The function having the factors (x+1), (x-1) and (x-4) is x³-4x²-x+4 = 0
What are factors?
A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
Factors can be found using either division or multiplication. Rules of divisibility can also be applied.
Given, the factors of a function are (x+1), (x-1) and (x-4)
We know that if the factors of a function are (x-a) and (y-b), it would mean that the function is (x-a)(y-b) = 0
Similarly, taking the above factors given in a function, the function would be:
(x+1)(x-1)(x-4)=0
⇒ (x²-1)(x-4)=0
⇒ x³-4x²-x+4 = 0
Hence, the function having the factors (x+1), (x-1) and (x-4) is x³-4x²-x+4 = 0
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Question 2
What is the length of the line segment with endpoints P(2, 1,-4) and Q(-1,5,3)?
The length of the line segment with endpoints P(2, 1, -4) and Q(-1, 5, 3) is 8.60 units
How to find the length of a line segment?To find the length of a line segment with endpoints P(x1, y1, z1) and Q(x2, y2, z2) in three-dimensional space, we can use the distance formula:
length = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)
Substituting the coordinates of P and Q into the formula, we get:
length = √((-1 - 2))² + (5 - 1))² + (3 - (-4)))² )
= √((-3))² + (4))² + (7))² )
= √(9 + 16 + 49)
= √(74)
= 8.60 units
Therefore, the length of the line segment is 8.60 units
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The graph of a relation is shown.
A coordinate plane with a straight line. The line starts in the lower left quadrant and continues up through the uppercase right quadrant. The line passes through the y-axis slightly below the origin, and then passes through the x-axis slightly to the right of the origin.
Which of these values could be the slope of the line? Select two options.
–2
0
3
$0.67 per book
$1.07 per book
$1.50 per book
The possible slope of the line is (c) 3
How to determine the possible slope of the lineFrom the question, we have the following parameters that can be used in our computation:
Start position = lower leftOther location = upper right quadrantThis means that the line is ascending from left to right in which case, the slope of the line is positive.
So, the possible values of the slope include the set of numbers greater than 0.
From the options, we have (c) 3
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PLS HELP W/ THESE LAST FEW QUESTIONS IM STRUGGLING THANK UU!!! (47 PNTS)
1) a
Obtuse and scalene
b
Isosceles and scalene
c
Acute and right
d
Right and scalene
e
Right and equilateral
2)Find the measure of the missing angle.
3)Find the measure of the missing angle.
6) t= ; ∠X
8) x=
10) m∠R = ; SR
Answer:
1. Scalene Triangle
2. 135 degrees
3. 80 degrees
I don't have much time for the rest, i'm sryyyyy
I hope i could helppp :3
Find the table that follows this rule: multiply by 8 and add 5.
A.
Input 5 6 7 8 9 10
Output 40 48 56 64 72 80
B.
Input 5 6 7 8 9 10
Output 45 53 61 69 82 90
C.
Input 5 6 7 8 9 10
Output 45 53 61 59 67 75
D.
Input 5 6 7 8 9 10
Output 45 53 61 69 77 85
Answer:
D
Step-by-step explanation:
multiply by 8 and add 5.
so,
we need to do this for every unit value and see, if the result is the same as the listed output value.
5 -> 5×8 + 5 = 45
6 -> 6×8 + 5 = 53
7 -> 7×8 + 5 = 61
8 - > 8×8 + 5 = 69
9 -> 9×8 + 5 = 77
10 -> 10×8 + 5 = 85
so, D is the correct answer.
The table shows the production budgets and worldwide gross revenues of eight 2018 films. Which statement gives the correct value and interpretation of r?
A. As budgets increased, the gross revenue increased; r = 0.38.
B. For every budget increase of $1 billion, gross revenue increased $0.38 billion; r = 0.38.
C. As budgets increased, the gross revenue increased; r = 0.62.
D. For every budget increase of $1 billion, gross revenue increased $0.62 billion; r = 0.62.
The correct option regarding the correlation coefficient of the data-set is given as follows:
C. As budgets increased, the gross revenue increased; r = 0.62.
What is the correlation coefficient and how to obtain it?The correlation coefficient is an index between -1 and 1 that measures the relationship between two variables, as follows:
negative coefficient: inverse relationship.positive coefficient: direct relationship.absolute value greater than 0.6: strong relationship.absolute value less than 0.6: weak relationship.The coefficient is obtained with a correlation coefficient calculator, inserting the points of the data-set into the calculator.
From the table given by the image, the points are given as follows:
(0.3, 2.05), (0.25, 0.39), (0.2, 1.35), (0.2, 1.24), (0.2, 0.63), (0.18, 0.79), (0.18, 0.53), (0.18, 0.35).
Inserting these points into a calculator, the value of the coefficient is given as follows:
r = 0.62.
Meaning that there is a positive relation amount the variables, and option C is correct.
Option D would be correct if 0.62 was the slope of the line of best fit, hence this is not the case.
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Answer:
answer is attached.
Step-by-step explanation:
Please Hurry ASAP!!!!!
The values of of the functions f(x)=3x+2 and g(x)=x²-x are: (14) 14, (15) 26, (16) -4, (17) 2, (18)12, (19) 42 (20)7, (21)2, (22)2, (23)5 (24) 3x+5 (25) 9b²-3b
How to determine the values of the functions?We should know that in each of the functions, we have to substitute the given values
The given functions are
f(x)=3x+2
g(x)=x²-x
(14) f(x)=3x+2
Substitute for x
f(4)=3*4+2
f(x)=12+2=14
(15) f(8)=3x+2
f(8)=3*8+2
Substitute for x
f(x)=24+2 = 26
(16) f(-2)=3*-2+2
Substitute for x
f(-2)=-6+2
f(x)=-4
(17) g(2)=2²-2
Substitute for x
g(x)=4-2
g(x)=2
(18) g(-3)=3²-(-3)
Substitute for x
g(x)=9+3 = 12
(19)g(-6)=-6²-(-6)
g(x)=36+6 = 42
(20) f(2)+1
Substitute for x
=2*3+1
=6+1
=7
(21) f(1)-1
3*1-1 = 2
(22) g(2) -2
2²-2
4-2=2
23 = g(-1)+4
-1²+4
1+5=5
(24) f(x+1)
Substitute for x
= 3(x+1)+2
=3x+3+2
=3x+5
(25) g(3b)
Substitute for x
=(3b)²-3b
9b²-3b
In conclusion, the values of the values of of the functions f(x)=3x+2 and g(x)=x²-x are: (14) 14, (15) 26, (16) -4, (17) 2, (18)12, (19) 42 (20)7, (21)2, (22)2, (23)5 (24) 3x+5 (25) 9b²-3b
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Mr.eder’s dog is on a special diet from the vet. The dog is to eat 1/4 kg of food per day. Me.Eder buys a 6 pound bag of dog food. If mr.Eder follows the vet’s diet, how many days will this bag of food last
For 10 days that bag will last when Mr. Eder's buys 6 pound bag of dog food, using kg to pound conversion and simple basic arithmetic operation.
How to convert kg to pound ?
We know that 1 Kg = 2.20 pound.
The dog is to eat 1/4 * 2.20 = 0.55 pound food
Weight of bag brought by him = 6 pound
The basic operations are :
Addition : (+) To get sum of two or more values
e.g. a = 3, b = 5
Addition = 3+5
= 8
Subtraction : (-) The result of subtraction is the “difference”
e.g. Subtraction of a and b = a-b
= 3-5
= -2.
Multiplication : (*) The result of multiplication is the “product”
e.g. Multiplication of a and b = 3*4
= 12
Division : (/) The result of division is the “quotient”
e.g. Division of 4 and 2 is = 4/2
= 2.
so, the number of days bag can be used = 6/0.55
= 10.90
So, the bag can be used for complete 10 days.
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if the odds on a particular football team winning a bowl game are 2:3 that means the percent chance that the team will win is:
There will be 40% chance that the team will win.
Odds, are given as (chances for success) : (chances against success) or vice versa.
If odds are stated as an A to B chance of winning then the probability of winning is given as P(winning) = A / (A + B) while the probability of losing is given as P(Losing) = B / (A + B).
For 2 to 3 odds for winning:
P(winning) = 2/2+3
= 2/5
= 0.4
⇒ The percent chance of winning is 40.
Therefore, 40% is the required answer.
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The probability of winning a certain game is 0. 5. If at least 70 percent of the games in a series of n games are won, the player wins a prize. If the possible choices for n are n=10, n=20, and n=100, which value of n should the player choose in order to maximize the probability of winning a prize?.
0.117 Or 11.7% chance of n should the player choose in order to maximize the probability of winning a prize.
What is the binomial theorem on probability?The probability of precisely x successes on n further trials in an experiment with two potential outcomes is referred to as the binomial probability (commonly called a binomial experiment).
When a procedure is performed a certain number of times (for example, in a group of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of witnessing a defined number of "successes."
The probability of winning a prize remains the same for. n = 10 or n=20 or n = 100; the probabilities are the same.
Given that,
p = 0.5, So, q = 1 - 0.5 = 0.5.
If 70% of 'n' games are won then 30% of n games must be lost.
Let n = 10.
Therefore, P ( x = 3) = [tex]^{10}C_3p^7q^3[/tex]
or, P ( x = 3) = [tex]^{10}C_3(0.5)^7(0.5)^3[/tex]
or, P (x = 3) = 120×0.0078×0.125.
or, P (x = 3) = 0.117 Or 11.7% chance.
Now, Changing the value won't have any effect as all the 'n's are multiple of 10 and we'll have same probability.
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Santiago creates a playlist of Latin dance music. The playlist contains bachata, salsa, and mambo tracks, as shown in the table. Santiago puts the playlist on shuffle mode. What is the probability that the first track he hears is a salsa track?
Santiago creates a playlist of Latin dance music. The playlist contains bachata, salsa, and mambo tracks, as shown in the table. Santiago puts the playlist on shuffle mode. What is the probability that the first track he hears is a salsa track?
Answer:8/20
Step-by-step explanation:i did the quiz and it is correct
0.55 / 2what is the probability that neither a nor b will happen? (round your answer to 2 decimal places.)
(a) The probability of either A or B occurring is 0.81.
(b) The probability that neither A nor B will happen is 0.19.
In the given question,
P(A)=0.39 P(A) = 0.39 and P(B)=0.42. P(B) = 0.42
(a) We have to find the probability of either A or B occurring.
P(A)=0.39
P(B)=0.42.
Since, events A and B are mutually exclusive
P(A and B) = 0
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.39 + 0.42 - 0
P(A or B) = 0.81
Probability of either A or B occurring is = 0.81
(b) Now we have to find the probability that neither A nor B will happen.
P(A or B) = 0.81
Probability that neither A nor B will happen = 1 - P(A or B)
Probability that neither A nor B will happen = 1 - 0.81
Probability that neither A nor B will happen = 0.19
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The right question is:
The events A and B are mutually exclusive. Suppose P(A)=0.39 P(A) = 0.39 and P(B)=0.42. P(B) = 0.42.
(a) What is the probability of either A or B occurring? (Round your answer to 2 decimal places.)
(b) What is the probability that neither A nor B will happen? (Round your answer to 2 decimal places.)
For this lab, you will find the area of an irregularly shaped room with the shape as shown above.
Ask the user to enter the values for sides A, B, C, D, and E and print out the total room area.
Remember the formula for finding the area of a rectangle is length * width and the area of a right triangle is 0.5 * the base * height.
Please note the final area should be in decimal format.
Sample Run
Enter side A: 11
Enter side B: 2
Enter side C: 4
Enter side D: 7
Enter side E: 1
Sample Output
Room Area: 53.5
The python program code is written to find the area of the shape.
What is meant by area?The size of a region on a planar or curved surface is expressed mathematically as area. The term "surface area" refers to the area of an open surface or the perimeter of a three-dimensional object, whereas "plane area" refers to the area of a shape or planar lamina.
The program is given as:
print('Please, enter sides lengths:')
# Getting sides lengths
a, b, c, d, e = map(float, (input('A = '), input('B = '), input('C = '), input('D = '), input('E = ')))
# Finding a rectangle area
rect_area = a * b
# Finding a triangle area
triang_height = (c**2 - (a / 2)**2)**0.5
triang_area = 0.5 * a * triang_height
# Sum area
area = rect_area + triang_area
print('Total room area: %f' % area)
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2 ^ (x + 3) * 3 ^ (x + 4) = 18
The value of the variable x is -2
What is an algebraic expression?An algebraic expression can be defined as an expression made up of terms, variables, coefficient, factors and constants.
These expressions are also made up of arithmetic or mathematical operations, which includes;
SubtractionAdditionMultiplicationDivisionBracketParentheses, etcFrom the information given, we have;
2 ^ (x + 3) * 3 ^ (x + 4) = 18
Now, let's find the factors of 18 in 2's and 3's, we have;
2 ^ (x + 3) * 3 ^ (x + 4) = 2^1 × 3^ 2
Collect the common factors, we get;
x+ 3 + x + 4 = 1 + 2
collect like terms
2x = 3 - 7
2x = -4
make 'x' the subject of formula
x = - 2
Hence, the value is -2
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Please help me with this
the value of y is 3 when the value of x is 8.
what is proportional relationship?
When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.
Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.
Given y is inversely proportional to x
When x=3, y=1/x = 8
So when x = 8 the value of y =3
Hence the value of y is 3 when the value of x is 8.
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Which number line shows the solutions to n > -2?
++++
+
-6-5-4-3-2-1 0 1 2 3 4 5 6
←++++
H
-6-5-4-3 -2 -1 0 1 2 3 4 5 6
+++
++++++
-6-5-4-3-2-1 0 1 2 3 4 5 6
+++++
-6-5-4-3-2-1 0 1 2
3 14 5 6
Done -
2
PLEASE HELP URGENT WITH 4 AND 6
The solution is
a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01
b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125
The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96
What is Compound Interest?
Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
a)
Let the principal be P = amount after first period = $ 402
Now , the rate of interest r = 6 %
The compound interest is calculated by compounding monthly
Now , the interest for the second period = ( PRT / 100 x 12 )
Substituting the values in the equation , we get
The interest for the second period = ( 402 x 6 x 1 ) / 1200
The interest for the second period = $ 2.01
The amount after the second period = amount after first period + interest for the second period
The amount after the second period = 402 + 2.01
The amount after the second period = $ 404.01
b)
Let the principal be P = $ 18260
The rate of interest r = 2.5 %
The compound interest is calculated by compounding quarterly
Now , the interest for the first period = ( PRT / 4 x 100 )
Substituting the values in the equation , we get
The interest for the first period = ( 18260 x 2.5 ) / 400
The interest for the first period = 45650 / 400
The interest for the first period = $ 114.125
The amount for the first period = 18260 + 114.125
The amount for the first period = $ 18,374.125
Now , the principal for the second period = interest + amount of first period
The principal for the second period = $ 18,374.125
The rate of interest = 2.5 %
The interest for the second period = ( PRT / 4 x 100 )
Substituting the values in the equation , we get
The interest for the second period = ( 18374.125 x 2.5 ) / 400
The interest for the second period = 45935.3125 / 400
The interest for the second period = $ 114.83828125
The amount for the second period = 18,374.125+ 114.84
The amount for the second period = $ 18,488.96
Hence , the amount and interest is calculated
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Lily convinced her parents to have her birthday party at Flyzone Trampoline park. As soon as she gets there , lily spends 3/4 of an hour eating birthday cake with her friends in all , lily spends 2 1/4hours at Fly zone .
Answer: 1.5 hours
Step-by-step explanation:
I assume you’re trying to find how much time she is doing other activity.
2 1/4 - 3/4 is equal to:
2.25-0.75
That equals 1.5.
HELP ME PLEASE!!
I HAVE NO IDEA WHAT IM DOING!!
A. 36
B. 54
C. 72
D. 18
Answer:
72
Step-by-step explanation:
We are told that line AC divides angle BAE in half or "bisects" it. We are also told that line AD divides angle CAE in half as well. Lastly we are giving the value of angle DAE which is 36.
Since line DA split angle CAE in half and we have half of the value, that means that the measure of angle CAE is 36 times 2 which is 72.
72 happens to be our answer for angle BAC because angle BAC is half of the largest angle BAE, which was divided in two by line AC.
Hope this helps!
Lindsey's Cafe uses 5 bags of coffee every day. How many days will 1/2 of a bag of coffee last?
When she uses 5 bags of coffee every day at her café, half of a bag of coffee lasts for 10 days.
What is division?Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The basic purpose of splitting is to determine how many equal groups develop or how many people are in each group when distributing equally. Division is a basic operation that divides an integer. It's best to imagine of it as a group of things being distributed among a group of individuals, as in the preceding example.
Here,
number of bags needed in a day=5
number of days 1/2 bag last,
=5÷1/2
=10 days
Half of bag of coffee last for 10 days when she uses 5 bags of coffee every day in her café.
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if the average height of a male in the u.s. is 70 inches and the standard deviation of male heights is 3 inches, what is the probability that a randomly selected male will be between 70 and 73 inches? (assume a normal distribution.)
The probability of men whose height falls between 70 and 73 inches is 0.273. Therefore, the percent of men whose height falls between 70 and 73 inches is 27.3%. Therefore, the solution is 27.3%.
The standard deviation is a quantity that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.
We are informed that the heights of men in the U.S are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. We need to determine the percent of men whose height falls between 70 and 73 inches. We would first evaluate the probability that the height of a randomly selected individual would fall between 70 and 73 inches;
This can be done in stat-crunch;
Click Stat, highlight on Calculators then click Normal
In the pop-up window that appears click Between
Enter the given values of mean and standard deviation; 70 and 3 respectively
Enter the values 70 and 73 in the next set of boxes in that order
Finally, click on compute;
Stat-Crunch returns a probability of 0.273. Therefore, the percent of men whose height falls between 70 and 73 inches is 27.3%. Therefore, the solution is 27.3%.
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Using composition of functions, determine if the two functions are inverses of each other. , x ≥ 0 , x ≥ 2 A. No, because the functions contain different operations. B. No, because the composition does not result in an answer of x. C. Yes, because F(x) is equal to –G(x). D. Yes, because the composition results in an answer of x for x ≥ 2.
The correct option regarding whether the two functions are inverse functions is given as follows:
B. No, because the composition does not result in an answer of x.
How to verify if the two functions are inverses of each other?Two functions are inverses of each other if the composition of these two function has a result of x.
From the image given at the end of the answer, the two functions in this problem are defined as follows:
[tex]F(x) = \sqrt{x} + 4, x \geq 0[/tex]G(x) = x² - 4, x ≥ 2.Their composition is given as follows:
[tex](G \circ F)(x) = G(\sqrt{x} + 4)[/tex]
[tex](G \circ F)(x) = (\sqrt{x} + 4)^2 - 4[/tex]
[tex](G \circ F)(x) = x + 8\sqrt{x} + 16 - 4[/tex]
[tex](G \circ F)(x) = x + 8\sqrt{x} + 12[/tex]
The composition does not result in x, hence the two functions are not inverses and the correct statement is given by statement B.
The problem is given by the image shown at the end of the answer.
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What number does B stand for
What number does C stand for
Answer:
B=20
C = 40
These are the answers
w write the total area as a product
ing the GCF as one of the factors.
54+42 = (6.9) + (6-7)
6
+7)
The area expression as products is 7 * (8 + 6)
How to rewrite the area expression as productsFrom the question, we have the following parameters that can be used in our computation:
Area = 54 + 42
Express 54 as a product of 7 and 8
So, we have the following representation
Area = 7 * 8 + 42
Express 42 as a product of 7 and 6
So, we have the following representation
Area = 7 * 8 + 7 * 6
Factor out 7
This gives
Area = 7 * (8 + 6)
Hence, the expression using GCF is 7 * (8 + 6)
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HELP ME PLEASE AND ONLY RIGHT ANSWERS!
The length of a cell phone is 1.4 inches and the width is 3.4 inches. The company making the cell phone wants to make a new version whose length will be 1.54 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answer: 3.74 inches.
Step-by-step explanation: We can use the following to help us solve this proportion:
1.4 / 1.54 = 3.4 / x (where x is the unknown value that we are trying to solve)
1.54 / 1.4 = 1.1
x / 3.4 = 1.1
The only number that can make the following above true is 3.74, so that is your answer.
Let me know if this is right! :)
solve the question attached
Answer:
B) y = 4a------------------------------
Given:
[tex]log_2 \ y = 2+ log_2\ x[/tex]Find y if x = a:
[tex]log_2 \ y = 2+ log_2\ a[/tex][tex]log_2 \ y =2 log_2\ 2+ log_2\ a[/tex][tex]log_2 \ y = log_2\ 2^2+ log_2\ a[/tex][tex]log_2 \ y = log_2\ 4+ log_2\ a[/tex][tex]log_2 \ y = log_2\ (4*a)[/tex][tex]log_2 \ y = log_2\ (4a)[/tex][tex]y=4a[/tex]Correct choice is B.
Shahina has 550g of apples and plenty of the other ingredients.
Can she make apple crumble for 6 people?
Explain how you got your answer.
By the way for 8 people it is:
700g of apple, 40g butter, 240g sugar and 180g flour
Shahina can make apple crumble for 6 people with 550g of apple
How to determine if she can make apple crumble for 6 people?From the question, we have the following parameters that can be used in our computation:
For 8 people it is:
700g of apple, 40g butter, 240g sugar and 180g flour
This means that the grams of apple for 1 person is
Apple unit rate = 700g of apple/Number of people
Substitute the known values in the above equation, so, we have the following representation
Apple unit rate = 700g of apple/8
For 6 people, we have the following equation
Amount = Apple unit rate * Number of people
Substitute the known values in the above equation, so, we have the following representation
Amount = 6 * 700g of apple/8
Evaluate
Amount = 525g of apple
525g of apple is less than 550g of apple
Hence, she can make apple crumble for 6 people
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you are skiing down a mountain with a vertical height of 2900 feet. the distance from the top of the mountain to the base is 5800 feet. to the nearest degree, what is the angle elevation from the base to the top of the mountain?
Answer:
30°
Step-by-step explanation:
You want the angle of elevation to a point 2900 feet up that is 5800 feet distant on a straight line.
SineThe sine of the angle is the ratio of the height to the straight-line distance.
sin(θ) = h/d = 2900/5800 = 1/2
θ = arcsin(1/2) = 30°
The angle of elevation is 30° from the base to the top.
Answer: When doing a problem like this I always draw an example so I can see it. If you do that you see a right triangle with the hypothenuse, 2500 feet, is the distance from the top to the base. The opposite side is 1250 feet. Then remember sine= o/h, (opposite side over hypothenuse). So divide 1250/2500 and you get .5 Now take your calculator and use "inv" or sin-1 button to get the answer of the angle. x = 30
sinθ 1250/2500 = 1/2; θ = sin-1(1/2) = 30°
Step-by-step explanation:
PLEASE HELP ASAP IM GONNA FAIL:(
Answer:
The first answer on the bottom goes with the picture on top.
The second answer on the bottom goes with the table on the bottom.
Step-by-step explanation:
It is just asking you to list the x values and the y value. The x values are the domains and the y values are the ranges. That's it.
suppose a sample of a radioactive substance weighs 32 mg. one year later, the sample weighs 25.5 mg. what is the half-life of this substance? (round your answer to two decimal places.)
Solving this equation gives us a half-life of approximately 1.36 years. Rounded to two decimal places, the half-life of this substance is 1.36 years.
What is half life of the substance?The half-life of a substance is the amount of time it takes for half of the atoms in a sample of the substance to decay.
What is formula to calculate half-life?To find the half-life, you can use the following formula:
half-life = (time) * ln(2) / ln(initial mass / final mass)
half-life = (1 year) * ln(2) / ln(32 mg / 25.5 mg)
Solving this equation gives us a half-life of approximately 1.36 years.
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rotation 90 degrees counterclockwise about the origin
As per the sign system of the Cartesian plane coordinates of A' will be (x,-y).
What is the cartesian plane?The cartesian plane is defined in mathematics as a two-dimensional coordinate plane formed by the intersection of the x- and y-axes. The origin is the point where the x- and y-axes intersect perpendicularly.
What are the quadrants?Quadrant one (QI) is the top right fourth of the coordinate plane, where all coordinates are positive. Quadrant two (QII) is the coordinate plane's top left fourth. Quadrant three (QIII) is the fourth from the bottom left. Quadrant four (QIV) is the fourth from the bottom right.
Given:
The direction of rotation = clockwise, (from the first quadrant to forth quadrant then third quadrant, and so on)
Angle of rotation = 90° about the origin
According to the question, let's take our start point as A(x, y)
So, A( x, y) will lie in the first quadrant.
After 90° rotation about the origin A' will lies in fourth quadrant.
As per the sign system of the Cartesian plane coordinates of A' will be (x,-y).
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