Answer:
Step-by-step explanation:
If J can paint a room in 3 hours, in 1 hour she gets [tex]\frac{1}{3}[/tex] of the job done.
If A can paint a room in 4 hours, in 1 hour she gets [tex]\frac{1}{4}[/tex] of the job done. We need to find out how long it takes them if they paint together. The equation for this is:
[tex]\frac{1}{3}+\frac{1}{4}=\frac{1}{x}[/tex] where x is the number of hours it takes them to get the job done together. Multiply everything through by 12x to get
4x + 3x = 12 so
7x = 12 and
x = 1.7 hours to get the room painted together.
The diameter of one circle is represented by 12x. The diameter of another circle is represented by 6x2y what is the ratio of the radiu of the two circles. 2:x3y 2x:y x:2y 2:xy
9514 1404 393
Answer:
(d) 2 : xy
Step-by-step explanation:
A common factor of 6x can be removed from the elements of the ratio. The ratio of radii is the same as the ratio of diameters.
12x : 6x²y = (6x)(2) : (6x)(xy) = 2 : xy
Answer:D
Step-by-step explanation:
Points A, B, C, and D lie on a line in that order. If AD/AC = 2/1 and AD/AB = 3/1, what is the value of AC/BD?
9514 1404 393
Answer:
3/4
Step-by-step explanation:
It might be easier to start by expressing the ratios with AD as the denominator.
AD/AC = 2/1 ⇒ AC/AD = 1/2
AD/AB = 3/1 ⇒ AB/AD = 1/3
From the latter, we have ...
(AD -AB)/AD = 1 -1/3 = 2/3 = BD/AD
Then the desired ratio is ...
AC/BD = (AC/AD)/(BD/AD) = (1/2)/(2/3) = (3/6)/(4/6)
AC/BD = 3/4
It has been determined that 60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon. A recent survey was conducted from 1000 of these individuals. For the sampling distribution of the sample proportion to be reasonably Normal, the sample must have been obtained in the right way (ideally, a simple random sample) and the sample size must be large (so that at least 10 or more successes and failures). Are these conditions met
Answer:
Random sample, [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], so yes, both conditions were satisfied.
Step-by-step explanation:
60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon.
This means that [tex]p = 0.6[/tex]
A recent survey was conducted from 1000 of these individuals.
This means that [tex]n = 1000[/tex]
Also, a random sample, so the first condition was satisfied.
The sample size must be large (so that at least 10 or more successes and failures).
[tex]np = 1000*0.6 = 600 \geq 10[/tex]
[tex]n(1-p) = 1000*0.4 = 400 \geq 10[/tex]
So yes, both conditions were met.
a. A CD is discounted by 10%, and then from the already discounted price, a further 15% discount is given. If the price now is $12.93, find the original price.
b. What is the total discount percent as compared to the original price?
Answer:
a. $16.90
b. 23.5%
Step-by-step explanation:
a. After the two discounts, the original price is multiplied by ...
(1 -10%)(1 -15%) = 0.90×0.85 = 0.765
Then the original price is found from ...
$12.93 = 0.765 × original price
original price = $12.93 / 0.765 ≈ $16.90
__
b. The effective discount from the original price is ...
1 -0.765 = 0.235 = 23.5%
Perimeter of a square with side 4 square root of 5
Answer:
16[tex]\sqrt{5}[/tex]
Step-by-step explanation:
[tex]4\sqrt{5}[/tex]+[tex]4\sqrt{5}[/tex]+[tex]4\sqrt{5}[/tex]+[tex]4\sqrt{5}[/tex]
16[tex]\sqrt{5}[/tex]
The perimeter of the square is 16√5 units.
We have,
The concept used here is straightforward: to find the perimeter of a square, you sum the lengths of all four sides because all sides of a square are equal in length.
In this case, the side length is given as 4√5, so you multiply it by 4 to calculate the total perimeter.
To find the perimeter (P) of a square with a side length of 4√5 units, you simply add up all four sides of the square, as all sides of a square are equal in length.
So,
P = 4 * side length
P = 4 * 4√5
P = 16√5 units
Thus,
The perimeter of the square is 16√5 units.
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1. Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute.
a. What is the mean or expected number of customers that will arrive in a five-minute period?
b. Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period.
c. Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur?
2. In the Willow Brook National Bank waiting line system (see Problem 1), assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customers per minute. Use the exponential probability distribution to answer the following questions:
a. What is the probability that the service time is one minute or less?
b. What is the probability that the service time is two minutes or less?
c. What is the probability that the service time is more than two minutes?
Answer:
1.
a. 2
b. 0.1353 probability that exactly 0 customers will arrive during a five-minute period, 0.2707 that exactly 1 customer will arrive, 0.2707 that exactly 2 customers will arrive and 0.1805 that exactly 3 customers will arrive.
c. 0.1428 = 14.28% probability that delays will occur.
2.
a. 0.4512 = 45.12% probability that the service time is one minute or less.
b. 0.6988 = 69.88% probability that the service time is two minutes or less.
c. 0.3012 = 30.12% probability that the service time is more than two minutes.
Step-by-step explanation:
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Question 1:
a. What is the mean or expected number of customers that will arrive in a five-minute period?
0.4 customers per minute, so for 5 minutes:
[tex]\mu = 0.4*5 = 2[/tex]
So 2 is the answer.
Question b:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]
[tex]P(X = 1) = \frac{e^{-2}*2^{1}}{(1)!} = 0.2707[/tex]
[tex]P(X = 2) = \frac{e^{-2}*2^{2}}{(2)!} = 0.2707[/tex]
[tex]P(X = 3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1805[/tex]
0.1353 probability that exactly 0 customers will arrive during a five-minute period, 0.2707 that exactly 1 customer will arrive, 0.2707 that exactly 2 customers will arrive and 0.1805 that exactly 3 customers will arrive.
Question c:
This is:
[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]
In which:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
The values we have in item b, so:
[tex]P(X \leq 3) = 0.1353 + 0.2707 + 0.2707 + 0.1805 = 0.8572[/tex]
[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.8572 = 0.1428[/tex]
0.1428 = 14.28% probability that delays will occur.
Question 2:
[tex]\mu = 0.6[/tex]
a. What is the probability that the service time is one minute or less?
[tex]P(X \leq 1) = 1 - e^{-0.6} = 0.4512[/tex]
0.4512 = 45.12% probability that the service time is one minute or less.
b. What is the probability that the service time is two minutes or less?
[tex]P(X \leq 2) = 1 - e^{-0.6(2)} = 1 - e^{-1.2} = 0.6988[/tex]
0.6988 = 69.88% probability that the service time is two minutes or less.
c. What is the probability that the service time is more than two minutes?
[tex]P(X > 2) = e^{-1.2} = 0.3012[/tex]
0.3012 = 30.12% probability that the service time is more than two minutes.
Lara says that she can use this picture to show that two pairs of congruent angles and
one pair of corresponding congruent sides is enough information to prove that two
triangles are congruent. Is Lara correct?
Answer:
Bottom left
Step-by-step explanation:
Mark brainliest please
Yes, Lara is correct.
Congruent triangleTwo triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are equal in measureTriangles are congruent when they have exactly the same three sides and exactly the same three angles.How to solve this problem?The steps are as follow:
Since there is a series of rigid motions that will match the triangles up exactly.Also, Lara is correct only if the corresponding congruent side is in between the two anglesThis would be "ASA" triangle congruceny which means Angle Side Angle congrucenySo Lara is correct
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Help me find the domain and range please!
Answer:
Domain: (-∞, 1]
Range: (-∞, 3]
Step-by-step explanation:
The function starts at point (1, 3) and goes to the left and down forever.
Domain: (-∞, 1]
Range: (-∞, 3]
Answer:
Domain: [tex](-\infty, 1][/tex]
Range: [tex](-\infty, 3][/tex]
Step-by-step explanation:
The domain of a function represents the range of x-values that are part of the function, read left to right. We can see that the function goes forever to the left and stops at [tex]x=1[/tex] when we read left to right. Therefore, the domain of this function is [tex]\boxed{(-\infty, 1]}[/tex].
The point at [tex]x=1[/tex] is a filled-in solid dot so it is included as part of the function. Use square brackets to denote inclusive.
The range of a function represents all y-values that are part of the function, read bottom to top. The function continues down forever and stops at [tex]y=3[/tex] when read bottom to top. Therefore, the range of this function is [tex]\boxed{(-\infty, 3]}[/tex]. Similar to the domain, we use a square bracket on the right to indicate that [tex]y=3[/tex] is included in the function. If the dot was not filled-in, then we would use a parenthesis to indicate that [tex]y=3[/tex] would not be part of the function.
Can someone help me with this problem?
2.What is the value of x if x/4 + 12 = 4 ?
Answer:
Step-by-step explanation:
Answer:
hope it will help u
PLEEEASEEEE HEEELPPP!!!
Answer: About 72%
Step-by-step explanation:
It's a conditional probability.
(Number of graduates on financial aid)/(Number of graduates)
[tex]\frac{1879}{2610} =0.7199[/tex]
0.7199 = 71.99% ≈ 72%
Algebraically show that each of the given combinations are equivalent to the given functions.
h(x) + j(x) is equivalent to k(x) given:
h(x) = 2x – 3;j(x) = - 4x + 6; k(x) = – 2x + 3
h(x) + j(2) =
Is h(x) + j(x) equivalent to k(x)? yes
Answer:
YES, they are equal
Step-by-step explanation:
Given the expressions
h(x) = 2x – 3;j(x) = - 4x + 6; k(x) = – 2x + 3
h(x) + j(x) = 2x – 3 + (-4x + 6)
h(x) + j(x) = 2x - 3 -4x + 6
h(x) + j(x) = 2x - 4x -3 + 6
h(x) + j(x) = -2x + 3 = k(x)
This shows that h(x) + j(x) = k(x)
it is estimated that 50% of emails are spam emails. Some software has been applied to filter these spam emails before they reach your inbox. A certain brand of software claims that it can detect 99% of spam emails and the probability for a flase positive is 5%. What is the probability that an email is detected as spam
Answer:
0.52 = 52% probability that an email is detected as spam.
Step-by-step explanation:
Probability that an email is detected as spam:
99% of 50%(are spam).
5% of 100 - 50 = 50%(false positives, that is, e-mails that are not spam but are detected as spams).
What is the probability that an email is detected as spam?
[tex]p = 0.99*0.5 + 0.05*0.5 = 0.52[/tex]
0.52 = 52% probability that an email is detected as spam.
Heeelp please!!! Picture included
Answer:
2nd choice
Step-by-step explanation:
The length of a rectangle is 6 inches more than the width. The perimeter is 28 inches. Find the length and the width (in inches).
Answer:
The length of the rectangle is 10 inches, and the width is 4 inches.
Step-by-step explanation:
Given that the length of a rectangle is 6 inches more than the width, and the perimeter is 28 inches, the following calculation must be performed to find the length and the width:
(X + X + 6) x 2 = 28
2X + 2X + 12 = 28
4X = 28 - 12
X = 16/4
X = 4
Therefore, the length of the rectangle is 10 inches, and the width is 4 inches.
evaluate:(0.0001)-¾
Answer:
0.001
Step-by-step explanation:
(0.0001)^-3/4=((0.1)⁴)^-3/4
(0.1)^4×-3/4
0.1^‐3
0.001
Solve the given system by the substitution method.
3x + y = 14
7x - 4y = 20
Answer:
(4, 2 )
Step-by-step explanation:
Given the 2 equations
3x + y = 14 → (1)
7x - 4y = 20 → (2)
Rearrange (1) making y the subject by subtracting 3x from both sides
y = 14 - 3x → (3)
Substitute y = 14 - 3x into (2)
7x - 4(14 - 3x) = 20 ← distribute parenthesis and simplify left side
7x - 56 + 12x = 20
19x - 56 = 20 ( add 56 to both sides )
19x = 76 ( divide both sides by 19 )
x = 4
Substitute x = 4 into (3) for corresponding value of y
y = 14 - 3(4) = 14 - 12 = 2
solution is (4, 2 )
Answer:
[tex]3x + y = 14 \\ y = 14 - 3x \\ substitute \: y \: into \: equation \: 2\\ 7x - 4(14 - 3x) = 20 \\ 7x - 56 + 12x = 20 \\ 19x = 76 \\ x = \frac{76}{19} =4 \\ y = 14 - 3( 4 ) = 2 \\ [/tex]
The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean of $38,000 and a standard deviation of $1,000. About 68 percent of the incomes lie between what two incomes
Answer:
68% is a special
value for these problems
empirical rule suggests ± 1 standard deviation
z = (x - μ)/σ
1 = (x - 38000)/1000
Between $37,000 and $39,000
Step-by-step explanation:
How long will it take her to travel 72 miles? use the unit ratio to solve the following problem.
Answer:
It will take Noshwa 3 hours and 36 minutes to travel 72 miles.
Step-by-step explanation:
Since Noshwa is completing the bike portion of a triathlon, assuming that she travels 40 miles in 2.5 hours, to determine how long will it take her to travel 72 miles, the following calculation must be performed:
40 = 2.5
72 = X
72 x 2.5 / 50 = X
180/50 = X
3.6 = X
1 = 60
0.6 = X
0.6 x 60 = X
36 = X
Therefore, it will take Noshwa 3 hours and 36 minutes to travel 72 miles.
Find the distance between the two points.
(3,-9) and (-93,-37)
Answer:
d(A,B)=100
Step-by-step explanation:
The distance between two points A([tex]x_A,y_A[/tex]) and B=([tex]x_B,y_B[/tex]) is:
d(A,B)=[tex]\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}[/tex]
In this case:
[tex]x_B = - 93\\x_A = 3\\y_B = -37\\y_A = -9[/tex]
In this case:
[tex]d(A,B)=\sqrt{( - 93 -3)^2+( - 37 - (-9))^2} =\\=\sqrt{( - 96)^2+(-28)^2} =\\=\sqrt{9.216+784} \\=\sqrt{10000}=\\=\sqrt{10^4} =\\=100[/tex]
convert the fraction 3/8 to a decimal WITHOUT the use of a calculator. Show your method clearly. SHOW ALL STEPS!
here you go it's too easy
Step-by-step explanation:
Explanation is in the attachment .
Hope it is helpful to you ❣️☪️❇️
Which are correct representations of the inequality -3(2x-5) <5(2 - x)? Select two options.
Answer:
-6x+15 < 10-5x
x>5
third equation, first graph
Step-by-step explanation:
A bottle maker believes that 23% of his bottles are defective. If the bottle maker is accurate, what is the probability that the proportion of defective bottles in a sample of 602 bottles would differ from the population proportion by less than 4%
Answer:
0.9802 = 98.02% probability that the proportion of defective bottles in a sample of 602 bottles would differ from the population proportion by less than 4%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A bottle maker believes that 23% of his bottles are defective.
This means that [tex]p = 0.23[/tex]
Sample of 602 bottles
This means that [tex]n = 602[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.23[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.23*0.77}{602}} = 0.0172[/tex]
What is the probability that the proportion of defective bottles in a sample of 602 bottles would differ from the population proportion by less than 4%?
p-value of Z when X = 0.23 + 0.04 = 0.27 subtracted by the p-value of Z when X = 0.23 - 0.04 = 0.19.
X = 0.27
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.27 - 0.23}{0.0172}[/tex]
[tex]Z = 2.33[/tex]
[tex]Z = 2.33[/tex] has a p-value of 0.9901
X = 0.19
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.19 - 0.23}{0.0172}[/tex]
[tex]Z = -2.33[/tex]
[tex]Z = -2.33[/tex] has a p-value of 0.0099
0.9901 - 0.0099 = 0.9802
0.9802 = 98.02% probability that the proportion of defective bottles in a sample of 602 bottles would differ from the population proportion by less than 4%
for a science fair project javier is recording the amount of water that evaporate from a bucket in a month he creates a table like this i will give point for the best answer
week 1 2/16 inch
week 2 1/16 inch
week 3 3/16 inch
week 4 2/16 inch
how much water had evaported from the bucket at the end of week 2
what was the total amount of water that evaported in the four weeks
if javier orignally put 4 inches of water in the bucket how many inches of water were left after the experment was completed
Answer: [tex]\dfrac{3}{16},\ \dfrac{1}{2}, \dfrac{7}{2}\ \text{inch}[/tex]
Step-by-step explanation:
Given
Javier created a table for the amount of water evaporated in each week
After two weeks, the amount of water evaporated is
[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}\\\\\Rightarrow \dfrac{2+1}{16}=\dfrac{3}{16}\ \text{inch}[/tex]
Total amount of water evaporated in four weeks is
[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}+\dfrac{3}{16}+\dfrac{2}{16}\\\\\Rightarrow \dfrac{2+1+3+2}{16}=\dfrac{8}{16}\\\Rightarrow \dfrac{1}{2}\ \text{inch}[/tex]
If Javier originally puts 4 inches of water, amount of water left in the bucket
[tex]\Rightarrow 4-\dfrac{1}{2}\\\\\Rightarrow \dfrac{4\times 2}{2}-\dfrac{1}{2}\\\\\Rightarrow \dfrac{8-1}{2}=\dfrac{7}{2}\ \text{inch}[/tex]
3. Express the strength of a solution both as a ratio and as a percentage if
2 L of the solution contain 400 mg of solute.
Answer:
1 : 5000
0.02%
Step-by-step explanation:
A solution = solute + solvent
A 2 Litre solution = (2 * 1000) = 2000 mg
Having, 400 mg of solute ;
Recall ;
1 mg = 0.001 ml
400 mg = (0.001 * 400) = 0.4 ml
The strength of the solution :
Amount of solute / Amount of solution
0.4 / 2000
As a ratio :
0.4 / 2000 = (0.4 * 10) / (2000*10) = 4 / 20000 = 1 / 5000 = 1 : 5000 (as a ratio)
0.4 / 2000
= 0.0002
(0.0002 * 100%) = 0.02% (As a percentage)
is this a direct variation
y=2x + 3
pls give an explanation if you don’t have one still pls give an answer
Answer:
No.
Step-by-step explanation:
y/x has to be the same number no matter what except at point (0 0) which it must also include for it to be a direct variation.
*y=2x+3 is not a direct variation because you can not write it as y/x=k where k is some constant number. If we were y=2x, then yes since y/x=2.
*You could also take two points and see if they are proportional. That is, you can see if y2/x2 gives the same value as y1/x1 where (x1,y1) and (x2,y2) are points on the line y=2x+3. This must work for every pair of points on the linear relation except at x=0 (where you would or should have y=0 if it is directly proportional).
Let's try it out. If x=1, then y=2(1)+3=5.
5/1=5
If x=2, then y=2(2)+3=7
7/2=3.5
As you can see 5 doesn't equal 3.5.
*For it to be a direct variation, it also must contain the point (0,0) and be a diagonal line when graphed. It can also be written in form y=kx where k is a constant number. This fails two of the the things I mentioned. It doesn't contain point (0,0) because y=2(0)+3=3 not 0. It cannot be written in form y=kx because of the plus 3.
If it were y=2x, then the answer would be yes.
Can someone please help?
Step-by-step explanation:
So, so, to attempt this, we need to use the formula :-
2 (l + b) × h ---> For Lateral surface area
2(30+30) h = 7200
2×60×h = 7200
120 × h = 7200
h = 7200/120
h = 60 cm
Now, volume = l×b×h
= 30×30×60
= 54000 cm³ is the required answer.
Hope it helps! :D
why no one helping me please help please please please please please
Answer:
a) A
b) C and E
c) C, D and F
d) two
e) Equal
ABCD-EFGH what does y=?
Answer:
y = 3
Step-by-step explanation:
Given that the shapes are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{AB}{EF}[/tex] = [tex]\frac{CD}{GH}[/tex] , substitute values
[tex]\frac{3}{2}[/tex] = [tex]\frac{4.5}{y}[/tex] ( cross- multiply )
3y = 9 ( divide both sides by 3 )
y = 3
What is the answer??
Answer:
Step-by-step explanation:
Let AC = x
AB - AC = 4 cm
AB = 4 +x ----------------(I)
Pythagorean theorem
AB² + AC² =BC²
(4 + x)² + x² = 9²
Use the identity (a + b)² = a² + 2ab + b² where a = 4 & b = x
4² +2*4*x +x² + x²= 81
16 + 8x + 2x² = 81
2x² + 8x + 16 - 81 = 0
2x² + 8x - 65= 0
a = 2 ; b = 8 ; c = -65
D = b² - 4ac
= 8² - 4*2*(-65)
= 64 + 520
D = 584
√D = √584 = 24.16
[tex]x=\frac{-b+\sqrt{D}}{2a} \ or \ x =\frac{-b-\sqrt{D}}{2a}\\\\x= \frac{-8+24.16}{2*2} \ or \ x = \frac{-8-24.6}{2*2}[/tex] {Ignore this as it is negative.}
x = 16.16/4
x = 4.04
AC = 4.04 Cm
AB = 4 + 4.04 = 8.04 cm
Area of triangle ABC = [tex]\frac{1}{2}* base * height[/tex]
[tex]=\frac{1}{2}*4.04 *8.04\\\\= 2.02 * 8.04[/tex]
= 16.24 sq.cm
