A circle is centered on point B. Points A, C and D lie on its circumference.
If ZABC measures 40°, what does ZADC measure?
Answers
Given:
A circle is centered on point B.
Points A, C and D lie on its circumference.
If [tex]m\angle ABC[/tex] measures 40°.
To find:
The [tex]m\angle ADC[/tex].
Solution:
Central angle theorem: According to this theorem, the central angle is equal to the twice of inscribed angle on the same intercepted arc.
In the given figure [tex]\angle ABC[/tex] is the central angle and [tex]m\angle ADC[/tex] is the inscribed angle on the same arc AC.
Using central angle theorem, we get
[tex]m\angle ABC=2m\angle ADC[/tex]
[tex]40^\circ=2m\angle ADC[/tex]
[tex]\dfrac{40^\circ}{2}=m\angle ADC[/tex]
[tex]20^\circ=m\angle ADC[/tex]
Therefore, the measure of angle ADC is 20°.
Related Questions
Find the value of x.
Answers
9514 1404 393
Answer:
x = 20
Step-by-step explanation:
The external angle at V is half the difference of the subtended arcs:
(65° -25°)/2 = x° = 40°/2
x = 20
on monday 600 cars of different colours were produced in a factory. of these cars, 155 were red cars. a pie cart is to he drawn for the numbers of cars of the different colours produced on monday.
calculate the size, in degrees, of the angle of the sector in the pie chart for res cars.
Answers
Answer:
It is 69 degrees in a pie chart
Step-by-step explanation:
115 out of 600 = 115/600 or 23/120, 69/360
Solve the system of equations. 2y-y=5 and 3x+2y=4
Answers
Answer:
Step-by-step explanation:
Answer:
y=5 x=-2
Step-by-step explanation:
Paisley has $540 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
She buys a new bicycle for $446.60.
• She buys 3 bicycle reflectors for $4.09 each and a pair of bike gloves for $35.82.
• She plans to spend some or all of the money she has left to buy new biking outfits
for $72.82 each.
Which inequality can be used to determine x, the maximum number of outfits Paisley
can purchase while staying within her budget?
O 540 < 494.69% + 72.82
72.82x + 494.69 > 540
Submit Answer
72.82x + 494.69 < 540
540 > 494.69x + 72.82
Answers
The inequality that can be used to determine the maximum budget that can be spent on outfits is 72.82x + 494.69 < 540.
The first step is to determine the total cost of the items bought.
Cost of the bicycle = $446.60.
Cost of the 3 bicycle reflectors = $4.09 x 3 = $12.27
Cost of the bike gloves = $35.82
Total cost = $494.69
The amount left that can be spent on the new biking outfits = $540 - $494.69 = $45.31
The amount of money left is not sufficient to buy the new biking outfits.
To learn more about inequality, please check: https://brainly.com/question/5031619
How many terms are in 3x + 2y - 5?
Answers
Answer:
3
Step-by-step explanation:
3x=1 term
+2y= 2 term
-5= 3 term
Answer:
there are 3 terms in this equation
Step-by-step explanation:
3x --- this is the 1st term
2y --- this is the 2nd term
5 --- this is the 3rd term
(brainliest plz)
A bird is 50 feet above sea level, a fish is swimming 23 feet below sea level. What's the distance between the bird and the fish
Answers
Answer:
73 feet
Step-by-step explanation:
50 + 23 = 73 feet
find x to the nearest 10th help pls
Answers
Answer:
5.9
Step-by-step explanation:
HELP ASAP!!!!!!!!!!!!!!1
Answers
I think that’s the correct answer.
How do you solve:
g(x) = x - 2
( I think the answer is 2 but how?!)
Answers
Answer:
x-2 =0
x=2
Step-by-step explanation:
we take -2 to the anther side it becomes 2
Answer:
-2
Step-by-step explanation:
A function is a rule for working out the values y for the given values x
For example, h = 3x and y = x^2 are functions. The notation g(x) is read as g of x. g is the function. g(x) = 3x means the function of x is 3x
So, when solving to find the value of x, you must substitute x for any given value.
For example, f(x) = 10/x. Work out f(5), you must substitute the 5 into the denominatior of the fraction 10/x . This becomes 10/5, which equals to 2.
But for your question, to find the value of x, substitute x with 0
You end up with -2
Hope this helps
BtW. the above statements are just notes. i thought they might help.
ed made a large cube by gluing together a number of identical small cubes together
Answers
Answer:
thats cool not realy a question tho can I have brainlest
Step-by-step explanation:
Ed painted 95 faces of a large cube.
What is the Cubic equation?Cubic equations are polynomials of degree 3. That means the maximum degree of the polynomial is three.
And the standard form of the cubic equation is;
f(x) = ax³ + bx² +cx +d, where a, b, c, and d are constant coefficients a ≠ 0.
Let's assume that the original cube that Ed made had n small cubes along each edge.
Then the total number of small cubes in the large cube is n³.
Let p be the number of faces that Ed painted.
Each small cube has 6 faces, and if a face is painted, it will not be visible after the large cube is assembled.
So the total number of unpainted faces is 6n³ - p.
When Nicole drops the cube, each small cube will be separated from the others, and all painted faces will become visible.
So the total number of painted faces is equal to p minus the number of small cubes that don't have any painted faces, which is 45.
Therefore, we have a cubic equation:
p - 45 = 6n³ - p.
Simplifying this equation, we get:
2p =6n³ + 45
p = 3n³ + 22.5
We know that p is an integer, so 3n³ + 22.5 must be an integer.
This means that n³ must be a multiple of 2/3.
The smallest integer value of n that satisfies this condition is n = 3.
So Ed made a cube with 3 small cubes along each edge, and he painted:
the value of the cubic equation at 27,
p = 3n³ + 22.5 = 3(27) + 22.5 = 94.5 ≈ 95 faces of the large cube.
Therefore, 95 faces of the large cube.
To learn more about the cubic equation;
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The complete question:
Ed made a large cube by gluing together a number of small identical cubes and then he painted some of the faces of the large cube. His sister Nicole dropped the cube and it broke into the original small cubes. 45 of these small cubes didn't have any painted faces. How many faces of the large cube did Ed paint?
The function N(t) = 100e^−0.023t models the number of grams in a sample of cesium-137 that remain after t years. On which interval is the sample's average rate of decay the fastest?
Answers
Options:
A. [1,10] B. [10,20] C. [15,25] D. [1,30]
Answer:
A. [1,10]
Step-by-step explanation:
Given
[tex]N(t) = 100e^{-0.023t}[/tex]
Required
Interval with the fastest rate of decay
The rate of change over [a,b] is calculated as:
[tex]Rate = \frac{N(b) - N(a)}{b - a}[/tex]
So, we have:
A. [1,10]
[tex]Rate = \frac{N(10)-N(1)}{10 - 1}[/tex]
[tex]Rate = \frac{N(10)-N(1)}{9}[/tex]
Calculate N(10) and N(1)
[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]
[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]
So:
[tex]Rate = \frac{79.45-97.73}{9} = \frac{-18.28}{9} = -2.03[/tex]
B. [10,20]
[tex]Rate = \frac{N(20)-N(10)}{20 - 10}[/tex]
[tex]Rate = \frac{N(20)-N(10)}{10}[/tex]
Calculate N(20) and N(10)
[tex]N(20) = 100e^{-0.023*20} = 100e^{-0.46} = 63.13[/tex]
[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]
So:
[tex]Rate = \frac{63.13 - 79.45}{10} = \frac{-16.32}{10} = -1.632[/tex]
C. [15,25]
[tex]Rate = \frac{N(25)-N(15)}{25 - 15}[/tex]
[tex]Rate = \frac{N(25)-N(15)}{20}[/tex]
Calculate N(25) and N(15)
[tex]N(25) = 100e^{-0.023*25} = 100e^{-0.575} = 56.27[/tex]
[tex]N(15) = 100e^{-0.023*15} = 100e^{-0.345} = 70.82[/tex]
So:
[tex]Rate = \frac{56.27 - 70.82}{10} = \frac{-14.55}{10} = -1.455[/tex]
D. [1,30]
[tex]Rate = \frac{N(30)-N(1)}{30 - 1}[/tex]
[tex]Rate = \frac{N(30)-N(1)}{29}[/tex]
Calculate N(30) and N(1)
[tex]N(30) = 100e^{-0.023*30} = 100e^{-0.69} = 50.16[/tex]
[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]
So:
[tex]Rate = \frac{50.16 - 97.73}{29} = \frac{-47.57}{29} = -1.64[/tex]
By comparing the values of the calculated rates,
-2.03 is the smallest, in other words; the fastest rate
Hence, the interval [1,10] has the fastest rate of decay
The required average rate of change is the fastest on [tex][1,10][/tex].
The average rate of change :The formula for the average rate of change on the interval [tex][a,b][/tex] is,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{b-a}[/tex]
Now, applying the given function into the above function is,
Now, [tex]a=1,b=10[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{10-1} =-2.03[/tex]
Now, [tex]a=10,b=20[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{20-10} =-1.6325[/tex]
Now, [tex]a=15,b=25[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{25-15} =-1.455[/tex]
Now, [tex]a=1,b=30[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{30-1} =-1.64[/tex]
So the average rate of change is fastest on [tex][1,10][/tex]
Learn more about the topic of the average rate of change:
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Look at the graph shown below the blue line represents an _______ of the graph
Answers
Given:
The graph of a function and a blue line.
To find:
The correct name for the blue line.
Solution:
Domain: It is the set of inputs. These are the x-values for which the function is defined.
Range: It is the set of outputs. These are the y-values for the function.
Asymptote: The function approaches to a line as x approaches to -∞ or ∞ but not intersect the line, then the line is known as asymptote.
y-intercept: It is the intersection point of the function and the y-axis.
From the given graph it is clear that the function approaches to the blue line as x approaches to -∞ but not intersect the blue line.
So, the blue line is an asymptote of the function.
Look at the graph shown below the blue line represents an asymptote of the graph.
the graph shows the function y=3x-1. What are the cordinates of intercepts
Answers
Answer:
[tex]y \: intercept : when \: x = 0 \\ y = (3 \times 0) - 1 = - 1 \\ = > (0, - 1) \\ x \: intercept : when \: y = 0 \\ 0 = 3x - 1 \\ x = \frac{1}{3} \\ = > ( \frac{1}{3} ,0) \\ intercepts : (0, - 1) \: and \: ( \frac{1}{3} ,0)[/tex]
What is the cost of 1 pound of grapes?
Answers
*escribir todos los números que cumplen la siguientes condiciones* a) su modulo es cinco b) es positivo y su módulo es menor que cuatro C) es negativo y su módulo es menor que seis D) su módulo es menor que siente y mayor que tres
Answers
I need help with this asap
Answers
Answer:
C
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
What is the value of x in this equation?
8x + 40 = 180
Answers
Answer:
17.5
Step-by-step explanation:
180 = 40+ 8x
140 = 8x
17.5 = x
Answer:
17.5 is the correct answer to the question
Step-by-step explanation:
8x+40=180
8x=180-40
8x=140
X=140/8
X=17.5
Is this correct???
I’m really worried this is a test worth 100 points?? Pls help if I made a mistake!!???
Answers
Answer:
There's supposed to be nothing in the 7 and 8 columns
Step-by-step explanation:
You were good, but there aren't any in the 7 or 8 columns, making 9 an outlier.
hope this helps:)
A plane is at cruising altitude of 10,200 feet. If the angle of depression to the run way is 18 degrees, what is the distance, to the nearest foot, from the plane to the run way
Answers
Answer: [tex]33,007.9\ ft[/tex]
Step-by-step explanation:
Given
The plane is cruising at an altitude of [tex]h=10,200\ ft[/tex]
The angle of depression is [tex]\theta=18^{\circ}[/tex]
Suppose the distance of the plane to the runway is x
from figure
[tex]\Rightarrow \sin 18^{\circ}=\dfrac{h}{x}\\\\\Rightarrow \sin 18^{\circ}=\dfrac{10,200}{x}\\\\\Rightarrow x=33,007.9\ ft[/tex]
Al resolver la suma de ¾ + 5/4 obtenemos como resultado
Answers
Answer:
2
Step-by-step explanation:
3/4+5/4=8/4=2
Which set of ordered pairs is included in this relation?
A {(-5, 4), (-3, 2), (2, -1), (3, 0)}
B {(-4, 1), (-2, -5), (1, -2), (5, 2)}
C {(-3, -2), (0, 3), (1, -2), (4, 1)]
D {(-2,-5), (-1, 4), (2, -1), (3, 0)}
Answers
Mathmerica Bank offers 2.1% interest compounded yearly
if you open a savings account with them and invest a
minimum of $2,500 dollars.
Answers
Answer:
Total = 2,500 (1.021)^t
Step-by-step explanation:
There is no question but the formula for compound interest is
Total = amount (1 + rate)^time
Total = 2,500 (1.021)^t
find the missing side
please please i need help
Answers
Answer:
6.40312424
Step-by-step explanation:
5^2 + 4^2 = c^2
25 + 16 = c^2
41 = c^2
sqrt41 = c
c is equal to about 6.40312424 (round it if you need to)
Answer:
a^2+b^2=c^2
Step-by-step explanation:
5^2+4^2=6.403^2
c= 6.4
An amusement park charges an entrance fee of $20 and the rides cost $4 each. Suppose you write a function for the total cost for entering the park and riding a. Number of the rides. What is the domain of the function based on the given context?
Answers
Answer:
With the information provided, you can say that the total cost is equal to the entrance fee plus the price per ride for the number of rides, which would be:
C(x)=20+4x,where:
x is the number of rides
The domain of the function refers to all the inputs that the function can have and in this case, the domain consists of all real numbers greater than or equal to zero since x refers to the number of rides and it can't have a negative number.
The density of an object is equal to the quotient of its mass, and volume. An object has a density of 10g per liter and a volume of 40 liters. What is its mass in grams.
Answers
Answer:
400 grams
Step-by-step explanation:
If the equation is density = mass / volume, fill it out to find mass
10 = x / 40
400 = x
x = 400 g
Which is a solution to the system of linear
inequalities? Select all that apply.
y > 2x + 5
y<-3x+5
a. (-5, -1)
b. (0, 2)
c. (-4,1)
d. (-3,0)
Answers
Jeremy is participating in a school fundraiser selling
books and magazines. He sells two fewer magazines
than one-half the number of books he sells. He sells a
total of 16 books and magazines in all. Solve a system
of equations graphically to find the number of books
Jeremy sold.
A) sold 12 books
B) sold 4 books
C) sold 2 books
D) sold 14 books
Answers
Answer:
A
Step-by-step explanation:
12/2 = 6 , 6-2=4 . 12+4 =16
Solve ∣3x−2∣+4=0. Write your smaller answer first.
Answers
Answer:
wrong
Step-by-step explanation:
Find the measure of angle N
Help
Answers
Answer:
direct answer 20
Step-by-step explanation:
What is the measure of each angle if x = 13?
A. 42°, 38°
B. 527, 26°
C 429, 269
D. 527, 38°
The measures of two angles are 4x° and (2x + 12) °
Answers
hope that helps!! pls mark brainliest ☺️