The leading coefficient of a third-degree function that has the output of -110 x=3 and has zeros of 14, I, -I is 10
How to find the leading coefficient of a third-degree functionIf a third-degree function has zeros 14, I, and -I, it can be factored as: f(x) = a(x - 14)(x - I)(x + I)
'a' denotes the leading coefficient.
We may use the knowledge that the function's output is -110 when x = 3 to calculate the value of 'a'.
Substituting x = 3 into the function's factored form yields:
f(3) = a(3 - 14)(3 - I)(3 + I) = -110
When we simplify this equation, we get:
a(-11)(3 - I)(3 + I) = -110
a(-11)(9 - I^2) = -110
a(-11)(9 + 1) = -110 (since I2 = -1)
a(-11)(10) = -110
-110a = -1100
a = 10
Hence , the third-degree function's leading coefficient is 10.
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Answer the following questions.
Answer:
A=60
B=27
Step-by-step explanation:
Please solve As soon as possible.
An equation to match the graph include the following: f(x) = |x + 1| + 1.
What is a translation?In Mathematics and Geometry, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
Since the parent function is f(x) = |x|, g(x) would be created by translating f(x) the parent function one unit to the left and one unit upward as follows;
f(x) = |x|
g(x) = |x + 1| + 1
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What is the value of the shaded area of the total diagram?(both squares). Please see attached image.
A.0.148
B.0.148 repeated
C. 0.3
D.0.3 repeated
Special right triangles puzzle
Here’s are the instructions:
1. Find each missing value for x and y.
2. Round all answers to the nearest tenth.
3. Organise all of your work in a notebook/sheet of paper.
4. Give the answer in simplest radical form (root form).
5. If may be helpful to zoom in on pieces to see the diagrams clearly.
6. Box D is the first box in the upper left corner of the template! Drag this box over.
7. Continue dragging boxes onto the template and arrange them so that their edges meet with corresponding answers.
D x = 7.8
√7.82
E y = 11.1
√11.12
F x = 5.1
√5.12
G y = 24.3
√24.32
H x = 9.1
√9.12
I y = 15.4
√15.42
J x = 13.7
√13.72
K y = 20.2
√20.22
L x = 11.9
√11.92
M y = 18.3
√18.32
N x = 21
√21
O y = 17.5
√17.52
giving brainlest. Bobby believes his video game scores are clustered closer to his median than Amelia's are to her median. Explain why you agree or do not agree with Bobby.
Write a response.
Sample Response: Bobby’s interquartile range is 113, while Amelia’s is 179. A lower interquartile range means Bobby’s scores are closer to the median.
I cannot agree or disagree with personal beliefs. However, based on statistical principles, if the range of Bobby's scores is narrower than Amelia's range, then it is likely that Bobby's scores are closer to his median. Alternatively, if Amelia's scores are spread out more, her median may not be a good representation of the typical score, and her scores may not cluster closely around it. Ultimately, without more information on the distribution of the scores, it is impossible to determine who has scores clustered closer to their median.
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:
A. x² + (y - 3)² = 36.
D. x² + (y + 8)² = 36.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.
Based on the information provided above, we have the following parameters:
Radius, r = diameter/2 = 12/2 = 6 units.
Center, (h, k) = (0, 3).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 3)² = 6²
x² + (y - 3)² = 36.
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The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:
A. x² + (y - 3)² = 36.
D. x² + (y + 8)² = 36.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.
Based on the information provided above, we have the following parameters:
Radius, r = diameter/2 = 12/2 = 6 units.
Center, (h, k) = (0, 3).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 3)² = 6²
x² + (y - 3)² = 36.
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Review the information given based on a principal balance of $8,000 to answer the question:
FICO Score Simple Interest Rate Total # of Payments Total Amount Paid
800–850 12% 29 $9,256.00
740–799 15% 33 $9,812.00
670–739 18% 38 $10,554.00
580–669 21% 48 $11,891.00
300–579 28% 60 $14,945.00
Calculate how much more a household with a credit score of 525 will pay compared to a household with a credit score of 675.
a household with a credit score of 525 would pay $4,280.82 more than a household with a credit score of 675 for a principal balance of $8,000.
what is principal balance ?
Principal balance refers to the amount of money that you still owe on a loan or debt, not including any interest or fees that have accrued. When you make a payment towards your loan or debt, a portion of the payment goes towards paying down the principal balance,
In the given question,
To calculate the difference in payment between a household with a credit score of 525 and one with a score of 675, we need to compare the total amount paid for each score range.
For a principal balance of $8,000, based on the given information:
A household with a credit score of 525 would have a simple interest rate of 28%, and would make 60 payments of $249.08 each, for a total amount paid of $14,945.00.
A household with a credit score of 675 would have a simple interest rate of 18%, and would make 38 payments of $280.61 each, for a total amount paid of $10,664.18.
The difference in payment between these two scores would be:
$14,945.00 - $10,664.18 = $4,280.82
Therefore, a household with a credit score of 525 would pay $4,280.82 more than a household with a credit score of 675 for a principal balance of $8,000.
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What is the vertex of the quadratic function?
Answer:
1,-6
Step-by-step explanation:the vertex is the lowest/highest point, as you can see here it is at 1,-6
Using these sets, find the following: (D NE) UF=
D = {b, a, c, k}
• E = {t, a, s, k}
. F = {b, a, t, h}
Using the information regarding the set, it should be noted that (D NE) UF will be {b, a, t, h, s, t}
How to explain the informationD U E = {b, a, c, k} U {t, a, s, k}
= {b, a, c, k, t, s}
Next, we need to find the complement of set D with respect to set E, which is denoted as D NE. This is the set of all elements in E that are not in D: D NE = E \ D = {t, s}
(D NE) UF = {t, s} U {b, a, t, h}
= {b, a, t, h, s, t}
In conclusion, Using the information regarding the set, it should be noted that (D NE) UF will be {b, a, t, h, s, t}
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I NEED HELP WITH THIS TRIG QUESTION
The angle of elevation from the player's eyes to the center of the rim is approximately 16.2 degrees.
What is unit circle in trigonometry?A circle having a radius of 1 that is centred at the origin of a coordinate plane is known as the unit circle. The sine, cosine, and tangent values for every angle in the unit circle are frequently defined in trigonometry.
A radian-measured angle that begins at the positive x-axis and rotates anticlockwise around the circle can be used to represent each point on the unit circle. (Cos, Sin) are the coordinates of the point on the unit circle that corresponds to the angle.
For the given triangle first determine the value of the height from, the player to the top of the baseball pole as follows:
10 - 5.8 = 4.2 units
Now, using the trigonometric identity of tangent we have:
tan θ = opposite / adjacent
tan θ = 4.2 / 15
θ = tan⁻¹(4.2 / 15)
Hence, the angle of elevation from the player's eyes to the center of the rim is approximately 16.2 degrees.
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please answer questions on picture
The probability that William does his homework is 25/44
Let A be the event that William walks the dog after school, and let B be the event that he does his homework.
We are given:
P(A) = 8/11
P(B|A) = 1/2 (the probability of doing homework given that he walks the dog)
P(B|A') = 3/4 (the probability of doing homework given that he doesn't walk the dog)
We want to find P(B), the probability that William does his homework. We can use the law of total probability, which states that:
P(B) = P(A)×P(B|A) + P(A') × P(B|A')
Substituting the values we have, we get:
P(B) = (8/11) × (1/2) + (3/11) × (3/4)
= 4/11 + 9/44
=16+9/44
= 25/44
Therefore, the probability that William does his homework is 25/44
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K
The eccentricity of an ellipse is defined as e = c/a. For an ellipse, 0
5
Find an equation of an ellipse with vertices (0,-6) and (0,6) and e=
6
The equation of an ellipse which satisfies the given conditions is
(Type your answer in standard form.)
close to 0, an ellipse
The equation of the ellipse is y² = 35 (1 - x²)
How did we get this ?The given ellipse has vertices at ( 0, -6) and ( 0 , 6), which lie on the y - axis.
The distance between the centr of the ellipse (which also lies on the y - axis) and each vertex is 6 units. So since we hve
c = 6
and the eccentricity of the ellipse is also given as e = 6
we can use the r elationship between e, a, and c to find the value of a....
e = c/a
6 = 6/a
a = 1
Using the value of A and C, we find the equation of the ellipse, we can use the standard form
( x² / a²) + (y² / b²) = 1
Since the center of the ellipse is at the origin, know that
x / a² + y² / b ² = 1
Substituting a and c, ......
x² / 1² + y² / b² = 1
y² / b² = 1 - x²
y² = b² (1 - x²)
We need to find the value of b. We know that the distance between the center and each co-vertex of the ellipse is 5 units. So we state this as
b² = c² - a²
b² = 6² - 1 ²
b² = 35
Substituting the value of b² in the equation we got earlier, we get
y² = 35( 1 - x²)
Therefore, the equation of the ellipse is:
y² = 35 (1 - x² )
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HELPPPPPPPPPP PLEASEEEEEE!!!!!!!!!!
Answer:C is your answer
Step-by-step explanation:This is not a 90 degree angle or 360 degree shape
Jazmin is flying a kite but it got caught at the top of a 24 ft tree. If she let out 100 ft of string, what is the angle of elevation from Jazmin to the top of the tree (round to the nearest degree)?
The angle of elevation from Jazmin to the top of the tree is 14°.
We are given that;
Top of tree= 24ft
String= 100ft
Now,
We can use any trigonometric ratio that involves opposite and hypotenuse sides, such as sine or cosine. Let’s use sine for this example.
sin θ = opposite / hypotenuse
sin θ = 24 / 100
sin θ = 0.24
θ = sin^-1 (0.24)
θ = 13.9° (rounded to the nearest degree)
Therefore, by the angle the answer will be 14°.
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. The perimeter of a rectangle is twice its area. If the perimeter is 32L and the breadth is the square of its length, L, find a. length b. Breadth c. Perimeter d. Area of the rectangle.
The rectangle have length = 4, breath = 16, perimeter = 40, and area = 64.
How to evaluate for the length, breadth, perimeter, and area of the rectangleThe perimeter of a rectangle is the sum of length of its four sides or the sum of its length and breadth, multiplied by two. While the area is the length multiplied by the breadth.
Perimeter = 2(L + B)
Area = L × B
From the question;
2(L + B) = 2LB
32L = 2L(L²)...(1) {since B = L²}
from equation (1), L = 4 by solving for L
so;
B = 4² = 16
perimeter of the rectangle = 2(4 + 16) = 40
area of the rectangle = 4 × 16 = 64
Therefore, the rectangle have length = 4, breath = 16, perimeter = 40, and area = 64.
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In a recent year, women spent $2 million on swimwear and purchased 92,000 swimsuits. During the same year, men spent $500,000 on swimwear and purchased 37,000 swimsuits.
a. Find the ratio of the amount men spent on swimwear to the amount women spent on swimwear.
b. Find the ratio of the amount men spent on swimwear to the total amount men and women spent on swimwear. Write the ratios as fractions in simplest form.
Ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. It is also the comparison of two like or similar quantities.
How to determine this,
The ratio of the amount men spent on swimwear to the amount women spent on swimwear
When the amount men spent on swimwear = $500,000
Amount women spent on swimwear = $2,000,000
Ratio = 500,000 : 2,000,000
Ratio = 500,000/2,000,000
Ratio = 1/4
Ratio = 1 : 4
The ratio as a fraction = 1/4
b. To find the ratio of the amount men spent on swimwear to the total amount men and women spent on swimwear.
Amount men spent on swimwear = $500,000
Total amount men and women spent on swimwear
= $2,000,000 + $500,000
= $2,500,000
Ratio = $500,000 : $2,500,000
Ratio = 500,000/2,500,000
Ratio = 1/5
Ratio = 1 : 5
Ratio expressed as a fraction = 1/5
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If the sides of a square are increased by 11, the area becomes 400. What is the length of the original side?
Answer: The length of the original side of the square is 22 units.
Step-by-step explanation:
Let x be the length of the original side of the square.
If the sides are increased by 11, the new side length is x + 11.
The area of the new square is given as 400, so we have:
(x + 11)^2 = 400
Expanding the left side: x^2 + 22x + 121 = 400
Subtracting 400 from both sides: x^2 + 22x - 279 = 0
Using the quadratic formula:
x = (-22 ± sqrt(22^2 - 41(-279))) / (2*1)
x = (-22 ± sqrt(12100)) / 2
x = (-22 ± 110) / 2
Taking the positive solution:
x = (-22 + 110) / 2
x = 44 / 2
x = 22
HELP PLS ASAPPP!!!
algebra problem; solving linear inequalities !!! :)
Answer: x = -3/2
Step-by-step explanation:
Supplementary angles
The angle that is supplementary to <DEA is DEC
How to determine the angleTo determine the angle that is supplementary to <DEA , we need to consider the following;
Supplementary angles are described as angles that sum up to 180 degreesIt is described as the pair of angles on a straight lineSum of angles on a straight line is 180 degreesThe supplementary angles must be pairTangent lines forms supplementary anglesFrom the information given, we have that;
<DEA is supplementary to <DEC that is sum of angles on a straight line.
Then,
<DEA + <DEC = 180 degrees
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help
I need an answer
The correct option that indicates the quadrant that contains the translation of the shaded figure is the option B
B. III
What is a translation transformation?A translation is a transformation in which the size, relative position of the points on the pre-image, are preserved but the location of the pre-image changes to obtain the image.
The shape of the shaded figure is an L-shape
The geometric figure in quadrant II and IV are a reflection of the shaded figure, across the y-axis and across the x-axis, respectively which is not a translation transformation.
The geometric figure in quadrant III can be obtained from the shaded figure by a translation 4 units to the left and 5 units downwards, which can be expressed as <-4, -5>, which is a translation transformation, therefore;
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Solve the system of linear equation given by 2x − 2y = 7 and −x + y = −2
The system of linear equations has no solutions.
How to solve the system of linear equations?Here we want to solve the system of linear equations:
2x- 2y = 7
-x + y = -2
One could easily identify that the two lines are parallel, but let's prove it. To do so, we can multiply the second equation by -2.
Then we will get:
-2*(-x + y) = -2*-2
2x - 2y = 4
Then the system of equations is:
2x- 2y = 7
2x - 2y = 4
The coefficients in the left side are the same ones and the constants in the right side are different. Thus, the lines are parallel, and thus, the system has no solutions.
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The width of the rectangle is 5 units less than the length if the area is 36 square units then find the dimension of the rectangle
Answer:
The dimensions of the rectangle are approximately 8.54 units by 3.54 units.
Step-by-step explanation:
Let's start by using algebra to represent the information given in the problem.
Let L be the length of the rectangle.
Then, the width of the rectangle is 5 units less than the length, which means the width can be expressed as L - 5.
The area of a rectangle is given by the formula A = L * W, where A is the area, L is the length, and W is the width. In this case, we are given that the area is 36 square units. So we can write:
A = L * (L - 5)
36 = L * (L - 5)
Expanding the right-hand side of the equation, we get:
36 = L^2 - 5L
Moving all the terms to the left-hand side of the equation, we get:
L^2 - 5L - 36 = 0
Now we can use the quadratic formula to solve for L:
L = (-(-5) ± sqrt((-5)^2 - 4(1)(-36))) / (2(1))
Simplifying this expression, we get:
L = (5 ± sqrt(229)) / 2
We can discard the negative solution since the length of a rectangle cannot be negative.
So, the length of the rectangle is approximately 8.54 units (rounded to two decimal places).
To find the width, we can substitute this value of L into the expression we derived earlier for the width:
W = L - 5
W = 8.54 - 5
W ≈ 3.54 units (rounded to two decimal places)
Therefore, the dimensions of the rectangle are approximately 8.54 units by 3.54 units.
how much to subtract from 53/6 to make 8
Answer:
We need to subtract 41/6 from 53/6 to get 8. Alternatively, we can say that 8 is 41/6 less than 53/6.
Step-by-step explanation:
To determine how much to subtract from 53/6 to make 8, we need to perform the following calculation:
53/6 - x = 8
where x is the amount we need to subtract.
To isolate x, we need to isolate it on one side of the equation. We can do this by subtracting 53/6 from both sides:
53/6 - x - 53/6 = 8 - 53/6
Simplifying the left-hand side gives:
-x = 8 - 53/6 + 53/6
Simplifying the right-hand side gives:
-x = 41/6
Multiplying both sides by -1 gives:
x = -41/6
Therefore, we need to subtract 41/6 from 53/6 to get 8. Alternatively, we can say that 8 is 41/6 less than 53/6.
Please help me solve the photo
I need to know the order asap
The inverse of the function f(x) = 3 · x / (8 + x) is f⁻¹(x) = 8 · x / (3 - x).
How to find the inverse of a function
In this problem we must determine the inverse of a function, this can be done by means of algebra properties. First, write the entire function:
f(x) = 3 · x / (8 + x) (Step 0)
y = 3 · x / (8 + x) (Step 1)
Second, use the following substitutions:
x → y
y → x
x = 3 · y / (8 + y) (Step 2)
Third, clear y within the expression:
x · (8 + y) = 3 · y (Step 3)
8 · x + x · y = 3 · y
8 · x = 3 · y - x · y (Step 4)
8 · x = y · (3 - x)
y = 8 · x / (3 - x)
Fourth, use final notation:
f⁻¹(x) = 8 · x / (3 - x) (Step 5)
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48 POINTS PLEASE HELP ME ASAP!
The function f(x) = -0.05(x^2-18x -40) represents the path coming out of the cannon. If x is the horizontal distance from the cannon, what does f(x) represent? Recall that f(x) is a notation for the y-values of the function.
The function f(x) = -0.05(x²-18x -40) represents the "height" of the projectile fired from the cannon at a "horizontal-distance" of x.
The function which represents the path, coming out of the cannon is f(x) = -0.05(x²-18x -40);
The term inside the bracket is : (x²-18x -40) is a quadratic expression that represents the shape of the projectile's path.
Now, let us consider the "negative-coefficient" (-0.05) in front of the quadratic expression.
This means that the function will be reflected about the x-axis, which means that the height of the projectile will be measured downwards from a reference point.
Therefore, f(x) represents the height of the projectile.
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Find the derivative of y = ((2x - 1) ^ 3)//√(3x + 1)
The derivative of the function y = ((2x - 1)³)/√(3x + 1) is dy/dx = (2x - 1)²[3x + 6]/(2[√(3x + 1)]³)
What is the derivative of a function?The derivative of a function is the limit as the change in x tnds to zero of the change in y over the change in x.
To find the derivative of the function y = ((2x - 1)³)/√(3x + 1), we use the quotient rule.
dy/dx = (vdu/dx - udv/dx)/v²
where u = (2x - 1)³ and v = √(3x + 1)
So, du/dx = 3(2x - 1)² and dv/dx = 3/[2√(3x + 1)]
Substituting the values of the variables into the equation, we have that
dy/dx = (vdu/dx - udv/dx)/v²
dy/dx = (√(3x + 1) × 3(2x - 1)² - (2x - 1)³ × 3/[2√(3x + 1)])/[√(3x + 1)]²
dy/dx = (3√(3x + 1)(2x - 1)² - 3(2x - 1)³/[2√(3x + 1)])/[√(3x + 1)]²
= (3√(3x + 1)√(3x + 1)(2x - 1)² - 3(2x - 1)³/[2√(3x + 1)])(3x + 1)²
= [3(3x + 1)(2x - 1)² - 3(2x - 1)³/[2√(3x + 1)])(3x + 1)²
= (2x - 1)²[3(3x + 1) - 3(2x - 1)/[2√(3x + 1)])(3x + 1)²
= (2x - 1)²[9x + 3 - 6x + 3]/[2√(3x + 1)])(3x + 1)²
= (2x - 1)²[3x + 6]/(2[√(3x + 1)]³)
So, dy/dx = (2x - 1)²[3x + 6]/(2[√(3x + 1)]³)
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QUESTION 10
The following headline refers to change. Identify the change as absolute or relative.
"Enrollments at Northeastern University are expected to increase by 1,700 students"
The change referred to in the headline is an absolute change. An absolute change is a difference or increase in a quantity that is measured without reference to the original or initial value.
In this case, the headline states that enrollments at Northeastern University are expected to increase by 1,700 students. This means that the actual number of students is expected to increase by 1,700 from its current or previous level, without any reference to the original number of students enrolled at Northeastern University.
An absolute change is usually expressed in units of the quantity being measured, such as students, dollars, or meters. In contrast, a relative change is expressed as a percentage or ratio of the original or initial value. A relative change indicates how much a quantity has changed in proportion to its initial value.
For example, if enrollments at Northeastern University were expected to increase by 10%, this would be a relative change because it represents a percentage of the current or previous level of enrollment. However, the headline specifies an absolute increase of 1,700 students, which does not depend on the current or previous level of enrollment.
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A pole that is 3.2 m tall casts a shadow that is 1.3 m long. At the same time, a nearby tower casts a shadow that is 46.75 m long. How tall is the tower? Round your answer to the nearest meter. Please help /:
Answer:
115 meters
Step-by-step explanation:
Think of this like a ratio [tex]\frac{3.2}{1.3} =\frac{x}{46.75}[/tex]
Then solve for x [tex](\frac{3.2}{1.3} )*46.75 = 115.08[/tex]
A teacher asks her students to find an expression for the number of tiles needed to
surround such a square pool, and sees the following responses from her students:
4(s+1)
s²
4s+4
2s+2(s+2)
4s
Is each mathematical model correct or incorrect? How do you know?
The correct mathematical expression to find the number of tiles needed to surround a square pool would depend on how the tiles are arranged and how the dimensions of the pool and the tiles are related.
4(s+1): This expression appears to be correct if we assume that each side of the square pool is surrounded by a row of tiles, and each corner requires an additional tile.
So, the expression can be simplified to 4s+4. This is a valid expression for the number of tiles needed to surround the pool.
s²: This expression does not appear to be correct, as it only gives the area of the square pool, and does not take into account the dimensions of the tiles or the need to surround the pool.
4s+4: This expression is the same as the first expression, 4(s+1), and is a valid expression for the number of tiles needed to surround the pool.
2s+2(s+2): This expression appears to be incorrect, as it gives the total perimeter of the pool plus an additional 4 units, but does not take into account the size of the tiles or the need to surround the pool.
4s: This expression is incorrect, as it only gives the perimeter of the pool and does not take into account the need to surround the pool with tiles.
Thus, two of the given expressions (4(s+1) and 4s+4) are correct, one expression (s²) is incomplete, and two expressions (2s+2(s+2) and 4s) are incorrect.
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