If the number of bacteria doubles every 234 hours, we can use the exponential growth formula to find the population at a future time t:
N(t) = N0 * 2^(t/T)
where N(t) is the population at time t, N0 is the initial population, T is the doubling time (234 hours in this case), and t is the time elapsed.
We are given that the initial population is 15,500 bacteria. We want to find the population 936 hours from now. Therefore, we can substitute the values into the formula:
N(936) = 15,500 * 2^(936/234)
N(936) = 15,500 * 2^4
N(936) = 15,500 * 16
N(936) = 248,000
Therefore, the population of bacteria in the colony will be 248,000 after 936 hours.
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Find explicit formulas for sequences of the form a1, a2, a3, ... with the initial terms given
0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7
This formula generates the sequence 0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7, ...
Notice that the sequence alternates between positive and negative terms and that the denominators of each term increase by 1 while the numerators increase by 1 or -1. To find the explicit formula, we can write it in terms of its general form:
a1 = 0
a2 = -1/2
a3 = 2/3
a4 = -3/4
a5 = 4/5
a6 = -5/6
a7 = 6/7
We can see that the numerator of each term is equal to its index number, n, if n is even and equal to -n if n is odd. The denominator of each term is equal to n+1 for all terms.
Using this observation, we can write the explicit formula for the sequence as:
an = (-1)^(n+1) * n / (n+1)
where (-1)^(n+1) is equal to -1 if n is odd and 1 if n is even. This formula generates the sequence 0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7, ...
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Algebraic Inequalities
Help due today
Answer: i am certain that the answer is -6
PLS HELP WILL GIVE BRAINLIEST
Triangle FUN has vertices located at F (-1, -4), U (3, -5), and N (2, 6).
Part A: Find the length of UN. Show your work.
The length of the segment UN is 11.05 units.
How to find the length of the segment UN?For any pair of points (x₁, y₁) and (x₂, y₂), the distance between the two points is given by the formula:
distance = √( (x₂ - x₁)² + (y₂ - y₁)²)
Here we know that the points are:
U = (3, -5)
N = (2,6)
The distance between these two points is then:
distance = √( (3 - 2)² + (-5 - 6)²)
distance = √122 = 11.05
The length of the segment is 11.05 units.
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Angle PQR is isosocles with PQ=PR= 7. 5cm and QR = 9cm. The height PS from P to QR,is 6cm. Find the area of Angle PQR. What will be the height from R to PQ that is RT
The height RT from R to PQ is approximately 3.16 cm.
To find the area of triangle PQR, we can use the formula:
Area = 1/2 * base * height
Since PQR is isosceles with PQ = PR, the base is PQ or PR. We can choose PQ as the base. Then the height is PS.
Area of PQR = 1/2 * PQ * PS
Since PQ = PR = 7.5 cm and PS = 6 cm, we can substitute these values into the formula and simplify:
[tex]Area of PQR = 1/2 * 7.5 cm * 6 cm[/tex]
[tex]Area of PQR = 22.5 cm^2[/tex]
Therefore, the area of triangle PQR is [tex]22.5 cm^2[/tex].
To find the height RT from R to PQ, we can use the Pythagorean theorem.
Let's draw a perpendicular line from R to PQ, intersecting at T. Then we have a right triangle PRT with hypotenuse PR and legs PT and RT.
Since PQR is isosceles, we can also see that angle PQR is equal to angle PRQ. Therefore, angles PQR and PRQ are equal and each is approximately 69.3 degrees (using inverse cosine function).
Using the sine function, we can find the length of PT:
sin(69.3) = PT / 7.5
PT = 7.5 * sin(69.3)
PT ≈ 6.93 cm
Using the Pythagorean theorem, we can find the length of RT:
[tex]RT^2 + PT^2 = PR^2[/tex]
[tex]RT^2 = PR^2 - PT^2[/tex]
[tex]RT^2 = 7.5^2 - 6.93^2[/tex]
RT ≈ 3.16 cm
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HELP ASAP!!!!!!!!!!!!
Which cannot be the angle measurements of triangle ABC?
Measure of angle A = 55 degrees, measure of angle B = 65 degrees, measure of angle C = 60 degrees
Measure of angle A = 60 degrees, measure of angle B = 60 degrees, measure of angle C = 60 degrees
Measure of angle A = 57 degrees, measure of angle B = 58 degrees, measure of angle C = 65 degrees
Measure of angle A = 61 degrees, measure of angle B = 57 degrees, measure of angle C = 61 degrees
Answer:
A=61
B=57
C=61
Step-by-step explanation:
The sun of the three angles must give us 180 degrees. so the sum of these three angles is giving us 179 wrong degrees.
−6(3/8+3/4)= ??????????????????????????????????
AS A FRACTION
Answer:
-27/4
3/8+3/4=3/8+(3×2)(3×2)
3/8+4/8=7/8
-6×7/8
=-27/4
In the figure, m∠1= (5x)°, m∠2= (4x + 10)° and, m∠3= (10x − 5)°. What is m∠3,
in degrees?
Answer: I think this is a triangle because there are 3 angles.
All triangles have the entire sum 180*
(5x) + (4x + 10) + (10x-5) = 180
x = 175/19
Answer - 1750/19 (Decimal: 92.105263)
Step-by-step explanation:
10 (175/19)
10/1 * 175/19
10 175
1 19
= 1750
19
help me plsss
Which function is graphed here?
Of(x)=√x-2
Of(x)=√x+2
Of(x)=-3√x-2
Of(x) = -√√x+2
Answer:
I'm pretty sure it's C. isnnxixiab
Three identical small circles are drawn inside one large circle, as shown in the diagram.
The centres of the small circles lie on the diameter of the large circle.
Therefore, the radius r of each of the small circles multiplied by [tex](3sqrt(3)/2)[/tex] to get the length of the diameter AB of the big circle.
what is circle ?A circle is a geometric form made up of all points that are spaced apart by a predetermined amount, known as the radius, from a specific point known as the center. The circumference of a circle is determined by the formula C = 2r, where r denotes the radius and (pi) denotes a mathematical constant roughly equivalent to 3.14159. Numerous areas of mathematics, science, and daily living frequently involve circles. They have a number of crucial characteristics that make them helpful in a variety of applications.
given
The line section PQ is the following length:
PQ is equal to [tex]sqrt(3r2/4) = sqrt(3)/r.[/tex]
In a similar manner, we can determine how long the line section QR is:
OQ2 - OR2 = QR2 = r2/4 - r2 = QR2 = -3r2/4
Therefore, QR is a line that goes beyond the spot R rather than a line segment.
The length of the large circle's diameter AB is determined by adding the lengths of PQ, QR, and RP, each of which is equivalent to (sqrt(3)/2)r. As a result, we have:
[tex]AB = 3 * (sqrt(3)/2) (3sqrt(3)/2)r = r[/tex]
Therefore, the radius r of each of the small circles multiplied by [tex](3sqrt(3)/2)[/tex] to get the length of the diameter AB of the big circle.
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the yoko fund earns 11.2% during the year while the risk-free rate is 3.1%. the yoko fund has a beta of 1.20 and a standard deviation of 17.5%. the treynor ratio is closest to: a. 0.463 b. 0.640 c. 6.750 d. 9.333
For the Yoko Fund, the Treynor ratio is 6.0%, although none of the answer choices provided is a close approximation, we can choose option c. 6.750
The Treynor ratio measures the excess return earned by an investment per unit of systematic risk (i.e., beta). It is calculated as the difference between the return of the investment and the risk-free rate, divided by the investment's beta.
The formula for the Treynor ratio is:
Treynor Ratio = (Return of the Investment - Risk-Free Rate) / Beta
In this case, the return of the Yoko Fund is 11.2%, the risk-free rate is 3.1%, the beta is 1.20, and we are given the standard deviation of the Yoko Fund's returns, which is 17.5%.
Using the formula, we get:
Treynor Ratio = (11.2% - 3.1%) / 1.20
= 6.0%
Therefore, the Treynor ratio for the Yoko Fund is 6.0%.
None of the answer choices is exactly equal to 6.0%, but the closest one is (c) 6.750.
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A person places $398 in an investment account earning an annual rate of 9.7%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years.
A person has $785.35 after 7 years in the account.
What is continuous compound interest?Interest that is compounded continuously to the principal amount. This interest rate provides exponential growth for a period of time.
The formula of continuous compound interest rate;
[tex]V = Pe^{rt}[/tex],
Where P is the principal amount, r is the interest rate and t is the time period.
A person places $398 in an investment account earning an annual rate of 9.7%, compounded continuously.
Using the formula:
[tex]V = Pe^{rt}[/tex], where P = $398, r = 0.097 (9.7% as a decimal), and t = 7 years, we can calculate the value of the account after 7 years as:
V = 398[tex]e^(0.0977)[/tex]
V = 398[tex]e^{0.679}[/tex]
V = 784.818126761
V = $785.35 (rounded to the nearest cent)
Therefore, the amount of money in the account after 7 years is $785.35.
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Last year, 89 musicians attended a jazz camp, and 15 of them were bassists. What is the experimental probability that the first musician to sign up will be a bassist?
There is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.
What is experimental probability?Experimental probability is a type of probability that is based on actual observations or experiments. It is also called empirical probability
According to question:The ratio of the frequency of an occurrence to the total number of trials or observations is known as the experimental probability. In this case, the event is the first musician to sign up being a bassist.
Since there were 15 bassists out of 89 musicians who attended the camp last year, the experimental probability of the first musician to sign up being a bassist is:
Experimental probability = Number of bassists / Total number of musicians
Experimental probability = 15 / 89
Experimental probability = 0.1685 or approximately 16.85%
As a result, there is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.
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this is simple i dont need no words js the work pls and thankyou <33
Rewrite in simplest rational exponent form square root of x times the fourth root of x. Show each step of your process.
Unpacking the expression we have,
[tex](\sqrt{x})(\sqrt[4]{x})[/tex]
Its better to work with this in terms of exponents so we rewrite the expression as [tex]x^{\frac{1}{2}}*x^{\frac{1}{4}}[/tex]. (cause [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]) This can be a little tricky when learning it for the first time.
Then by the exponent sum rule [tex]x^{\frac{1}{2}}*x^{\frac{1}{4}}=x^{\frac{1}{2}+\frac{1}{4}}=x^{\frac{3}{4}}[/tex] (more straightforward, you probably know this from class).
I assume this is what you mean by rational exponent form. But you could also write it as [tex]\sqrt[4]{x^3}[/tex].
Which point has coordinates -4, -3)?
A J
B K
C N
D Q
Answer: K
Step-by-step explanation:
Answer:
Step-by-step explanation:
k
assume that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. using the propensity scoring method, their responses would be
The propensity scoring method is a statistical technique used to adjust for differences in the characteristics of groups being compared in a study. In this case, we want to adjust for the fact that respondents aged 70 or older are underrepresented in an internet sample.
To do this, we can assign a propensity score to each individual in the sample based on their likelihood of being in the sample, given their age. We can then use this score to weight their responses to account for the underrepresentation of older individuals.
In this case, we know that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. This means that we can assign a propensity score of 3 to each individual aged 70 or older in the sample, and a propensity score of 1 to everyone else.
Using these propensity scores, we can weight the responses of each individual in the sample. Responses from individuals with a propensity score of 3 would be weighted by a factor of 3, while responses from individuals with a propensity score of 1 would be weighted by a factor of 1.
By adjusting for the underrepresentation of older individuals in this way, we can obtain more accurate estimates of the characteristics of the population being studied, and reduce the potential for bias in our analysis.
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2.40 in a certain binary communication channel, it is equally likely to send a 1 or a 0 (both probabilities are equal to 1/2). the probability of an error given that a 1 is sent is 2/9, while the probability of an error given a 0 is sent is 1/9. (a) what is the probability that a 1 is received? (b) what is the (unconditional) probability that an error occurs? (c) what is the probability that a 1 was sent, given a 1 was received?
(a) The probability that a 1 is received is 4/9.
(b) The (unconditional) probability that an error occurs is 1/6.
(c) The probability that a 1 was sent, given that a 1 was received, is 7/8.
To solve this problem, we can use Bayes' theorem and conditional probability.
(a) The probability that a 1 is received can be found using the law of total probability. We can calculate it by considering the probabilities of two mutually exclusive events: receiving a 1 when a 1 is sent and receiving a 1 when a 0 is sent.
Let P(1) be the probability that a 1 is sent and P(0) be the probability that a 0 is sent. Both probabilities are equal to 1/2 since they are equally likely.
The probability of receiving a 1 when a 1 is sent is 1 minus the probability of an error when a 1 is sent, which is 1 - (2/9) = 7/9.
The probability of receiving a 1 when a 0 is sent is the probability of an error when a 0 is sent, which is 1/9.
Using the law of total probability:
P(1 received) = P(1 sent) x P(1 received | 1 sent) + P(0 sent) x P(1 received | 0 sent)
P(1 received) = (1/2) x (7/9) + (1/2) x (1/9)
P(1 received) = 7/18 + 1/18
P(1 received) = 8/18
P(1 received) = 4/9
Therefore, the probability that a 1 is received is 4/9.
(b) The (unconditional) probability that an error occurs can be calculated by considering the probabilities of two mutually exclusive events: an error occurs when a 1 is sent and an error occurs when a 0 is sent.
Using the law of total probability:
P(Error) = P(1 sent) x P(Error | 1 sent) + P(0 sent) x P(Error | 0 sent)
P(Error) = (1/2) x (2/9) + (1/2) x (1/9)
P(Error) = 2/18 + 1/18
P(Error) = 3/18
P(Error) = 1/6
Therefore, the (unconditional) probability that an error occurs is 1/6.
(c) The probability that a 1 was sent, given that a 1 was received, can be calculated using Bayes' theorem:
P(1 sent | 1 received) = (P(1 sent) x P(1 received | 1 sent)) / P(1 received)
P(1 sent | 1 received )= (1/2) x (7/9) / (4/9)
P(1 sent | 1 received) = (1/2) x (7/9) * (9/4)
P(1 sent | 1 received) = 7/8
Therefore, the probability that a 1 was sent, given that a 1 was received, is 7/8.
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I need help asap pls!!
Answer:
First, we need to calculate the daily interest rate on the credit card. We can do this by dividing the annual percentage rate (APR) by the number of days in a year:
Daily interest rate = APR / 365
Daily interest rate = 0.2445 / 365
Daily interest rate = 0.00067 or 0.067%
Next, we can calculate the interest that will accrue over the course of one month, which is approximately 30 days:
Interest = Balance * Daily interest rate * Number of days
Interest = $1,359 * 0.00067 * 30
Interest = $27.42
Adding the interest to the outstanding balance, we get:
Balance after one month = $1,359 + $27.42
Balance after one month = $1,386.42
Therefore, the balance on the credit card after one month will be approximately $1,386.42.
4cd - 5cd + 3c + 8d simplify
Answer:
-cd+3c+8d
Step-by-step explanation:
4cd - 5cd + 3c + 8d
Combine like terms
(4cd - 5cd) + 3c + 8d
-cd+3c+8d
Answer:
3c + 8d - cd
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The expression is,
→ 4cd - 5cd + 3c + 8d
Let's simplify the expression,
→ 4cd - 5cd + 3c + 8d
→ 3c + 8d + 4cd - 5cd
→ (3c) + (8d) + (4cd - 5cd)
→ 3c + 8d + (-cd)
→ 3c + 8d - cd
Hence, answer is 3c + 8d - cd.
Activity 2 Synthesis
1. Precious says you can estimate the area of a circle by calculating 32. What do you think
each part of her expression means?
2. Do you agree with Precious? Use your earlier work to help support your thinking.
D
114°
A
в
56°
C
HURRRRRYYY PLEASEEEE
The calculated value of the angle x is 58 degrees
How to calculate the value of xfrom the question, we have the following parameters that can be used in our computation:
The triangle
Using the sum of opposite external angles, we have the following equation
114 = 56 + x
When the like terms are evaluated, we have
x = 114 - 56
Evaluate
x = 58
Hence, the value of x is 58
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Which lines are parallel? check all that apply. lines b, c, d, e, f are cut by transversal a. clockwise from top left, the angles formed by lines b and a are blank, 89.5 degrees, blank, blank; by lines c and a are blank, blank, blank, 91.5 degrees; by lines d and a are blank, blank, 89.5 degrees, blank; by lines e and a are 88.5 degrees, blank, blank, blank; by lines f and a are blank, blank, 90.5 degrees, blank. b is parallel to f b is parallel to d c is parallel to e c is parallel to d d is parallel to f e is parallel to f
The lines which are parallel are given below :
Line b is parallel to line f, line b is parallel to line d, line c is parallel to line e, line c is parallel to line d and line d is parallel to line f.
Line b is parallel to line f because they both have a pair of alternate angles that are congruent which is 89.5 degrees and 90.5 degrees.
Line b is parallel to line d because they both have a pair of alternate angles that are congruent at 89.5 degrees.
Line c is parallel to line e because they both have a pair of alternate angles that are congruent at 91.5 degrees.
Line c is parallel to line d because they both have a pair of alternate angles that are congruent: 89.5 degrees.
Line d is parallel to line f since they have corresponding angles of 89.5 degrees and 90.5 degrees, respectively
Therefore, the correct answer is :
Line b is parallel to line f, line b is parallel to line d, line c is parallel to line e, line c is parallel to line d and line d is parallel to line f.
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What is the area of the following composite figure? Round to the nearest whole.
Answer:
The answer to your problem is 53 in ^2
Hope it helps
a charger has a power rating of 12 w. if you charge 6 cents per kilowatt hour, how much do you make in 1 day
The earnings made in 1 day when charging a device with a power rating of 12 W at a rate of 6 cents per kilowatt hour is 0.01728.
Given, Power rating of charger = 12 W. Charge per kilowatt hour = 6 cents = 0.06/kWh.To calculate the earnings in 1 day, we need to calculate the power consumed by the charger in 1 day first.
P = Power rating of charger = 12 Wt = Time = 1 day = 24 hours. Energy consumed = Power x Time. E = P x t= 12 W x 24 hours= 288 Wh = 0.288 kWh. Therefore, energy consumed by the charger in 1 day = 0.288 kWh.
Now, we can calculate the earnings in 1 day as follows: Charge per unit = 0.06/kWh. Earnings = Energy consumed x Charge per unit. Earnings = 0.288 kWh x 0.06/kWh= 0.01728.
Therefore, the earnings made in 1 day when charging a device with a power rating of 12 W at a rate of 6 cents per kilowatt hour is 0.01728.
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Which three side length best describes the triangle in the diagram
Answer:
i think that it is d or c just guessing
i do not understand please help asap
Step-by-step explanation:
Lets assume this is a right triangle.
If you use pythagorean theorem, lets assume the tower is the longest line on the triangle.
If this is true, lets say that 9^2 (distance from end of slide to base of tower) + x^2 (length of slide) = 23^2 (height of tower)
we get the length of the slide is 21.2 meters.
Help ASAP due today!!
The least common multiple (LCM) of two or more integers is the smallest positive integer that is a multiple of all of them. In other words, it is the smallest number that is divisible by each of the given numbers without leaving a remainder. [tex]3(5/8) + 2(3/8) = 6.[/tex]
What is the integer?To add the mixed numbers 5 3/8 and 3 2/8, we need to convert them to fractions with a common denominator. Since both have a denominator of 8, we can add the whole numbers to the fractions to get:
[tex]5 3/8 = 5 + 3/8 = 40/8 + 3/8 = 43/8[/tex]
[tex]3 2/8 = 3 + 2/8 = 24/8 + 2/8 = 26/8[/tex]
Now we can add these fractions:
[tex]5 3/8 + 3 2/8 = 43/8 + 26/8 = 69/8[/tex]
So the sum of [tex]5 3/8[/tex] and [tex]3 2/8[/tex] as a fraction is [tex]69/8[/tex] .
The LCM is often used when adding or subtracting fractions with different denominators, since we need to find a common denominator to perform the operation. To do this, we can find the LCM of the denominators and use it as the common denominator.
To write equivalent fractions with a common denominator, we need to find the least common multiple of the denominators, which in this case is 8.
For [tex]3(5/8)[/tex] :
[tex]3(8/8) + 5/8 = 24/8 + 5/8 = 29/8[/tex]
For [tex]2(3/8):[/tex]
[tex]2(8/8) + 3/8 = 16/8 + 3/8 = 19/8[/tex]
To add these fractions, we simply add their numerators:
[tex]3(5/8) + 2(3/8) = 29/8 + 19/8 = 48/8 = 6[/tex]
Therefore, [tex]3(5/8) + 2(3/8) = 6.[/tex]
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Can you help me with this
Answer:c
Step-by-step explanation:
Answer: C
Step-by-step explanation:
Part D When the membrane potential of a neuron begins returning to normal, resting levels, the cell membrane experiences summation repolarization depolarization Ohyperpolarization rest Submit Request Answer Part E Saltatory conduction allows for faster and more efficient conduction because action potentials are confined to which part of a neuron? Cell body Dendrites Axon terminal Axon hillock Nodes of Ranvier Submit Request Answer
The action potential "jumps" from node to node, allowing it to travel faster and with less energy loss than if it had to propagate along the entire length of the axon.
Part D: When the membrane potential of a neuron begins returning to normal, resting levels, the cell membrane experiences hyperpolarization.
During hyperpolarization, the membrane potential becomes more negative than the resting potential, making it more difficult to trigger an action potential.
Part E: Saltatory conduction allows for faster and more efficient conduction because action potentials are confined to the Nodes of Ranvier.
The Nodes of Ranvier are small gaps in the myelin sheath that covers the axon of some neurons. Because the myelin sheath insulates the axon, action potentials can only occur at the nodes, where the membrane is exposed. This means that the action potential "jumps" from node to node, allowing it to travel faster and with less energy loss than if it had to propagate along the entire length of the axon.
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Determine weather the series is arithmetic or geometric,then find the indicated sum
The series, based on the general terms, can be found to be arithmetic. The indicated sum is - 544.
How to determine if a series is arithmetic or geometric ?To determine if the series is arithmetic or geometric, we must first find the common difference (arithmetic) or common ratio (geometric).
Term 1 (p=1): 19 - 2(1) = 17
Term 2 (p=2): 19 - 2(2) = 15
Term 3 (p=3): 19 - 2(3) = 13
There is a common difference of -2 so this is arithmetic.
The formula for the sum of an arithmetic series is:
Sum = (n x (a1 + an)) / 2
The series is: ∑ (p = 1 to 34) (19 - 2p)
To find the last term, we plug in p = 34:
an = 19 - 2(34)
= 19 - 68
= -49
The sum is therefore:
Sum = (34 x (17 + (-49))) / 2
Sum = -544
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A rectangle has an area of 15 square yards. The width is 2 yards less than the length. What is the length, in yards, of the rectangle?
A: 2 yards
B: 3 yards
C: 5 yards
D: 15 yards
Answer:
The correct answer would be option (A).
Step-by-step explanation:
Answer: 5
Step-by-step explanation:
length = x
Width=x-2
Area=lw
15=(x)(x-2)
15=x^2-2x
0=x^2-2x-15
Quadratic formula:
X=-15
X=5
the length is 5 because the length can’t be negative