The percentage of students earned a B in the statistics course is 22.5%. So, the correct option is B).
To find the percentage of students who earned a B in the course, we need to determine the total number of students who took the course and the number of students who earned a B.
Using the information given in the bar chart, we can determine that there were a total of 40 students who took the statistics course. The number of students who earned a B is given as 9 in the bar chart. Therefore, the percentage of students who earned a B is (9/40) x 100%, which simplifies to 22.5%.
The total number of students who took the statistics course is:
Y = A + B + C + D + F = 5 + 9 + 11 + 8 + 7 = 40
The percentage of students who earned a B is:
(B/Y) x 100% = (9/40) x 100% = 22.5%
Therefore, the correct answer is (B) 22.5%.
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The area of a rectangular window is 3816 cm
If the length of the window is 72 cm, what is its width
Answer: The width of the rectangular window is 53 cm.
Step-by-step explanation:
We know that the area of a rectangle is given by the formula:
Area = Length x Width
Substituting the given values, we have:
3816 cm² = 72 cm x Width
To solve for the width, we can divide both sides by 72 cm:
Width = 3816 cm² ÷ 72 cm
Width = 53 cm
Therefore, the width of the rectangular window is 53 cm.
TRUE/FALSE. Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" Ris a linear transformation. If Ic.B = Tç, e then B = E = C.
Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" R is a linear transformation. If Ic.B = Tç, e then B = E = C.
The above statement is True.
In mathematics, and more specifically in linear algebra, a linear map (also called a linear map, a linear transformation, a vector space homomorphism, or in some cases a linear function) is a map between two vector spaces V → W, which performs the conservation of operations on vectors. Addition and scalar multiplication. The same names and definitions are also used for the more general case of modules over rings; see the homomorphism of modules.
A linear map is called a linear isomorphism if it is a bijection. In the case V=W, the linear map is called linear automorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily that V = W, where V is the space of functions, which is a common convention in functional analysis.
Sometimes the term linear function has the same meaning as linear map, but not in analysis.
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taking a whole number, how do you know if there is a number that you can multiply by itself to get it
If a whole number has a whole number square root, it means that there exists a number that you can multiply by itself to get that number.
Let us understand this statement by taking example, the whole number 9 has a whole number square root, which is 3. This means that 3 multiplied by itself gives 9: 3 x 3 = 9. Similarly, the whole number 16 has a whole number square root, which is 4. This means that 4 multiplied by itself gives 16: 4 x 4 = 16.
However, not all whole numbers have whole number square roots. For example, the whole number 2 does not have a whole number square root, which means that there is no whole number you can multiply by itself to get 2. In this case, we would say that 2 is an "irrational" number, because its square root is not a whole number or a fraction of whole numbers.
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Find the nth term of this quadratic sequence 6, 16, 32, 54, ...
Answer:
3n squared+n+2
Answer:
the nth term of the sequence is 2n² + 4T
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Step-by-step explanation:
he sequence represents a quadratic function, the nth term of the sequenceis 2n² + 4
The nth term of a quadratic sequence is :an² + bn + c c = zeroth term ; a = second difference ÷ 2
From the sequence :First difference = 6, 10, 14, 18Second difference = 4, 4, 4
First difference between terms in position 1 and 0 :6 - 4 = 2
Zeroth term = First term in sequence - 2 = 6 - 2 = 4a = 4/2 = 2
Plugging the values into the equation :2n² + bn + 4 Using the 2nd term :n = 22(2)² + 2b + 4 = 128 + 2b + 4 = 12 2b = 12 - 12 2b = 0b = 0
Hence, the nth term of the sequence is 2n² + 4
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2.4x − 1.5y = 0.3
1.6x + 0.5y = −1.3
The system of equations above is graphed in the xy -plane. What is the x -coordinate of the intersection point (x , y) of the system?
The given system of equations above is graphed in the xy -plane, then the x-coordinate of the intersection point (x, y) is -1.0625.
What is the system of equations?
A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously.
There are different methods to find the solution of a system of two equations in two variables, but one common one is to use elimination or substitution. Here, we will use substitution.
From the first equation, we can isolate x in terms of y by adding 1.5y to both sides and dividing by 2.4:
2.4x - 1.5y = 0.3
2.4x = 1.5y + 0.3
x = (1.5/2.4)y + 0.3/2.4
x = 0.625y + 0.125
Now we substitute this expression for x into the second equation and solve for y:
1.6x + 0.5y = −1.3
1.6(0.625y + 0.125) + 0.5y = −1.3
1.0y = −1.8
y = −1.8/1.0
y = −1.8
Finally, we substitute this value of y back into either equation to find the corresponding x-coordinate:
x = 0.625y + 0.125
x = 0.625(-1.8) + 0.125
x = −1.0625
Therefore, the x-coordinate of the intersection point (x, y) is -1.0625.
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PLEASEE help!!!! Urgent!!!!!
Answer:
Step-by-step explanation:
Solve for x
(x-14)+(2x+8)= 180
3x-14+8=180
3x-6=180
3x=186
x=62degrees
Solve for y
(7y-15)+62=180
7y+47=180
7y=180-47
7y=133
y=19degrees
If the area of one side of this cube is 25 cm^2
2
, what is the area of the whole surface of the cube?
cm^2
2
Answer:
150 cm2
Step-by-step explanation:
Given side of cube's area = 25. Since Side's a square,
Edge^2 = 5^2 = 5 cm
Total surface area: 6*a² = 6*5*5 = 150 cm2
report error suppose and are isosceles triangles. also suppose that and . what is the sum of all possible lengths for ?
The possible values of TP in isosceles triangle are between 5.5 and infinity.
Let TP = x. Then we have:
TI = TP = x (isosceles triangle)
PI = TP - PI = x - 7 (isosceles triangle)
PO = TP + OP = x + 11 (triangle inequality)
Using the fact that the sum of any two sides of a triangle must be greater than the third side, we have:
x + x > 11 --> x > 5.5
x + 11 > x --> 11 > 0
x + 7 > 5 --> x > -2
Therefore, the possible values of x are between 5.5 and infinity. The sum of all possible values of x is infinity since there is no upper bound on the possible values.
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_____The given question is incomplete, the complete question is given below:
Suppose triangle TIP and triangle TOP are isosceles triangles. Also suppose that TI=5, PI=7, and PO=11. What is the sum of all possible lengths for TP?
g suppoe x follows a distribution with pdf given by...show that the moment generating function of x is mx(t)
The distribution of Z=X+Y is gamma(1,10), which has a probability density function f(z) = 10 × e^(-10z), 0 ≤ z.
The moment generating function (mgf) of Z=X+Y can be found by taking the product of the mgfs of X and Y
Mz(t) = Mx(t) × My(t) = (e^(-4+4t))×(e^(-6+6t)) = e^(-10+10t)
We recognize that Mz(t) is the mgf of the gamma distribution with shape parameter k=1 and rate parameter λ=10. Therefore, Z=X+Y follows a gamma distribution with shape parameter k=1 and rate parameter λ=10.
In summary, the distribution of Z is gamma(1,10), which has a probability density function f(z) = λ^k × z^(k-1) × e^(-λz) / Γ(k) where k=1 and λ=10. Therefore, the probability density function of Z is f(z) = 10 × e^(-10z), 0 ≤ z.
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I have solved the question in general, as the given question is incomplete.
The complete question is:
What is the distribution of Z and the value of the parameter?
15. In the figure, ABCD is a trapezoid. Given
that length of BE equals to the length
CE, find the area of triangle ADE.
Triangle ADE has a surface area of 75 cm².
What is the triangular area formula?Triangle area determination. Use the equation area = 1/2 * base * height to determine a triangle's surface area. Decide which side will serve as the triangle's base, then calculate the triangle's height from that base.
Using similarity to determine y's value
AD/BD = AE/BE
y/(a-x) = y/x
yx = y(a-x)
x = a/2
This fact can be used to determine the height of the trapezoid:
h = √(BC² - [(AB-DC)/2]²)
= √(10² - [2²]²)
= 8
Now that we know how long MD is, we can:
As a result of the triangles ADE and BDE's resemblance, we can now determine the value of y:
y/BD = AE/BE
y/(a-x) = y/x
yx = y(a-x)
x = a/2
Substituting x = a/2 and BD = AB - DC = 10 - 6 = 4, we get:
y/4 = AE/(a/2)
y = 2AE/a
Substituting y = 2AE/a in the above equation, we get:
(2AE/a)/4 = AE/(a/2)
AE = (a/2)²/2
We may now apply the triangle's area formula, ADE:
Area of ADE = (1/4) x y x (a+b)
= (1/4) x 2AE/a x (a+b)
= (1/8) x (a²/2) x (a+b)
= (1/16) x a² x (a+b)
Substituting a = 10 and b = 6, we get:
Area of ADE = (1/16) x 10² x (10+6)
= 75 cm².
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A person invests 5500 dollars in a bank. The bank pays 4.5% interest compounded
annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 6700 dollars?
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = the final amount (6700 dollars)
P = the principal amount (5500 dollars)
r = the annual interest rate (4.5% or 0.045)
n = the number of times the interest is compounded per year (once annually)
t = the time period (in years) for which the money is invested
Substituting these values in the formula, we get:
6700 = 5500(1 + 0.045/1)^(1t)
Dividing both sides by 5500, we get:
1.21818181818 = 1.045^t
Taking the logarithm (base 10) of both sides, we get:
t = log(1.21818181818) / log(1.045)
Solving this equation using a calculator, we get:
t ≈ 4.4
Therefore, the person must leave the money in the bank for approximately 4.4 years (to the nearest tenth of a year) until it reaches 6700 dollars.
ANSWER ASAP!!!!! You will be brainliest!!! To play a game, a 12 sided number cube with faces numbered 1,1,2,2,3,3,3,4,4,4,5,5 is rolled. As a percennt rounded to the nearest tenth, what is the probability of rolling either a 3 or a 5?
Answer:
41.7%----------------------------------
There are 3 of 3's and 2 of 5's out of 12 sides.
The probability of rolling either 3 or 5 is:
(3 + 2)/12 = 5/12 = 41.7% (rounded to the nearest tenth)Answer:
36
9
1/4
Step-by-step explanation:
hope I helped ya :]
please help asap!!!!!!!
To remove the y-term in the given linear equation in two Variable multiply the equation by 4 then add these two equations.
What is linear equation in two Variable;
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable. As a result, this equation has a single solution, x = 5/2. Yet, there are two solutions to a linear equation with two variables.
According to given question;
5X+8y=5 ……..eqn 1.
3x-2y=3 ………eqn 2.
Multiply by 4 in the eqn 2.
We get
12x-8y=12 ……..eqn 3 .
When we add eqn 1 and eqn 3 we get ;
17x =17
X =1
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After eliminating the y-term in the given equations i.e 5x+8y=5 and
3x-2y=3, The solution to the system of equations is x = 1, y = 0.
What is elimination method?The elimination method is the technique used to solve systems of linear equations. It involves adding or subtracting equations in a system to eliminate one variable and find the value of the other variable.
To eliminate the y-term in these equations, you can multiply the second equation by 4, which will give you:
12x - 8y = 12
Now, you can add this equation to the first equation:
5x + 12x + 0y = 5 + 12
Simplifying the left side gives you 17x, and simplifying the right side gives you 17. So, you have the equation:
17x = 17
Solving for x gives you x = 1.
Now that you have found the value of x, you can substitute it into one of the original equations to solve for y. Using the first equation, you get:
5(1) + 8y = 5
Simplifying this equation gives you:
8y = 0
Solving for y gives you y = 0.
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A special bag of Starburst candies contains 20 strawberry, 20 cherry, and 10 orange. We will select 35 pieces of candy at random from the bag. Let X = the number of strawberry candies that will be selected. a. The random variable X has a hypergeometric distribution with parameters M= , and N= n= b. What values for X are possible? c. Find PCX > 18) d. Find PX = 3) e. Determine E[X] or the expected number of strawberry candies to be selected. f. Determine Var[X]. The Binomial Distribution input parameters output The mean is The number of trials n is: The success probability p is: Binomial Probability Histogram dev. is: 1 Enter number of trials Must be a positive integer. Finding Probabilities: 0.9 0.8 Input value x fx(x) or P(X = x) Fx(x) or P(X 3x) 0.7 0.6 Input value x fx(x) or P(X = x) Fx(x) or P(X sx) 0.5 0.4 Input value x fx(x) or PCX = x) Fx(x) or P(X sx) 0.3 0.2 0.1 Input value x fx(x) or PCX = x) Fx(x) or P(X sx) 0 0 0 0 0 0 0 0 0 0 0
It involves selecting 35 candies from a bag containing 20 strawberry, 20 cherry, and 10 orange Starburst candies. X is the number of strawberry candies selected. X has a hypergeometric distribution, with possible values from 0 to 20. P(X > 18) is 0.0125, and probability mass function P(X = 3) is 0.0783. The expected value of X is 14, and the variance of X is approximately 5.67.
X has a hypergeometric distribution with parameters M=40 (20+20), N=50 (20+20+10), and n=35.
X can take on values from 0 to 20, since there are only 20 strawberry candies in the bag.
Using the cumulative distribution function for the hypergeometric distribution, we have P(X > 18) = 0.0125.
Using the probability mass function for the hypergeometric distribution, we have P(X = 3) = 0.0783.
The expected value of X is E[X] = np = 35(20/50) = 14.
The variance of X is Var[X] = np(1-p)(N-n)/(N-1) = (35)(20/50)(30/49)(40/49) ≈ 5.67.
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calculat the following multiplication
[tex]483 \times 25[/tex]
Answer:
12075
Step-by-step explanation:
Simply multiply both terms together
483 x 25 = 12075
to calculate the workload of a resource that serves different flow unit types, one must know which of the following?
The workload of the resource is 20.5 units.
To calculate the workload of a resource that serves different flow unit types, one must know the amount of flow units, the processing time for each flow unit, and the number of resources available. This is best calculated using Little's Law, which states that the average number of flow units in a system is equal to the average rate of flow units multiplied by the average time they spend in the system.
For example, if a resource is serving 3 flow unit types, A, B and C, with 10, 8 and 5 units respectively, and a processing time of 2 minutes, 1 minute and 3 minutes respectively, with 2 resources available, the workload can be calculated as follows:
Workload = (10*2 + 8*1 + 5*3) / 2
= 41 / 2
= 20.5 units
Therefore, the workload of the resource is 20.5 units.
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Complete question
What are the flow unit types that the resource is serving?
7.4y-2.9y
pls lmk....
4.5y
subtract 2.9y from 7.4y, and you get 4.5y
Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch. I need help
D: Please !!!!
Answer:
We can use the formula for the area of a rectangle to solve this problem. Let's assume that the length of the top of the bookcase is L and the width is b. Then, we can write:
L × b = 300
Solving for b, we get:
b = 300 / L
Since we don't know the length L, we cannot find the exact value of b. However, we can use the given information to make an estimate. Let's say that the length of the bookcase is 60 inches. Then, we have:
b = 300 / 60 = 5
So, if the length of the bookcase is 60 inches, the width needs to be at least 5 inches to accommodate Bria's soap carving collection. However, if the length is different, the required width will also be different.
Write a sentence of interpretation for each point given.
When coffee beans sell for p dollars per pound, producers supply q million pounds. (5, 9); (15, 40)
When coffee beans sell for $5 per pound, producers supply 9 million pounds. This indicates that at a higher price, producers are willing to supply a larger quantity of coffee beans.
This means that at a lower price, producers will supply a smaller quantity of coffee beans. Conversely, when the price of coffee beans increases to $15 per pound, producers supply 40 million pounds.
The relationship between price and quantity supplied is a fundamental concept in economics. When prices are lower, producers may not have enough incentive to produce and supply goods. On the other hand, when prices are higher, producers may have more incentive to produce and increase their supply. This is often referred to as the law of supply.
Understanding this relationship is important for businesses and policymakers to make informed decisions about pricing and production. By analyzing market trends and the behavior of producers, they can adjust prices to maintain a balance between supply and demand. For example, if prices are too high, it may lead to a surplus of goods that cannot be sold, while prices that are too low may result in shortages or supply constraints.
In conclusion, the relationship between price and the supply of coffee beans reflects a broader economic principle that is essential for understanding how markets work. By examining the supply curve, we can gain insights into how producers respond to changes in price, and use this information to make informed decisions about pricing and production.
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Plss help due today!!!
The survey contained 10 questions (translated into multiple languages) which resulted in categorical and quantitative data being collected. Some examples are below:
What language do you primarily speak?
Are you aware of the 2020 recipient of the European Lifetime Achievement Award in Writing? Yes or No
What is your age (in years)?
How many books did you read last year?
Do you agree with the following statements: “The European Lifetime Achievement Award recognizes authors of a variety of races and ethnicities”: Strongly Disagree, Disagree, Neither Agree nor Disagree, Agree, Strongly Agree, Do not know.
13) Which variables are quantitative?
14) Give an example of a survey question they might want to include that would result in a categorical response (include the categories).
15) What decisions might they be making with the results of the survey? Why are they interested in these questions?
Answer:
The quantitative variables in the survey are age and the number of books read last year.An example of a survey question that would result in a categorical response could be "What is your gender?" with categories such as male, female, and non-binary.The results of the survey will help the writer's guild understand the opinions and demographics of European book buyers regarding their lifetime achievement award process. Based on the responses, they may make decisions about whether to continue their current process or make changes to better align with the desires of their audience. For example, if the majority of respondents are not aware of the award or do not believe it is inclusive enough, the guild may choose to increase advertising efforts or make changes to their nomination and selection process.
Which set of numbers could represent the lengths of the sides of a right triangle?
Responses
A: 15, 18, 21
B: 9, 11, 14
C: 8, 9, 10
D: 7, 24, 25
Answer:
C: 8, 9, 10
Step-by-step explanation:
Do not put any punctuation (other than a necessary decimal place) or spaces into your answer.
When Claudia borrowed $6400 at 11% compounded semiannually for three years, the value of the rate per period was
Caludia needs to pay 2917.6128 as a payment of compound interest capital+interest.
What is compound interest?
compound interest is interest on principal + interest and this denotes to the addition of interest to the principal amount of a loan or deposit.
Capital(p) = $6400
Rate of interest(r) = 11%
Years(n) = 3
The general formula of compound interest is [tex]A= p(1+\frac{r}{100}})^n[/tex].
Now
[tex]A= 6400(1+\frac{11}{100}})^3\\A=6400 \times \frac{111}{100} \times \frac{111}{100} \times \frac{111}{100}\\A= 8752.8384[/tex]
The entire amount (Capital+interest) is equal to $8752.8384.
If we take 1 year as a period then Claudia needs to pay [tex]\frac{8752.8384}{3}\\=2917.6128[/tex]
Therefore, Claudia needs to pay 2917.6128 as a payment of compound interest capital+interest.
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A sequence is shown as follows:
points at (1,32), (2,8), (3,2), (4,0.5)
Assuming the pattern continues, what is the formula for the nth term?
Answer: an = 128 * (1/4)^n
Step-by-step explanation:
The given sequence is not an arithmetic or geometric sequence, but we can try to find a pattern using algebra. Let's assume that the formula for the nth term is of the form:
an = a * b^n
where a and b are constants to be determined. We can find these constants by using the first two points:
a * b^1 = 32 (when n = 1)
a * b^2 = 8 (when n = 2)
Dividing the second equation by the first, we get:
b^1 = (8/32) / (1/2) = 1/4
Substituting this value of b in the first equation, we get:
a * (1/4)^1 = 32
a = 128
Therefore, the formula for the nth term is:
an = 128 * (1/4)^n
We can check this formula using the other given points:
a2 = 128 * (1/4)^2 = 8
a3 = 128 * (1/4)^3 = 2
a4 = 128 * (1/4)^4 = 0.5
So the formula holds for all the given points.
type the correct words in the blanks. two radicals are said to be radicals if they have the same and the radicand.
Two radicals are said to be radicals if they have the same indices and the radicand.
In mathematics, a radicand is an expression, a number, or a variable that is enclosed in a root symbol. The factor for which we are determining the root is quantity. As we study exponents and roots, the word "radicand" is utilised. Therefore, the radicand in 2 has a value of 2. Following are some radicand examples:
3√(pq) → pq is the radicand
√(a+b) → a + b is the radicand
4√15 → 15 is the radicand
A radical is a symbol used to represent a number's root. It is symbolised as. The word or phrase that appears after the radical symbol is known as the radicand. Hence, it may be claimed that the radical represents the radicand. Alternatively said, the radicand sign is √.
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Complete question:
Type the correct words in the blanks:
Two radicals are said to be radicals if they have the same and the radicand.
Find the 45th derivative of y = cos(2x)
Answer:
Step-by-step explanation:
y=cos2x
y1=-2sin2x=2cos(2x+π/2)
y2=-2*2sin (2x+π/2)=2²cos(2x+π/2+π/2)=2²cos(2x+2*π/2)
y3==2²*-2sin(2x+2*π/2)=2³cos(2x+2*π/2+π/2)=2³cos(2x+3π/2)
......................................................................................................
y45=2^{45}cos(2x+45π/2)
Daniel opens a new savings account and makes an initial deposit of $1,200.
If the account earns 2.5%
annual interest, which equation shows how much money is in the account in 9
months?
Responses
A x=1,200+1,200(0.25)(0.75)
x is equal to 1 comma 200 plus 1 comma 200 0 point 2 5 0 point 7 5
B x=1,200+1,200(0.025)(0.75)
x is equal to 1 comma 200 plus 1 comma 200 0 point 0 2 5 0 point 7 5
C x=1,200+1,200(0.25)(9)
x is equal to 1 comma 200 plus 1 comma 200 0 point 2 5 9
D x=1,200+1,200(0.025)(9)
Answer:
D) x = 1,200 + 1,200(0.025)(9)
In this equation, 1,200 is the initial deposit, 0.025 is the decimal representation of the annual interest rate, and 9 represents the time period in months. The multiplication of 0.025 and 9 gives the proportion of interest earned in 9 months, which is then multiplied by the initial deposit and added to it to give the total amount in the account after 9 months.
Simplifying the equation:
x = 1,200 + (1,200)(0.025)(9)
x = 1,200 + 270
x = 1,470
Therefore, there would be $1,470 in the account after 9 months
The figure shows an angle with a measure of 52 degrees.
A. Find the complement of the angle shown.
B. Find the supplement of the angle shown.
Show all your work.
a. The cοmplement οf the given angle is 38 degrees.
b. The supplement οf the given angle is 128 degrees
What is cοmplementary and supplementary angles?Twο angles are said tο be cοmplementary if their measurements sum up tο 90 degrees. They are, in οther wοrds, angles that "cοmplete" οne anοther tο create a right angle. As an illustratiοn, if οne angle is 30 degrees, its cοunterpart is 60 degrees.
Twο angles are said tο be supplementary if their sums equal 180 degrees. They are, in οther wοrds, angles that "cοmplete" οne anοther tο create a straight line. If οne angle is 120 degrees, fοr instance, its cοmplement is 60 degrees.
Given the measure οf the angle is 52 degrees.
The cοmplement οf the angle is, when it is added with a angle and the result is 90.
Thus,
90 - 52 = 38
The supplement οf an angle is when the result οf additiοn is 180 degrees.
Thus,
180 - 52 = 128
Hence, the complement of the given angle is 38 degrees. b. The supplement of the given angle is 128 degrees
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Let f(x) = 2x2 + 5x -19 and g(x) = x - 1. Perform the function operation and then find the domain.
(f + g)(x)
(Simply your answer.)
Answer:
(f + g)(x) = 2x² + 5x - 19 + x - 1 = 2x² + 6x - 20Domain: all real numbersURGENT. PLS HELP ME FILL IN THE CHART. Simplify the given polynomials. Then, classify each polynomial by its degree and number of terms.
The polynomial's value is Degree: 2 (because x has a maximum power of 2), Degree: 2 (since x has a maximum power of 2), and Degree: 1 (since x has a maximum power of 1).
What qualifies as a polynomial?A polynomial is an equation made up of exponents, constants, and variables that is combined using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).
Expanding the provided expression, we obtain: Polynomial 1
6x2 + 2x - 24x - 8 = (x-4)(6x+2) = 6x2 - 22x - 8
When we condense the phrase, we get:
3
(3x² - 11x - 4)
Level: 2
Amount of terms: 1
2nd polynomial:
(7x² + 3x) Degree: (21x2 - 12) = 7x2 + 3x - (21x2 + 12) = -14x2 + 3x + 12 2 (because the maximum power of x is 2)
Polynomial 3: 2(-10x2 + 18x + 13) + 4(5x2 + 9x + 7) = 20x2 + 36x + 28 - 20x2 + 36x + 26 = 72x + 54
Grade: 1
There is one term.
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Graph to solve the system: y=-3/2 and y=(1/2) × -1 At what x-values are the equations equal?
the x-value that makes the two equations equal is x = -1. and x=0.
equation defineAn equation consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), connected by an equals sign (=). The LHS and RHS may contain one or more variables, which are values that can change or vary.
The first equation, y = -3/2, is a horizontal line with a y-intercept of -3/2. This means that no matter what x-value we plug in, the corresponding y-value will always be -3/2.
The second equation, y = (1/2) x - 1, is the equation of a line with slope 1/2 and y-intercept -1. To find the x-value(s) where this equation equals -3/2, we can set the two equations equal to each other:
-3/2 = (1/2) x - 1
Adding 1 to both sides, we get:
-1/2 = (1/2) x
Multiplying both sides by 2, we get:
-1 = x
At x=0, two equation satisfy the condition.
Therefore, the x-value that makes the two equations equal is x = -1 and 0.
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