : cosx = sin (90 - x)
sin( x -70) = sin (90 - x)
x-70 = 90 - x
2x = 160
x = 80
In parallelogram ABCD, what is BDC?
Answers
Answer:
25
Step-by-step explanation:
<ABD=<BDC
Check it out
Answer:
∠ BDC = 25°
Step-by-step explanation:
Since ABCD is a parallelogram , then
AB and DC are parallel , so
∠ BDC = ∠ ABD = 25° ( alternate angles )
A fruit seller bought 160 kg of apples at Rs. 32 per kg. He sold one fourth of them at Rs. 40 per kg and sold the rest at Rs. 31 per kg. Find his profit or loss.
Answers
Answer:
A fruit seller bought 160 kg of apples at Rs. 32 per kg. He sold one fourth of them at Rs. 40 per kg and sold the rest at Rs. 31 per kg. Find his profit or loss.
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can you please help me with this.
Answers
Answer:
Step-by-step explanation:
The equation for an arithmetic sequence is
[tex]a_n=a_1+d(n-1)[/tex] where n is the position of the number in the sequence, a1 is the first number in the sequence, and d is the difference between the numbers in the sequence.
Our first number is 2, so a1 = 2; to get from 2 to 5 we add 3, to get from 5 to 8 we add 3. That means that d = 3. Filling in the standard form of the equation:
[tex]a_n=2+3(n-1)[/tex] which simplifies to
[tex]a_n=2+3n-3[/tex] and a bit more to
[tex]a_n=3n-1[/tex] (which should tell you that arithmetic sequences are lines!)
Finding the 13th number simply requires that we replace n with 13 and solve:
[tex]a_{13}=3(13)-1[/tex] so
[tex]a_{13}=38[/tex]
Answer:
38
Step-by-step explanation:
This isn't the most efficient way but it's the best I can do.
2, 5, 8, 11....
The pattern is that we add 3 every time.
2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38,
1 , 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
We can see that 38 is the 13th term of the sequence.
Answer ASAP please!
…
Answers
Answer:
"A" seems to be incorrect....
Step-by-step explanation:
"A" seems to be incorrect....
[tex]\frac{\left(\sin \left(60^{\circ \:}\right)\cdot \:300\right)}{\sin \left(90^{\circ \:}\right)}=150\sqrt{3}\quad \begin{pmatrix}\mathrm{Decimal:}&259.80762\dots \end{pmatrix}[/tex]
Angela has a rectangular piece of paper and cuts a rectangle out of a corner what are the area and perimeter of the resulting shape help me find the perimeter only
Answers
The perimeter of a shape is the summation of the visible lengths of the shape. The area; however, is the product of the length and the width of the shape
The perimeter of the figure is 74cm and the area of the figure is 231 square cm
I've added shape as an attachment.
The perimeter is the sum of all side lengths. So, we have:
[tex]Perimeter = 6cm + 7cm + 15cm + 9cm + 21cm + 16cm[/tex]
[tex]Perimeter = 74cm[/tex]
To calculate the area, we split the shape into 2.
The first has the following dimension:
[tex]Length = 6cm[/tex]
[tex]Width = 7cm[/tex]
While the second has the following dimension
[tex]Length = 21cm[/tex]
[tex]Width = 9cm[/tex]
The area of the shape is:
[tex]Area = 6cm \times 7cm + 21cm\times 9cm[/tex]
[tex]Area = 231cm^2[/tex]
Hence, the shape has a perimeter of 74cm and an area of 231 square cm
Read more about area and perimeters at:
https://brainly.com/question/11957651
Correct answer gets 5 star
Answers
Answer:
Step-by-step explanation:
A
