In the figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC = 55° and ∠BAC 45°, Find ∠BCD.
Answers
Given,
ABCD is a cyclic quadrilateral in which AC and BD are its diagonals.
[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
[tex] \sf∠DBC= 55° and ∠BAC = 45°[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
[tex] \sf∠CAD = ∠DBC= 55° (Angles \: in \: the \: same \: segment)[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
Thus,
[tex] \sf∠DAB=∠CAD + ∠BAC[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= 55° + 45° [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \sf= 100°[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
We know that the opposite angles of a cyclic quadrilateral are supplimentary.
[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
[tex] \sf ∠DAB +∠BCD = 180°[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
[tex] \sf∠BCD = 180°-100° =80°[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
[tex] \pink{\boxed{\sf{∠BCD = 80°}}}[/tex]
Answer:
∠BCD = 80°
Step-by-step explanation:
Given -ABCD is a cyclic Quadrilateral.
∠DBC = 55°
∠BAC = 45°
To find -∠BDC
Solution..BC is a segment and angles of same segment are equal.=> ∠BAC = ∠BDC
=> 45° = ∠BAC { Angles of same segment BC}
In Triangle BCD
=> ∠BDC + ∠DBS + ∠BCD = 180°
=> 45° + 55° + ∠BCD = 180°
=> 100° + ∠BDC = 180°
=> ∠BDC = 180-100
=> 80° ans.
Related Questions
Drag numbers to the table so it shows a proportional relationship between x and y.
PLEASE HELP
Answers
Answer:
See below ~
Step-by-step explanation:
Finding the proportionality constant, k :
y = kxTake the point (0.5, 3)3 = 0.5kk = 6Table :
[tex]\left[\begin{array}{ccc}0.5&3\\1.5&9\\4.5&27\end{array}\right][/tex]
4m=6m-2/5
First answer get to be brainliest!
Answers
Answer:
m = 1/5Step-by-step explanation:
4m = 6m - 2/5
-2m = -2/5
m = 2/5 : 2
m = 1/5Which of the following figures uses the SSS theorem to prove that AEFG SAHIJ?
Answers
Answer:
W.
Step-by-step explanation:
SSS, or Side-Side-Side is used to prove two triangles similar
Figure W. is the only one that uses three side marks, all of the others use at least one angle to prove them similar.
In a recent survey, 8 people were each asked the number of times they have been on an airplane. Here is a list of the responses.
9, 21, 7, 11, 13, 21, 5, 14
Find the range of the data set.
Answers
Explanation: Range is the difference between the highest and lowest number.
21 - 5 = 16.
Answer: The range of the data set is: " 16 " .
______
Explanation:
The range is calculated by subtracting the lowest value in the given data set from the highest value in the data set.
______
Given: The data set: 9, 21, 7, 11, 13, 21, 5, 14 ;
Let us organize these numbers from lowest value to highest value:
" 5, 7, 9, 11, 13, 14, 21, 21 " ;
Note: This is done by inspection. Note that all eight (8) values are accounted for.
So, we subtract the lowest value in our given data set: "5" ;
from the highest value in our given data set: "21" ; to get the "range":
→ " 21 − 5 = 16 " ;
______
The range is: " 16 " .
______
Hope this is helpful! Best wishes!
The diameter of the circle is 5 inches, the circumference is 15.70 inches, and the area is 19.625 square inches.
Use the formula for area and solve for the value of pi for the circle.
Answers
Answer:
it is approximately 19.63.
Step-by-step explanation:
Area= pi r^2
Noemi decide hacer una cadena de solidaridad. Para esto
ella pide $500 a tres amigos, al día siguiente cada uno de los
amigos pide $500 a otros tres amigos y así sucesivamente.
A) ¿Cuánto dinero se habrá recaudado al 5° día?
B) ¿Cuántas personas colaboraron durante los primeros 5
días?.
Answers
The amount of money collected after 5 days is $181,500
The number of people that collaborated during the first 5
days is 363 people
Calculations and Parameters:To solve this problem, we would use the Geometric Progression with the formula:
[tex]\frac{a(r^n -1)}{r-1} \\[/tex]
Where:
r= 3
a= 3
n= 5
[tex]\frac{3(3^5 - 1)}{3-1} \\[/tex]
= [tex]\frac{3(243 -1)}{2}[/tex]
121 * 3 = 363 people.
Therefore, the amount contributed is $500 * 363= $181,500
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The kinetic energy (K) that an object has varies jointly with its mass (m) and the square of its velocity (v). The equation that represents this relationship is given by [tex]K=kmv^2[/tex] where k is the kinetic energy constant. If a bowling ball of mass 5 kilograms is traveling at 2 meters per second, its kinetic energy is 10 Joules. What is the kinetic energy of a bowling ball of mass 3 kilograms traveling at 2.6 meters per second?
Answers
The kinetic energy of the bowling ball with the mass and traveling at the given velocity is 10.14 Joules.
What is Kinetic Energy?Kinetic energy is simply a form of energy a particle or object possesses due to its motion.
It is expressed as;
K = (1/2)mv²
Where m is mass of the object and v is its velocity.
Given that;
Mass of the bowling ball m = 3kgVelocity of the bowling ball v = 2.6m/sKinetic energy K = ?We substitute the given values into the above equation.
K = (1/2)mv²
K = 0.5 × 3kg × (2.6m/s)²
K = 0.5 × 3kg × 6.76m²/s²
K = 10.14kgm²/s²
K = 10.14J
Therefore, the kinetic energy of the bowling ball with the mass and traveling at the given velocity is 10.14 Joules.
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5 cm
3 cm
5 cm
8 cm
2 cm
7 cm
what is the volume of the prism? show your thinking. organize it so it can be followed by others.
Answers
8400
Step-by-step explanation:
use multiplication
I cant reveal any more things that I know
Find the equation of a line that passes through point (2,4) and has a gradient of 3
Answers
Answer:
y=3x-2
Step-by-step explanation:
y-y0=m(x-x0)
y-4=3x-6
y=3x-2
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
Find the equation of a line that passes through (2,4) and has a gradient of 3.
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
First, let's take a look at our provided information.
| Provided information:-
Point (2,4)Gradient 3What we need to find:-the line's equationHow to find it using our provided information (gradient & point)? write the equation of the line in point-slope form
point-slope form:-[tex]\sf{y-y_1=m(x-x_1)}[/tex]how to solve:-Replace y₁ with 4Replace m with 3 (m is the gradient)Replace x₁ with 2therefore,[tex]\sf{y-4=3(x-2)}[/tex]
[tex]\bigstar[/tex] On simplification,
[tex]\sf{y-4=3x-6}[/tex][tex]\bigstar[/tex] On further simplification,
[tex]\sf{y=3x-6+4}[/tex]Which results in:-
[tex]\sf{y=3x-2}[/tex]Good luck with your studies.[tex]\rule{300}{1}[/tex]
Using the net below, find the surface area of the triangular prism 5 cm 5 cm 4 cm 4 cm 3 cm 3 cm 3 cm 5 cm
Answers
Answer:
54000
Step-by-step explanation:
use multiplication
do ur own work if you want to see if I'm wrong
PLEASE HELP QUICKLY!
Part A: Abe rented a bike at $36 for 5 days. If he rents the same bike for 8 days, he has to pay a total rent of $48.
Write an equation in the standard form to represent the total rent (y) that Abe has to pay for renting the bike for x days. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
(10 points)
Answers
Answer:
(5,36)(8,48)slope = (48 - 36) / (8 - 5)
Step-by-step explanation:
Answer: Equation of the system is y = 4x + 16 and in function form is f(x) = 4x + 16.
Explanation
9 in.
5 in.
4
5 in.
What is the volume of a square pyramid that has a
base length of 5 inches and a height of 9 inches?
cubic inches
Volume of a pyramid: V = Bh Where "B" is the area of the pyramid's base)
Answers
Answer:
75
Step-by-step explanation:
1/3 * 5² * 9 = V
1/3 * 25 * 9
= 75
Tasha has foam blocks stored in a box that measures 214 ft long by 2 ft wide by 2 ft tall.
Each foam block is a cube with 12ft edge length.
How many blocks can fit into the box?
Answers
A line that passes through the points (x, 4) and (6, -1) has a slope of 56. what value of x will yield the given slope?
Answers
The value of x that yields a slope of 56 is 6.09
How to determine the value of x?The given parameters are:
Slope = 56Points: (x,4) and (6,-1)The slope of two points is:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
This gives
[tex]\frac{-1 -4}{6 -x} = 56[/tex]
Evaluate the difference
[tex]\frac{-5}{6 -x} = 56[/tex]
Cross multiply
56(6 - x) = -5
Divide both sides by 56
6 - x = -0.09
Make x the subject
x = 6 + 0.09
Evaluate
x = 6.09
Hence, the value of x that yields a slope of 56 is 6.09
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A survey asked 200 Grade 4 students about their reading preferences. Based on Graph #1, about how many of them would you expect prefer comic books?
i added the graph
Answers
Answer:
D. 80
Step-by-step explanation:
The graph shows that about 3/8 ( 37.5% ) of the students enjoy comic books.
200 × .375 = 75
75 rounded to the nearest tens value is 80
Here are two rectangles. the area of the shaded rectangle is 1/4 the area of the large rectangle. work out the value of x
Answers
The area of the rectangle is the product of length and width. The value of the variable x is 3.6 cm
What is the area of the rectangle?Let L be the length and W be the width of the rectangle.
Then the area of the rectangle will be
Area of the rectangle = L × W square units
The diagram is given below.
Let A₁ be the area of the small rectangle and A be the area of the large rectangle.
A₁ = 1/4 A
4A₁ = A
4 × 2× (12 - x) = 12 × (x + 2)
8(12 - x ) = 12x + 24
96 - 8x = 12x + 24
72 = 20x
x = 3.6
Then the value of the variable x is 3.6 cm
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100 PTS AND WILL GIVE BRAINLY!!!
THE SCENARIO
The Tortoise and the Hare finally have their long awaited rematch. The Tortoise gets a
300 m lead and runs at 0.2 m/s. The Hare begins at the starting line and runs at a rate of 2 m/s. There is also a rat in this race. The Rat starts 350 m ahead of the Hare and runs back towards the starting line at a rate of 0.6 m/s.
THE CALCULATIONS
Create a table of values for each runner in the race. The domain for the race will be 0 ≤ t ≤ 200 seconds. You can decide on 5 time intervals for your table.
Answers
Answer:
Tortoise:
Hare:
Rat:
All will be shown later
Step-by-step explanation:
Equation for Torotise: f(x)=0.2(x)+300
Equation for the Hare: f(x)=2(x)
I hope it helps! I will show you screenshots in the comments
The length of a
rectangle is 12 cm
more than the width.
The perimeter is 44
cm. What is the
length of the
rectangle?
Answers
Answer:
length= 5+ 12= 17
Step-by-step explanation:
will take width as x
then the length is x+12
perimeter = x+ x+12+x+x+12= 44
=4x= 44-24= 36
x= 20/4
x= 5
Consider the function f(x) = log x. Which two transformations can be used to move
the graph of f(x) to the graph of -f(x+4)?
Select all that apply
Answers
The parent function will translate 4 units to the left and reflect over the x-axis option (C) and (E) are correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = log x
First transformation:
Replace x → (x+4)
The parent function will shift left side by 4 units.
Second transformation:
Multiply the function with -1
The function will reflect over x-axis
The function becomes:
g(x) = -log(x+4)
Thus, the parent function will translate 4 units to the left and reflect over the x-axis option (C) and (E) are correct.
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You toss a nickel a penny and a dime what is the probability that the nickel comes up heads
Answers
The penny can land two ways. The nickel can land two ways. The dime can land two ways. The quarter can land two ways. The total number of ways that all of them can land is (2x2x2x2)= 16 possibilities. Only ONE result shows no heads . . . TAIL-TAIL- TAIL-TAIL. All of the other 15 possibilities include at least one HEAD. So the probability is 15/16 = 93.25% .
The figures below are similar. What is v?
Answers
Answer:
v = 16 mm
Step-by-step explanation:
since the figures are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{v}{20}[/tex] = [tex]\frac{28}{35}[/tex] ( cross- multiply )
35v = 560 ( divide both sides by 35 )
v = 16
can someone help me with this
Answers
angles in a triangle always equal to 180° so:
1. all the angles are equal to each other
180°÷3=60°
2.
•we know 1 angle, 68°
• straight lines are 180°-> 180°-126°= 54°
180°-68°-54°= 58°
Write standard form of the equation of the line through the given point with the given slope
through: (4, -4), slope = -1
Answers
Answer:
x+1y=-4
Step-by-step explanation:
use ax+by=c
please help me out!!!
A trapezoid with short base fourteen centimeters, long base thirty-eight centimeters, height sixteen centimeters, and diagonal side lengths twenty centimeters.
320 square centimeters
608 square centimeters
416 square centimeters
560 square centimeters
Answers
Answer:
416 square centimeters
Step-by-step explanation:
Formula for finding area of a trapezoid :
A = 1/2 x (a + b) x h
a and b = parallel sides of the trapezoidh = height of the trapezoidSolving :
A = 1/2 x (38 + 14) x 16A = 8 x 52A = 416 square centimetersAnswer:
416 cm²
Step-by-step explanation:
The figure we are given, is a trapezoid. Let's apply the "area of trapezoid" formula to determine the area of the trapezoid provided.
[tex]\boxed{\text{Area of trapezoid:} \ \dfrac{a_1 + a_2}{2} h}[/tex]
[Where a₁ and a₂ are the measure of the parallel sides and h is the height]
Let's plug the height and the parallel sides into the formula and simplify it:
[tex]\text{Area of trapezoid} = \dfrac{38 + 14}{2} \times 16}[/tex]
[tex]\text{Area of trapezoid} = \dfrac{52}{2} \times 16}[/tex]
[tex]\text{Area of trapezoid} = 26 \times 16}[/tex]
[tex]\boxed{\text{Area of trapezoid} = 416 \ \text{cm}^{2}}[/tex]
Therefore, the area of the trapezoid is 416 cm².
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a drawer contains black socks and white socks. 70% of the socks are black socks.
Answers
Answer:
30% are white socks
Step-by-step explanation:
percent - per 100
100- 70 = 30
=> 30% of the 100 are white socks.
A solid glass sphere is cast with a diameter of 30 cm. find the volume of the sphere. please leave in terms of pi.
a. v = 20pie cm^3
b. v = 40pie cm^3
c. v = 4,500pie cm^3
d. v=14,137pie cm^3
Answers
Answer:
C
Step-by-step explanation:
Recall that the volume of a sphere is given by:
[tex]\displaystyle V = \frac{4}{3}\pi r^3[/tex]
Because the sphere has a diameter of 30 cm, its radius is 15 cm. Therefore, its volume is:
[tex]\displaystyle \begin{aligned} V & =\frac{4}{3}\pi(15\text{ cm})^3 \\ \\ & = \frac{4}{3}\pi(3375\text{ cm}^3) \\ \\ & = 4500\pi\text{ cm}^3 \end{aligned}[/tex]
In conclusion, our answer is C.
what is -3(4+(-7) + (-2( 5) -17) with examples please
Answers
Answer:
90
Step-by-step explanation:
◄) There were 60 dogs at the dog park last Saturday, and 30 of them were purebreds.
Considering this data, how many of the next 18 dogs to arrive at the park next Saturday
should you expect to be purebreds?
purebreds
Submit
Answers
30!outcof 60 were purebreds 30/60 = 1/2
1/2 of the dogs were purebreds.
18 x 1/2 = 9
Answer: 9 dogs
Answer:9 points
Step-by-step explanation:in the hyperproberbillity of things it’s this answer.
what is the approximate of this cone
Answers
Answer:
so the volume of our cone is exactly π ! As we all know, this can be approximated as volume ≈3.14159
Hi everyone i hope you can help with this exercise
Answers
s = area = 11.76
p = perimeter = 16.8
r=2*11.76/16.8=23.52/16.8=1.4
r=1.4
a= 90 degrees
b=36.87 degrees
c=53.13 degrees
triangle is in a circle
Circumradius: R = 3.5