Answer:
circumference = 8 inches
Step-by-step explanation:
75% = 75/100 = 3/4
Let C be the circumference
3/4 C = 6
Multiply both sides by 4/3
C =
Y=4x^2;estimate dy/dx x=2
Answer:
Below
Step-by-step explanation:
y = 4x^2
dy/dx = 8x
at x = 2 this is 16 <===== not sure what they mean by 'estimate' !
PLEASE HELP PLEASE ASAP PLEASE HELP
What are the coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin?
The coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin are R' (2, 1), S' (4, 2), T' = (5, 4), and U' = (3, 3).
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise to the vertices of triangle RSTU, the coordinates of the vertices of the image are as follows:
(x, y) → (-y, x)
Ordered pair R = (1, -2) → Ordered pair R' = (-(-2), 1) = (2, 1).
Ordered pair S = (2, -4) → Ordered pair S' = (-(-4), 2) = (4, 2).
Ordered pair T = (4, -5) → Ordered pair T' = (-(-5), 4) = (5, 4).
Ordered pair U = (3, -3) → Ordered pair U' = (-(-3), 3) = (3, 3).
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The newborn baby, Jake, needs some supplies. Jake’s mom gave you this list of things he needs. You and your friend have agreed to spend $115 of the $300 on Jake. You spend 15% of it on a new blanket, 25% of it on toys, and 40% of it on clothes. How much money do you have left to spend on diapers for Jake?
Things for Jake
Diapers
Blanket
Clothes
Toys
You have $28.75 left to spend on diapers for Jake.
What is the percentage?
Percentage refers to a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, if 30 out of 100 students in a class are girls, the percentage of girls in the class is 30%. Percentages are commonly used in many fields, such as finance, statistics, and science, to express proportions, rates, and changes over time.
The total percentage of money spent on the blanket, toys, and clothes is 15% + 25% + 40% = 80%.
Therefore, the amount of money spent on Jake's supplies is $115, which is 80% of the total budget. We can set up the equation:
0.8x = 115
Solving for x, we get:
x = 115 ÷ 0.8 = $143.75
So, the total budget for Jake's supplies is $143.75.
To find out how much money is left for diapers, we need to subtract the amount spent on blanket, toys, and clothes from the total budget:
$143.75 - 15% of $143.75 - 25% of $143.75 - 40% of $143.75
= $143.75 - $21.56 - $35.94 - $57.50
= $28.75
Therefore, you have $28.75 left to spend on diapers for Jake.
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Figure ABCD is reflected across the x-axis. What are the coordinates of A′, B′, C′, and D′? Enter your answer by filling in the boxes. A′ (−1, −4) B′ (, ) C′ (−5, −4) D′ (−4, −2)
The coordinates of A′, B′, C′, and D′ for the reflection across the x-axis is given as: A'(2, -3), B'(5, -5), C'(7, -3), and D'(5, -2).
Explain about the reflection across the x-axis?One of the many transformations we can do on a geometric figure is reflection. By using an axis of symmetry, the original position is reversed.The x-coordinate remains constant when a point is reflected across the x-axis, but still the y-coordinate is assumed to correspond to the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).A(2, 3) ⇒ A'(2, -3),
B(5, 5) ⇒ B'(5, -5),
C(7, 3) ⇒ C'(7, -3),
D(5, 2) ⇒ D'(5, -2).
Thus, the coordinates of A′, B′, C′, and D′ for the reflection across the x-axis is given as: A'(2, -3), B'(5, -5), C'(7, -3), and D'(5, -2).
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The correct question is-
Figure ABCD is reflected across the x-axis. What are the coordinates of A′, B′, C′, and D′?
The figure is attached.
Find the area of the shaded region shown below and choose the appropriate result.
A 48 in²
B 96 in²
C 92 in²
D 144 in²
[tex]A = 9(12) - 4^{2} = 108 - 16 = \bf 92 \ in^{2}[/tex]
Latanya needs to order some new supplies for the restaurant where she works. The
restaurant needs at least 739 glasses. There are currently 390 glasses. If each set on
sale contains 6 glasses, which inequality can be used to determine x, the minimum
number of sets of glasses Latanya should buy?
A. 739 6x + 390
B. 390x+6739
C.390x+6> 739
D. 739 2 6x +390
Submit Answer
The inequality that can be use to represent the situation is 390 + 6x ≥ 739.
How to represent expression with inequality?Latanya needs to order some new supplies for the restaurant where she works. The restaurant needs at least 739 glasses. There are currently 390 glasses. Each set on sale contains 6 glasses.
Therefore, the inequality that can be used to determine x, the minimum number of sets of glasses Latanya should buy can be calculated as follows:
Hence,
390 + 6x ≥ 739
where
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11. You place $4,000.00 in a bank account with an interest rate of 5.25% APR and another $2,000.00 in an account with an interest rate of 6.00% APR. after 6 months, what is the difference in interest that the accounts earn?
Answer:
$45
Step-by-step explanation:
I = prt
I = interest earned
p = principal = amount invested
r = interest rate; 5.25% = 5.25/100 = 0.0525
t = time in years; 6 months = 0.5 years
$4,000.00 at 5.25% interest
I = 4000 × 0.0525 × 0.5 = 105
$105 interest in 6 months
$2,000.00 at 6.00% interest
I = 2000 × 0.06 × 0.5 = 60
$60 earned in 6 months
$105 - $60 = $45
The difference is $45.
Find the volume of a sphere whose radius is 20.8 centimeters. Leave your answer in form.
π cm³
Type the answer in terms of pi by putting the number BEFORE pi in the box, rounded to the nearest thousandth.
For example, "47" would look like 4
V=
H
Answer: its really simple the answer is 478cm^3
Step-by-step explanation:
Answer:
478cm^3
Step-by-step explanation:
Faster please!! thank u!! If the length of side DF = 4 ft., what is the length of side GH?
The length of GH on the triangle is 12 units
How to determine the length of GHFrom the question, we have the following parameters that can be used in our computation:
The similar triangles
Assuming that
The smaller triangle with length DF gives the larger triangle with length GH
This means that
GH = 3 * DF
Substitute the known values in the above equation, so, we have the following representation
GH = 3 * 4
So, we have
GH = 12
Hence, the length is 12 units
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Answer:
12 ft
Step-by-step explanation:
keep it simple, just givin' the answer :)
Help what is the answer
The the estimated answer is 42 and the actual answer is 41.91. The answer 41.91 is very close to the estimated answer of 42, so it looks sensible.
How to answer the question on estimateWhen rounding to one significant figure, we keep only the leftmost digit that is not zero. Therefore, rounding 33.72 and 8.19 to one significant figure gives 34 and 8 respectively so the estimated answer is;
34 + 8 = 42
Actual answer answer is derived as;
33.72 + 8.19 = 41.91
In conclusion, the estimated answer is 42 and the actual answer is 41.91. The answer 41.91 is very close to the estimated answer of 42, so it looks sensible.
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The mango mania drinks company has a new design for the juice boxes. Each box will have a square base of an area of 22 cm². The height will be 12 cm. What is the volume of one of these new juice boxes.
By answering the supplied question, we may infer that the response is square Because 1 cm³ = 1 mL, one of the new juice cartons has a capacity of 264 cubic centimeters or 264 milliliters.
What is a square?
According to Euclidean geometry, a square is an equilateral quadrilateral having four equal sides and four equal angles. It is sometimes referred to as a rectangle with two adjacent sides of the same length.
A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are those that are 90 degrees or straight.
The diagonals of the square are also equally spaced and divided at a right angle. a nearby rectangle with two sides of identical length.
a quadrilateral with four equal-length sides and four right angles. two neighboring, equal sides that create a right angle in a parallelogram. an equilateral rhombus.
By dividing the base area by the height, one may get the volume of a square-based box. Thus, we can use the following formula to determine the juice box's volume:
Volume equals base area times height.
We may enter the numbers 22 cm² for the base area and 12 cm for the height into the formula to obtain the following results:
Volume equals 22 x 12 cm²
These values are multiplied together to produce:
Size = 264 cm³
Hence, Because 1 cm³ = 1 mL, one of the new juice cartons has a capacity of 264 cubic centimeters or 264 milliliters.
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Answer this composite function:
Answer:
-21
Step-by-step explanation:
given
To evaluate (h.g(5)), we first need to find g(5) and then apply h to the result.
g(x) = 4x + 3, so g(5) = 4(5) + 3 = 23.
Now we apply h to g(5):
h(g(5)) = h(23) = -(23) + 2 = -21
Therefore, (h.g(5)) = -21.
Answer:
Step-by-step explanation:
To find (h o g)(5), we need to first find g(5), and then evaluate h at that value.
We are given that g(x) = 4x + 4, so we can find g(5) by substituting x = 5:
g(5) = 4(5) + 4 = 24
Now we evaluate h at g(5):
h(g(5)) = h(24)
We know that h(x) = -x + 2, so we can evaluate h(24) by substituting x = 24:
h(g(5)) = h(24) = -(24) + 2 = -22
Therefore, (h o g)(5) = -22.
Draw a triangle with an area of 21 square units in a coordinate plane where the vertices are not all in the same quadrant?
The graph of the triangle is on the image at the end.
How to draw the triangle?Remember that the area of a triangle of base B and height H is:
A = B*H/2.
Here we want to have an area of 21, then we can use:
B = 6
H = 7
Then:
A = 6*7/2
A = 3*7 = 21
So we must have a base of 6 units and a height of 7 units, then the vertices that we can have are:
(-3, 0), (3, 0), (-3, 7)
So we will have a right triangle such that the vertices are on the first and second quadrant, the graph of the vertices is below.
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Please anyone help me with this ?!!! Thank you:))!!
The solution is, he had 68 marvels.
What is addition?
Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
given that,
he added 36 marvels, now, he has 104 in total,
we have to find that, how many he had.
let, he had = x
so, we know, added = 36
i.e. now total is = x+36
ATQ, we get,
x+36 = 104
or, x = 104 - 36
or, x = 68
Hence, The solution is, he had 68 marvels.
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Four transformations of the function ()
f
(
x
)
are given below.
For each transformation, drag the graph that shows the result of that transformation into the box under it.
On a coordinate plane, a line f goes through (0, 1) and (1, negative 1).
CLEAR CHECK
On a coordinate plane, a line f begins at the top of the second quadrant, extends downward toward the fourth. The line is shifted 4 units to the right.
On a coordinate plane, a line f begins at the top of the second quadrant, passes through (0, 1), and extends toward the bottom of the fourth. The line is shifted 4 units up.
On a coordinate plane, a line f begins at the top of the second quadrant, goes through (0, 1), and extends toward the bottom of the fourth. The line is shifted 4 units down.
On a coordinate plane, a line f begins at the top of the second quadrant and extends toward the bottom of the fourth. The line is shifted 4 units to the left.
On a coordinate plane, a line f begins at the top of the second quadrant, passes through (0, 1), and extends toward the bottom of the fourth. The line is shifted 3 units up.
()=(−4)
m
(
x
)
=
f
(
x
-
4
)
()=()−4
n
(
x
)
=
f
(
x
)
-
4
()=(4+)
p
(
x
)
=
f
(
4
+
x
)
()=4+()
q
(
x
)
=
4
+
f
(
x
)
On a coordinate plane, a line f begins at the top of the second quadrant, passes through (0, 1), and extends toward the bottom of the fourth. The line is shifted 5 units down.
NEXT
CLOSE
Reference
calculator
formulas
glossary
CLOSE
Language
Changes the language of the audio snippets and the glossary
ENGLISH
Answer:
Step-by-step explanation:
300000000000000000000000000
Three right triangles surround a shaded triangle; together they form a rectangle measuring 12 units by 14 units. The figure below shows some of the dimensions but is not drawn to scale. Is the shaded triangle a right triangle?
Answer:
To determine whether the shaded triangle is a right triangle, we need to use the fact that the three right triangles together form a rectangle.
Let's label some of the dimensions as shown in the diagram:
[asy]
unitsize(0.25cm);
pair A = (0,0), B = (10,0), C = (8,6), D = (6,0), E = (8,0), F = (10,6), G = (8,2);
draw(A--B--F--C--cycle);
draw(D--E);
draw(C--G);
label("$10$", (A+B)/2, S);
label("$6$", (C+F)/2, N);
label("$8$", (B+E)/2, E);
label("$2$", (C+G)/2, E);
label("?", (D+G)/2, NE);
label("$?$", (G+E)/2, S);
fill(C--G--D--cycle, gray(0.7));
[/asy]
The dimensions of the rectangle are 12 units by 14 units, so we know that:
\begin{align*}
10 + 8 &= 18 \\
6 + 2 + ? &= 14
\end{align*}
Simplifying the first equation, we get $8 = 14 - 6$. Substituting this into the second equation, we get:
$$2 + ? = 8$$
Therefore, the length of the shaded side of the triangle is 6 units. Now we can use the Pythagorean theorem to determine whether the shaded triangle is a right triangle. Letting $x$ be the length of the other leg of the shaded triangle, we have:
\begin{align*}
x^2 + 6^2 &= 8^2 \\
x^2 + 36 &= 64 \\
x^2 &= 28 \\
x &= 2\sqrt{7}
\end{align*}
Since $2\sqrt{7}$ is not an integer, we can conclude that the shaded triangle is not a right triangle.
(-2,-3), m=0
How do you get to -3
Answer:
y = -3
Step-by-step explanation:
You want the equation of a line with slope 0 through the point (-2, -3).
Point-slope formThe point-slope form equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
Adding k to both sides gives the "y =" form ...
y = m(x -h) +k
ApplicationWhen m=0 and (h, k) = (-2, -3), this becomes ...
y = 0(x -(-2)) + (-3)
y = -3 . . . . . . simplified
__
Additional comment
Anything times 0 is 0. So, the product 0(x +2) is 0.
Anything added to 0 is unchanged. So, the sum y = 0 -3 is y = -3.
When the slope is zero we get y= -3.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
As, the Point-slope form
The point-slope form equation for a line with slope m through point (h, k) is
y = mx + b
When m=0 and (h, k) = (-2, -3)
y = 0(x -(-2)) + (-3)
y = -3
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Eight students in Ms. Reese's class decided to purchase their textbook from two different sources. Some of the students purchased the textbook from the colleg
bookstore for $16.50. The rest of the students purchased the textbook from an online discount store for $11.00 per book. If the total amount spent by the eight
students is $121.00, how many students purchased the book online?
students purchased the book online.
If the total amount spent by the eight students in Ms. Reese's class is $121.00, using a system of equations, the number that purchased from the:
College Bookstore = 6Online = 2.What is a system of equations?A system of equations is two or more equations solved at the same time or concurrently.
It is also known as simultaneous equations.
The total number of students in Ms. Reese's class who decided to purchase their textbook from two different sources = 8
The unit cost per textbook from the college bookstore = $16.50
The unit cost per textbook from an online discount store = $11.00
The total spending by the eight students = $121.00
Let the number of students who purchased from the college bookstore = x
Let the number of students who purchased from an online discount store = y
Equations:x + y = 8 …Equation 1
16.5x + 11y = 121 …Equation 2
Multiply Equation 1 by 11:
11x + 11y = 88 …Equation 3
Subtract Equation 3 from Equation 2:
16.5x + 11y = 121
-
11x + 11y = 88
5.5x = 33
x = 6
Substitute x = 6 in either equation:
x + y = 8
6 + y = 8
y = 2
Thus, 6 students purchased their textbooks from the college bookstore while 2 purchased online.
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The three oldest children need shoes. You find a store that has shoes on sale. All shoes in the store are marked $10 per pair. You have a choice of “Three for the price of two” or “Buy one and get 25% off the second.” Which of these is the best deal? Explain your reasoning.
Pls help I’m not sure about this data
Answer: D - The mean of the date is greater than the median
Step-by-step explanation:
First, you line all the numbers up from least to greatest:
25, 26, 31, 33, 38, 39, 48, 58
Next, you find the median, or in this case, 35.5
Now you find the mean, and do that by adding all the numbers up (298) and then divide that by the number of people, or 8, which would be 37.25
Thus, the mean is greater than the median
Answer:
D
Step-by-step explanation:
Original data set:
25, 26, 31, 39, 33, 56, 38, 48
Data in increasing order:
25, 26, 31, 33, 38, 39, 48, 56
mean = (25 + 26 + 31 + 39 + 33 + 56 + 38 + 48)/8 = 37
median = (33 + 38)/2 = 35.5
mode = no mode
Answer: D
A cat adoption facility takes in an average of 6 cats per day. The facility has to keep their cat occupancy below 300. Currently, the facility has 258 cats. If none of their cats get adopted, how many more days, x, can the facility continue to take in cats? Select the inequality that includes the largest number of days this facility can continue to take in cats without exceeding its occupancy limit.
A. x < 5
B. x < 7
C. x < 42
D. x < 36
The highest number of days this institution can continue to accept cats without going over its allowed occupancy is included in the inequality (C) x<42.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
The majority of the time, size comparisons between two numbers on the number line are made.
In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other.
Hence, inequality emerges from a lack of balance.
So, what we can do is add 6 in 285 till it reaches 300.
258 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 300
6 is added 7 times, then:
6*7 = 42
Then the correct inequality would be x < 42.
Therefore, the highest number of days this institution can continue to accept cats without going over its allowed occupancy is included in the inequality (C) x<42.
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Can you solve this for me I’m stuck?
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{65}~,~\stackrel{y_1}{149})\qquad (\stackrel{x_2}{105}~,~\stackrel{y_2}{221}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{221}-\stackrel{y1}{149}}}{\underset{\textit{\large run}} {\underset{x_2}{105}-\underset{x_1}{65}}} \implies \cfrac{ 72 }{ 40 } \implies \cfrac{ 9 }{ 5 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{149}=\stackrel{m}{ \cfrac{ 9 }{ 5 }}(x-\stackrel{x_1}{65})\implies y-149=\cfrac{ 9 }{ 5 }x-117 \\\\\\ y=\cfrac{ 9 }{ 5 }x-117+149\implies \boxed{y=\cfrac{ 9 }{ 5 }x+32} \\\\\\ \stackrel{\textit{Celsius is 70, so x = 70}}{y=\cfrac{ 9 }{ 5 }(70)+32}\implies \boxed{y = 158}[/tex]
The function f is graphed below. Determine the intervals on which f is increasing and decreasing.
The function is decreasing on the interval -6 < x < 0
increasing on the interval 0 < x < 4, and increasing on 4 < x < 9
solve the system 2xy+3=4y 3xy+2=5y
The solution to the system 2xy+3=4y 3xy+2=5y is (x, y) = (22/5, -30/29).
How to solve the system equation?Starting with the first equation:
2xy + 3 = 4y
We can rearrange it to solve for one of the variables in terms of the other:
2xy - 4y = -3
2y(x - 2) = -3
y = -3/(2(x - 2))
Now we can substitute this expression for y into the second equation:
3x(-3/(2(x - 2))) + 2 = 5(-3/(2(x - 2)))
Multiplying both sides by 2(x - 2) to clear the fraction:
-9x + 4(x - 2) = -30
-9x + 4x - 8 = -30
-5x = -22
x = 22/5
Now we can use this value of x to solve for y:
y = -3/(2(22/5 - 2))
y = -30/29
Therefore, the solution to the system is (x, y) = (22/5, -30/29).
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why does it make sense to arrange the twelve 1 tiles in 3 rows of 4 instead of any other arrangement of twelve 1 tiles, such as 2 rows of 6?
Arranging the twelve 1 tiles in 3 rows of 4 instead of any other arrangement of twelve 1 tiles, such as 2 rows of 6, makes sense because it allows for more flexibility and creativity in exploring mathematical concepts and creating visual representations.
What is arrangement?An arrangement is a way of organizing or arranging a set of objects in a specific order or sequence.
When arranging the tiles in 3 rows of 4, there are more possible ways to create rectangular arrays using the tiles. For example, you could create a 4x3 array, a 3x4 array, a 2x6 array, a 6x2 array. These different arrays can be useful in a variety of mathematical contexts, such as exploring multiplication and division.
Therefore, arranging the twelve 1 tiles in 3 rows of 4 instead of any other arrangement of twelve 1 tiles, such as 2 rows of 6, makes sense because it allows for more flexibility and creativity in exploring mathematical concepts and creating visual representations.
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Core Assessment 35. Choose all the expressions that have as a product. 0 1/2 x 1/1/201 17/10 × 1/100 X 07/3 × 19/0 3 01 × 1/2 36. i need this by tonight pls help me i will give u 30 pionts
The ratio of the number of bar magnet to horse shoe magnet is 2 to 5. If there are 10 bar magnets, find the number of horse shoe magnets? Explain your answer
Answer:
25 horse shoe magnets
Step-by-step explanation:
What is a ratio?A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
If the ratio is 2: 5 (bar magnet: horse shoe magnet) then we can use this ratio to solve for how many horse shoe magnets there are if there are 10 bar magnets.
10: ?To solve for '?', we can use this expression:
5 × 5 = 25Why do we multiply by 5?We multiply by 5 because in order to go from 2 to 10 (2: 5, 10: ?), we multiply the 2 by 5.
Therefore, for every 10 bar magnets, there are 25 horse shoe magnets.
work out the size of angle x
The measurement of angle x in the given figure is 11°
What is an angle?An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes.
Given is a figure, we need to find the measure of angle x,
The labeled figure is attached,
We have,
∠ 1 = 85° [vertically opposite angles]
∠ 3 = 96° [corresponding angles between parallel lines]
∠ 2 + ∠ 3 = 180° [linear pair angles]
∠ 2 = 180°-96°
∠ 2 = 84°
Now,
∠ 1 + ∠ 2 + x = 180° [angles sum property of a triangle]
85° + 84° + x = 180°
x = 180°-169°
x = 11°
Hence, the measurement of angle x in the given figure is 11°
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Find the inverse of the function f(x)=√x+3.
Answer:
The inverse of the function is
[tex]f^{-1} (x)=x^2-3[/tex]
Step-by-step explanation:
Given
[tex]f(x)=\sqrt{x+3}[/tex]
Find the inverse.
Write the function as an equation equal to [tex]y[/tex].
[tex]y=\sqrt{x+3}[/tex]
Interchange the variables.
[tex]x=\sqrt{y+3}[/tex]
Square both sides of the equation.
[tex]x^2=y+3[/tex]
Subtract [tex]3[/tex] from both sides of the equation.
[tex]y=x^2-3[/tex]
Replace [tex]y[/tex] with [tex]f^{-1} (x)[/tex].
[tex]f^{-1} (x)=x^2-3[/tex]
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The perimeter of a rectangular fence is to be at least 82 feet and no more than 124 feet. If the width of the fence is 14 feet, what is the range of values for the length of the fence?
The range of values for length when the perimeter is between 82 feet and 124 feet is: 27 ≤ l ≤ 48
What is meant by perimeter?A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter. The perimeter of the shape can be calculated by summing the measurements of its sides and edges. A rectangle's perimeter is equal to twice the product of its length and width.
Given a rectangular fence.
The perimeter P is at least 82 feet and is no more than 124 feet.
82 ≤ P ≤ 124
The width is 14 feet.
The range of values of the length is to be found.
Now,
Perimeter of rectangle = 2( length + width)
The lowest value of the perimeter is 82
82 = 2(l + 14)
82 = 2l + 28
54 = 2l
l = 27
The highest value of perimeter is 124
124 = 2(l + 14)
124 = 2l +28
96 = 2l
l = 48
Therefore the range of values for length when the perimeter is between 82 feet and 124 feet is:
27 ≤ l ≤ 48
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