We have the following response after answering the given question: inequality {x | x ≥ ∛9} or [∛9, ∞) in interval notation.
What is inequality?A connection between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. The not equal symbol is often used to indicate that two values are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two sides until just the variables are left, one may solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.
[tex]x^3[/tex] - 8 ≥ 1
Adding 8 to both sides, we get:
[tex]x^3[/tex] ≥ 9
Taking the cube root of both sides, we get:
x ≥ ∛9
Since ∛9 is approximately 2.08, the inequality is satisfied for all values of x greater than or equal to 2.08. Therefore, the set of all possible values of x that satisfy the inequality is:
{x | x ≥ ∛9} or [∛9, ∞) in interval notation.
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a highway has at least one rest stop every 25 miles. Write solve and graph an inequality to represent the number of rest stops in the first 200 miles of the highway.
In a linear equation, The number of rest stops in the first 200 miles would be 8 or more.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
25x > 200
25 25
x > 8
The number of rest stops in the first 200 miles would be 8 or more.
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In a different plan for area codes,the first digit could be any number from 3 through 7, the second digit was either 6,7,or8, and the third digit could be any number except 6 or 7. With this plan, how many different area codes are possible?
Answer:
Step-by-step explanation:
According to the given plan for area codes, the first digit can be any number from 3 through 7, the second digit can be 6, 7, or 8, and the third digit can be any number except 6 or 7.
There are 5 possible choices for the first digit (3, 4, 5, 6, or 7), 3 possible choices for the second digit (6, 7, or 8), and 8 possible choices for the third digit (0, 1, 2, 4, 5, 8, 9). This is because there are 10 possible digits in total, but we cannot use 6 or 7 for the third digit.
Using the multiplication principle of counting, we can multiply these choices together to find the total number of possible area codes:
5 x 3 x 8 = 120
Therefore, there are 120 different area codes possible with this plan.
Jose receives a dividend of $1.36 on each of his 398 shares. How many shares can he buy at $15.88?
Answer:
Jose can buy 0.086 shares at $15.88 with his dividend of $1.36 on each of his 398 shares.
Step-by-step explanation:
A square scarf has a side length of 34 yard on each side.
What is the area of the scarf?
Enter your answer in the boxes as a fraction in simplest form.
la surface de l'écharpe est de 1 1 56 cm² car la formule pour calculer l'air d'un carré est A= coté * coté soit coté²
donc : Aécharpe=34²=1156
Which of the following expressions is equivalent to 3^2x − 3?
Answer:
3(3x−1)
Step-by-step explanation:
Identify the part-to-whole ratio that describes the location of point P(3, 1) on the directed line segment AB, with coordinates A(-2, 6) and B(4, 0).
The part-to-whole ratio that describes the location of point P(3, 1) on the directed line segment AB, with coordinates A(-2, 6) and B(4, 0) is given as follows:
5/6.
How to obtain the part-to-whole ratio?The part-to-whole ratio that describes the location of point P(3, 1) on the directed line segment AB, with coordinates A(-2, 6) and B(4, 0) is obtained applying the proportions in the context of the problem.
We have that both the x-coordinate and the y-coordinate of A and B have a difference of 6 units.
We also have that both the x-coordinate and the y-coordinate of point P(3,1) have a difference of five units from the coordinates of the starting point of the segment A.
Then the ratio is given as follows:
5/6.
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a set of data with a mean of 45 and a standard deviation of 5 is normally distributed. find each value, given its distance from the mean
A set of data with a mean of 90 and a standard deviation of 3.5 is normally distributed. Find each given value, given its distance from the mean
For the given information, the standard deviation are 30 and 103.25 respectively.
What is standard deviation?
The standard deviation measures the amount of variability or dispersion in the data set. It is the square root of the average of the squared deviations from the mean.
We can use the properties of a normal distribution to find the values given their distance from the mean. In particular, we can use the standard deviation to determine how far a given value is from the mean in terms of the number of standard deviations.
For the set of data with a mean of 45 and a standard deviation of 5:
A value that is 1 standard deviation above the mean is at 45 + 5 = 50
A value that is 2 standard deviations above the mean is at 45 + 2(5) = 55
A value that is 3 standard deviations below the mean is at 45 - 3(5) = 30
For the set of data with a mean of 90 and a standard deviation of 3.5:
A value that is 1 standard deviation above the mean is at 90 + 3.5 = 93.5
A value that is 2 standard deviations below the mean is at 90 - 2(3.5) = 83
A value that is 3.5 standard deviations above the mean is at 90 + 3.5(3.5) = 103.25
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40. Social Security Numbers
A Social Security number is used to identify each resident of the United States uniquely. The number is of the form xxx-xx-xxxx, where each x is a digit
from 0 to 9.
(a) How many Social Security numbers can be formed?
(b) What is the probability of correctly guessing the Social
Security number of the president of the United States?
There are 10⁹(1 billion) possible Social Security numbers that can be formed. The probability of correctly guessing the Social Security number of the president of the United States is practically zero. This is because there are so many possible combinations, and it is highly unlikely that anyone would guess the correct number.
What is number?Number is a mathematical object used to count, measure, and label. It is used to express amounts, or magnitude of a quantity. Numbers are used in almost every field of life, such as science, engineering, economics, finance, and many other areas. Numbers are used in a wide range of contexts and are essential to modern life. They are used to communicate information, to measure time, and to represent values. Furthermore, numbers are used to represent abstract ideas, such as the probability of an event occurring. Numbers are also used to create patterns, which are essential to understanding complex systems. Without numbers, it would be impossible to measure anything, make estimates, or draw conclusions.
(a) There are a total of 10^9 (1 billion) possible Social Security numbers. This is calculated by multiplying the 10 possible digits (0-9) for each of the nine positions in the number, which gives 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10⁹.
(b) The probability of correctly guessing the Social Security number of the president of the United States is 1 in 10⁹. This is because there are a total of 10^9 possible Social Security numbers, and the president's number is only one of those.
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Can you please help on this question
Answer: It would be 10.5
Step-by-step explanation:
You are inputting R or radius into question the radius is given to you which is 10.5
11.
Jolie’s time at work increases from 25 hours per week to 30 hours per week. By what percentage did the time at work per week increase?
Show your mathematical calculations below. Describe how you determined the percentage that Jolie's time at work increased.
Jolie's working time increased by 20 %
What is percentage?A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
Given that, Jolie’s time at work increases from 25 hours per week to 30 hours per week, we need to find that by what percentage did the time at work per week increase,
Using the concept of percentage,
Initial working hours = 25 hours per week
Final working hours = 30 hours per week
Increased hour = 30 - 25 = 5 hours
Percentage increased = 5 / 25 x 100 = 20%
Hence, Jolie's working time increased by 20 %
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Describe an activity for Grade R to teach Subtraction that will accommodate each type of learning modality
Grade R learners can be best taught using hands-on experience, thus use physical beads or objects to practically teach subtraction.
How should learners in grade R be taught?A manipulatives-based project can be a fantastic method to teach subtraction to grade R students, who frequently learn best via hands-on experiences. This activity can be modified to accommodate students who learn better visually, aurally, or kinesthetically.
The activity that can be used to teach grade R learners to subtract is by using physical objects, and asking them to count the initial number.
Remove some items and recount them.
The objects removed will denote the subtraction.
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'Paraphrasing'
Original: Scientists are quick to state that the presence of these organic molecules is not sufficient evidence for ancient life on Mars, as the molecules could have been formed by non-living processes.
A- Scientists cannot agree whether the discovery of organic material on Mars is proof that creatures lived on Mars or not in the past.
B- Scientists quickly say that the existence of these organic materials is not sufficient proof for ancient life on Mars, as the molecules could have been formed by other non-living methods.
C- Scientists claim life on Mars was not possible, and that natural processes are responsible for discovering any organic molecules.
D- Science experts are not strongly convinced that the discovery of organic materials on Mars is proof that living creatures existed before on Mars. It is possible the organic matter was created naturally due to different natural causes.
The presence of these organic elements, according to scientists, is insufficient evidence for the existence of ancient life on Mars since the molecules been created via other non-living processes. This assertion true.
What kinds of things are organic materials?Everything that includes carbon compounds produced by living things is considered to be organic matter. Lawn trimmings, leaves, twigs, branches, moss, algae, lichens, any animal parts, sewage, dust, insects, earthworms, and bacteria are just a few examples of what it includes.
Which three categories best describe organic materials?Carbohydrates, lipids, protein, and nucleic acids are the four main kinds of organic substances that are found in all living organisms.
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The height of this right circular cylinder is 3 feet and its base has a radius of 5 feet. What is the surface area of this cylinder in terms of π?
The surface area of this cylinder will be 80π ft².
What is Total surface area ?
Total surface area is the total area, which includes the curved portion and any bases. It refers to the entire surface area of the thing. The total area will be equal to the sum of the two areas if the shape has a curved base and surface.
Given : height of cylinder = 3 ft
radius of base of cylinder = 5 ft
We know that, Total surface area of cylinder = 2πrh + 2πr²
= 2πr(h+r)
So, The surface area of given cylinder = 2π × 5 ( 3+5)
= 10π (8)
= 80π ft²
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Five years have passed and Jamie Lee, 34, is considering taking the plunge--not only is she engaged to be married, but she is also deciding on whether to purchase a new home. Jamie Lee’s cupcake café is a success! It has been open for over a year now and has earned itself rave reviews in the local press and from its regular customers who just cannot get enough of her delicious varieties of cupcakes. One such customer, who stopped by on a whim in the café’s first week of business, is Ross. After a whirlwind courtship, Ross, a self-employed web designer, proposed, and Jamie Lee agreed to be his wife. The bungalow that Jamie Lee has been renting for the past five years is too small for the soon-to-be newlyweds, so Jamie Lee and Ross have purchased a brand new three-bedroom, 2 ½ bath home in a quiet neighborhood for $276,000. Use the provided information and the table below to calculate the affordable mortgage amount that would be suggested by a lending institution based on Jamie Lee and Ross’s income. You will need to make note of the purchase price (above) of their home for future questions. Use the following for Jamie Lee and Ross's calculations: 10% down payment $650 per month for estimated combined property taxes and insurance 5% interest rate for 30 years Refer to Exhibit 7-7 for current mortgage rates
Therefore , the solution of the given problem of interest comes out to be $882.75 monthly affordable mortgage amount recommended by a lending organisation .
What does interest actually mean?To determine simple interest, divide the sum by the cost of borrowing, the amount of time left, and other factors. Principal plus interest plus hours is the straightforward return strategy in marketing. The simplest approach to calculate interest is to use this method. The most popular method of calculating revenue is as a fraction of the principal amount.
Here,
We can use an internet mortgage calculator to determine the affordable monthly mortgage payment. With the provided data, we can determine the monthly mortgage payment to be $1,187.25 using a mortgage calculator.
Assume that Jamie Lee and Ross earn $8,000 per month in gross revenue.
Affordable debt amount
=> $1,837.25 ($8,000 x 0.43)
=> $2,720 - $1,837.25
is an affordable mortgage sum.
=> $882.75 is an affordable mortgage sum.
This indicates that the $882.75 monthly affordable mortgage amount recommended by a lending organisation based on Jamie Lee and Ross's income.
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The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rate
T.
P = $2300, A = $2762, t = 6 months
The loan's simple interest is %.
***
Based on the information provided, it can be concluded the loan's simple interest is 4.01%.
What is the loan's simple interest?The simple interest is the difference between the future value of the loan and the loan amount.
Simple interest = future value - loan amount $2762 - $2300 = $462
The simple interest rate is a linear function of the loan amount, the interest rate, and the duration of the loan. The simple interest that is paid is the same each year for each period of the duration of the loan.
Simple interest = loan amount x time x interest rate
Interest rate = simple interest / (loan amount x time) = 462 ÷ (6/12 x 2300) = 0.401= 4.01%
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reduce 42/84 what is the answer
Answer:
1/2
Step-by-step explanation:
42/84=1/2
3x^2+42x+72 Student 1 Student 2 (X+2)(x+12). 3(x+2)(x+12) Which answer is the correct answer? What was wrong with that is incorrect? Explain what they did wrong. What important note can you make about factoring that you’ve learned from mistakes made on this problem?
Answer:
3(x + 12)(x + 2)
Step-by-step explanation:
Given
3x² + 42x + 72 ← factor out 3 from each term
= 3(x² + 14x + 24) ← factor the quadratic
Consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term.
The factors are + 12 and + 2, since
12 × 2 = 24 and 12 + 2 = 14, thus
x² + 14x + 24 = (x + 12)(x + 2) and
3x² + 42x + 72
= 3(x + 12)(x + 2) ← in factored form
Emmy watson is buying a new oven for 915.00. She made a down payment of 20% and financed the remainder. How much did she finance
Answer:
$732.00
Step-by-step explanation:
Down payment 20% of 915.00
20% = 0.2
915 x 0.2 = $183.00
Down payment = $183.00
Financed the remainder:
915.00 - 183.00 = $732.00
So, she finance $732.00
Which of these cannot be an r2-value?
The value given that cannot be an r ² value is A. - 0.75.
What is the r ² value ?The r² value, also known as the coefficient of determination, is a statistical measure that represents the proportion of variance in the dependent variable that can be explained by the independent variable(s). It is a value between 0 and 1, with higher values indicating a better fit of the regression model to the data.
It is not possible for the r² value to be negative because it is the square of the correlation coefficient. - 0.75 cannot possibly be a value of r ² as a result.
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Assuming and y are both positive, write the following expression in simplest
radical form.
4xy³√ 27x^2y^5
Answer:
We can simplify the given expression using the rules of exponents and radicals:
4xy³√ 27x^2y^5
= 4xy * ³√(27x^2y^5) (since y and ³√(27) cannot be simplified further)
= 4xy * ³√(3^3 * x^2 * y^3 * y^2)
= 4xy * 3xy * ³√y^2
= 12x^2y^2 * ³√y^2
Therefore, the expression 4xy³√ 27x^2y^5 simplifies to 12x^2y^2 * ³√y^2.
Step-by-step explanation:
When 16 is subtracted from the square of a number, the result is 6 times the number. Find the positive solution.
The positive solution is t = 8.
What are quadratic equations?A quadratic equation is a polynomial which has variables in which one has the highest power of 2.
Considering the question, let the unknown number be represented by t. So that;
16 is subtracted from the square of a number = t^2 - 16;
the result is 6 times the number = 6t
So that;
t^2 - 16 = 6t
t^2 - 6t - 16 = 0
t^2 + 2t - 8t - 16 = 0
(t^2 + 2t)(-8t - 16) = 0
t(t + 2)-8(t + 2)
So that
(t + 2)(t - 8) =0
t + 2 = 0 or t - 8 = 0
t = -2 or t = 8
Thus the positive solution is t = 8.
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HELPPP! A yard plan includes a rectangular garden that is surrounded by bricks. In the drawing, the garden
is 7 inches by 4 inches. The length and width of the actual garden will be 35 times larger than the
length and width in the drawing.
(a) What is the perimeter of the drawing? Show your work.
(b) What is the perimeter of the actual garden? Show your work.
(c) What is the effect on the perimeter of the garden with the dimensions are multiplied by 35?
Show your work.
Can you help me with this problem??
a) The finance charge for the financing of the company airplane priced at $250,000 with 15% down payment is $66,308.
b) The monthly payments Vista's aircraft loan are $4,646.80.
How are the finance charge and monthly payments computed?The finance charge and the monthly payments can be determined using an online finance calculator as follows:
The finance charge represents the total interest and other fees that the financier charges for the loan.
The monthly payments are the periodic payments that must be made to settle the loan and compounded interest with the installment period of 60 months.
Company Airplane Price = $250,000
Down Payment = 15%
Loan Term = 60 months (5 years x 12)
Interest Rate = 11.25%
Results:
Monthly Payment (PMT): $4,646.80
House Price = $250,000
Down Payment = $37,500 ($250,000 X 15%)
Loan Amount = $212,500 ($250,000 - $37,500)
Total of 60 Mortgage Payments = $278,808
Total Interest (Finance Charge) = $66,308 ($278,808 - $212,500)
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The area of each figure can be calculated using the given dimensions. Which of the
figures has an area formula that is a linear function?
The figure that has an area formula that is a linear function is the rectangle.
What is area?Area is the size or measurement of a two-dimensional space. It is usually expressed in square units such as feet, meters, or kilometers. Area is a fundamental concept in mathematics, and is used to measure the size of shapes and surfaces. Area is also used to calculate the amount of material or resources needed to cover a given space. In addition, it can be used to measure the cost or value of a piece of land.
The formula for the area of a rectangle is A=lw, where l is the length and w is the width. This formula is a linear equation because it is a product of two variables, where the relationship between the two variables is a constant. Thus, the area of a rectangle is a linear function of its dimensions.
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You are taking a survey to determine the most popular pizza ordered at the local pizza shop. Which of the examples below will give a random sample of the population? Select all that apply. A) Watching people order pizza one night each week for a month B) Asking your friend what his favorite pizza is C) Having 50 customers rate their favorite pizza as they order D) Asking 5 people at the pizza shop what they ordered Hint Video This feature does not work with a screen reader. Please use shapes, lines, or other tools available below to annotate the page. Pressing enter on this button enables or disables the feature. Pen Tools Answer checkboxes A
Answer:
AStep-by-step explanation:
It is A because people will order what they want.B will not be a random sample because it is your friend, not a random person.
C a customer may be ordering another pizza that is not their favorite.
D Five is not enough and you may be bias (Ex: You need to ask 1 more person and there are 2 people: one with a dog, and one without. Let's say you like dogs, than you may go to the dog person more likely)
Find the minimum sample size n needed to estimate μ for the given values of c, σ, and E.
c = 0.95, σ = 9.1, E = 1
Answer:
The formula to calculate the minimum sample size required to estimate the population mean is given as:
n = (z^2 * σ^2) / E^2
Where,
z = the z-value for the given confidence level, which is 1.96 for c = 0.95
σ = the population standard deviation
E = the maximum error of estimate, also known as the margin of error
Plugging in the values, we get:
n = (1.96^2 * 9.1^2) / 1^2
n = 301.63
Rounding up to the nearest whole number, the minimum sample size required is 302.
Therefore, a sample size of at least 302 is needed to estimate the population mean with a 95% confidence level, assuming a population standard deviation of 9.1 and a maximum error of estimate of 1.
Step-by-step explanation:
Josh wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, Josh can pay $35 per month, plus $2 for each group class he attends. Alternately, he can get the second membership plan and pay $34 per month plus $3 per class. If Josh attends a certain number of classes in a month, the two membership plans end up costing the same total amount. What is that total amount? How many classes per month is that?
Therefore, if Josh attends 1 group class per month, both membership plans will cost him a total of $37 per month.
What makes up a number's fundamental unit?In mathematics, the first 10 integers are referred to as the fundamental numbers. From 0 to 9, these foundational numbers are listed. The 0 to 9 range of basic integers includes 0 through 1, 2, 3, 4, 5, 6, 7 and 8.
Let's start by defining some variables. Let:
x be the number of group classes Josh attends per monthT1 be the total cost of the first membership plan (which charges $35 per month, plus $2 for each class)T2 be the total cost of the second membership plan (which charges $34 per month, plus $3 for each class)We can write the equations for the total cost of each plan as:
T1 = 35 + 2x
T2 = 34 + 3x
Since we know that the two plans end up costing the same total amount when Josh attends a certain number of classes in a month, we can set T1 equal to T2 and solve for x:
35 + 2x = 34 + 3x
35 = 34 + x
1 = x
So if Josh attends 1 group class per month, the two membership plans will cost the same total amount. Let's substitute x = 1 into our equations for T1 and T2 to find out what that total amount is:
T1 = 35 + 2(1) = 37
T2 = 34 + 3(1) = 37
Therefore, if Josh attends 1 group class per month, both membership plans will cost him a total of $37 per month.
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i don’t know what to do
The table of values for the equation of line y = ( -3/4 )x + 3 is given by
x = { -4 , 0 , 4 , 8 }
y = { 6 , 3 , 0 , -3 }
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = ( -3/4 )x + 3
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope m = -3/4
when x = -4
y = ( -3/4 ) ( -4 ) + 3
y = 3 + 3
y = 6
when x = 0
y = ( -3/4 ) ( 0 ) + 3
y = 0 + 3
y = 3
when x = 4
y = ( -3/4 ) ( 4 ) + 3
y = -3 + 3
y = 0
when x = 8
y = ( -3/4 ) ( 8 ) + 3
y = -6 + 3
y = -3
Hence , the table of values are x = { -4 , 0 , 4 , 8 } and y = { 6 , 3 , 0 , -3 }
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Give an example of data that would show direct and positive correlation explain in one to two sentences the data and why it’s direct and positive correlation
The relationship between hours worked and income earned is an example of data that shows a direct and positive correlation. As the number of hours worked increases, so does the amount of money earned. This is a direct correlation because the variables (hours worked and earnings) are positively related; as one variable rises, so does the other. The correlation is positive because the relationship between the variables is directional, i.e., as one variable increases, so does the other.
Answer:
Step-by-step explanation:
An example of data that would show direct and positive correlation is the relationship between the number of hours studied for an exam and the grade received on the exam. As the number of hours studied increases, the grade received on the exam also increases, indicating a direct and positive correlation between the two variables.
Find the measure of the three missing angles in the parallelogram below.
Answer:
[tex]x[/tex] = 67 , [tex]y[/tex] = 113 , [tex]z[/tex] = 67
Step-by-step explanation:
What we need to know:
A parallelogram has two pairs of equal angles
Opposite angles are equal
Angles in a quadrilateral add up to 360
1) Find out as many angles we can
We know that the opposite angles are equal, this means that y would be equal to 113
y = 1132) Find the remaining angles
We already know that two of our angles are 113, this means that our total is 226 for now. We have two angles left which are equal so to find them we have to subtract 226 by 360 then divide by 2
360 - 226 = 134134 ÷ 2 = 67[tex]x[/tex] = 67[tex]z[/tex] = 67Hope this helps, have a lovely day! :)
Answer:
x = 67
y = 113
z = 67
Step-by-step explanation:
The properties of a parallelogram are:
The opposite sides are equal and parallel.Opposite angles are congruent.Adjacent angles are supplementary (sum to 180°).Two angles are said to be adjacent when they share a common vertex.
Therefore, both angle x and angle z are adjacent to the angle that measures 113°.
Since adjacent angles in a parallelogram are supplementary:
⇒ x° + 113° = 180°
⇒ x° = 67°
⇒ x = 67
Similarly:
⇒ z° + 113° = 180°
⇒ z° = 67°
⇒ z = 67
As opposite angles in a parallelogram are equal:
⇒ y° = 113°
⇒ y = 113