y = 2x + 1...so sub in 2x + 1 for y in the other equation
x + 3y = 10
x + 3(2x + 1) = 10
x + 6x + 3 = 10
x + 6x = 10 - 3
7x = 7
x = 1
y = 2x + 1
y = 2(1) + 1
y = 2 + 1
y = 3
the difference : there can be 1 possible answer for this..
y - x = 3 - 1 = 2
If vec r =3 hat i -2 hat j +6 hat k , find the value of ( vec r * hat j ).( vec r * hat k )-12
Answer: We can first find the dot product of vec r with hat j and hat k:
vec r * hat j = (3 hat i - 2 hat j + 6 hat k) * (- hat j) = -2
vec r * hat k = (3 hat i - 2 hat j + 6 hat k) * hat k = 6
Substituting these values into the expression given, we get:
(vec r * hat j).(vec r * hat k) - 12 = (-2) * (6) - 12 = -24
Therefore, the value of (vec r * hat j).(vec r * hat k) - 12 is -24.
Step-by-step explanation:
For each of the following propositions, either i. use a case-based proof to demonstrate that the proposition holds true or ii. Use a counterexample to demonstrate the proposition does not hold.
(a) Assume x is an integer that is not divisible by 3, and y is an integer that is not divisible by 3. Then the sum of x and y cannot be divisible by 3.
(b) Assume x is an integer that is not divisible by 3, and y is an integer that is divisible by 3. Then the sum of x and y cannot be divisible by 3.
In both cases, the sum of x and y is not divisible by 3, we have demonstrated that the proposition is true. and the proposition is false, and we have shown a counterexample where the sum of two integers, one of which is not divisible by 3 and the other is divisible by 3, can be divisible by 3.
(a) To prove that the sum of two integers, x and y, neither of which is divisible by 3, cannot be divisible by 3, we can use a case-based proof.
Case 1: x and y leave a remainder of 1 when divided by 3.
Let x = 3m + 1 and y = 3n + 1, where m and n are integers. Then, the sum of x and y is 3m + 3n + 2, which leaves a remainder of 2 when divided by 3. Therefore, x + y is not divisible by 3.
Case 2: x and y leave a remainder of 2 when divided by 3.
Let x = 3m + 2 and y = 3n + 2, where m and n are integers. Then, the sum of x and y is 3m + 3n + 4, which leaves a remainder of 1 when divided by 3. Therefore, x + y is not divisible by 3.
Since in both cases, the sum of x and y is not divisible by 3, we have demonstrated that the proposition is true.
(b) To prove that the sum of two integers, x and y, where x is not divisible by 3 and y is divisible by 3, cannot be divisible by 3, we can use a counterexample.
Let x = 2 and y = 6. Then, x is not divisible by 3 and y is divisible by 3. However, x + y = 8, which is not divisible by 3.
Therefore, the proposition is false, and we have shown a counterexample where the sum of two integers, one of which is not divisible by 3 and the other is divisible by 3, can be divisible by 3.
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PLEASE HELP ME ON THIS QUESTION
0-24- Tally (1)
25-49 Tally (4)
50-74 Tally (5)
75-99 Tally (2)
What’s 9 X 3/9 answer…………………………………….
Answer:
9 x 3/9
= 39 ⋅ 3= 2727/9
27 ÷ 9
= 3Step-by-step explanation:
You're welcome.
Can someone please help
Answer:
1.11
2.4
3.5
pls correct me if I'm wrong
Answer:
38. (b) 11
39. (c) 4
40. (c) 5
Step-by-step explanation:
38.)
[tex]\implies \: \sf \sqrt{3xx - 8} = 5 \\ \\ \implies \: \sf 3xx - 8 = {(5)}^{2} \\ \\ \implies \: \sf 3xx - 8 = 25 \\ \\ \implies \: \sf 3xx = 25 + 8 \\ \\ \implies \: \sf 3xx = 33 \\ \\ \implies \: \sf xx = \dfrac{33}{3} \\ \\ \implies \: \sf xx = 11\\ [/tex]
Hence, Required answer is option (b) 11.
39.)
[tex]\implies \: \sf \sqrt{4xx -7 } - 3 = 0 \\ \\ \implies \: \sf \sqrt{4xx - 7} = 3 \\ \\ \implies \: \sf 4xx - 7 = {(3)}^{2} \\ \\ \implies \: \sf 4xx - 7 = 9 \\ \\ \implies \: \sf 4xx = 9 + 7 \\ \\ \implies \: \sf 4xx = 16 \\ \\ \implies \: \sf xx = \dfrac{16}{4} \\ \\ \implies \: \sf xx = 4 \\ [/tex]
Hence, Required answer is option (c) 4.
40.)
[tex]\implies \: \sf \sqrt{6xx + 6} - 6 = 0 \\ \\ \implies \: \sf \sqrt{6xx + 6} = 6 \\ \\ \implies \: \sf 6xx + 6 = {(6)}^{2} \\ \\ \implies \: \sf 6xx + 6 = 36 \\ \\ \implies \: \sf 6xx = 36 - 6 \\ \\ \implies \: \sf 6xx = 30 \\ \\ \implies \: \sf xx = \dfrac{30}{6} \\ \\ \implies \: \sf xx = 5 \\ [/tex]
Hence, Required answer is option (c) 5.
a friend has an 81% average before a final exam. The score includes everything but the final, which counts for 15% of the grade. What is the minimum to earn 75% for the course?
Answer:
57
Step-by-step explanation:
Okay, So we have this person That has 81% average before the quiz. For a course That score includes everything, but the final, which counts for 25% of the course grade, was the best course grade you your friend can earn. Okay, The best course grade given to me makes me. Mhm. 100. So we have .81 times. Actually we'll keep this as 81, times .75 right Plus 100 times. Excuse ME, Time 0.25. This is equivalent to 81 times 0.75. Mhm. This is equivalent to 81 times .75 plus 100 times 0.25, Which equals 85.75%. Now that's for part one. Report to we have what is the minimum score? Turn to 75%. So we have 75 equal to 81 times 0.75 Plus X. Times zero 25. So 81 times 0.75 equals 60.75 75- is value mhm. Is equal to 14.25. So we have 0.25 x. And if we divide 14.25 over 0.25, we isolate X. So the minimum score to get a 75 is a 57
What triangles are similar to triangle ABC?
Answer:
A right angled triangle is similar to triangle ABC
Step-by-step explanation:
If you tilt the triangle and put it straight, you'll see that angle C is equal to 90°
And if a triangle has one angle of 90° then it is a right angled triangle
Hope you understand :)
FILL IN THE BLANK Random variation in a process indicates __________; whereas non-random variation indicates process __________.
Random variation in a process indicates natural variation ; whereas non-random variation indicates process variation
Random variation in a process refers to the natural variation or randomness that occurs in a process due to various factors that are not controlled or predictable. For example, in a manufacturing process, random variation can be caused by factors such as differences in raw materials, operator error, or environmental conditions that are not controlled.
On the other hand, non-random variation in a process refers to the variation that is not due to chance and is likely caused by specific factors that are affecting the process. Non-random variation is also known as special cause variation. Special cause variation can be caused by factors such as a change in machine settings, a change in process parameters, or a change in the process inputs.
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Help please! I have no idea!!!!
The values of the function from the graph are h(7) = 10, h(0) = 9, h(t) = 8, t = 5 and h(t) = 0, t = 4
How to determine the value of the functionGiven that the graph is the graph of height as a function of time
To calculate the values of h(t) from the graph of g(x), we need to follow these steps
Identify the value of t on the x-axis where you want to calculate the value of h(t)Locate that point on the graphWrite the values from the pointUsing the above, we have the following
h(7) = 10
h(0) = 9
h(t) = 8, t = 5
h(t) = 0, t = 4
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Represent each number line by an inequality.
Answer:
Step-by-step explanation:
The inequality in the first equation is x > 8.
The inequality for the second graph is x ≤ -4 since it's a dot.
This problem explores some questions regarding the fishery model
dt
dP
=P(1−P)−h
If you have not yet run the Jupyter notebook please do so now. Find analytical expressions for the two fixed points of the model, in terms of
h
. Give an expression for the stable fixed point. You may assume that the larger fixed point is the stable one. For what values of
h
does there exist a fixed point?
a) The expression for the stable fixed point is P* = (1 + sqrt(1 - 4h)) / 2
b) There exists a fixed point for all values of h less than or equal to 1/4.
The fixed points of the model are the values of P at which dP/dt = 0. Therefore, we need to solve the equation
P(1-P) - h = 0
Expanding the left-hand side, we get
P - P^2 - h = 0
Rearranging, we get a quadratic equation
P^2 - P + h = 0
Using the quadratic formula, the two solutions for P are
P = (1 ± sqrt(1 - 4h)) / 2
a) The larger root is the stable fixed point, as it corresponds to a minimum of the fish population growth function. Therefore, the expression for the stable fixed point is
P* = (1 + sqrt(1 - 4h)) / 2
b) For the model to have a fixed point, the quadratic equation must have real roots. This occurs when the discriminant (the expression inside the square root) is non-negative
1 - 4h ≥ 0
Solving for h, we get
h ≤ 1/4
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The given question is incomplete, the complete question is:
This problem explores some questions regarding the fishery model
dP/dt =P(1−P)−h
If you have not yet run the Jupyter notebook please do so now. Find analytical expressions for the two fixed points of the model, in terms of h
a) Give an expression for the stable fixed point. You may assume that the larger fixed point is the stable one. b) For what values of h does there exist a fixed point?
The graph of triangle has coordinates E(1,4) F(-1,1) and G(2,-1). Graph triangle of EFG and it’s image after a translation of 3 units left and 1 unit down.
Answer:
Step-by-step explanation:1.4 -1, 1 2, -1
assume x and y are int variables. write an expression that evaluates to true if x is greater than y.
If x and y are integer variables, then the expression that evaluates to true if x is greater than y is "x>y".
In Java, symbol of ">" is used for "greater-than" operator. So, the expression which evaluates to "true" if integer "x" is greater than integer "y" is "x > y".
This expression compares the values of x and y and returns a Boolean value of "true" if x is greater than y, and "false" otherwise.
The expression can be used in conditional statements, loops, and other constructs that require a Boolean value as a condition. It is important to note that the ">" operator only works with primitive types such as int, long, double, etc.
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1) The school bake sale needs to make at least $200.
If each cake is sold for $10, how many cakes should
they sell to beat their goal? Let x represent the
number of cakes. Identify the inequality that
represents this situation.
a) 10x ≥ 200
b) 10x ≤ 200
10
c)
d)
X
-> 200
10
x
< 200
If we solve this inequality for x, we get x 20, which indicates the school equation bake sale must sell at least 20 cakes in order to meet their $200 objective.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
10x ≥ 200 accurately portrays the scenario.
To explain why, consider the following:
Because each cake costs $10, the total amount earned from selling x cakes is 10x.
The aim is to raise at least $200, thus the total amount must be larger than or equal to $200.
As a result, we may describe the circumstance by writing the inequality 10x 200.
If we solve this inequality for x, we get x 20, which indicates the school bake sale must sell at least 20 cakes in order to meet their $200 objective.
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Instructions: Use the following data set to find the sample statistics for the
following data set. (Round answers to the nearest hundredth, if necessary.
{51, 48, 42, 43, 48, 48, 46, 15, 29, 45,
47, 55, 46, 35, 47, 48, 54, 26, 53, 42}
1.
2.
<<>>
11
4. Mode =
(>>
3. Median =
=
11
By using sample standard deviation - (1) N or n = 20
(2) X or μ = 43.4
(3) σ = 9.78 and s = 10.04
Why does sample standard deviation exist?
When we talk about a sample standard deviation, we're not talking about population standard deviation. The average amount by which a group of values deviates from their mean is shown by the statistical measure of variability known as the standard deviation.
We are given with the following data set below;
{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}
(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.
(2) The formula for calculating Mean of the data, i.e. X or μ is given by;
Mean = 51 +48+ 42+ 43+ 48 + 48 + 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42/20
= 868/20 = 43.4
So, the value of X or μ is 43.4.
(3) The formula for calculating population standard deviation () is given by;
Standard deviation, σ = √(51 - 43.4)² + (48 - 43.4)² + .........+(42 - 43.4)²/20
= 9.78
Similarly, the formula for calculating sample standard deviation (s) is given by;
Sample Standard deviation, s =
√(51 - 43.4)² + (48 - 43.4)² + .........+(42 - 43.4)²/20 - 1
= 10.04
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The simple interest formula 1 =
PRT
100
gives the interest I on a principal P
invested at a rate of R% per annum for
Tyears.
a) Find the interest when GH 2500 is
invested at 5% p.a. for 4 years.
b) Find the principal that gains an interest
of GH 2590 in 5 years at 7% per
annum,
The interest earned on GH 2500 at 5% p.a. for 4 years is GH 500.
The principal that gains an interest of GH 2590 in 5 years at 7% per annum is approximately GH 7400.
What is simple interest ?
Simple interest is a type of interest that is calculated on the principal amount of a loan or investment at a fixed rate for a specified period of time. It is based only on the principal amount, and does not take into account any interest earned on previous periods.
The formula for simple interest is:
I = P * R * T
where:
I is the interestP is the principal amountR is the interest rate per periodT is the number of periodsAccording to the question:
a) Using the simple interest formula, we have:
I = (P * R * T) / 100
Substituting P = GH 2500, R = 5%, and T = 4 years, we get:
I = (2500 * 5 * 4) / 100 = 500
Therefore, the interest earned on GH 2500 at 5% p.a. for 4 years is GH 500.
b) Using the same formula, we can solve for the principal P:
I = (P * R * T) / 100
2590 = (P * 7 * 5) / 100
2590 = (35P) / 100
35P = 2590 * 100
P = (2590 * 100) / 35
P ≈ GH 7400
Therefore, the principal that gains an interest of GH 2590 in 5 years at 7% per annum is approximately GH 7400.
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Fill in the missing values to make the equations true.
i need help i forgot how to do this
Step-by-step explanation:
For RIGHT triangles : sin ( angle) = opposite LEG / Hypotenuse
so sin B = 32 / 68 = 8 / 17
Please help ASAP!!!! The average of two numbers is 13.One number is 10.What is the other number?
Answer:16
Step-by-step explanation:
average is similar to mean
you get the Total value and divide it with the number of values added
Can someone help quick i have 6 questions left
Answer:
Step-by-step explanation:
long leg = 78 (means that 26√3*√3 = 26√9 = 26*3 = 78
for x: Short leg= 26√3
Hypotenuse= 2*26√3 = 52√3 for y
Write the equation of the circle centered at (4,-1) that passes through (13,8).
Answer:
[tex](x-4)^2+(y+1)^2=162[/tex]
Step-by-step explanation:
Determine r² by using the equation of a circle and plugging in the center (h,k)->(4,-1) as well as (x,y)->(13,8):
[tex](x-h)^2+(y-k)^2=r^2\\(x-4)^2+(y-(-1))^2=r^2\\(13-4)^2+(8+1)^2=r^2\\9^2+9^2=r^2\\81+81=r^2\\162=r^2\\[/tex]
Hence, the equation of the circle that meets these criteria is[tex](x-4)^2+(y+1)^2=162[/tex]
please help me 60 points
Answer:
Matt would walk 8 miles in to hours.
Step-by-step explanation:
15 minutes is 1/4 of an hour, meaning it would be 1/8 of 2 hours.
1 mile times 8 = 8 miles
Hope that helps!
10 POINTS!!!NEED HELP ASAP PLEASE HELP FIND THE AREA AND THE PERIMETER!!
Answer: Area: 460.48 ft^2 Perimeter: 90.12 ft
Step-by-step explanation:
The area is 1/2 * 3.14 * (16 / 2)^2 (area of semicircle)
+ 10 * 12 / 2 (area of triangle)
+ 20 * 15 (area of rectangle)
= 460.48
The perimeter is 1/2 * 16 * 3.14 (perimeter of semicircle)
+ 10 (perimeter of triangle)
+ 20 + 15 + 20 (perimeter of rectangle)
= 90.12
Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. y 0 1 2 3 4 ply) 0.60 0.20 0.15 0.03 0.02 (a) Calculate and interpret Hy My = 0.20 (b) In the long run, for what proportion of cartons is the number of broken eggs less than jy? (Round your answer to two decimal places). Enter a number. Does this surprise you? Yes O No 0 + 1 + 2 + 3 + 4 (c) Explain why sy is not equal to = 2.0. 5 This computation of the mean is incorrect because the value in the denominator should equal the maximum y value. This computation of the mean is incorrect because it does not take into account that the number of broken eggs are all equally like O This computation of the mean is incorrect because it includes zero in the numerator which should not be taken into account when O This computation of the mean is incorrect because it does not take into account the number of partially broken eggs.
a) The value of Hy = 1.15
b) The proportion of cartons with less than 1.15 broken eggs is 0.60
c) The answer is B)This computation of the mean is incorrect because it does not take into account that the number of broken eggs are not all equally like.
(a) Hy = 0.67, which means that on average, there are 0.67 broken eggs per carton.
Hy = (0*0.60 + 1*0.20 + 2*0.15 + 3*0.03 + 4*0.02)/1
= 0.67
(b) The proportion of cartons with less than 0.67 broken eggs is 0.60 which is probability of 0 broken eggs.. This may be surprising as the probability of having less than 0.67 broken eggs is only 0.60, but this is due to the fact that the distribution is skewed towards higher values.
(c) Hy is not equal to the simple average of 0, 1, 2, 3, and 4 because the distribution is not symmetrical. The probabilities are weighted towards higher values, which increases the mean. Additionally, the value of zero should be included in the calculation, as it represents a possible outcome. Therefore, the correct formula for Hy is (0*0.60 + 1*0.20 + 2*0.15 + 3*0.03 + 4*0.02)/1 = 0.67.
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--The question is incomplete, answering to the question below--
"Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs.
y 0 1 2 3 4
p(y) 0.60 0.20 0.15 0.03 0.02
(a) Calculate and interpret Hy
(b) In the long run, for what proportion of cartons is the number of broken eggs less than Hy? (Round your answer to two decimal places).
Does this surprise you?
Yes
No
(c) Explain why Hy is not equal to (0 + 1 + 2 + 3 + 4)/5 = 2.0.
A. This computation of the mean is incorrect because the value in the denominator should equal the maximum y value.
B. This computation of the mean is incorrect because it does not take into account that the number of broken eggs are not all equally like
C. This computation of the mean is incorrect because it includes zero in the numerator which should not be taken into account when
D. This computation of the mean is incorrect because it does not take into account the number of partially broken eggs."
K
Factor the four-term polynomial by grouping.
x³ +9x² + 3x + 27
The factorization of the polynomial x³ + 9x² + 3x + 27 by grouping is:
x³ + 9x² + 3x + 27 = (x + 9)(x² + 3)
What is grouping?In algebra, "grouping" refers to a method of factoring polynomials that involves grouping together pairs of terms within the polynomial, in order to factor out a common factor.
What is polynomial?In mathematics, a polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
In the given question,
To factor the four-term polynomial by grouping, we can follow these steps:
Step 1: Group the first two terms and the last two terms together.
x³ + 9x² + 3x + 27
= (x³ + 9x²) + (3x + 27)
Step 2: Factor out the common factor from each group.
= x²(x + 9) + 3(x + 9)
Step 3: Notice that the expression (x + 9) is a common factor of both terms, and factor it out.
= (x + 9)(x² + 3)
Therefore, the factorization of the polynomial x³ + 9x² + 3x + 27 by grouping is:
x³ + 9x² + 3x + 27 = (x + 9)(x² + 3).
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Part B
Draw
parallel to
. You can draw
any length and place it anywhere on the coordinate plane, but not on top of
.
Find and record the ratio, n, of the length of
to the length of
. Then, multiply the lengths of
and
by n and record the resulting lengths.
In a diagram,
Then,
[tex]\dfrac{DE}{BC}=n[/tex]
For example, suppose that n=2; thus,
[tex]DE=2BC\longrightarrow2\times CA[/tex]
We can form a new triangle DEF whose side EF is parallel to CA; therefore,
[tex]\longrightarrow EF=2CA[/tex]
Scenario #3:
Imagine you find a map with a scale of 1:63,360. On that map, you see your hiking destination is
seven inches from your current location.
(a) How far away is that in reality (in miles)?
(b) Explain how you arrived at this decision.
SHOW YOUR WORK! This includes the potential for partial value, if incorrect.
Answer:
7 miles
Step-by-step explanation:
Note there are 63,360 inches in a mile.
So, rewrite scale as 1 inch: 1 mile, where inch replaces the unit.
Therefore 7 inches: 7 miles.
Plsss help due today!!
The writer’s guild only gives a lifetime achievement award out every 5 years and was curious to see how the population in Europe felt about their process.
They decided to conduct an opinion survey by selecting a random sample of 500 Europeans who made book purchases online in 2022. They emailed the survey to all 500 randomly selected online shoppers and received 127 responses.
9) Describe the population of interest.,
10) Describe the sample.
11) Give an example of a parameter they might be interested in calculating from the survey.
12) Give an example of a statistic they might report based on the parameter you gave above.
Answer:
The population of interest is all Europeans who make book purchases online in 2022.The sample is the randomly selected 500 Europeans who make book purchases online in 2022, to whom the survey was emailed, and the 127 who responded to the survey.A parameter they might be interested in calculating from the survey is the proportion of all Europeans who make book purchases online in 2022 who support the writer’s guild's process of giving a lifetime achievement award out every 5 years.A statistic they might report based on the parameter above is the proportion of the 127 respondents who support the writer’s guild's process of giving a lifetime achievement award out every 5 years, and an estimate of the proportion of all Europeans who make book purchases online in 2022 who support this process, based on the sample data.Whenever we construct a confidence interval for the population mean, the margin of error includes the standard error of x bar and theA. sampling biasB. nonresponse biasC. z or t value associated with a 95% confidence levelD. desired level of confidence
The margin of error in a confidence interval for the population mean includes the standard error of the sample mean and the z or t value associated with a certain level of confidence, usually 95% or 99%. Therefore, the correct answer is (C).
Sampling bias and nonresponse bias are potential sources of error in survey or study design and data collection, but they are not directly related to the construction of a confidence interval.
The desired level of confidence is a key input for determining the z or t value used in the calculation of the margin of error, but it is not included in the margin of error itself. The correct answer is z or t value associated with a 95% confidence level.
So, the correct option is (C).
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Answer the question below: *
Tasha is planning an expansion of a square flower garden in a city park. If each side of the original garden is
increased by 5 m, the new total area of the garden will be 121 m². Find the length of each side of the original garden.
O 6 meters
O 6.6 meters
O 11 meters
O 16 meters
Sea "x" la longitud de cada lado del jardín original en metros.
La superficie del jardín original es x^2 m².
Si cada lado del jardín original se aumenta en 5 m, el nuevo lado del jardín será de (x+5) metros, y la nueva superficie será (x+5)^2 m².
Según el problema, la nueva superficie total es de 121 m²:
(x+5)^2 = 121
Tomando la raíz cuadrada en ambos lados:
x+5 = 11
Restando 5 en ambos lados:
x = 6
Por lo tanto, la longitud de cada lado del jardín original es de 6 metros.
Por lo tanto, la respuesta correcta es O 6 metros.
x - the length of each side of the original garden
A = x²
( x + 5 )² = 121 /√
x + 5 = 11, or x + 5 = - 11;
x = 11 - 5
x = 6 ( another solution in negative )
Answer:
A ) 6 m
