Restaurants A, B, C, and D lie on a circular lake. Restaurants A and Care near the
road. The angle between the two roads is 70°.
The dashed segments show the path of a boat which sails between the restaurants
and transports guests.
Answers
Answer:
10
Step-by-step explanation:
Angle α in the given problem comes to be 125°.
∠ATC =70°(given)
Suppose the center of the circle is O while both the tangents intersect at T.
As we know quadrilateral ATCO is a cyclic quadrilateral because a quadrilateral constructed by tangents, corresponding points of tangency, and the center of a circle is a cyclic quadrilateral.
What is a cyclic quadrilateral?A quadrilateral with all its vertices on the circumference of the circle is called a cyclic quadrilateral. The sum of opposite angles is always 180° in a cyclic quadrilateral.
So, ∠AOC = 180 - ∠ATC
∠AOC = 180 - 70
∠AOC = 110°
We know that angle made by an arc at the circumference is half of the angle made by the same arc on the center.
So, ∠ABC = 110/2 = 55°.
Quadrilateral ABCD is a cyclic quadrilateral
So, α =180- ∠ABC
α =180-55
α=125°
Therefore, angle α in the given problem comes to be 125°.
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Related Questions
A rectangle has vertices at: A(0, 0), B(0, 9), C(4, 9), D(4, 0) What is the perimeter of the rectangle?
Answers
Answer:
Rectangle Perimeter = 26
Step-by-step explanation:
Rectangle ABCD , Length = parallel horizontal sides are AB & CD, Breadth = parallel vertical sides = BC & AD
AB segment joining A (0,0) - B (0,9) = 9 units. CD joining C (4, 9) & D (4,0) = 9 units. So, Length = 9 units
BC segment joining B (0,9) - C (4,9) = 4 units. AD joining A (0,0) - D (4,0) = 4 units. So, Breadth = 4 units
Perimeter of rectangle = 2 (Length + Breadth)
= 2 (9 + 4)
= 13 x 2 = 26
A random number generator is used to select a number from 1 to 50 (inclusively). What is the probability of selecting the number 28?
(Type an integer or a decimal. Do not round.)
Answers
Answer:
the answer is 1/50
Step-by-step explanation:
A random number generator is used to select an integer from 1 to 50. Since random number generator generates any number randomly, all the numbers from 1 to 50
is this a proportional relationship?
3 2
6 4
9 6
12 8
15 10
Answers
Answer:
Yes
Step-by-step explanation:
I got it right.
Write the equation of the line that passes through (−3,1) and (2,−1) in slope-intercept form
Answers
Answer:
[tex]y=-\frac{2}{5}x-\frac{1}{5}[/tex]
Step-by-step explanation:
The equation of a line is y = mx + b
Where:
m is the slopeb is the y-interceptFirst, let's find what m is, the slope of the line.
Let's call the first point you gave, (-3,1), point #1, so the x and y numbers given will be called x1 and y1.
Also, let's call the second point you gave, (2,-1), point #2, so the x and y numbers here will be called x2 and y2.
Now, just plug the numbers into the formula for m above, like this:
[tex]m = -\frac{2}{5}[/tex]
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
[tex]y=-\frac{2}{5}x + b[/tex]
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(-3,1). When x of the line is -3, y of the line must be 1. (2,-1). When x of the line is 2, y of the line must be -1.Now, look at our line's equation so far: [tex]y=-\frac{2}{5}x + b[/tex]. [tex]b[/tex] is what we want, the -[tex]-\frac{2}{5}[/tex] is already set and x and y are just two 'free variables' sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-3,1) and (2,-1).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!
You can use either (x,y) point you want. The answer will be the same:
(-3,1). y = mx + b or [tex]1=-\frac{2}{5} * -3 + b[/tex], or solving for b: [tex]b = 1-(-\frac{2}{5})(-3)[/tex].[tex]b = -\frac{1}{5}[/tex]. (2,-1). y = mx + b or [tex]-1=-\frac{2}{5} * 2 + b[/tex], or solving for b: [tex]b = 1-(-\frac{2}{5})(2)[/tex]. [tex]b = -\frac{1}{5}[/tex].See! In both cases, we got the same value for b. And this completes our problem.
The equation of the line that passes through the points (-3,1) and (2,-1) is [tex]y=-\frac{2}{5}x-\frac{1}{5}[/tex]
how many perfect squares are there between 2 and 140
Answers
Answer:
11
Step-by-step explanation:
4, 9, 16, 25, 36, 49, 64, 81, 100, 121
There are 10 numbers who are perfect squares.
What is Square of a number?When an integer is multiplied by the same integer, the resultant number is known as a square number. For example, when we multiply 5 × 5 = 52, we get 25. Here, 25 is a square number. Square numbers are always positive, they cannot be negative because when a negative number is multiplied by the same negative number, it results in a positive number.
Properties of Square NumbersThe properties of square numbers are listed below which helps to identify them easily.
Square numbers always end with the digits 0, 1, 4, 5, 6, and 9. For example, 25, 49, 81, 100, etc are perfect squares, whereas, 37, 48, 22, etc are not considered to be perfect square numbers.The number of zeros at the end of a square number is always even. This means if a number has an odd number of zeros at the end, then the number is not a square number. For example, 400, 3600 are square numbers, whereas, 10, 250, and 360 are non-square numbers.If a number has 1 or 9 as its last digit, then its square number ends with 1. For example, the square of 9 is 81, and the square of 11 is 121.If a number has 4 or 6 as its last digit, then its square number ends with 6. For example, the square of 4 is 16, and the square of 26 is 676.The square of even numbers is always even, and the square of odd numbers is always odd. For example, the square of 12 is 144, and the square of 13 is 169.Square numbers are always positive because two negative signs multiplied by each other result in a positive sign. For example, (-6)2 = -6 × -6 = 36 . Here, the product is 36 and it is a positive square number.Given:
2 and 140
Now, the perfect squares are:
√4=2
√9=3
√16 =4
√25=5
√36=6
√49=7
√64=8
√81=9
√100=10
√121=11
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29 , 58 , 116 , 7th term
Answers
Answer:
The 7th term is 1856.
Step-by-step explanation:
The equation of this is n * 2 for the next of every variable. So with this knowledge,
first term = 29
Multiply by 2.
second term = 58
Multiply by 2.
third term = 116
Multiply by 2.
fourth term = 232
Multiply by 2.
fifth term = 464
Multiply by 2.
sixth term = 928
Multiply by 2.
seventh term = 1856.
FACTOR this trinomial: 2x^2+17x+35
**show step by step explanation or no brainliest**
Answers
Answer:
which class question ???????
Step-by-step explanation:
and which chapter...........
Answer:
(2x+7)(x+5)
Step-by-step explanation:
2 x ² + 17 x +35=2 x ² + 7 x + 10 x +35=x(2x+7)+5(2x+7)=(2x+7)(x+5)
.Find the area of the figure
Answers
Answer:
Area of the figure = 171 in²
Step-by-step explanation:
Composite figure given in the picture comprises of three figures, two right triangles and one rectangle.
Area of the composite figure = Area of two right triangles + Area of the rectangle at the center
Area of one right triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(12)(9)[/tex]
= 54 in²
Area of the rectangle = Length × Width
= 7 × 9
= 63 in²
Area of the composite figure = 2(54) + 63
= 108 + 63
= 171 in²
Algebra 2 will mark brainliest. 4 pictures 4 questions
Answers
Answer:
decreasing because x is negative.
1. A student has a rectangular block. It is 2 cm wide, 3 cm tall, and 25 cm long. It has a
mass of 600 g. Determine the density of the block to the nearest unit.
8.9
Answers
Answer:
20 gcm^3
Step-by-step explanation:
Density = mass / volume
Volume = 3 X 2 X 25 = 30 cm
600 / 30 = 20
not 100 % sure though
What are the formulas for a 90, 180, 270, and 360 rotation?
Answers
[tex]3 + 3 + 3 = [/tex]
[tex]5 + 5 + 5 + 5 = [/tex]
[tex]5 + 5 + 3 = [/tex]
[tex]3 + 3 + 3 + 5 = [/tex]
[tex]5 + 5 + 5 = [/tex]
[tex]5 + 5 + 3 - 3 = [/tex]
[tex]5 + 5 + 3 + 3 + 3 = [/tex]
NO FILES PLEASE
Answers
Answer:
[tex]3 + 3 + 3 =9 [/tex]
[tex]5 + 5 + 5 + 5 =20 [/tex]
[tex]5 + 5 + 3 =13 [/tex]
[tex]3 + 3 + 3 + 5 = 14[/tex]
[tex]5 + 5 + 5 =15 [/tex]=15
[tex]5 + 5 + 3 - 3 =10 [/tex]
[tex]5 + 5 + 3 + 3 + 3 =19 [/tex]
Answer:
Step-by-step explanation:
3+3+3=9
5+5+5+5=20
3+3+3+5=14
5+5+5=15
5+5+3-3=10
5+5+3+3+3=19
Please Help! Will give Brainliest!!
Write with our the absolute value sign
Answers
Since y is less than -5, -6 would work,
The absolute sign changes the - into a positive so 6+5 = 11
Simplify the expression 3.4(-2) + 10
Answers
choose the monetary amount that is equivalent to 1 7/100
$ 1.70
$ 0.07
$ 1.07
$ 0.70
plsssssssssssssssssssssssssssssssssssss answer
Answers
Answer:
c. $1.07 is equivalent to 1 7/100
Step-by-step explanation:
hope this helps :)
Mr. Kumar is getting his house renovated. 1/5 th of the work has been completed in 2 months. How much time will it take for the entire work to be completed?
Answers
Answer:
10 months
Step-by-step explanation:
If it takes 2 months to do 1/5th, it will take 4 months to do 2/5, 6 months to do 3/5, 8 months to do 4/5, and 10 months to do 5/5 or in other words the whole thing.
The remaining work will take 8 month.
What is Algebra?Algebra is the branch of mathematics that represents problems in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
Given:
As, 1/5 th of the work has been completed in 2 months.
let the total time taken to complete the work is 'x' month.
1/5 * x = 2
x= 5*2
x=10 month
Hence, remaining work will take (10 - 2) = 8 month.
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Please help with this its confusing somehow :(
Answers
Answer:
x=4 and y=2
Step-by-step explanation:
What is the value of 4.2(46-65). A.798 b.-79.8 C.79.8 D.798. I just need the answer you don’t have to work it out
Answers
Answer:
b. -79.8.
Step-by-step explanation:
We calculate what's in the brackets first:
46 - 65
= -19
Now multiply by 4.2:
-19 * 4.2
= -79.8.
18. Hoping to lure more shoppers downtown, a city
builds a new public parking garage in the central business
district. The city plans to pay for the structure through
parking fees. During a two-month period (44 weekdays),
daily fees collected averaged $126, with a standard
deviation of $15.
Answers
Answer:
The responses to these question can be described as follows:
Step-by-step explanation:
Please find the complete question in the attached file.
For the random condition:
If other regular fees have been chosen at random, I'd claim I'm satisfactory.
State of autonomy:
Truly content, since the 44 daily fees represent less than 10% of the total population of daily payments, the community must have more than 440 daily fees.
In the Normal Condition:
Since the sample size of 44 is 30 or more, the distribution of the sample means is roughly Normal (as per the total probability theorem).
need help asap! solve for x, the measure of the altitude in the given triangle
Answers
Answer:
3.9
Step-by-step explanation:
[tex]8^{2} -7^{2} =15[/tex]
[tex]\sqrt{15} =3.9[/tex]
Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of bottles she needs to sell to earn $100. 1.25x + 1.49 = 100 What error did Barbara make in writing the equation? the number of bottles of water.
Answers
Answer:
she didnt write an x next to the 1.49 in her equation. she is writing an equation for how many bottles she is selling but according to her equation she is selling water for 1.25$ times x amount of bottles and selling only one ice tea
56 = -48 - 8y
Please answer quickly
Answers
rearrange them first add 48 to both sides of equations. simplify them 104 = 8y y=-13
Step-by-step explanation:
hope this helps
First: opposite operation
Second: add
Third: division
And you will get your answer.
56 = -48 - 8y
+48. +48
104 = 8y
8. 8
Y= 13
2) What is the five-digit number, no zeroes, in which the second digit is three times the first, the third is one more than the second, the fourth is four
times the first and the last is one-half more than the second?
Answers
the five digit number:
let the first digit be x
x _ _ _ _
x 3x _ _ _
x -3x- 3x+1- 4x- 3x+1.5x
This is the structure of the digit:x -3x- 3x+1- 4x- 3x+1.5x
Please please answer this for me
Answers
BRAINLIEST TO CORRECT ANSWER!!! NO links as answers, or you will be reported!! (question 4)
Answers
Answer:
Hello! Your answer would be, C) Divide by 2
Step-by-step explanation:
And plz don't be mean. :(
Hope I helped! Brainiest plz!♥ Have a nice afternoon. Hope you make a 100%! -Amelia
Out of the 90 customers at Eva's boutique35 wore a size extra-large. What is the probability that a randomly selected customer wore a size extra-large? Write your answer as a fraction or whole number. P(extra - large) =
Answers
Answer: 7/18
Step-by-step explanation:
Number of customers at Eva's boutique = 90
Number of customers who wore a size extra-large = 35
The probability that a randomly selected customer wore a size extra-large will be:
= Number of customers who wore a size extra-large / Number of customers at Eva's boutique
= 35 / 90
= 7/18
Therefore, the probability that a randomly selected customer wore a size extra large is 7/18.
12 points
1. FIND THE SLOPE
A. 2
6
4
B.
-2
2
-6
1-2
-4
X
0
D.
Ο Α
Answers
Answer:
i think it's 1, but I don't know if I'm right
Answer:
1
Step-by-step explanation:
2/2 = 1
Help please! Will give brainiest!!!!!!!
Write an equation in slope-intercept form of the line that passes through the given points.
Answers
Answer:
y = -1/2x+1
Step-by-step explanation:
Please help me ☹️☹️♀️
A picture below
Answers
Answer
Step-by-step explanation:
So first things First You are going to put a Dot on 2 on the y-axes, then the fraction is you Slope- Rise over- run
so you're going up 4 and over 5
Hope this helps !
Answer:
See attachment :)
Step-by-step explanation:
The given equation is in slope-intercept form, which lists the slope and the y-intercept of the line.
Slope-intercept form is [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept. The y-intercept, 2, is a point on the y-axis where the line intersects with the axis. So, we can graph the given intercept on the y-axis, (0,2).
The slope, [tex]m[/tex], is [tex]\frac{4}{5}[/tex]. The slope is the rise of the line over the run, or [tex]\frac{rise}{run}[/tex]. For this equation, then, we rise 4 units and run 5.
We'll start from the y-intercept, a point we know will be on our line. From this point, move up 4 units, and right 5. A negative slope would run to the left, but this is a positive line, so the run will go to the left. Now, we are on the point (5,6). From this point, we can repeat this [tex]\frac{rise}{run}[/tex].
A few of the following points are (10,10), (14,15), and (18,20). Now, draw a line connecting these points. This line is a graph of our equation.
I've attached a photo of the graphed line.
Good luck :)
please dont guess. need the answer asap
Answers
WILD ANSWER - 35% possibility it could be wrong. Please check with other answer first.
Answer: X=15.4
Step-by-step explanation:
Cos 39 = x/26
12 x = 0.77714596
x = 15.44111479
X=15.4