There are 2 music classes. This is a problem of combination. We can use the formula:
combinations = (n!) / (r! * (n-r)!)
Where n is the total number of choices and r is the number of choices in each combination.
We know that Sam can make 36 possible combinations and that he has 4 language classes, and 3 art classes to choose from.
Let's assume that there are x music classes.
So the total number of classes is 4 + 3 + x = x + 7
We can substitute these values into the formula:
36 = (x+7)! / (3! * (x+7-3)!)
36 = (x+7)(x+6)(x+5) / (321)
We can simplify it to
36 = (x+7)(x+6)(x+5)
We can find the value of x by solving the above equation.
x = 2
Therefore, there are 2 music classes.
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Is 0 a negative number?
a unit vector lies in the xy plane, at an angle of 155 degrees from the x axis, with a positive y component. what is the unit vector? (it helps to draw a diagram.)
The unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).
A unit vector is a vector with a magnitude of 1. To find the unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component, we can use the formula for a two-dimensional vector in polar coordinates:
r = (cos(θ), sin(θ))
where r is the unit vector, θ is the angle in radians, and cos(θ) and sin(θ) are the x and y components, respectively.
First, we need to convert the angle from degrees to radians:
θ = 155° * (π / 180°) = 2.68 radians
Next, we can plug in the values into the formula:
r = (cos(2.68), sin(2.68)) = (0.4237, 0.9055)
So, the unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).
To summarize, the process for finding a unit vector in the xy plane at an angle from the x axis is:
Convert the angle from degrees to radians
Use the formula for a two-dimensional vector in polar coordinates: r = (cos(θ), sin(θ))
Plug in the values into the formula to find the unit vector
Note: Keep in mind that the angle of a unit vector is relative to the positive x axis, with positive angles going counterclockwise and negative angles going clockwise.
Therefore, The unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).
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The unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).
A unit vector is a vector with a magnitude of 1. To find the unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component, we can use the formula for a two-dimensional vector in polar coordinates:
r = (cos(θ), sin(θ))
where r is the unit vector, θ is the angle in radians, and cos(θ) and sin(θ) are the x and y components, respectively.
First, we need to convert the angle from degrees to radians:
θ = 155° * (π / 180°) = 2.68 radians
Next, we can plug in the values into the formula:
r = (cos(2.68), sin(2.68)) = (0.4237, 0.9055)
So, the unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).
To summarize, the process for finding a unit vector in the xy plane at an angle from the x axis is:
Convert the angle from degrees to radians
Use the formula for a two-dimensional vector in polar coordinates: r = (cos(θ), sin(θ))
Plug in the values into the formula to find the unit vector
Note: Keep in mind that the angle of a unit vector is relative to the positive x axis, with positive angles going counterclockwise and negative angles going clockwise.
Therefore, The unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).
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in most cases, the product of a monomial and a binomial is a ___.
If we multiply monomial and binomial, then it is become polynomial.
Perfect Squares: The Square of a Difference Squaring a binomial every time results in a trinomial.
In other words, if we find the product of 6 and 3 by simply calculating 6 times 3 which equals 18.
A monomial is a statement of the form k⋅xⁿ, where k is a real number and n is a positive integer. It is essentially a polynomial with a single term.
When we are multiplying two monomials, we can rewrite the product as a single monomial using properties of multiplication and exponents.
A polynomial equation with two terms normally joined by a plus or minus sign is called a binomial.
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help video
Alexander drove 184 miles in 4 hours. Fill out a table of equivalent ratios and plot the
points on the coordinate axes provided.
Miles Hours
1
184
414
4
A table of equivalent ratios for the number of miles and hours that Alexander drove is as follows:
Miles Hours
46 1
184 4
414 9
The data points are plotted on the coordinate axes of the graph shown in the image attached below.
What is a proportional relationship?In Mathematics, a proportional relationship can be represented by the following mathematical expression:
x = ky
Where:
x represents the number of miles.y represents the number of hours.k represents the constant of proportionality.In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality. Therefore, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = x/y
Constant of proportionality (k) = 184/4
Constant of proportionality (k) = 46.
When hours y = 1, the number of miles x is given by:
x = ky
x = 46 × 1
x = 46 miles.
When miles x = 414, the number of hours y is given by:
y = x/k
y = 414/46
y = 9 hours.
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Which value of x would make line segment f g is parallel to line segment b c? 1 3 6 9
The value of x is 9 would make line segment fg is parallel to line segment bc.
It is given that FG || BC.
From the diagram,
If a transversal line intersect two parallel lines then the corresponding angles are same. There in triangle ACB and AGF.
If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary, i.e. they add up to 180°. When two lines intersect each other, then the opposite angles, formed due to intersection, are called vertical angles or vertically opposite angles.
∠GFA=∠CBA
∠AGF=∠ACB
If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.
Angle A is common is both triangles.
[tex]$$\begin{aligned}& \frac{F A}{B A}=\frac{G A}{C A} \\\\& \frac{x+1}{(x+1)+(x+6)}=\frac{x-1}{(x-1)+(x+3)} \\& \frac{x+1}{(2 x+7}=\frac{x-1}{(2 x+2)} \\& (x+1)(2 x+2)=(x-1)(2 x+7) \\& 2 x^2+4 x+2=2 x^2+5 x-7 \\& 4 x+2=5 x-7 \\& x=9\end{aligned}$$[/tex]
Therefore, the value of x is 9.
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i’m timed, this is stressing me out. please someone help
Answer:
Step-by-step explanation:
(f+g)(x) = -12x^3-10-6x+2
= -12x^3-6x-8
Since the problem asks for (f+g)(x), plug in the value 12 to get your answer.
(f+g)(12)=-20736-72-8 = -20816
Next, (f-g)(x).
(f-g)(x)=-12x^3-10+6x-2
=-12x^3+6x-12
=6144-48-12
=6084
Different varieties of field daisies have numbers of petals that follow a fibonacci sequence. Three varieties have 13, 21, and 34 petals. How many petals do the next two varieties of field daisy have?.
The next two varieties of field daisy have 55 and 89 petals.
We know that the Fibonacci Sequence is the series of numbers such that:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
Here, the next term of the sequence is found by adding up the two numbers before it.
For exa., the fourth term 2 is the sum of (1+1),
the fifth term 3 is the sum of (1+2)
In this question the numbers of petals of field daisies follow a Fibonacci sequence.
The three varieties have 13, 21, and 34 petals.
The next variety of field daisy would be the sum of 21 and 34
21 + 34 = 55
And the fifth variety of field daisy would be the sum of 34 and 55
34 + 55 = 89
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Line m||n cut by transversals t and s if m<2= 98 degrees m<13=120 degrees and m<9=2x-5 find the value of x and the measure of angle y
The missing values of the angles x and y of the given diagram are; x = 32.5° and y = 22°
What is the measure of the angle?
From the attached image, we can see that angle 12 and 13 are corresponding angles and as such;
m∠12 = m∠13
Similarly, angles 6 and 2 are corresponding angles and we can say that;
m∠6 = m2
We know that sum of angles on a straight line is 180 degrees and as such since m<9 = 2x - 5, then we have;
m<9 = 180 - m<12
= 180 - 120
= 60°
Therefore,
2x - 5 = 60
2x = 65
x = 65/2
x = 32.5°
m<8 = m<6 = 98° because they are vertically opposite angles
Thus;
y + m<9 + m<8 = 180 ( sum of angles of a triangle is 180 degrees)
y + 60 + 98=180
y + 158 = 180
y = 22°
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Brody's new home had a purchase price of $187,500. He got a 30-year fixed mortgage for 95% of the purchase price. The interest rate on the loan is 3. 875%
a. The monthly payment would be $1,061.76.
b. Total amount paid would be $382,636.16.
c. The cost of the loan would be $195,136.16.
A mortgage is a type of loan used to purchase a property or real estate. The borrower (in this case, Brody) uses the property as collateral for the loan, and makes monthly payments to the lender (usually a bank or mortgage company) to repay the principal (the amount borrowed) plus interest. Mortgages typically have a fixed interest rate, meaning the interest rate stays the same over the life of the loan, and a fixed term, typically 15 or 30 years.
a. To calculate the monthly payment for Brody's loan, you would use the formula for a fixed-rate mortgage, which is:
M = P [ i(1 + i)ⁿ ] / [ (1 + i)ⁿ ⁻ ¹]
Where M is the monthly payment, P is the principal (the amount borrowed), i is the interest rate (expressed as a decimal), and n is the number of payments (in this case, 30 years x 12 months/year = 360 payments).
Plugging in the numbers, the monthly payment would be:
M = $187,500 x [0.03875(1 + 0.03875)^360] / [(1 + 0.03875)³⁶⁰ ⁻ ¹]
M = $1,061.76
b. To calculate the total amount paid, you would multiply the monthly payment by the number of payments:
Total amount paid = $1,061.76 x 360 = $382,636.16
c. The cost of the loan is the total amount paid minus the amount borrowed:
Cost of the loan = $382,636.16 - $187,500 = $195,136.16
The complete question is shown below.
Brody's new home had a purchase price of $187,500. He got a 30-year fixed mortgage for 95% of the purchase price. The interest rate on the loan is 3.875%.
a. What is his monthly payment for the loan?
b. What is the total amount paid?
c. What is the cost of the loan?
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If 7x 3 = 24, what is the value of 5 - 4x? a. -23 b. -7 c. 1 d. 17 show steps pls
The value of 5 - 4x is 7/3, which is equivalent to option (d) d. 17
If 7x³ = 24, we can solve for x by taking the cube root of both sides:
[tex](7x^3)^{1/3} = (24)^{1/3} \\x = (24)^{1/3} \div7^{1/3}[/tex]
To find the value of 5 - 4x, we can substitute the expression for x into the second equation:
5 - 4x = [tex]5 - 4(24)^{1/3} \div 7^{1/3[/tex]
Simplifying, we get
5 - 4x = 5 - 4(2/3)
5 - 4x = 5 - (8/3)
5 - 4x = (15/3) - (8/3)
5 - 4x = 7/3
So the value of 5 - 4x is 7/3, which is equivalent to option (d) d. 17
The cube root of a number is a value that when multiplied by itself twice, produces the original number.
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need help fast please
For horizontal asymptote, for the graph function y=f(x) where the straight line equation is y=b, which is the asymptote of a function x → + ∞, if the following limit is finite.
what is the equation for the horizontal asymptoms?
A horizontal asymptote of a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞. A slant asymptote of a graph is a slanted line y = mx + b where the graph approaches the line as the inputs approach ∞ or –∞. If the degree of the numerator is less than the degree of the denominator (n<m), then f has a horizontal asymptote of y=0 as x→±∞.Horizontal Asymptote y=0 when f(x)=p(x)q(x),q(x)≠0 where degree of p<degree of q f ( x ) = p ( x ) q ( x ) , q ( x ) ≠ 0 where degree of p < degree of q . Case 2: If the degree of the denominator < degree of the numerator by one, we get a slant asymptote.To learn more about horizontal refers to:
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Which graph is a function of x?
PLEASE HELP IM BEING TIMED
The function of graph x is v shaped.
What is the function of graph?
The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We may alternatively say that the graph of f is the graph of y = f. (x). Consequently, a special case of an equation's graph is the graph of a function.
The relation depicted by the graph is not a function if any vertical line touches it more than once.
The given graph is non functional graph the right graph need is :
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The linear function
y
=
2
x
+
25
models the average cost of a haircut in a certain city, where
y
, is the average price of a haircut
x
years after 1985. Find the slope for the model. Then describe what this means in terms of the rate of change in the average cost of a haircut over time.
a)
m
=
2
b) The average cost of a haircut in this city increased (Enter: increased or decreased or not changed ) at a rate of per year after 1985.
Therefore , the solution of the given problem of function comes out to be $33 will be the price of haircut in 1997.
What is function?Mathematics is a science that investigates numbers, their variations, mathematics and the local tissues, shapes, and the both their actual and potential placements. Function describes the connection between a collection of inputs, each of which has an associated output. A function is an association domain of inputs that results in a single, distinctive output for each input. Each function is given a city or municipality or a scope, often known as a realm.
Here,
Given : c = 2y + 29
where c is the typical cost of the a haircut and
y is the number of years since 1995.
For the model, the slope is 2.
It implies that starting in 1995,
the average price of a haircut will rise by 2 each year.
=>1995 has y=0 and a cost of 29.
=> 1996's y=1 results in a cost of 29+2=31.
=>When y=2 in 1997, the price is 29+4 = 33, and so forth.
Therefore , the solution of the given problem of function comes out to be $33 will be the price of haircut in 1997.
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PLSPLSPLS HELP WITH THIS QUESTION I NEED TO SUBMIT THE ASSIGNMENT RLLY SOON
For the given equation, values to get equal the value of w equals [tex]\frac{7}{16}[/tex].
Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.
The three primary forms of linear equations are point-slope, standard, and slope-intercept.
A simple equation is a mathematical formula that expresses the relationship between two expressions on both sides of the "equal to" sign.
These equations contain a variable, which is frequently written as x or y. It is frequently necessary to rearrange simple equations in order to solve them.
Given, the equation is
[tex]2 \frac{2}{3} w = 1 \frac{1}{6}[/tex]
Simplifying the equation,
[tex]\frac{8}{3}w = \frac{7}{6}[/tex]
[tex]w = \frac{7}{6} \times \frac{3}{8}[/tex]
[tex]w = \frac{7}{16}[/tex]
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Find the sun of 268 and 479
Answer:
The sum is 747.
Step-by-step explanation:
Sum is addition, 268 + 479 eauals 747.
please answer fast on a time limit
Answer:
2
Step-by-step explanation:
functions mean that each input can only have one output.
if we do 2 as the input it will have both 7 and -5 a the output making it not a function
hopes this helps
Answer: B
Step-by-step explanation:
LaVelle buys a jumbo package of 84 candies to 12 make favor bags for her son's birthday party. If she wants to make bags, how many candies should she put in each bag?
What do you say about the lines represented by 2x 3y 9 0 and 4x 6y 18 0?
The equation 1(2x+3y−9=0) and 2(4x+6y−18=0) we can say that both line are coincident lines. So the option 4 is correct.
In the given question, we have to find what we say about the lines represented by 2x+3y−9=0 and 4x+6y−18=0.
The given lines are
2x+3y−9=0..............(1)
4x+6y−18=0..............(2)
We can common 2 from the second line. Now the line is
2(2x+3y-9) = 0
Divide by 2 on both side, we get
2x+3y-9 = 0
Now we can see that the both lines are same. The second line is the two time the first line.
So from the equation 1 and 2 we can say that both line are coincident lines. So the option 4 is correct.
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The complete question is:
What do you say about the lines represented by 2x+3y−9=0 and 4x+6y−18=0?
(1) Intersecting lines
(2) Perpendicular line to each other
(3) Parallel Lines
(4) Coincident lines
What is the slope when 0 /- 5?
The slope is 0 when 0/(-5) and it means, the line with this slope must be coincident or parallel to the x-axis
We know that the slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate.
The slope of the line describes the steepness of a line.
Also, if a line makes an angle θ with the positive direction of the x-axis, then the slope of the line will be tangent of angle θ
m = tan θ
Here we have been given a slope 0/(-5)
As we know 0/(-5) = 0
So, the slope is 0.
The slope is 0 when 0/(-5)
Let m be the slope of the line, m = 0
From definition of slope of line,
0 = tan θ
θ = arctan(0)
θ = (nπ) where n = 0, 1, 2, . . .
This means, the slope 0/(-5) represents that for every fiveunits of horizontal distance crosses there is no change of vertical distance.
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You bike for 2 hours at a speed no faster than 16.6 miles per hour. The bike portion
of an Ironman Triathlon is 112 miles. You want to complete the bike portion in less
than 6.4 hours. If you continue to bike at the same speed, will you reach your goal?
Explain.
No, you will not reach your goal. At 16.6 miles per hour, it would take you 6.74 hours to complete the bike portion of the Ironman Triathlon. This is more than the 6.4 hours you want to complete it in.
Will you accomplish your objective if you ride your bike at the same speed?No, if you continue to bike at the same speed of 16.6 miles per hour, you will not reach your goal of completing the bike portion of the Ironman Triathlon in less than 6.4 hours.In 2 hours, you would only cover 33.2 miles.To cover the full 112 miles in 6.4 hours, you would need to maintain an average speed of 17.5 miles per hour for the entire bike portion.If you are currently biking at 16.6 miles per hour, you will need to increase your speed by at least 1 mile per hour in order to complete the bike portion in 6.4 hours or less. This can be difficult, as it will require you to push yourself and maintain a faster speed for a longer period of time.However, it is not impossible. You can work on increasing your speed by doing shorter and faster rides, or incorporating interval training into your rides.Additionally, you can work on increasing your endurance and stamina, so that you can maintain a faster speed for a longer period of time.With the right training and dedication, you can reach your goal of completing the bike portion of the Ironman Triathlon in less than 6.4 hours.To learn more about the time/distance/speed equation refer to:
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Find the sum of the next numbers in the
sequence below.
8, 9, 12, 18, 28,__,__
Answer:
the two next numbers are 43 and 64 , sum = 107
Step-by-step explanation:
see attachment
so the next two nos. of the sequence would be 43 and 64
And we are done!
-Rishabh
10,5,5/2 find 6th term
Answer:
Hey there!
Arithmetic sequences are made up of terms that are added or subtracted, and geometric sequences are made up of terms that are multiplied or divided.
Given this info, we can see that we go from 10 to -5. Because we know that this is geometric, we see that we must divide by -2 in our sequence.
We can see that this is true because -5/-2=5/2.
Now, we could simply continue dividing by negative two to get our answer, which is -5/16.
You could easily do that with a calculator, but if you had to find a term that was farther from the first term, that would take forever to do with a calculator, so there is an equation that you can use and plug in your numbers to find the answer quickly.
, where is the number of term in the sequence (6 in this problem), a is the first term of the sequence (10), and r is the common ratio (-1/2).
I hope this helps!
Step-by-step explanation:
How do you find the distance between two points in Class 11?
To calculate the distance between two places, we can apply the distance formula d=((x2 - x1)² + (y2 - y1)²).
What is the distance?The distance of an object is its overall motion, regardless of direction.
Distance is the amount of space that an object has covered, regardless of where it began or concluded.
By understanding how far an object is from us, we may calculate its actual size.
It is possible to calculate the area that an object takes up in the sky.
The actual size of an object can then be determined by taking into account its distance.
The further away something is, the smaller it appears.
The distance between two locations on a plane is the length of the line segment connecting them.
The formula d=((x2 - x1)2 + (y2 - y1)2) is frequently used to calculate the separation between two points.
Therefore, to calculate the distance between two places, we can apply the distance formula d=((x2 - x1)² + (y2 - y1)²).
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Circle C is centered at the origin. Is point (5, 5) on the circle?
Answer:
no, the origin is located at 0,0
how can i solve this
a. The value of a is 5500. b. The value of r is 0.92. c. There are 2022 trees still alive till 1st October 2023.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
a) The value of a is 5500.
b) To find the value of r, we can use the equation N = ar where N is the number of trees still alive t years after 1st October 2018. We know that N = 5060 on 1 October 2019, so we can substitute these values into the equation:
5060 = 5500 r
r = 5060/5500
r = 0.92
c) To find the predicted percentage decrease in trees still alive between 1 October 2018 and 1 October 2030, we can use the equation:
[tex]N = ar^t[/tex]
Here a = 5500, r = 0.92 and t = 12
We can now substitute the values, then we get
N = 5500 × (0.92)¹² ≈ 2021.67
N = 2022
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24x^(4)y^(3)z^(4)-32x^(3)yz^(5)
Answer: 8x^3yz^4(3xy^2-4z)
Step-by-step explanation:
Factor out the greatest common factor: [tex]8[/tex]
8 x 3 = 24
8 x 4 = 32
Factor out the smallest powers from both sides: [tex]x^3 yz^4[/tex]
Leave the remaining x, y, and z values
[tex]8x^3yz^4(3xy^2-4z)[/tex]
Consider the following expression: (1+x)^2.
A) Use the Binomial Theorem to find the first four terms of this polynomial.
B) Why is 1 + nx a good approximation of this expression when x is less than 1?
Answer:
Step-by-step explanation:
A) The Binomial Theorem states that for any positive integer n and any real numbers a and b, the expression (a + b)^n can be expanded as a sum of the form:
(a + b)^n = C(n,0)a^n b^0 + C(n,1)a^(n-1)b^1 + C(n,2)a^(n-2)b^2 + ... + C(n,n)a^0b^n
where C(n,k) = n!/(k!(n-k)!) is the binomial coefficient.
Applying this to the expression (1 + x)^2, we have:
(1 + x)^2 = C(2,0)1^2 x^0 + C(2,1)1^1 x^1 + C(2,2)1^0 x^2
= 11^21 + 21x + 1*x^2
The first four terms of the polynomial are: 1, 2x, x^2
B) The binomial theorem states that the first term is a constant term and the second term is linear. When x is less than 1, the linear term 2x is much smaller than the constant term 1, so the linear term can be ignored as a good approximation. Therefore, 1 + nx will be a good approximation of the expression (1+x)^2 when x is less than 1.
For the given central angle, determine the distance traveled along the unit circle from the point (1, 0). -112 degrees a. 0. 98 units c. 0. 62 units clockwise b. 0. 62 units d. 1. 95 units clockwise
-112° = 1.95 units clockwise. This can be solved using the concept of central angle.
Correct option is: d
What is central angle?A circle's central angle is the angle formed by two of its radii. The circle's two places of intersection (Note: The opposite end of the radii meets at the circle's centre) together make up a section known as the arc Length.
A central angle is an angle whose legs (sides) are radii intersecting the circle at two different places, A and B, and whose apex (vertex) is the center O of a circle. The central angle is the angle created by the two radii of the circle. A 360° angle is completed by the circle. A circle's central angle has a value between 0 and 360°.
For the given central angle,
-112° = d 1.95 units clockwise
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heyyy guys sometimes some of the answers are wrong
Answer:
6.1 x 10⁴
that is the answer for you sir
Find two consecutive even integers such that the sum of the larger and 3 times smaller is 234
The number of the largest series and 3 times the smallest is 234 would be = 58 and 60.
What is an integer?An integer is a whole number, regardless of sign, that goes from 0 to infinity or to minus infinity.
Let's suppose the first integer is x then the second will be x + 2
Sum of the larger and 3 times the smaller is 234
(x + 2) + 3x = 234
4x + 2 = 234
4x = 232
x = 58 so x + 2 = 60
Therefore, both consecutive even integers such that the sum of the larger and 3 times the smaller is 234 is 58 and 60.
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