The limit of the function As x → - ∞, f(x) → 2.
What is the limit of a function?The limit of a function is the value the function tends to as the independent variable tends to a given value.
Given the graph of the function above, to find the limit of the function As x → -∞, f(x) →? We proceed as follows
Looking at the graph, we see that f(x) has a horizontal asymptote at y = 2. Now, we see that As x → -∞, f(x) approaches 2.
So, As x → - ∞, f(x) → 2.
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Identify which year’s population will hit zero
The year when the population becomes zero is 2020.2
Which year the population will reach zero?We know that the population decreases at a constant rate, so it is modeled by a line:
y = ax + b
Where a is the slope and b is the y-intercept.
Here we have two points (2010, 5100) and (2012, 4100)
The slope is the quotient between the differences of the y-values and the x-values, then:
a = (4100 - 5100)/(2012 - 2010) = -1000/2 = -500
We can write.
y = -500*x + b
We know that when x = 2010, y = 5100, replacing that we get:
5100 = -500*2010 + b
b = 5100 + 500*2010 = 1,010,100
Then:
y = -500*x + 1,010,100
And it is zero when:
0 = -500*x + 1,010,100
x = 1,010,100/500
x = 2020.2.
That is the year when the pópulation becomes zero.
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What is the solution to x – 5 + 2 < 20? –7 < x < 15 –13 < x < 23 x < –7 or x > 15 x < –13 or x > 23
Answer:
Therefore, the correct answer is: x < 23.
Step-by-step explanation:
To solve the inequality x - 5 + 2 < 20, we can simplify it step by step:
x - 5 + 2 < 20
Combine like terms:
x - 3 < 20
Add 3 to both sides of the inequality:
x - 3 + 3 < 20 + 3
Simplify:
x < 23
The solution to the inequality is x < 23.
Therefore, the correct answer is: x < 23.
Answer and Step-by-step explanation:
Please see the photo for the solution :)
7. At age 20, Heather began investing $3000 annually
into an account earning 7.5% interest compounded
annually. Lesley invested $6000 annually into a similar
account but began at age 40. They both stopped
contributing at age 65.
a) How much money did Heather and Lesley contribute
to their account?
b) What is the value of each of their investments when
they are 65 years old?
c) At age 65, when the investments mature, who has
more money and by how
much?
a) Heather contributed $135,000 and Lesley contributed $150,000 to their accounts.
b) Heather's investment is approximately $273,714.17, while Lesley's investment is approximately $191,048.18 when they are 65 years old.
c) Heather has more money by approximately $82,665.99 at age 65.
a) To find out how much money Heather and Lesley contributed to their accounts, we need to calculate the total contributions made by each of them.
Heather:
Heather started investing at age 20 and stopped at age 65, contributing $3000 annually. The number of years she contributed is (65 - 20) = 45 years.
Total contributions by Heather = $3000 × 45 = $135,000.
Lesley:
Lesley started investing at age 40 and stopped at age 65, contributing $6000 annually. The number of years she contributed is (65 - 40) = 25 years.
Total contributions by Lesley = $6000 × 25 = $150,000.
Therefore, Heather contributed $135,000 and Lesley contributed $150,000 to their respective accounts.
b) To calculate the value of their investments at age 65, we can use the formula for compound interest:
Future Value = Principal × (1 + interest rate)^number of years
Heather:
Principal (initial investment) = $3000
Interest rate = 7.5% = 0.075 (converted to decimal)
Number of years = 65 - 20 = 45
Future Value of Heather's investment = $3000 × (1 + 0.075)^45
Lesley:
Principal (initial investment) = $6000
Interest rate = 7.5% = 0.075 (converted to decimal)
Number of years = 65 - 40 = 25
Future Value of Lesley's investment = $6000 × (1 + 0.075)^25
Calculating these values:
Future Value of Heather's investment = $3000 × (1.075)^45 ≈ $273,714.17
Future Value of Lesley's investment = $6000 × (1.075)^25 ≈ $191,048.18
c) To determine who has more money at age 65 and by how much, we compare the future values of their investments.
Heather's investment value at age 65 = $273,714.17
Lesley's investment value at age 65 = $191,048.18
Therefore, Heather has more money at age 65, and the difference in their investments is approximately $273,714.17 - $191,048.18 = $82,665.99.
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Five clubs at Johnson School raised $2000. The incomplete circle graph shows what percent of the money was raised by each club. How much money did the Math Club raise?
$500
$600
$200
$400
$300
The Math Club raised $400.
To find out how much money the Math Club raised, we need to determine the percentage of the total amount raised that corresponds to the Math Club's portion.
Let's assume the Math Club raised "x" amount of money. The total amount raised by all five clubs is $2000.
According to the incomplete circle graph, the Math Club's percentage is missing, but we know the percentages for the other clubs: Computer Club raised 15%, Gardening Club raised 18%, Art Club raised 30%, and Spanish Club raised 17%.
To find the missing percentage for the Math Club, we subtract the percentages of the other clubs from 100%:
Missing percentage = 100% - (15% + 18% + 30% + 17%) = 100% - 80% = 20%
Now we can set up a proportion to determine the amount raised by the Math Club:
(x / $2000) = 20% / 100%
Cross-multiplying:
x = ($2000 * 20%) / 100%
Simplifying:
x = $400
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0.059 and 0.01 which is greater?
Toula owns the Pita Pan restaurant. She needs to order supplies for the upcoming weekend rush. She needs 150 bags of pita bread. The bread come in crates of 50, and each crate costs $15.00. She also needs 65 containers of hummus dip. There are 5 containers in a box, and each box costs $20.00 What expressions can Toula use to determine how much the pita bread and hummus dips will cost? What will the total be?
The total cost of the pita bread and hummus dips will be $305.00.
To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:
Cost of pita bread:
Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates
Cost of each crate = $15.00
Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00
Cost of hummus dips:
Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes
Cost of each box = $20.00
Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00
Therefore, the expressions Toula can use to determine the costs are:
Cost of pita bread = 3 crates × $15.00/crate
Cost of hummus dips = 13 boxes × $20.00/box
The total cost will be the sum of the costs of pita bread and hummus dips:
Total cost = Cost of pita bread + Cost of hummus dips
Total cost = $45.00 + $260.00
Total cost = $305.00
Therefore, the total cost of the pita bread and hummus dips will be $305.00.
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Two cyclists, 54 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
Answer:
In summary, the faster cyclist cycles at a speed of 18 mi/h since they travel 36 of the 54 miles in 2 hours while cycling twice as fast as the slower cyclist.
Explanationn:
The two cyclists are 54 miles apart and heading toward each other.
One cyclist cycles 2 times as fast as the other. We will call the faster cyclist A and the slower cyclist B.
They meet 2 hours after starting. This means they travel a total distance of 54 miles in 2 hours.
Since cyclist, A cycles 2 times as fast as cyclist B, cyclist A travels 2/3 of the total distance, and cyclist B travels 1/3 of the total distance.
In two hours, cyclist A travels (2/3) * 54 miles = 36 miles.
We need to find the speed of cyclist A in miles per hour.
Speed = Distance / Time
So the speed of cyclist A is:
36 miles / 2 hours = 18 miles per hour
Therefore, the speed of the faster cyclist is 18 mi/h.
Enter the number that belongs in the green box
The angle C in the triangle is 34.05 degrees.
How to use cosine law to find angles in a triangle?
The sum of angles in a triangle is 180 degrees. The angle in a triangle can be found using cosine law as follows:
Therefore, let's find the unknown angle in the triangle as follows;
c² = a² + b² - 2ab cos C
Hence,
4² = 5² + 7² - 2 × 7 × 5 cos X
16 = 25 + 49 - 70 cos X
16 = 74 - 70 cos X
16 - 74 = -70 cos X
-58 = -70 cos X
cos X = 58 / 70
X = cos⁻¹ 0.82857142857
X = 34.0478785629
X = 34.05 degrees
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A merchant mixed 12 lb of a cinnamon tea with 5 lb of spice tea. The 17-pound mixture cost $28. A second mixture included 14 lb of the cinnamon tea and 6 lb of the spice tea. The 20-pound mixture cost $33. Find the cost per pound of the cinnamon tea and of the spice tea.
Cinnamon tea costs $1.50 per pound, and spice tea costs $2.75 per pound.
To solve this problem, we can set up a system of equations based on the given information.
Let's denote the cost per pound of the cinnamon tea as C, and the cost per pound of the spice tea as S.
From the first mixture, we know that the total weight is 17 pounds, so we can write the equation:
12C + 5S = 28 ----(Equation 1)
From the second mixture, we know that the total weight is 20 pounds, so we can write the equation:
14C + 6S = 33 ----(Equation 2)
To solve this system of equations, we can use a method like substitution or elimination.
Let's use the elimination method to eliminate the variable C:
Multiply Equation 1 by 2 and Equation 2 by -3 to eliminate the C terms:
24C + 10S = 56 ----(Equation 3)
-42C - 18S = -99 ----(Equation 4)
Add Equation 3 and Equation 4:
-18C - 8S = -43
Solve for S:
8S = 43 - 18C
S = (43 - 18C)/8 ----(Equation 5)
Now substitute Equation 5 into Equation 1:
12C + 5((43 - 18C)/8) = 28
Multiply through by 8 to eliminate the fraction:
96C + 215 - 90C = 224
6C = 9
C = 9/6 = 1.5
Substitute the value of C back into Equation 5 to find S:
S = (43 - 18(1.5))/8 = 2.75
Therefore, the cost per pound of the cinnamon tea is $1.50, and the cost per pound of the spice tea is $2.75.
In summary, the cost per pound of the cinnamon tea is $1.50, and the cost per pound of the spice tea is $2.75.
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A round pencil is sharpened to a cone shape at both ends.calculate the volume of the pencil if the two radius is 1.2 and heights are 8cm
Answer:
A round pencil is sharpened at both ends the hight of the pencil is 16cm the length of the pencil is 1cm the radius of the two sharpened ends is 16cm 1.2cm
Calculate the volume using the value 22/7.
Step-by-step explanation:
se logarithms to solve the problem.
The rule of 70 is a rule of thumb for estimating the doubling time of a quantity (e.g., investment, GDP, population) experiencing growth that is compounded continuously. The rule states that if the growth rate is r% per year, then the time it takes for the quantity to double is approximately 70/r years.
(a)
Use the rule of 70 to estimate the time it takes for an investment to double in value if it grows at the rate of 5% per year compounded continuously.
yr
(b)
What is the exact time it will take for the investment in part (a) to double in value? (Round your answer to two decimal places.)
yr
a. The investment to double in value take about 14 years for the funding to double in value.
b. The genuine time it will take for the funding to double in fee is about 13.86 years.
(a) To estimate the time it takes for an funding to double in cost the use of the rule of 70, we want to decide the increase rate. In this case, the increase price is given as 5% per 12 months compounded continuously.
Using the rule of 70, we can calculate the estimated doubling time:
Time to double ≈ 70 / boom rate
Time to double ≈ 70 / 5
Simplifying, we have:
Time to double ≈ 14 years
Therefore, it would take about 14 years for the funding to double in value.
(b) To decide the genuine time it will take for the funding to double in value, we can use the formulation for non-stop compounding:
Doubling time (exact) = ln(2) / (ln(1 + r))
where r is the increase fee as a decimal.
In this case, the increase charge is 5% per year, or 0.05 as a decimal.
Doubling time (exact) = ln(2) / (ln(1 + 0.05))
Doubling time (exact) ≈ 13.86 years (rounded to two decimal places)
Therefore, the genuine time it will take for the funding to double in fee is about 13.86 years.
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quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 62
minutes with a mean life of 606
minutes.
If the claim is true, in a sample of 99
batteries, what is the probability that the mean battery life would be greater than 619
minutes? Round your answer to four decimal places.
Answer:
Step-by-step explanation:
Select all the statements that are true for the following systems of equations.
System A
2x-3y = 4
4x - y = 18
00
System B
3x - 4y = 5
y = 5x +3
All three systems have different solutions.
Systems B and C have the same solution.
System C simplifies to 2x-3y=4 and 4x-y=18 by dividing the second equation by three.
Systems A and B have different solutions.
Systems A and C have the same solution.
Reset
System C
2x-3y=4
12x-3y = 54
Next
The statements that are true about the system of equations are: Options C, D, and E.
How to Find the Solution to a Systems of Equations?Let's analyze each statement and determine whether it is true or false for the given systems of equations:
System A
2x - 3y = 4
4x - y = 18
System B
3x - 4y = 5
y = 5x + 3
System C
2x - 3y = 4
12x - 3y = 54
A. All three systems have different solutions.
To determine if the systems have different solutions, we need to solve them. Solving system A gives the solution x = 5 and y = -6. Solving system B gives the solution x = -1 and y = -2. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is false because systems A and C have the same solution.
B. Systems B and C have the same solution.
As mentioned above, solving system B gives the solution x = -1 and y = -2. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is false because systems B and C have different solutions.
C. System C simplifies to 2x-3y=4 and 4x-y=18 by dividing the second equation by three.
To simplify system C, we can divide the second equation by 3, resulting in:
2x - 3y = 4
4x - y = 18
This is exactly the same as system A. Therefore, this statement is true.
D. Systems A and B have different solutions.
As mentioned earlier, solving system A gives the solution x = 5 and y = -6. Solving system B gives the solution x = -1 and y = -2. Therefore, this statement is true.
E. Systems A and C have the same solution.
As mentioned earlier, solving system A gives the solution x = 5 and y = -6. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is true.
In summary:
A. False
B. False
C. True
D. True
E. True
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Complete Question:
Select all the statements that are true for the following systems of equations.
System A
2x - 3y = 4
4x - y = 18
System B
3x - 4y = 5
y = 5x +3
System C
2x - 3y = 4
12x - 3y = 54
A. All three systems have different solutions.
B. Systems B and C have the same solution.
C. System C simplifies to 2x-3y=4 and 4x-y=18 by dividing the second equation by three.
D. Systems A and B have different solutions.
E. Systems A and C have the same solution.
Which linear equation shows a proportional relationship?
y equals negative one sixth times x
y equals one sixth times x minus 8
y = −6x + 1
y = 6
Answer:
y = (-1/6)x represents a proportional relationship.
Find the slope and the y-intercept of the following linear equation. 5. 3x + 2y = 14
Answer:
slope = - [tex]\frac{3}{2}[/tex] , y- intercept = 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
3x + 2y = 14 ( subtract 3x from both sides )
2y = - 3x + 14 ( divide through by 2 )
y = - [tex]\frac{3}{2}[/tex] x + 7 ← in slope- intercept form
with slope m = - [tex]\frac{3}{2}[/tex] and y- intercept c = 7
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An output value for (fog)(x) is 55/(x² + 2x).
Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.
How to determine the corresponding composite function?In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;
(fog)(x) = 5/(x + 2) × 11/x
(fog)(x) = 55/x(x + 2)
(fog)(x) = 55/(x² + 2x)
For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;
x² + 2x ≠ 0
x² ≠ -2x
x ≠ -2
Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.
In conclusion, we can reasonably infer and logically deduce that x must not be equal to 0 and -2.
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What is the volume of the triangular prism?
3 in.
15 in.
13 in.
Which of the following steps indicates the addition property of equality while solving the equation –1 – 6x = x – 15?
A) x = 14∕2
B) –1 – 6x = x – 15
C) 23 – 6x – 24 = x – 15
D) –1 – 6x + 15 = x – 15 + 15
Answer:
-1 - 6x = x - 15
Add 15 to both sides using the addition property of equality.
14 - 6x = x
14 = 7x
2 = x
D) -1 - 6x + 15 = x - 15 + 15
Answer and Step-by-step explanation:
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Arc BC on circle A has a length of 115,
- inches. What is the radius of the circle?
115/6 pi
138°
The radius of the circle is 25 inches. The length of arc with a central angle of 138° is 115π/6 in
What is an equation?An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.
The length of an arc with a central angle Ф with circle radius (r) is given by:
Length of arc = (Ф/360) * 2πr
Given the length of arc as 115π/6 in and angle of 138°, hence:
Length of arc = (Ф/360) * 2πr
Substituting:
115π/6 = (138/360) * 2πr
r = 25 inches
The radius of the circle is 25 inches.
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A gaming system costs $600 and is on sale for 15% off. After the discount, there is a 5% tax. What is the final price of the gaming system?
Answer$535.50
Step-by-step explanation:
15% is equal to .15
So, multiply 600.00x .15=90
600.00 - 90.0=510.
510. 00x .05=25.50
510.00+25.50=535.50
Your answer is $535.5
The axis of symmetry for the function f(x) = -x² - 10x + 16 is x = -5. What are the coordinates of the vertex of the
graph?
A. (-5,41)
B. (-5,56)
C. (-5,76)
D. (-5,91)
Answer:
A
Step-by-step explanation:
the axis of symmetry passes through the vertex
its equation x = - 5 is the x- coordinate of the vertex
substitute x = - 5 into f(x) for corresponding y- coordinate
f(- 5) = - (- 5)² - 10(- 5) + 16
= - 25 + 50 + 16
= - 25 + 66
= 41
coordinates of vertex = (- 5, 41 )
A shop sells phone covers in 3 colours: red, blue and green. There are 4 more green covers than blue covers. There are twice as many blue covers as red covers. There are 104 covers altogether. how many green covers are there
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
D = {x|x is a whole number} E = {x|x is a perfect square between 1 and 9} F = {x|x is an even number greater than or equal to 2 and less than 9} Which of the following is an element of D ∩ (E ∩ F)? 16 3 6 4
The element 4 is an element of D ∩ (E ∩ F).
To find the intersection of sets D, E, and F, we need to determine the elements that are common to all three sets.
Set D consists of all whole numbers, so any whole number can be an element of set D.
Set E consists of perfect squares between 1 and 9. The perfect squares in this range are 1, 4, and 9.
Set F consists of even numbers greater than or equal to 2 and less than 9.
The even numbers in this range are 2, 4, 6, and 8.
Taking the intersection of sets E and F, we find that the common element is 4, as it is the only number that satisfies both conditions of being a perfect square and an even number in the given range.
Finally, taking the intersection of set D with the intersection of sets E and F, we find that the element 4 is also an element of set D ∩ (E ∩ F).
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Assume that Canes customer would buy. A maximum of 82000. Units of Alpha and62000 of beta assume that the raw material availability for production is limited to 162000 pounds how many units of each product should Cane produce to maximize profits
The units of each product that Cane should produce to maximize profits will be 62000 units of Beta and 7600 units of
Alpha.
Contribution margin per poundAlpha Beta
Selling price 130 90
Variable cost 78 48
Contribution margin 52 42
Pound per unit 5 2
Contribution margin per pound 10.4 21
Pound Unit
Beta 62000*2 = 124000 62000
Alpha 38000 38000/5 = 7600
Total 162000
Maximum contribution margin = (38000*10.4+124000*21) = 2999200
Highest price = 10.4+5 = 15.40 per pound
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PLEASE HELP AS SOON AS POSSIBLE
Answer:
B
Step-by-step explanation:
Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over x = −1.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−5, 5), M′(−2, 3), O′(−3, 7)
N′(3, 2), M′(0, 1), O′(1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).
To determine the vertices of the image N'M'O' after reflecting triangle NMO over the line x = -1, we need to apply the reflection transformation to each vertex.
For a reflection over the line x = -1, we can find the image of a point (x, y) by finding its reflection as (2(-1) - x, y).
Applying this transformation to each vertex of triangle NMO, we get:
N' = (2(-1) - (-5), 2) = (5, 2)
M' = (2(-1) - (-2), 1) = (2, 1)
O' = (2(-1) - (-3), 3) = (3, 3)
The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).
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Find the numbers with the following property three times the sum of four and a number is less than seven times the same number
Let's represent the number with the variable "x". According to the given property, we can write the following equation:
3(x + 4) < 7x
Now, let's solve this inequality to find the range of numbers that satisfy the property.
3x + 12 < 7x
Subtract 3x from both sides:
12 < 4x
Divide both sides by 4 (since the coefficient of x is 4):
3 < x
So, the range of numbers that satisfy the given property is x > 3.
Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:
Factorise the formula y = 4x² + 16x +15 in the form y = (2x +...)(2x + ...). help
Answer:
y = (2x + 5)(2x + 3)
Step-by-step explanation:
y = 4x² + 16x + 15
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × 15 = 60 and sum = + 16
the factors are + 10 and + 6
use these factors to split the x- term
y = 4x² + 10x + 6x + 15 ( factor the first/second and third/fourth terms )
y = 2x(2x + 5) + 3(2x + 5) ← factor out (2x + 5) from each term
y = (2x + 5)(2x + 3)
since multiplication is commutative , then could be
y = (2x + 3)(2x + 5)
Select the expression that is equivalent to (n²-25)
A. n² +10n - 25
B. n²-10-25
C. (n+5)(n-5)
D. (n-5) ²
Answer:
C. (n+5)(n-5)
Step-by-step explanation:
Select the expression that is equivalent to (n²-25)
Let's check each option. A and B are wrong, so we only check C & D.
C. (n + 5) (n - 5)
n² - 5n + 5n - 25
n² - 25
D. (n - 5)²
(n - 5) (n - 5)
n² - 5n - 5n + 25
n² - 10n + 25
So, the correct answer is C. (n+5)(n-5)
Given rhombus QRST, find the
perimeter if QU = 3 and RU equals 4.
Q
R
T
U
X
S
The perimeter of the rhombus in this problem is given as follows:
19.8 units.
What is the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
The diagonal length can be obtained as follows:
QU = US = 3.RU = UT = 4.RU + UT = 7.
Applying the Pythagorean Theorem, the side length is obtained as follows:
x² + x² = 7²
2x² = 49
[tex]x = \sqrt{\frac{49}{2}}[/tex]
x = 4.95.
Then the perimeter is given as follows:
P = 4 x 4.95
P = 19.8 units.
More can be learned about the perimeter of a polygon at https://brainly.com/question/3310006
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