Jacob's body metabolizes caffeine at a rate of 13.5% per hour.
a)Jacob's body will takes 4.77 ~5 hours to metabolize half of the 96 mg of caffeine.
b) If Jacob consumes an energy drink with 212 mg of caffeine in it, Jacob's body will take 4.77948 ~ 5 hours to metabolize half of the 212 mg of caffeine.
c) Jacob consumes a cup of coffee with c mg of caffeine in it. Jacob's body will take 4.77948~ 5 hours to metabolize half of the c mg of caffeine.
What is decay rate?The volume will slowly decrease at regular intervals and at a regular rate. This growth reduction is calculated using the exponential decay formula. The general form is y = a(1- r)ᵗ
We have, decay rate r = 13.5 % = 0.135
Initial value , a = 96 mg
plugging the value in formula we get,
y = 96(1 - 0.135)ᵗ --(1)
Now, Half of 96 is 48
so, 48 = 96(0.865)ᵗ --(2)
dividing equation by 96 we get
=> 48/96 = (0.865)ᵗ
taking natrual logarithm both sides,
=> ln(1/2) = ln ((0.865))
=> ln(1/2) = t In (0.865)
=> t = ln(1/2)/In (0.865)
=> t = 4.77948
Since, decay rate is constant so, half never changes for any .
a) 4.779~5 hours, long will it take for Jacob's body to metabolize half of the 96 mg of caffeine.
b) Jacob's body to metabolize half of the 212 mg of caffeine is 4.779~ 5 hours.
c) for Jacob's body to metabolize half of the cmg of caffeine is 4.77948.. So, we have 4.77948 ~ 5 hours is decay constant rate.
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Which BEST describes the decimal form of a rational number?
Responses
A either terminates in 0's or repeats.
B eventually repeats a non-zero digit
C neither terminates nor repeats
D always terminates in 0s
I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST PLS HURRY
Answer:
C
Step-by-step explanation:
A rational number can be written as a ratio of two integers. In decimal form, a rational number will either terminate or repeat a pattern.
let z be a standard normal variable. find p(-0.86 < z < 2.25). a) 0.1980 b) 0.7898 c) 0.7929 d) 0.7884 e) 0.7742 f) none of the above.
Using the Z- Distribution table, The answer is c) that is 0.7929.
What do you mean by probability distribution?A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.
What is Standard Normal Distribution?A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution. The standard normal distribution is centered at zero, and the standard deviation indicates how much a specific measurement deviates from the mean.
Following the Z-table,
P(-0.86<x<2.25) = 0.79288
The answer is c) 0.7929
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can someone help me figure out how to solve this problem
Answer:
To find the fourth term in the given sequence, we can use the formula for the nth term, which is a^n = 2 (a^n-1) + 4. We can then plug in the value of a^1, which is 3, and the value of n, which is 4, to find the fourth term:
a^4 = 2 (a^3) + 4
= 2 [2 (a^2) + 4] + 4
= 2 [2 [2 (a^1) + 4] + 4] + 4
= 2 [2 [2 (3) + 4] + 4] + 4
= 2 [2 [10] + 4] + 4
= 2 [24] + 4
= 52
Therefore, the fourth term in the sequence is 52.
Answer:
[tex]a_4 = 52\\[/tex]
Step-by-step explanation:
There is no way around this one. You just had to calculate each term until you got the fourth term.
[tex]a_2 = 2(a_1) + 4 = 2(3) + 4 = 10[/tex]
[tex]a_3 = 2(a_2) + 4 = 2(10) + 4 = 24[/tex]
[tex]a_4 = 2(a_3) + 4 = 2(24) + 4 = 52[/tex]
Find the distance AB:
A = (-2, 1) and B=(5,-4)
Simplify.
d =
= √(5--2)² + (-4-1)²
Answer:
now
Step-by-step explanation:
d= √(X2 _ X1) +(Y2 - Y1). = (5 -2 )+ (-4- 1)=
PLEASE PLEASE PLEASE HELP
a certain statistic will be used as an unbiased estimator of a parameter. let r represent the sampling distribution of the estimator for samples of size 35, and let s represent the sampling distribution of the estimator for samples of size 15. which of the following must be true about r and s ? responses the expected values of r and s will be equal, and the variability of r will be less than the variability of s. the expected values of r and s will be equal, and the variability of r will be less than the variability of s . the expected values of r and s will be equal, and the variability of r will be equal to the variability of s. the expected values of r and s will be equal, and the variability of r will be equal to the variability of s . the expected values of r and s will be equal, and the variability of r will be greater than the variability of s. the expected values of r and s will be equal, and the variability of r will be greater than the variability of s . the expected value of r will be greater than the expected value of s, and the variability of r will be greater than the variability of s. the expected value of r will be greater than the expected value of s , and the variability of r will be greater than the variability of s . the expected value of r will be greater than the expected value of s, and the variability of r will be less than the variability of s.
Using the Central Limit Theorem, it is found that the correct option is
a. The expected values of R and S will be equal, and the variability of R will be less than the variability of S.
What is the Central Limit Theorem?
A sufficiently high sample size from a population with a finite level of variance will result in a mean of all samples from that population that is roughly equal to the population mean, according to the CLT, a statistical theory.
According to the central limit theorem, the distribution of the sample means will be roughly normally distributed if you take sufficiently large random samples from a population with mean and standard deviation and replacement.
The samples in this issue were drawn from the same population, thus they all had the same expected value.
R has less variability because there are more samples available.
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Anyone know the answer?
0.08m^3 to kg
Answer:
hush Nikki
nnnnmm
nnnnn
The graph models the linear relationship between the number of monthly payments made on a loan and the remaining balance in dollars left to pay on the loan.
Which statement describes the x-intercept of the graph?
The x-intercept is 40 , which represents the initial balance in dollars of the loan.
The x-intercept is 30,000 , which represents the initial balance in dollars of the loan.
The x-intercept is 40 , which represents the number of monthly payments needed to repay the loan.
The x-intercept is 30,000 , which represents the number of monthly payments needed to repay the loan.
The x - intercept is 40 ,which represents the number of monthly payments needed to repay the loan .
Given :
The graph models the linear relationship between the number of monthly payments made on a loan and the remaining balance in dollars left to pay on the loan.
From the graph :
Two points are ( 6 , 25500 ) and ( 25 , 11250 )
x - intercept = 40
The x - intercept gives information about the variable represented on the x - axis of a graph which is the number of monthly repayments needed to cover the loan.
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a convex mirror, like the passenger-side rearview mirror on a car, has a focal length of -2.8 m. an object is 5.6 m from the mirror.
The image's distance from the mirror is -1.87, by using the mirror equation.
Note:- Although the question is missing, I believe the issue is asking where the image is located.
To find the solution to the problem, the mirror equation can be used:
Mirror equation = [tex]\frac{1}{f}+\frac{1}{d_{o} }+\frac{1}{d_{i} }[/tex]
Where,
f = mirror's focal length
[tex]d_{o}[/tex] = object's distance from the mirror
[tex]d_{i}[/tex] = image's distance from the mirror
The focal length is assumed to be negative for a convex mirror in our problem.
f = -2.8 m
The object's distance (do) = 5.6m
By using the mirror equation, the image's distance from the mirror can be determined
[tex]\frac{1}{f}+\frac{1}{d_{o} }+\frac{1}{d_{i} }[/tex]
i.e, [tex]\frac{1}{d_{i} } = \frac{1}{f} -\frac{1}{d_{o} }[/tex]
= [tex]-\frac{1}{2.8} -\frac{1}{5.6}[/tex] = [tex]-\frac{3}{5.6}[/tex]
= - 0.5357
[tex]d_{i} =[/tex] [tex]-\frac{5.6}{3}[/tex]
= -1.87 m
The virtual nature of the image is indicated by the negative sign (located behind the mirror)
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A line passes through point (5, –3) and is perpendicular to the equation y = x. What's the equation of the line?
Question 26 options:
y = –x + 2
y = x
y = x + 3
y = –x – 7
y= - x + 2.
Step-by-step explanation:1. Find the slope of the given line.The slope of any linear equation will always be the coefficient of the "x" variable when the equation is solved for "y". Since there isn't any number written to the left of "x", the slope of the line is 1.
2. Find the slope of the new line.When looking for the slope of a line perpendicular do another, take the value of the slope and find its multiplicative inverse and change the sign of this value as well. This is how you do it:
Original slope value: 1.
Multiplicative inverse: 1/1= 1
Changing the sign: -1
3. Form the new equation.Using the calculated value of the slope "m", which is -1, use the formula for calculating linear equations with both the slope and the values of the ordered pair:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
Substitute the values and simplify.
[tex]y-(-3) =(-1)(x-(5) )\\ \\y+3=(-1)(x)-(-1)(5)\\ \\y+3=(-1x)-(-5)\\ \\y+3=-1x+5\\ \\y=-1x+2\\ \\y=-x+2[/tex]
4. Conclude.A line that passes through point (5, –3) and is perpendicular to the equation y = x is y= - x + 2.
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6. Writing When you add a
one-digit number to a
decade number, what do you
notice about the ones place
digit of the sum?
When you add one-digit number to a decade number, you will notice that the ones place digit sum is interchanged in their positions
How to add a one-digit number to a decade number?You should know the word decade means ten. so a decade number is a number with ten digits. The digits of the decade number are
1,2,3,4,5,6,7,8,9
So write the number as
12345679
A digit number is say 9
123456789+9
= 123456798
Therefore when a digit number is added to a decade number, the last digits interchange their positions
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Which set of ordered pairs represents a function? {(-1, 3), (2, 6), (3, 9), (4, 12), (5, 20)} {(-7, 3), (-7, 6), (-7, 12), (-7, 18)} {(9, -3), (4, -2), (1, -1), (0, 0), (1, -3)}
From the given pairs of ordered pairs {(-1, 3), (2, 6), (3, 9), (4, 12), (5, 20)} it is a function.
What is a Function?The core concept of mathematics calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.
As per the set of ordered pairs given in the question,
1.
{(-1, 3), (2, 6), (3, 9), (4, 12), (5, 20)}
It is a function because every input has a single output.
2.
{(-7, 3), (-7, 6), (-7, 12), (-7, 18)}
It is not a function because 7 corresponds to two different images like 3, 6, 12, and 18.
3.
{(9, -3), (4, -2), (1, -1), (0, 0), (1, -3)}
It is not a function because 1 corresponds to two different images, like -1 and 3.
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4. in the above system of equations, d and b are nonzero constants. if the lines intersect at (2, b), what is the value of ,4?
The point (x, y) where the lines intersect is (0, 0).
What is lines intersect?
The empty set, a point, or another line can cross another line in Euclidean geometry. Examples of applications for identifying these circumstances and locating the intersection include computer graphics, motion planning, and collision detection.
We have the linear system:
y = r[tex]\times[/tex]x
y = s[tex]\times[/tex]x
We want to find the point where the lines intersect,
We know that
r[tex]\times[/tex]x = y = s[tex]\times[/tex]x
r[tex]\times[/tex]x = s[tex]\times[/tex]x
if r and s are different numbers (if r = s, this means that the two lines are the same line)
Then we have that the equality is only true when x = 0.
this means that the value of y is.
y = s[tex]\times[/tex]0 = r[tex]\times[/tex]0 = 0
So the point (x, y) where the lines intersect is (0, 0).
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The water tank at the institution is
full. A water truck begin to full the tank with
water at a rate of 8 litres per minute. After 15 minutes the tank was 5/2 full. Calculate
the number of litres of water that the tank can hold
Answer:
t = 48 litres when full
Step-by-step explanation:
The water tank at the institution is full. A water truck begin to full the tank with water at a rate of 8 litres per minute. After 15 minutes the tank was 5/2 full. Calculate the number of litres of water that the tank can hold.
8(15) = 5/2t
120 = 5/2t
240 = 5t
t = 48 litres when full
martin is 6 years younger than his sister. the sum of their ages is no more than 22 years. enter an inequality that can be used to represent this situation in the box, where x represents martin's sister's age.
Answer:
x ≤ 14
Step-by-step explanation:
x = age of Sis
x - 6 = Martin's age
x + (x-6) ≤ 22
2x - 6 ≤ 22
2x ≤ 28
x ≤ 28/2
x ≤ 14
Could somebody answer:
2 1/4 + 8/3
PLSSS
Answer:
4 11/12
Step-by-step explanation:
2 1/4 + 8/3
9/4 + 8/3
23/12 + 32/12
59/12
4 11/12
Hello, I need help with this problem.
Fill out the Venn Diagram and answer the questions.
Thank you.
Answer:
see the attachment for the Venn diagram
17949173182153248Step-by-step explanation:
Given the numbers of students in various combinations of three courses, you want the associated Venn diagram and some numbers associated with additional combinations of courses.
Venn diagramIt is often easiest to populate the numbers in a Venn diagram by starting with the center one: 286 are taking all three courses. (V. = 286)
Working outwards from there, the numbers taking two courses can be filled in: (II. = History & Dance - V. = 343; IV. = History & Math - V. = 319; VI. = Dance & Math - V. = 318.)
Finally, the number taking a single course can be found. (I. = History -II. -IV. -V.; III. = Dance -II. -V. -VI.; VII. = Math -IV. -V. -VI.)
Adding all the numbers found so far gives the total in History, Dance, or Math (question 4). The difference between the number surveyed and the number in courses is VIII, the number taking none of the courses (question 5).
History or Not DanceThe least arithmetic may be involved if you rewrite this expression to ...
H ∪ D' = (H'∩D)' = 2401 -(III +VI) = 2401 -(289 +318) = 1794
(History or Math) and Not DanceThis will be the sum of numbers I, IV, VII.
226 +319 +372 = 917
Dance and Math and Not HistoryThis is VI alone: 318
History, Dance, or MathThis is all but VIIII: 2401 -248 = 2153
None of the CoursesThis is VIII alone: 248
f(x) = 5 + x + x2 − x3
Answer:
[tex]\left(-\frac{1}{3},\:\frac{130}{27}\right) \:\mathrm{Maximum}\left(1,\:6\right)\\\\\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \: < x < \infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\\\\\Not sure if I did it right[/tex]
The coefficient of determination of a set of data points is 0.83 and the slope of the regression line is -1.38. Determine the linear correlation coefficient of the data.
The linear correlation coefficient of the data is calculated to be -0.911 as the slope of the regression line is -1.38
As the coefficient of determination that is (R^2) = 0.83 and the slope of the regression line = - 1.38, we can determine the linear correlation coefficient of the data as follows;
The Coefficient of determination (R^2) is the square of the linear correlation Coefficient (R) and is used to acquire the proportion of explained variance of the regression line.
Hence. To get the linear correlation Coefficient (R) from the Coefficient of determination (R^2); we take the square root of R^2 as follows;
R = √R^2
R = √0.83
R = 0.91104335791
R = 0.911
As the value of the slope is negative, therefore this represents a negative relationship between the variables, hence R will also be negative ;
Therefore, R = -0.911
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Solve for d.
-10 = -2 + ½ d
d= -16.
Step-by-step explanation:1. Write the expression.[tex]-10=-2+\frac{1}{2}d[/tex]
2. Add "2" to both sides if the equation.[tex]-10+2=-2+\frac{1}{2}d+2\neq \\\\ -8=\frac{1}{2}d[/tex]
3. Divide both sides by "1/2".[tex]\frac{-8}{\frac{1}{2}} =\frac{\frac{1}{2}d}{\frac{1}{2}} \\ \\-8*2=d\\ \\-16=d\\ \\d=-16[/tex]
4. Verify.[tex]-10=-2+\frac{1}{2}(-16)\\ \\-10=-2-8\\ \\-10=-10[/tex]
That's correct! The answer is d= -16.
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Doug can paint a room in 5 hours. Dave can paint the same room in 7 hours. Doug and Dave paint the room together and take a one-hour break for lunch. Let $t$ be the total time, in hours, required for them to complete the job working together, including lunch. Which of the following equations is satisfied by t?
On solving the provided question, Since rate multiplied by time gives output, 1/5+1/7 (t-1)=1
What is equation?A formula is a statement that the values of two expressions are equal. The formula essentially says that two things are equal. An equals sign or '=' indicates that. 8+2=12-2 is an example equation. According to the above formula, the left side of the formula is equal to the right side. So the equation is the statement "this is equal to that".
Doug can paint 1/5 of a room per hour, Dave can paint 1/7 of a room per hour, and the time they spend working together is t-1.
Since rate multiplied by time gives output, 1/5+1/7 (t-1)=1
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 7
The cone will fit in 4 times and the volume of the cone is 535.89 in³
Volume of a ConeA cone is a pyramid with a circular cross-section. A right cone is a cone with its vertex above the center of the base. It is also called right circular cone.
The formula of volume of a cone is given as;
V = 1/3πr²h
v = volume of the coner = radius of the coneh = height of the coneHowever, we have to calculate the volume of the sphere which is given as
V = 4/3 πr³
The volume of the ball = 4/3 * 3.14 * 8³ = 2143.57in³
The volume of the cone = 1/3 * 3.14 * 8² * 8 = 535.89 in³
The number of times it will fit into will be 2143.57 / 535.89 = 4
It will fit in 4 times
b)
The volume of the cone is 535.89in³
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the lucas primality test is based on one finding of this man who pioneered the method of infinite descent. that result is a specific case of a theorem that takes an element to the totient function of n-1, euler's theorem. numbers for which the converse of that theorem do not hold are called carmichael
The name of this man's "small" and "final" theorems are Pierre de Fermat
He was a French mathematician who is recognized for his work on inequality and other early advances that helped pave the way for infinitesimal calculus. He is praised in particular for his work on number theory and his original invention of a technique for determining the largest and smallest ordinates of curved lines that is comparable to differential calculus, which was previously unheard of. He made important advances in probability, optics, and analytical geometry.
The Taniyama-Shimura Conjecture, commonly known as the modularity conjecture, was employed in another theorem that bears this man's name.
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morgan bought new living room furniture for $6,500 on an installment plan. he made a down payment $500, and he has to make monthly payments of $210.00 for the next three years. how much interest will he pay?
Interest morgan will pay is $1560.
What is compound interest?Compound interest, also known as interest on principle and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Given, Morgan used a payment plan to purchase brand-new living room furnishings for $6,500. He put down $500, and over the following three years, he must pay a monthly payment of $210.00.
Hence he has to total pay = 500 + 210*12*3
The total money morgan has to pay is $8060.
Therefore total interest morgan has to pay is 8060-6500 = $1560.
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How would you limit the domain to make this function one to one f(x)=3-x^2
Answer:
x ≥ 0
Step-by-step explanation:
You want to know an appropriate limit on the domain of f(x) = 3 -x² so the function is one-to-one.
One to OneA function is one-to-one if it passes the "horizontal line test." That is, a horizontal line can intersect its graph in at most one place.
The function f(x) = 3-x² has a turning point at x=0 and is symmetrical about that line. In order to make the function be one-to-one, the domain must be restricted to one of ...
x ≥ 0, orx ≤ 0or any subset of either of those domains.
What is the value of q?
O 4√5
O 2√14
O 20√5
O 64√5
Found the answer thought I would help
Answer:
18
Step-by-step explanation:
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
9x2 + xy + 9y2 = 19, (1, 1) (ellipse)
y = ________________?
The equation of the tangent line to the ellipse 9x^2 + xy + 9y^2 = 19 at the point (1, 1) is y = -18x + 19, which can be found using implicit differentiation.
We can find the equation of the tangent line to the ellipse 9x^2 + xy + 9y^2 = 19 at the point (1, 1) using implicit differentiation. Firstly, we take the partial derivatives of both sides of the equation with respect to x and y, which gives us y' = (9x + y)/(9y +x). Then, we plug in the given point (1,1) into the equation for y' and solve for y'. This gives us y' = (9 + 1)/(9 + 1) = 10/10 = 1. This means that the slope of the tangent line at this point is 1. We can then use the point-slope form of a line equation, y - 1 = 1(x - 1), to find the equation for the tangent line at this point, which is y = -18x + 19.
y' = (9x + y)/(9y +x)
At the given point (1,1):
y' = (9 + 1)/(9 + 1) = 10/10 = 1
Equation of the tangent line:
y - 1 = 1(x - 1)
y = -18x + 19
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Evaulate the expression for (22+5) / (12 - 9) x 6
Step-by-step explanation:
remember the priorities of doing the calculation operations :
1. brackets
2. exponents
3. multiplications and division
4. addition and subtraction
so,
(22 + 5) / (12 - 9) × 6
(27) / (3) × 6
and to write it without any doubt :
(27 / 3) × 6
9 × 6 = 54
why is
(27 / 3) × 6
better than
(27) / (3) × 6 ?
because if you are really taking it literally, you could understand
27 / 3 × 6
as
27 / (3 × 6)
and then the result is different.
so, many greetings to your teacher ! if what your write here was really what your teacher gave you, he/she was sloppy. in real math documentation people would write that as
((22 + 5) / (12 - 9)) × 6
our leave extra space like
(22 + 5) / (12 - 9) × 6
Mrs.Lopez asked a Capenter to struck a rectangular bulletin board for her classroom . she told the carpenter that the board must be 12 square feet.
1.what are the possible length and width of bulletin board?Give at least 2 pairs
2. how did you determine the possible length and width of the bulletim board?
3.suppose the length of the board is 1 ft.longer that its width and let x be the width. how will you represent the length of bulletin board?
4. given the area of the illustration board which is 12 square feet,what equation represent the given Situation? hint. Area=(length) (width)
5. how would you describe the equation formulated?
6. do you think you can use the equation formulated to find the length and width of the bulletin board
Let us answer the individual questions as per the given conditions:
1. Since the area of the bulletin board is meant to be exactly 12 square feet, the 2 pairs for length and width would be 4feet and 3feet(first pair), 6 feet and 2 feet(second pair) respectively.
2. The possible length and width of the board were determined using trial and error method to find two numbers whose product equal to 12.
3. If width of the board were to be x , and the length be 1 greater than width, we can represent the length as x+1.
4. Given the area of illustration board as 12 sq ft. the equation that represents the given situation is :
5. The equation can be described as quadratic equation.
6. Yes, I think we can use the equation formulated to find the length and width of the bulletin board.
What is rectangle?
A quadrilateral with equal angles and parallel opposing sides is referred to as a rectangle. Around us, there are a lot of rectangle items. Two dimensions, the length and breadth, define any rectangle form.
What is the formula for calculating area of rectangle?
The formula for calculating the area of rectangle is given by:
A = L * B
where A - area of rectangle
L - Length of the rectangle
B - Width of the rectangle
According to the given question:
1. Using the formula for area of rectangle(length * width) , the two pairs of length and breadth can be found by finding two real positive numbers whose product equals to 12. Hence , we get 4 feet and 3 feet as first pair and 6 feet and 2 feet as second pair for length and width respectively.
2. The possible length and width pairs were determined by using the equation of area, A = L*B which is equal to 12 sq ft.
3. Since the width is given to be x by the question and x is mentioned to be 1 greater than width, hence length will be equal to x+1.
4. Using the equation for area of rectangle:
A = L * B
substituting the values as per the given conditions,
12 = x(x+1)
or, x2 + x = 12
or, x2+x-12 =0
Which is the required equation.
5. Since the highest power in the equation is 2. Hence the equation is described as quadratic equation.
6. Yes , we can use the equation formulated to find the length and width of the bulletin word, Simply solving the quadratic equation given above.
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Pls helpppppppppppppppppppppp
Answer:
0.875
Step-by-step explanation:
7/8 in decimal form is 0.875.