Answer:
Step-by-step explanation:
To set up a 2-month amortization table for Kelis and Nathan's $375,000, 15-year mortgage with an APR of 3.75%, we can use the following headings:
Month | Payment | Principal | Interest | Balance
To calculate the monthly payment amount, we can use the following formula:
P = L[c(1 + c)^n]/[(1 + c)^n - 1]
Where:
P = the monthly payment
L = the loan amount ($375,000)
c = the monthly interest rate (APR divided by 12)
n = the total number of payments (15 years multiplied by 12 months per year)
First, we need to calculate the monthly interest rate:
c = 3.75% / 12 = 0.003125
Next, we need to calculate the total number of payments:
n = 15 years x 12 months per year = 180
Now we can plug in these values to the formula:
P = 375000[0.003125(1 + 0.003125)^180]/[(1 + 0.003125)^180 - 1]
P = $2,719.06
So, Kelis and Nathan's monthly payment will be $2,719.06.
To complete the table for the first 2 months, we need to calculate the interest and principal amounts for each payment:
Month 1:
Payment = $2,719.06
Interest = $1,406.25 ($375,000 x 0.003125)
Principal = $1,312.81 ($2,719.06 - $1,406.25)
Balance = $373,687.19 ($375,000 - $1,312.81)
Month 2:
Payment = $2,719.06
Interest = $1,462.97 ($373,687.19 x 0.003125)
Principal = $1,256.09 ($2,719.06 - $1,462.97)
Balance = $372,431.10 ($373,687.19 - $1,256.09)
So, the completed table for the first 2 months would look like this:
Month | Payment | Principal | Interest | Balance
1 | $2,719.06 | $1,312.81 | $1,406.25 | $373,687.19
2 | $2,719.06 | $1,256.09 | $1,462.97 | $372,431.10
We can continue this process to complete the full 15-year amortization table.
7. Sharon is making a huge batch of lemonade
for her lemonade stand. Her recipe calls for 26
pints of water. There are approximately 3 liters
in every 6.5 pints. How much water does
Sharon need in liters?
A.
B. 169 liters
5
C.
78 liters
D.
56 liters
12 liters
The amount of water Sharon needs in liters is given by A = 12 liters
Given data ,
Sharon is making a huge batch of lemonade for her lemonade stand
Now , recipe calls for 26 pints of water
And , 6.5 pints = 3 liters
So , 1 pint = ( 3/6.5 ) liters
On simplifying the equation , we get
The amount of water in liters A = 26 pints
26 pints = 26 ( 3/6.5 ) Liters
26 pints = 12 liters
Hence , the equation is A = 12 liters
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what is the greatest three-digit positive integer n for which the sum of the first n positive integers is not a divisor of the product of the first n positive integers? (2019 amc 10a problem 9) (a) 995 (b) 996 (c) 997 (d) 998 (e) 999
The largest three-digit positive integer n for which the sum of the first n positive integers is not a divisor of the product of the first n positive integers is 995.
We have,
To solve this problem, let's consider the sum and the product of the first n positive integers separately.
The sum of the first n positive integers can be expressed as:
S = 1 + 2 + 3 + ... + n = (n(n+1))/2.
The product of the first n positive integers can be expressed as:
P = 1 x 2 x 3 x ... x n = n!.
We want to find the largest three-digit positive integer n for which S is not a divisor of P.
Since P = n! grows faster than S = (n(n+1))/2, we need to find a value of n where P is not divisible by S.
By observing the answer choices, we can start from the largest answer choice and work our way down until we find a value where P is not divisible by S.
Let's test the values of n given in the answer choices:
For n = 999:
P = 999! and S = (999(999+1))/2 = 499500.
In this case, S is not a divisor of P.
For n = 998:
P = 998! and S = (998(998+1))/2 = 498501.
In this case, S is not a divisor of P.
For n = 997:
P = 997! and S = (997(997+1))/2 = 497503.
In this case, S is not a divisor of P.
For n = 996:
P = 996! and S = (996(996+1))/2 = 496506.
In this case, S is not a divisor of P.
For n = 995:
P = 995! and S = (995(995+1))/2 = 495510.
In this case, S is not a divisor of P.
Therefore,
The largest three-digit positive integer n for which the sum of the first n positive integers is not a divisor of the product of the first n positive integers is 995.
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Find the surface area of the ff. cylinder
1.) d = 10m h = 8m
Pls give a solution and step-by-step explanation
Answer: To find the surface area of a cylinder, we need to add the areas of the top and bottom circles to the lateral surface area (the curved surface that connects the circles).
1.) Given that the diameter (d) of the cylinder is 10m and the height (h) is 8m.
First, let's find the radius of the cylinder (r):
r = d/2 = 10m/2 = 5m
Then, we can find the surface area of the cylinder:
The area of each circle is given by A = πr^2
A(top and bottom circles) = 2π(5m)^2 = 2π(25m^2) = 50πm^2
The lateral surface area is given by A = 2πrh
A(lateral) = 2π(5m)(8m) = 80πm^2
The total surface area is the sum of the areas of the top and bottom circles and the lateral surface area:
A(total) = A(top and bottom circles) + A(lateral)
A(total) = 50πm^2 + 80πm^2
A(total) = 130πm^2
Therefore, the surface area of the cylinder is 130π square meters (or approximately 408.4 square meters if you round to one decimal place).
Events A and B are independent, with P(A) = 0.25 and P(A and B) = 0.10
Answer:
Step-by-step explanation:
o.10
match the following items. 1 . circular permutation the product of all the natural numbers from an integer down to one 2 . factorial the indicated sum of the terms of an associated sequence 3 . series an order of elements of a set 4 . permutation an ordering of elements in a circle
Circular permutation refers to the ordering of elements in a circle, factorial refers to the product of all the natural numbers from an integer down to one, series refers to the indicated sum of the terms of an associated sequence, and permutation refers to the order of elements of a set. It is important to understand these terms in order to have a solid foundation in mathematics.
Circular permutation refers to an ordering of elements in a circle. Factorial, on the other hand, is the product of all the natural numbers from an integer down to one. It is denoted by the exclamation mark (!). Series, on the other hand, refers to the indicated sum of the terms of an associated sequence. Finally, permutation is an order of elements of a set.
To summarize, circular permutation refers to the ordering of elements in a circle, factorial refers to the product of all the natural numbers from an integer down to one, series refers to the indicated sum of the terms of an associated sequence, and permutation refers to the order of elements of a set. It is important to understand these terms in order to have a solid foundation in mathematics.
1. Circular permutation - an ordering of elements in a circle.
In a circular permutation, the arrangement of items is considered in a circular fashion rather than in a linear order. The number of circular permutations for 'n' elements can be calculated using the formula (n-1)!.
2. Factorial - the product of all the natural numbers from an integer down to one.
Factorial, denoted by the symbol '!', represents the product of all the positive integers from a given integer down to one. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.
3. Series - the indicated sum of the terms of an associated sequence.
A series is the sum of the terms in a given sequence, often represented by the summation symbol Σ. For example, the sum of the first 'n' natural numbers is represented as Σ(i=1 to n) i = n(n+1)/2.
4. Permutation - an order of elements of a set.
A permutation refers to the arrangement of elements in a specific order within a set. The number of possible permutations for a set of 'n' elements, taken 'r' at a time, can be calculated using the formula n!/(n-r)!.
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which two figures have the same shaded area?
The figures that have the same shaded area are Figure I and Figure IV. The correct option is A. Figure I and Figure IV
Calculating the area : Determining figures with same areaFrom the question we are to determine the figures that have the same area
Area of Figure I
Area = 12 m × 8 m
Area = 96 m²
Area of Figure II
Area = 1/2 × (12 m × 7.5 m)
Area = 45 m²
Area of Figure III
Area = π (12/2)²
Area = 3.14 × (6)²
Area = 3.14 × 36
Area = 113.04 m²
Area of Figure IV
Area = 1/2 × (6 m + 10 m) × 12m
Area = 1/2 × (16 m) × 12m
Area = 8 m × 12m
Area = 96 m²
Hence, Figure I and Figure IV have the same area
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(Chapter 13) If K(t) = 0 for all t, the curve is a straight line.
This statement is false. If K(t) = 0 for all t, it means that the curvature of the curve at any point is zero.
This does not necessarily imply that the curve is a straight line. A curve can have zero curvature at some or all points and still not be a straight line, for example, a circle. A straight line is characterized by having zero curvature everywhere, but having zero curvature does not necessarily mean that a curve is a straight line.
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Cynthia has measured the weight and miles per gallon of four different cars, listed the data in a table, and graphed the results on a scatterplot. She noticed the points fall closely on a line.
Weight, in hundreds of pounds Miles per Gallon (mpg)
5 32
10 27
12 25
15 22
Using the data values that Cynthia collected, select the correct slope and y-intercept.
Based on the data provided, we can calculate the slope and y-intercept of the line that fits the data points.
First, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). We can use the first two data points for this calculation:
m = (27 - 32) / (10 - 5) = (-5) / 5 = -1
Now, let's find the y-intercept (b) using the formula: y = mx + b. We can use the first data point (5, 32) and the slope we found:
32 = -1 * 5 + b
32 = -5 + b
b = 37
Therefore, the correct slope is -1, and the y-intercept is 37.
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Ari plays an online game that charges his debit card $16 per month. Which integer represents the change in Ari’s balance in dollars after paying to play the game for 3 months? Multiple choice question. cross out A)
Answer: The answer is A -48 dollars
Step-by-step explanation: you times 16 by 3 which make 48 and since its debt you take away so thats negative 48
Nasim invests money in an account paying a simple interest of 1. 3% per year. If he invests $70 and no money will be added or removed from the investment, how much will he have in one year, in dollars and cents?
If Nasim invests money in an account paying a simple interest of 1. 3% per year and he invests $70 and no money will be added or removed from the investment, the amount he will have in one year is 70 dollars and 91 cents
Simple interest refers to the interest that is calculated on the original amount or the principal. Simple interest is calculated by:
Interest = P * r * t
where P is the principal
r is the rate of interest (in decimal)
t is the time
Given in the question,
P = $70
r = 1.3% = 0.013
t = 1 year
Interest = 70 * 0.013 * 1
= $0.91
Amount = P + i
where P is principal
i is interest
A = 70 + 0.91
A = $70.91
The amount that Nasim has after 1 year is $70.91.
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Can someone help with this question please
The sine of the angle θ is given as follows:
sin(θ) = -16/65.
How to obtain the sine of angle θ?The trigonometric identity relating the cosine of an angle, along with the sine of the same angle, is given as follows:
sin²(θ) + cos²(θ) = 1.
In this problem, we have that cos(θ) = 63/65, hence the sine of θ is obtained as follows:
sin²(θ) + (63/65)² = 1
sin²(θ) = 1 - (63/65)²
sin(θ) = +/- sqrt(1 - (63/65)²)
sin(θ) = -16/65.
The sine has a negative sign as on the fourth quadrant, the sine is negative.
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In reference to line items, how many permutations are possible with the letters "ABC"?
So there are 6 permutations possible with the letters "ABC". These are: ABC, ACB, BAC, BCA, CAB, CBA.
Permutations are a way of arranging objects in a specific order. The number of permutations of a set of n distinct objects is given by n!, where n! denotes the factorial of n.
In the case of the letters "ABC", there are three distinct objects: A, B, and C. Therefore, the number of permutations possible with these letters is:
3! = 3 x 2 x 1 = 6
This means that there are 6 possible ways of arranging the letters "ABC" in a specific order. These permutations are:
ABC
ACB
BAC
BCA
CAB
CBA
To see why there are 6 possible permutations, consider the first position. There are three letters to choose from, so there are three possible choices for the first position. Once the first letter is chosen, there are two letters left to choose from for the second position. Finally, there is only one letter left to choose from for the third position. Therefore, the total number of permutations is:
3 x 2 x 1 = 6
In summary, the number of permutations of a set of n distinct objects is given by n!, and in the case of the letters "ABC", there are 3! = 6 possible permutations: ABC, ACB, BAC, BCA, CAB, and CBA.
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jenna borrows $8000 for college at a yearly simple interest rate of 6%. she takes 15 years to pay off the loan and interest. how much interest does she pay?
Answer: $7,200 So, Jenna pays a total of $7,200 in interest.
Step-by-step explanation:
we can multiply the yearly interest by the number of years: Total Interest = Yearly Interest × Number of Years Total Interest = $480 × 15 Total Interest = $7,200 So, Jenna pays a total of $7,200 in interest.
Answer:
Step-by-step explanation:
the interest she pays is $7,000
the total amount she pays is $15,200
the interest caclucuation:
= 6/100 × 8,000
= 0.06 × 8000
= 480
= 480 × 15
= $7200
the total amount she pays:
= $7200 +$8000
= $15,200
how do i find the missing length of a triangle the adjacent is 60
The missing length in the attached right triangle is 8.7
Find the missing length of a triangleThe missing length of a triangle can be calculated using any of the basic trigonometry function
To illustrate this, I will use the attached right triangle where the missing length is x
The value of x in the right triangle can be calculated using the following sine ratio
sin(75) = x/9
Cross multiply the equation
So, we have
x = 9 * sin(75)
Evaluate the products
x = 8.7
Hence, the value of missing length in the attached right triangle is 8.7
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What is the approximate carrying capacity of the
population?
In which year, did the population reach the carrying capacity?
About how many years did it stay at carrying capacity?
Answer:
The carrying capacity of a population refers to the maximum number of individuals that a particular ecosystem can sustainably support over the long-term. It is affected by factors such as the availability of resources like food, water, and shelter, as well as disease, predation, and other environmental factors.
The carrying capacity of a population can vary over time and depends on many different variables, including the species in question, the environment it lives in, and the management practices that are in place. Therefore, it is not possible to determine the approximate carrying capacity of a population without specific details about the particular species and ecosystem in question.
Similarly, it is impossible to determine when a population reached its carrying capacity or how long it stayed there without specific information about the population and its environment. Population data over time can help to estimate changes in population size and to understand how it may have been impacted by different factors, but a detailed analysis of the specific ecosystem and species is required to make accurate predictions about carrying capacity and population dynamics.
Step-by-step explanation:
Misha has a cube and a right-square pyramid that are made of clay. She placed both clay figures on a flat surface.
Select each box in the table that identifies the two-dimensional-plane sections that could result from a vertical or horizontal slice through each clay figure.
NEED ANSWER ASAP (THANKS)
The cube results in a square two-dimensional-plane section when slices horizontally or vertically.
The square right pyramid results in a square when sliced horizontally and a triangle when sliced vertically.
A cube has 6 faces which are all squares.
So when a cube is slice either parallel to the base or perpendicular to the base, the resulting section will be a square.
Whereas, a right square pyramid has a base square and 4 triangular faces joining at a common point.
So when the pyramid is cut vertically, it results in a triangle and when it cuts horizontally, it results in a square.
Hence the cube results in a square in either slices and right square pyramid results in a square or triangle.
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Find the exact value of sin 4π/3 using both double and half angle identities.
The exact value of sin 4π/3 using both double and half angle identities is: -¹/₂√3
How to use Trigonometric Identities?Trigonometric Identities are defined as the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle.
Using the trigonometric identity: sin 2A = 2sin A cos A
Thus:
sin 2(2π/3) = 2 sin (2π/3) cos (2π/3)
From trigonometric tables, we have:
= 2((√3)/2 * -1/2)
= -¹/₂√3
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Consider the following system of equations.
y=6x² +1
y-x²+4
Which statement describes why the system has two solutions?
Each graph has one y-intercept, which is a solution.
O Each graph has one vertex, which is a solution.
The graphs of the equations intersect the x-axis at two places.
O The graphs of the equations intersect each other at two places.
Note that the system of graphs has two y-intersects hence the two solutions. Note tht in the graph there ar etwo parabolas.
What is a y-intercept?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation meets the coordinate system's y-axis. This is done in analytic geometry using the usual convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points fulfill x = 0 because of this.
Replace x in the equation with 0 and then solve for y, keeping in mind that the y-intercept always has an associated x-value of 0. Finding the value of y at x=0 on a graph will reveal the y-intercept. The graph's intersection with the y-axis occurs at this location.
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Greg bought a jacket for $38.32, a flag for $12.25, and a glove for $12. 75. He paid $60 and the rest he borrowed from his friend. If Greg got $6.68 in change from the cashier, how much did he borrow
from his friend to pay for all the items?
Greg borrowed from his friend to pay for all the items.
Answer:
Greg borrowed $10 from his friend.
Step-by-step explanation:
[tex]38.32+12.25+12.75 = 63.32 \\ 63.32 - 60 = 3.32 \\ 3.32 + 6.68 = 10[/tex]
Write the appropriate equation
The equation of the parabola is
y = 5/3(x + 2) (x - 4)How to find the equation of the parabolaThe equation of the parabola is solved using the equation
y = a(x - r1) (x - r2)
where r1 and r2 are the roots or x-intercept
The roots of the equation is given as -2 and 4.
hence we have that
y = a(x + 2) (x - 4)
Using (-1, -3) we solve for a
-3 = a(-1 + 2) (-1 - 4)
-3 = a(1) (-5)
-3 = -5a
a = 3/5
Plugging this figure back into the original equation,
y = 5/3(x + 2) (x - 4)
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5^(x − 2) = 8 using the change of base formula log base b of y equals log y over log b.
The value of "x" in the expression 5ˣ⁻² = 8; by using the change of base formula is approximately 3.2920.
We have to find the value of "x" in the "logarithmic-expression" : 5ˣ⁻² = 8; for which we have to use the change-of-base formula, which is [tex]log_{b} (y) = \frac{log(y)}{log(b)}[/tex].
we take "log" on both sides of 5ˣ⁻² = 8;
We get,
⇒ (x-2)log(5) = log(8),
⇒ x-2 = log(8)/log(5),
By using the "change of base formula",
We get,
⇒ x-2 = log₅(8),
⇒ x-2 = 1.2920
⇒ x = 1.2920 + 2;
⇒ x ≈ 3.290,
Therefore, the value of x is approximately 3.2920.
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The given question is incomplete, the complete question is
Find the value of "x" in the expression 5ˣ⁻² = 8 . Using the change of base formula [tex]log_{b} (y) = \frac{log(y)}{log(b)}[/tex].
*Refer to image*
Pls answer I have so many SIMILAR unanswered questions for 20 brilliance too
The length of the segment VW, obtained using the relationship between similar triangles and Pythagorean Theorem is; VW = 5·√3
What are similar triangles?Similar triangles are triangles that have the same shape or in which in one of the triangles, two of the angles are congruent to two angles in the other triangle.
The common external tangent indicates that the radius WZ and XY are both perpendicular to the tangent [tex]\overline{VX}[/tex], therefore;
WZ and XY are parallel and triangles ΔVWZ and ΔVXY are similar triangles
VW/5 = VX/15
VW = 5 × (VX/15) = VX/3
ZY = 5 + 15 = 20
VY = VZ + ZY = VZ + 20
VZ = VY/3
VY = VY/3 + 20
VY - VY/3 = 20
(2/3) × VY = 20
VY = 20 × 3/2 = 30
Pythagorean Theorem indicates
VX = √(30² - 15²) = 15·√3
VX = 15·√3
VW = VX/3, therefore;
VW = 15·√3 ÷ 3 = 5·√3
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#9Change from standard form to vertex formy= -x²+4x-1
So the vector form of the equation is: y = -1(x - 2)² + 3.
To convert from standard form to vertex form, we complete the square by following these steps:
Factor out the coefficient of the x-squared term:
y = -x² + 4x - 1
= -1(x² - 4x) - 1
To complete the square inside the parentheses, add and subtract the square of half of the coefficient of the x-term (-4/2)^2 = 4:
y = -1(x² - 4x + 4 - 4) - 1
Simplify the expression inside the parentheses by factoring a perfect square:
y = -1((x - 2)² - 4) - 1
Distribute the -1 and simplify:
y = -1(x - 2)² + 3
Therefore, the vertex of the parabola is at (2, 3), and the negative coefficient of the x-squared term means that the parabola opens downwards.
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You start at (-4, 3). You move left 1 unit and right 2 units. Where do you end?
Answer:
(-3,3)
Step-by-step explanation:
left 1 = (-5,3)
right 2 = (-3,3)
Answer:
-3,3
Step-by-step explanation:
20 POINtS HELP PLEASE ASAP
Answer: B. 5.6 mi
Step-by-step explanation:
The want you to convert 9km to mi
you can multiply by conversion factors to convert
[tex]9km*\frac{1 mi}{1.61 km}[/tex] >The conversion factor is equivalent measurements. The
>measurement you want to cancel out goes on the bottom.
=5.6 mi
g if k < n - r, the value of max value(r, 0, k) should be the larger of two expressions. one of these expressions has -1 as the second parameter to maxvalue. what is it?
The larger of the two expressions is maxvalue(r, n - k - r, k).
The expression with -1 as the second parameter to maxvalue is maxvalue(n-k-r, -1, k).
To see why this is the case, let's consider the definition of maxvalue(r, a, b). This function returns the maximum value among r, a, and b.
Now, suppose that k < n - r. Then, we have:
n - k - r > n - (n - r) - r = r
This means that n - k - r is greater than r, so maxvalue(r, n - k - r, k) will return either n - k - r or k, whichever is greater.
On the other hand, since -1 is less than any non-negative integer, we have:
-1 < 0 <= r
Therefore, maxvalue(r, -1, k) will return either r or k, whichever is greater.
Since r is non-negative, we have:
maxvalue(r, -1, k) = max(r, -1, k) = max(r, k)
So, the larger of the two expressions is maxvalue(r, n - k - r, k).
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You buy one container each of strawberries,
blueberries, and cherries. Cherries are $1 more per container than blueberries, which are $1 more per container than strawberries. The product of the 3 individual prices is 5 times the total cost of one container of each fruit.
a. Write a polynomial function to model the cost of your purchase.
Answer: its 7 i took the quiz
A class of 27 students is standing in front of a Do-It-Yourself Photo Booth. "Let's get
a picture of every possible pair of us," suggested Bart. "Well, gee," answered Mandy,
"that'd be a lot of pictures." How many pictures exactly?
Answer:702
Step-by-step explanation:n*n-1
tan * 23 = 22/x. Hey
The solution of the given equation; tan 23 = 22 / x for the variable x as required is; 52.07.
What is the value of x in the given equation?It follows from the task content that the value of x in the given equation is to be determined.
Since the given equation is; tan (23) = 22 / x;
By multiplying both sides by; x / tan (23); we have that;
x = 22 / tan (23)
x = 22 / 0.4225
x = 52.07.
Ultimately, the solution of the equation for x is; 52.07.
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What is the permeter of the reepangle?
4m
4m
4m
4m
The perimeter of the rectangle is 16m
How to determine the perimeterIt is important that a rectangle has four sides, it also has four angles.
The formula for calculating the perimeter of a rectangle is expressed as;
Perimeter = 2(l + w)
Such that the parameters of the formula are;
P is the perimeter of the rectangle.l is the length of the rectangle.w is the width of the rectangle.From the information given, we have that;
Substitute the values
Perimeter, P = 2(4 + 4)
add the values
Perimeter = 2(8)
Expand the bracket
Perimeter = 16m
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