x = (12 ± √(-16)) / 4,The solutions would be complex numbers.
What is the quadratic formula?To solve quadratic equations of the form ax2 + bx + c = 0, use the quadratic formula. For this situation, your condition is as of now as a quadratic condition, with a = 2, b = - 12, and c = 20.
The quadratic formula is:
x = (-b ± √[tex](b^2 - 4ac)[/tex]) / 2a
Plugging in the values for a, b, and c, we get:
x = (-(-12) ± √[tex]((-12)^2 - 4(2)(20)))[/tex] / 2(2)
Simplifying the expression inside the square root:
x = (12 ± √[tex](144 - 160)[/tex]) / 4
x = (12 ± √(-16)) / 4
Since the square foundation of a negative number is definitely not a genuine number, this condition has no genuine arrangements. Complex numbers would provide the answers.
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This year, there are eight freshmen, nine sophomores, eight juniors, and ten seniors are eligible to be on a committee. In how many ways can a dance committee of 8 students be chosen?
To solve this problem, we can use the combination formula, which is:
n C r = n! / (r! * (n-r)!)
where n is the total number of students eligible for the committee, r is the number of students we want to choose, and ! denotes the factorial function.
In this case, we want to choose a committee of 8 students from a pool of 8 freshmen, 9 sophomores, 8 juniors, and 10 seniors. So, the total number of students eligible for the committee is:
n = 8 + 9 + 8 + 10 = 35
We want to choose a committee of 8 students, so r = 8. Therefore, the number of ways we can choose a committee of 8 students is:
35 C 8 = 35! / (8! * (35-8)!) = 35! / (8! * 27!) ≈ 1,121,112 ways
So there are approximately 1,121,112 ways to choose a dance committee of 8 students from the eligible pool.
The demolition of a condominium development produced 1,425 cubic meters of construction waste. A truck driver works Monday through Friday from 8 am - 4 pm with no
breaks. The dimensions of the driver's truck they can use to haul waste is 8'2" x 9'3" x 18'6", and one round trip to the landfill and back to the demolition site takes the driver an hour. If the driver starts hauling the construction waste to the landfill Monday (10/7) at 8 am, how many more days of work do they have to completely remove the construction waste from the demolition site at noon on Wednesday (10/9)? MUST SHOW ENGINEERING
METHOD BELOW.
What is your calculated answer most closely to?
a. 7 days
b. 4 days
c. 6 days
d. 9 days
Answer:
(c) 6 days
Step-by-step explanation:
First, we need to calculate how many trips the truck can make per day. We will assume that the truck is filled to its maximum capacity on each trip.
The volume of the truck can be calculated by multiplying its dimensions:
8.17 feet x 9.25 feet x 18.5 feet = 1,482.51 cubic feet
We need to convert this to cubic meters:
1,482.51 cubic feet x 0.0283 cubic meters per cubic foot = 42.01 cubic meters
Therefore, each round trip can transport 42.01 cubic meters of construction waste.
To calculate how many trips are required to remove all the waste, we divide the total volume of waste by the volume of waste per trip:
1,425 cubic meters / 42.01 cubic meters per trip = 33.89 trips
Since the driver can make one round trip per hour, it will take approximately 34 hours to transport all the waste to the landfill.
If the driver starts on Monday at 8 am, they will have 8 working hours that day, for a total of 8 trips. On Tuesday and Wednesday, they will have 8 working hours each day, for a total of 16 trips. Therefore, by noon on Wednesday, they will have made 24 trips, leaving 9.89 trips remaining.
Since each day the driver can make 8 trips, they will need approximately 2 more days of work to completely remove the construction waste from the demolition site. Therefore, the answer is (c) 6 days.
Note: This calculation assumes that there are no delays or complications in the transportation process, such as traffic or equipment malfunctions, which could affect the actual time required to remove all the waste.
A textbook store sold a combined total of 220 biology and sociology textbooks in a week. The number of biology textbooks sold was 76 more than the number of sociology textbook sold. How many textbooks of each type are sold.
Answer:
144
Step-by-step explanation:
we can use subtraction to solve this, subtracting 220 from 76 ends up with 144
Assume a > 0, b > 0 and 1 < ax < bx for all x < 0. Which of the following are true?
a. a < b < 1
b. 1 < a < b
c. a < 1 < b
d. b < a < 1
e. b < 1 < a
Explain how you got to the answer.
Answer:
there is somthing wrong of what you ask
because it is impossible to be thet a>0 and b>0 and x<0 and still ax>1 or bx>1
Teuta bought a car. Its price fell by 23% at the end of the first year. At the end of the first year, her car cost 6575.8 eu How much did Teuta buy the car?
Teuta bought the car for 8545.71 eu.
What is percent in math?
Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.
Let's assume that the initial price of the car is x.
After a 23% drop in price, the new price of the car is: x -0.23x = 0.77x
We know that the new price after the first year is 6575.8 eu: 0.77x = 6575.8
Solving for x, we get: x = 6575.8/0.77 8545.71
Therefore, Teuta bought the car for approximately 8545.71 eu.
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Find the LCM of 6(x – 1)2(x + 2)(x – 3) and 9(x – 1)(x + 2)2(x – 3).
Answer:
To find the LCM of the two expressions, we need to factor each expression completely and then take the product of the highest powers of each factor.
So, let's factor each expression:
6(x – 1)2(x + 2)(x – 3) = 2 × 3 × (x – 1) × (x – 1) × (x + 2) × (x – 3)
9(x – 1)(x + 2)2(x – 3) = 3 × 3 × (x – 1) × (x + 2) × (x + 2) × (x – 3)
Now, we can identify the highest powers of each factor.
The LCM will be the product of those highest powers:
LCM = 2 × 3 × 3 × (x – 1)2 × (x + 2)2 × (x – 3)
Therefore, the LCM of 6(x – 1)2(x + 2)(x – 3) and 9(x – 1)(x + 2)2(x – 3) is 54(x – 1)2(x + 2)2(x – 3).
Use what you know about triangles to find the measure of the third angle.
Angle A= 78º, B= 45º, C= x
x=?
Responses
49º
57º
61º
54º
Answer:
x = 57°
Step-by-step explanation:
Pre-SolvingWe are given a triangle, and we know that the angles in the triangle are <A, <B, and <C.
We know that m<A = 78° and m<B=45°. We want to find the measure of angle C, which we know currently as x.
SolvingRecall that all angles in a triangle add up to 180°. This means that m<A + m<B + m<C = 180°.
Substituting what we know into that equation, we get:
78° + 45° + x = 180°
We can add 78 and 45 degrees together.
123° + x = 180°
Subtract 123° from both sides.
x = 57°
So x, or m<C is 57°.
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Statements which are always true regarding the diagram are
1. m∠5 + m∠6 = 180° ...........Parallel Pair
2. External angle of a triangle is equal to 2+3 = 6.
3. Triangle Sum Property: m2 + m3 + m5 = 180°
Think of ABC as having outside angles.
∠ 1, ∠ 4 , and ∠ 6
Triangle's exterior angle property:
A triangle's exterior angle equals the sum of its internal angles.
Exterior 1 has the following
The exterior angle of a triangle is given by the formula: 1 = 5 + 3.
Similarly,
Exterior 4 consists of
∠ 4 = ∠ 5 + ∠ 2.................Triangle's Exterior Angle
Similarly,
Exterior 6 consists of
The exterior angle of a triangle is given by the formula: 6 = 2 + 3
Property Triangle Sum:
The total of the angles in a triangle equals 180°.
∴ m∠2 + m∠3 + m∠5 = 180° .....Sum Triangle Property
Linear Pair:
The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
∴ m∠5 + m∠6 = 180° ...........Linear Pair
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QUICK I’LL MARK YOU BRAINLIEST I NEED HELP SOLVING THIS!!
To solve for the value of x, x is 2.
What is a simple equation?
A given equation which has one unknown variable whose value is to be determined is called a simple equation. This requires the applications of some mathematical principles to know the value of the unknown.
In the given question, the common factor is 25. so divide by 25 to have;
125x - 150 = 100
divide by the common factor, we have;
125x/25 - 150/25 = 100/25
5x - 6 = 4
So that, solve in the usual manner;
5x = 4 + 6
= 10
5x = 10
x = 10/5
= 2
x = 2
After solving the equation, the value of x is 2.
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A cold front moves through the area quickly. In the morning, the temperature is 82
degrees F and after 6 hours the temperature has dropped to 58 degrees F. If the
temperature dropped at a steady rate, how much did it drop each hour?
The temperature dropped by 4 degrees Fahrenheit per hour during the 6-hour period.
What is the drop in temperature?The temperature drop each hour is calculated as follows;
temperature drop per hour = (change in temperature) / (time elapsed)
change in temperature = final temperature - initial temperature
change in temperature = 58 degrees F - 82 degrees F
change in temperature = -24 degrees F
The time elapsed = 6 hours
The change in temperature or drop in temperature is calculated as;
temperature drop per hour = (-24 degrees F) / (6 hours)
temperature drop per hour = -4 degrees F/hour
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Please help me find the answer
Using trigonometric ratios θ = 26.57°
What is a trigonometric ratio?A trigonometric ratio is the ratio of the sides of a triangle.
To find the value of θ, we notice that in the triangle, we have the hypotenuse side and the adjacent side.
Using the trigonometric ratio cosθ = adjacent/hypotenuse
where
adjacent = 6√5 and hypotenuse = 15So, substituting the values of the variables into the equation, we have that
cosθ = adjacent/hypotenuse
= 6√5/15
= 2√5/5
= 2 × 2.236/5
= 4.472
= 0.8944
cosθ = 0.8944
θ = cos⁻¹(0.8944)
= 26.57°
So, θ = 26.57°
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helpp pls ixl help tyyyy
Answer: Probability: 1.3%
Totals, 51, 155. 0 Accounts: 18. 1 Account: 24. 2 Accounts:18. 3 or more: 42.
2a. Find the volume of the model of Saturn.
2
Eliza made sphere-shaped
models of the Earth and Saturn
out of playdough for a science
project. The model of Earth has
a diameter of 4.8 cm and the
model of Saturn has a diameter
of 45.6 cm.
The volume of the model of Saturn is approximately 4,845.6 cm³.
please help me find this which one
Answer:
A
Step-by-step explanation:
Self explanatory
Answer: b
Step-by-step explanation: i just did this one on a algebra 1b assignment lol
find the zeros of the function. State the multiplicity of multiple zeros.
y=7x^3-7x select the correct choice below and if necessary fill in the boxes within your choice.
1. The numbers _ are zeros of multiplicity 3
2. The numbers _ are zeros of multiplicity 2
3. The numbers _ are zeros of multiplicity 1
4. The numbers _ are zeros of multiplicity 1 and the numbers _ are zeros of multiplicity 2.
(picture added if needed :))
The numbers 0, 1, and -1 are zeros of multiplicity 1.
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
To find the zeros of the function [tex]y=7x^3-7x[/tex], we can set y equal to zero and solve for x:
[tex]7x^3 - 7x = 0[/tex]
Factor out 7x:
[tex]7x(x^2 - 1) = 0[/tex]
Factor the quadratic expression:
7x(x - 1)(x + 1) = 0
The zeros of the function are the values of x that make y equal to zero. From the factored expression, we see that the zeros are:
x = 0 (with multiplicity 1)
x = 1 (with multiplicity 1)
x = -1 (with multiplicity 1)
Therefore, the correct choice is: The numbers 0, 1, and -1 are zeros of multiplicity 1.
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Find the Fourier transform of (without using Tables). Show details.
() = { 2
, − 1 < < 1
0 , ℎ
As a result, the following is the given function's Fourier transform:
F(ω) = (1/π) * (sin(ω) / ω)
What is the Fourier transform?The Fourier transform is a mathematical operation that separates the frequencies that make up a waveform, which is a function of time. The Fourier transform's output is a complex valued function of frequency.
We must assess the integral in order to determine the given function's Fourier transform, f(x):
F() is equal to 1/(2) * [from - to -] F(x) E(-i) X Dx
where the frequency parameter is and i is the fictitious unit.
We can simplify the integral bounds as follows since the function f(x) is non-zero only in the range -1 x 1.
F() is equal to 1/(2)*[from -1 to 1] F(x) E(-i) X Dx
Let's analyse this integral in stages.
The value of the function f(x) is zero for x -1 or x > 1. As a result, we can increase the integral limits to - and + without changing the integral's value:
F(ω) = 1/(2π) * ∫(from - to -) F(x) = E(-ix) dx = 1/(2*) * the range [- to -1] from -1 to 1 + 0 dx 2dxe(-ix)+[from 1 to ] 0 dx = 1/(2π) * 2 * ∫E(-ix) dx [from -1 to 1]
Let's concentrate on the central integral:
∫[in the range of -1 to 1] e(-ix) dx = (-1/i)* [e^(-iωx)](-1/i)* _[from -1 to 1] (e^(-iω) - e^(iω))
Adding this back into the formula for the Fourier transform results in:
F(ω) = 1/(2π) * 2 * (-1/iω) * (e^(-iω) - e^(iω)) = (1/π) * (sin(ω) / ω)
As a result, the following is the given function's Fourier transform:
F(ω) = (1/π) * (sin(ω) / ω).
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The Fourier transform of the given function f(x) is:
F(ω) = 2 [ - sin(ω) / ω ]
What is Fourier Analysis?
Fourier analysis is a branch of mathematics that deals with the study of the decomposition of a complex signal into simpler components, known as harmonics, using a mathematical tool called the Fourier transform.
To find the Fourier transform of the given function f(x), we need to use the following formula:
F(ω) = ∫ f(x) e^(-iωx) dx
where F(ω) denotes the Fourier transform of f(x) and ω is the frequency variable.
Let's apply this formula to the given function f(x):
F(ω) = ∫ f(x) [tex]e^{(-iωx)}[/tex] dx
= ∫[tex]-1^{1}[/tex] 2 [tex]e^{(-iωx)}[/tex] dx + ∫{-∞}^{∞} 0 [tex]e^{(-iωx)}[/tex] dx
= 2 ∫_[tex]{1}^{{1}}[/tex] [tex]e^{(-iωx)}[/tex] dx + 0
= 2 [ (1/iω) [tex]e^{(-iωx)}[/tex] ]_[tex]-1^{1}[/tex]
= 2 [ [tex]e^{(-iωx)}[/tex] - [tex]e^{(iω)}[/tex] / iω ]
Simplifying this expression, we get:
F(ω) = 2 [ (cos(ω) - i sin(ω)) / iω - (cos(-ω) - i sin(-ω)) / iω ]
= 2 [ (cos(ω) - i sin(ω)) / iω - (cos(ω) + i sin(ω)) / iω ]
= 2 [ -2i sin(ω) / (2iω) ]
= 2 [ - sin(ω) / ω ]
Therefore, the Fourier transform of the given function f(x) is:
F(ω) = 2 [ - sin(ω) / ω ]
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Which table represents a nonlinear function?
Answer:
D)
Step-by-step explanation:
The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore a seat belt.
The probability of not wearing a seat belt given that the driver survived a car accident is 28%.
What is the probability of not wearing a seat belt?The probability of not wearing a seat belt and that the driver survived a car accident will be calculated using Bayes' theorem.
The Bayes' theorem states that: P(A|B) = P(B|A) * P(A) / P(B) where A is the event of not wearing a seat belt and B is the event of the driver surviving a car accident.
Driver Survived/No seat belt = 168,132
Total Sample = 583,425
Plugging the values, we get:
P(A|B) = 168,132 / 583,425
P(A|B) = 0.288
P(A|B) = 28.8%.
Full question "The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore a seat belt: Wore Seat Belt 415,293 No Seat Belt Total Driver Survived Driver Died Total 168,132 583,425 521 415,814 1643 169,775 2164 585,589 Find the probability of not wearing a seat belt; given that the driver survived a car accident: The probability as a decimal is 0.288 (Round to three decimal places as needed.) The probability as a fraction is (Type an integer or a simplified fraction).
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laurel exercises and keeps track of how many minutes she spends participating in different exercise activities
Laurel spent a total of 65 minutes exercising across these activities.
How to solveTo calculate the total minutes Laurel spent exercising, we simply need to add the minutes spent on each activity:
Jogging: 30 minutes
Swimming: 20 minutes
Yoga: 15 minutes
Total minutes = 30 + 20 + 15 = 65 minutes
Laurel spent a total of 65 minutes exercising across these activities.
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How many minutes did Laurel spend exercising in total, if she participated in different activities for the following durations: 30 minutes of jogging, 20 minutes of swimming, and 15 minutes of yoga?
ill in the blanks below with the correct units.
(a) Keith's house is about 4?
(b) The can of soda held about 350 ?
✓ from school.
(c) Deandre bought a candy bar. Its mass was about 60?
Answer:
a. km
b.350 ml
c.60 gr
Step-by-step explanation:
the units may be bigger though to whats the options is
I don’t understand can someone help me please!
Answer: y = -|x| - 3
Step-by-step explanation:
It's an absolute value function that has been shifted down 3 and has been reflected
y = -|x| - 3
You wish to make an investment of $5,400 at 5.6% interest. How much will your investment be worth in 25 years at simple interest, compounded quarterly, and compounded continuously?
simple interest:
compounded quarterly:
compounded continuously:
Simple interest = $12,9600
Compounded quarterly = $12,9600
and compounded continuously = $21,686.49
What is simple interest?
Simple interest, often known as the yearly interest rate, is an annual payment based on a percentage of borrowed or saved money.
Here, we have
Given:
Investment = $5,400 at 5.6% interest.
t = 25 years
Final amount at simple interest: F = P(1+rt)
F = 5400(1+0.056×25)
F = 5400(2.4)
F = $12,9600
Final amount at compound interest: F= P(1+r/n)ⁿˣ
compounded quarterly(n=4)
F = P(1+r/n)ⁿˣ
F = 5400(1+0.056/4)⁴⁽²⁵⁾
F = 5400(1.014)¹⁰⁰
F = $21,686.49
Final amount at continuously compound interest: F= Peⁿˣ
F = 5400 e¹°⁴
F = $21,898
Hence,
simple interest = $12,9600
compounded quarterly = $12,9600
and compounded continuously = $21,686.49
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Paul bought a new rug in the shape of a regular decagon. Each side of the decagon is 4.25 feet. Find the area of the rug. Round to the nearest hundredth.
The area of the rug which has the shape of a decagon would be = 178.79ft²
How to find the area of the rug with the shape of a decagon?To calculate the area of the rug that has the shape of a decagon, the formula for the area of a decagon should be used. That is;
Area of decagon = 5/2a²√5+2√5
Where;
a = side length = 4.25 ft
area = 5/2(4.25)²√5+2√5
= 5/2(18.06)√5+2√5
= 45.15× √5+2√5
= 45.15 × √15.65247584
= 45.15× 3.96
= 178.79ft²
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A police officer invested $5,000 in a treasury bond paying 4.75% interest compounded quarterly. After 25 years, the value of the bond will be $16,280.08. If the police officer's investment was compounded continuously instead of four times per year, what would be the difference in the account balances after 25 years?
Answer:
114.29
Step-by-step explanation:
30m3n4-5m4complete factored form of the polynomial
Factor of polynomial m are 0, 6n⁴.
What is polynomial in maths?
A polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients, and it only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.
= 30m³n⁴ - 5m⁴
= 5m³(6n⁴ - m )
let 5m³(6n⁴ - m ) = 0
5m³ = 0
m = 0
6n⁴ - m = 0
m = 6n⁴
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Y=x^2-4x+8 write the equation in vertex form.
Answer:
y = (x - 2)² + 4
Step-by-step explanation:
y = x² - 4x + 8
using the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² - 4x
y = x² + 2(- 2)x + 4 - 4 + 8
= (x - 2)² + 4 ← in vertex form
Brent is designing a poster that has an area of 1 square foot. He is going to paste a photo collage on a section of the poster that is 1/3 foot wide and 3/5 foot long. What part of a square foot will the photo collage cover?
Show your work.
The part of the foot will the photo collage cover is 1/5 square foot
How to determine the photo collage cover?Recall that an area of a lawn is an area of soil-covered land planted with grasses and other durable plants such as clover which are maintained at a short height with a lawnmower (or sometimes grazing animals) and used for aesthetic and/or recreational purposes
The given parameters are
Area of the Poster =1 sq.ft.
The collage will cover a part of the poster that is
1/5ft wide and 3/5ft long
Area of the Photo Collage Section
=Length X Width
= 1/3 * 3/5
= 3/15 ft = 1/5foot
In conclusion, the photo cover will cover 1/5 of a square foot
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In 1940 the average size of a U.S. farm was 174 acres. Let’s say that the standard deviation was 55 acres. Suppose we randomly survey 38 farmers from 1940. The IQR for X is from ___ acres to ___.
40 divided by [2=3 (17=15)] evaluate
The inverse operation of division by zero is deemed undefined; therefore, significant analysis for this expression cannot take place.
How to solveIt appears there's some confusion regarding the expression you supplied. To better interpret it, please consider making further explanations visible.
Nonetheless, an attempt to interpret is provided below:
40 divided by [(2=3)(17=15)]
Essentially, the intention is to multiply the results of each step in this expression. Let us begin assessing the individual components:
The first, 2=3 proves false as a statement; thus, we can grant it a value of zero.
Likewise, 17=15 sets out to be incorrect which, rightfully so, can also assume a figure of nothingness.
Let us now multiply the outcomes of both statements:
(0)(0) = 0
Finally, we divide 40 - the stated number - by the result from before:
40 ÷ 0
Conclusively, the inverse operation of division by zero is deemed undefined; therefore, significant analysis for this expression cannot take place.
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Evaluate the following:
40 divided by [2=3 (17=15)]
A quadrilateral is shown below.
a) Which one of the words below describes
this shape?
Trapezium
Parallelogram Kite
b) Work out the size of angle y.
Rhombus
36°
133⁰
Rectangle
Y
#
Not drawn accurately
PLEASE DO AND DO MY ATHER QUESTIONS
Answer:
y = (360 - 117 - 75) / 2 = 84 degrees
Step-by-step explanation:
a) The shape shown in the image could be described as a kite.
b) Since the opposite angles in a kite are equal, we can find the measure of angle y by subtracting the measures of angles x and z from 360 degrees and then dividing by 2, since the sum of the interior angles of a quadrilateral is always 360 degrees. Thus, we have:
y = (360 - x - z) / 2
We can see from the figure that angle x has a measure of 117 degrees, since it is opposite to angle y in one of the congruent triangles formed by the diagonal of the kite. Similarly, angle z has a measure of 75 degrees, since it is opposite to angle y in the other congruent triangle. Substituting these values into the above equation, we get:
y = (360 - 117 - 75) / 2 = 84 degrees
Therefore, the measure of angle y is 84 degrees.
We can see that opposite sides of the quadrilateral are parallel and equal in length, which indicates that the shape is a parallelogram.
Work out the size of angle y?To find the size of angle y, we can use the fact that opposite angles in a parallelogram are equal. Let's call the angle at the bottom left corner of the parallelogram "x". Then, we know that:
x + y = 180° (because the two angles form a straight line)
We also know that the angle at the top left corner of the parallelogram is equal to x (because opposite angles in a parallelogram are equal). And since the four angles of a quadrilateral add up to 360°, we can write:
2x + 2y = 360°
Simplifying this equation gives:
x + y = 180°
x + y = 180° - x + y
2x = 180° - x
3x = 180°
x = 60°
Now we can substitute x = 60° into the equation x + y = 180° to solve for y:
60° + y = 180°
y = 180° - 60°
y = 120°
Therefore, the size of angle y is 120°.
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