The surface area of the toy box is 712 square centimeters.
Describe Surface Area?Surface area is the measure of the total area that the surface of an object occupies. In other words, it is the sum of the areas of all the faces or surfaces of the object.
For example, consider a rectangular prism with dimensions length (l), width (w), and height (h). The surface area of this object would be the sum of the areas of all six faces, which are:
Two rectangular faces with area lw
Two rectangular faces with area wh
Two rectangular faces with area lh
So the total surface area of the rectangular prism would be:
Surface area = 2lw + 2wh + 2lh
The concept of surface area is useful in various fields, such as architecture, engineering, and physics. For example, in construction, knowing the surface area of a structure can help estimate the amount of materials needed for construction, such as paint or roofing tiles. In physics, surface area is important in determining the heat transfer and rate of reaction of a substance.
The surface area of the toy box can be found by summing the areas of its six faces. From the given net, we can see that the toy box has dimensions of 14 cm by 10 cm by 9 cm.
The top and bottom faces have areas of 14 cm × 10 cm = 140 cm² each.
The front and back faces have areas of 14 cm × 9 cm = 126 cm² each.
The left and right faces have areas of 10 cm × 9 cm = 90 cm² each.
Therefore, the total surface area is:
2(140 cm²) + 2(126 cm²) + 2(90 cm²) = 280 cm² + 252 cm² + 180 cm² = 712 cm²
Thus, the surface area of the toy box is 712 square centimeters.
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5(2 +2f)
U need to simplify this expression how do I get the answer and what is the answer pls help I’m so stuck on this
in a hurry need help on these questions
The length of the ramp is approximately 4.95 meters and the angle the ladder makes with the ground is approximately 58.21 degrees.
Solving the equationTo solve x^2 + 8x - 20 = 0 using the Zero Product Property, we first need to factor the quadratic equation into two linear factors:
So, we have
(x + 2)(x - 10) = 0
This gives
x = -2 and x = 10
The length of the rampTo find the length of the ramp, we can use the trigonometric ratio of tangent.
We know that the vertical height (opposite side) of the ramp is 1.8 meters and the angle between the ramp and the ground (angle of elevation) is 20
So, we have
tan(20) = opposite / adjacent
tan(20) = 1.8 / adjacent
This gives
adjacent = 1.8/tan(20)
Evaluate
adjacent = 4.95
Therefore, the length of the ramp is approximately 4.95 meters.
The angle with the groundWe know that the ladder is 20 feet long and reaches a point 17 feet up the wall.
Let the angle the ladder makes with the ground be θ.
Using the trigonometric ratio of sine, we have:
sin(θ) = opposite / hypotenuse
sin(θ) = 17 / 20
Taking the arc sine of both sides, we get:
θ = sin^(-1)(17/20)
Using a calculator, we get:
θ ≈ 58.21 degrees
Therefore, the angle the ladder makes with the ground is approximately 58.21 degrees.
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In a recent year, 27.4% of all registered doctors were female. If there were 42,400 female registered doctors that year, what was the total number of registered doctors?
round answer to nearest whole number
the total number of doctors that were registered was about 154,744.
In a recent year, 27.4% of all registered doctors were female. If there were 42,400 female registered doctors that year,
Let's call the overall number of licensed physicians "x". We know that there were 42,400 female registered doctors in that year, making up 27.4% of all registered doctors.
To find x, we can construct the following equation:
0.274x = 42,400
x= 42,400 ÷0.274
x ≈ 154,744
Consequently, when rounded to the nearest whole number, the total number of doctors that were registered was about 154,744.
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If the equation of the normal to the curve f (X) at the point (2,-1) is X-2 y = 4 , then f (2) =
To find the value of f(2), we need to use the equation of the normal to the curve at the point (2,-1). We know that the normal to the curve is perpendicular to the tangent at that point.
From the given equation of the normal, we can determine the slope of the tangent line, which is -1/2.
Now we can use the point-slope form of a line to find the equation of the tangent line to the curve at (2,-1): y + 1 = (-1/2)(x - 2).
To solve for f(2), we need to find the y-coordinate of the point on the curve that lies on this tangent line. We can substitute x=2 into the equation of the tangent line to find the y-coordinate: y + 1 = (-1/2)(2 - 2) => y = -1.
Therefore, f(2) = -1.
(Need help please and thank you!)
the roots are 5/2, -5/2
please help me with math i’ll give you brainlist
The length of the longer leg of a right triangle is 22cm more than six times the length of the shorter leg. The length of the hypotenuse is 23cm more than six times the length of the shorter leg. Find the side lengths of the triangle.
The length of the shorter leg is 15cm, the length of the longer leg is 6x + 22 = 6(15) + 22 = 112cm, and the length of the hypotenuse is 6x + 23 = 6(15) + 23 = 113cm.
what is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
Let's denote the length of the shorter leg by "x".
According to the problem statement, the length of the longer leg is 22cm more than six times the length of the shorter leg, so:
longer leg = 6x + 22
Also, the length of the hypotenuse is 23cm more than six times the length of the shorter leg, so:
hypotenuse = 6x + 23
Now, we know that this is a right triangle, so we can use the Pythagorean theorem to relate the side lengths:
shorter leg² + longer leg² = hypotenuse²
Substituting the expressions we found earlier, we get:
x² + (6x + 22)² = (6x + 23)²
Expanding the squared terms and simplifying, we obtain:
x² + 36x² + 264x + 484 = 36x² + 276x + 529
Subtracting 36x² + 276x + 529 from both sides, we get:
x² - 12x - 45 = 0
Now, we can solve for x by factoring the quadratic equation:
(x - 15)(x + 3) = 0
So, either x = 15 or x = -3. Since we're dealing with lengths, we discard the negative solution and take x = 15.
Therefore, the length of the shorter leg is 15cm, the length of the longer leg is 6x + 22 = 6(15) + 22 = 112cm, and the length of the hypotenuse is 6x + 23 = 6(15) + 23 = 113cm.
So the side lengths of the right triangle are 15cm, 112cm, and 113cm.
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Trigonometry dba
100 points need in 1 hour
Answer: I thank it is 200 point in 2 hour
Step-by-step explanation:
Answer all the following with work shown
I hope this helps but i am not sure about the last qn.
Remika just got a new job!
• The job pays $8.50 per hour
During the first year, every 4 months there is a 2% raise in hourly pay.
At the end of one year, how much would Remika be paid hourly, to the nearest cent?
●
Do not enter the dollar sign ($).
Answer: 9.01
Step-by-step explanation: 8.5*0.02= 0.17 *3= 0.51+8.5=9.01
Given vectors u = (8, 1) and v = (-7, -1), find the sum u + v and write the
result in component form.
According to the solution we have come to find that, The sum of the given vectors u and v is (1, 0).
What is vector?In mathematics, a vector is a mathematical object that has both magnitude (or length) and direction. It is usually represented as a directed line segment, where the length of the segment corresponds to the magnitude of the vector, and the direction of the segment represents the direction of the vector.
A vector can be specified in terms of its components or coordinates, which are typically expressed as a sequence of numbers or symbols. For example, a two-dimensional vector can be written as (x, y), where x and y are the components of the vector along the x-axis and y-axis, respectively.
To find the sum of two vectors, we simply add their corresponding components.
So, for the given vectors u = (8, 1) and v = (-7, -1), their sum u + v can be computed as:
u + v = (8, 1) + (-7, -1) = (8 - 7, 1 - 1) = (1, 0)
Therefore, the sum of the given vectors u and v is (1, 0).
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Colby’s art class is 50 minutes. She spends 21 minutes cutting paper and the rest of the time making a collage. How much time did Colby spend making her collage?
Colby spends 29 minutes making her collage.
50 is the total amount of minutes and 21 minutes is a part of that total.
This means we have to subtract.
50 - 21 = 29.
PLEASE HELP ASAP ILL GIVE BRAINLY!!!
(a) Write the quadratic regression equation that models the data. Let x = time in seconds
and let y = height in feet. Round all numbers to the nearest hundredth. (b) Use the equation to estimate the height of rocket after Show your work. 3 seconds
(a) A quadratic equation is in the form: y = -12.87x² + 42.22x + 1.18
(b) The height of the rocket after 3 seconds would be 12.01 feet.
What is a quadratic equation?A quadratic equation is a polynomial equation with a maximum degree of two. Any equation that can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation.
Here, we have
Given: A rocket is launched upwards from the ground.
(a) A quadratic equation is in the form:
y = -12.87x² + 42.22x + 1.18
(b) When x = 3 seconds
y = -12.87(3)² + 42.22(3) + 1.18
y = 12.01 feet
Hence, the height of the rocket after 3 seconds is 12.01 feet.
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{2, 4, 4, 6, 9}
mean = 5
You add one number to this set.
Which number would change the mean the most?
O 20
O 1
O 5
Answer:
O 20
Step-by-step explanation:
when you add 1 and 5 the mean only changes by a little.
but, once you add the 20 it makes your answer go up drastically which makes
O 20
your correct answer.
The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an
elephant weighs 3300 pounds on Planet A, find the elephant's weight on Planet B.
using arithmetic sum formula
Find the sum of the first 6 terms.
2,5,8,11,14,17
Therefore, the sum of the first 6 terms of this arithmetic sequence is 57.
What is arithmetic sequence?An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed constant number to the previous term. The fixed constant number is called the common difference (d) of the sequence.
Here,
To find the sum of the first 6 terms of this arithmetic sequence, we can use the arithmetic sum formula:
Sn = n/2 * [2a + (n - 1)d]
where Sn is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.
In this case, we have:
a = 2 (the first term)
d = 3 (the common difference, since each term is 3 more than the previous term)
n = 6 (the number of terms)
Substituting these values into the formula, we get:
S6 = 6/2 * [2(2) + (6 - 1)3]
= 3 * [4 + 15]
= 3 * 19
= 57
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This is due at midnight can I have some help :>
The distance between town 1 and 2 is 83 miles
What is word problem?Word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.
The distance between Town 1 and 3 is 110 miles and the distance between Town 2 and town 3 is 27miles.
Therefore the distance between town 1 and 2 is the difference between distance between town 1 and 3 and distance between town 2 and 3
This means that distance between town 1 and 2 = 110-27 = 83 miles.
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Mrs. Vo is going to put wallpaper around her daughter's rectangular bedroom over the summer. What formula is needed to find the amount of border needed?
Answer: To find the amount of border needed to put wallpaper around a rectangular bedroom, the formula for the perimeter of a rectangle is needed. The formula for the perimeter of a rectangle is:
P = 2l + 2w
where P is the perimeter, l is the length, and w is the width of the rectangle.
Step-by-step explanation:
6x2+15x=0
use the quadratic formula to solve. and describe the solution. show work
Answer: x = -2.5
Step-by-step explanation:
I think you meant 6x^2 + 15x = 0
6x^2 + 15x = 0
3x(2x + 5) = 0
2x + 5 = 0
2x = -5
x = -2.5
A small business was founded by three friends whose capital shares are: Aries-$120, Gemini-$240, and Leo-$360.
Their profit for the week reached $540. The profit will be divided in proportion to their investment.
What percent of the capital shares was invested by Leo?
Much help is needed asap!
1. Identify each premise and the conclusion in the following argument. Determine whether the argument is an example of inductive or deductive reasoning.
Our house is made of brick. Both of my next-door neighbors have brick houses. Therefore, all houses in our neighborhood are made of brick.
Premises:
Conclusion:
Inductive or deductive?
2. Use the list of equations and inductive reasoning to predict the next multiplication fact in the list:
37 × 3 = 111, 37 × 6 = 222 , 37 × 9 = 333, 37 × 12 = 444 , ....
Use inductive reasoning to determine the probable next number in the list below. An arithmetic sequence adds or subtracts a fixed amount (the common difference) to get the next term in the sequence.
5, 9, 13, 17, 21, 25, 29, .....
3. Successive Differences
Use the method of successive differences to find the next number in the sequence.
(a) 20, 31, 45, 62, 82, ... (Hint: Start with 31 - 20 = 11, use the subsequent term subtract the previous term)
(b) 8, 6, 3, 1, 2, 8, 21, ... (Hint: start with 6 - 8= -2, use the subsequent term subtract the previous term)
4. Find the sum using the special sum formula.
1 + 2 + 3 + ... + 48
5. Use the formula given on the first section to find
a) the sixth pentagonal number.
b) the eighth triangular number.
6. A vending machine accepts nickels, dimes, and quarters. Exact change is needed to make a purchase. How many ways can a person with four nickels, three dimes, and two quarters make a 30-cent purchase from the machine?
7. Ronnie goes to the racetrack with his buddies on a weekly basis. One week he tripled his money, but then lost $12.
He took his money back the next week, doubled it, but then lost $40. The following week he tried again, taking his money back with him. He quadrupled it, and then played well enough to take that much home, a total of $224. How much did he start with the first week?
8. Use inductive reasoning to determine the units digit (or ones digit):
Example: Use inductive reasoning to determine the units digit of the number
3^55 .
The question is not about giving the exact value, but rather than applying the inductive reasoning to figure out the units digit.
The units digit in base 3 are 3, 9, 7, 1, 3, 9, 7, 1, ... repeating meaning that every power that is divisible by 4 will end in 1. 56 is divisible by 4. Using this inductive reasoning 3 to the 56th power would end in a 1, then moving backward to the 55th power would give you a units digit of 7. This is inductive reasoning because we are using the smaller sample size of 4 repeating unit digits to make broad theories about all powers of 3.
Another similar approach: The units digit in base 3 are 3, 9, 7, 1, 3, 9, 7, 1, ... repeating. If the power is a multiple of four, the units digit is 1. Power 52 is a multiple of 4 and it's close to power 55.
Power 52 ends with units digit of 1, next 53 ends with 3, 54 ends with 9, and 55 ends with 7
(a) The ones digit (also called the units digit) in 2^4000 . The question is not about giving the value to the expression,
but rather than applying the inductive reasoning to figure out the units digit. The answer is just a single digit.
(b) The units digit of the number 3^41
9. Kathy stood on the middle rung of a ladder. She climbed up 2 rungs, moved down 5, and then climbed up 6. Then she climbed up the remaining 4 rungs to the top of the ladder. How many rungs are there in the whole ladder?
10. If you ask Batman’s nemesis, Catwoman, how many cats she has, she answers with a riddle: “Five-sixth of my cats plus seven.” How many cats does Catwoman have?
11. A birdhouse for swallows can accommodate up to 8 nests. How many birdhouses would be necessary to accommodate 58 nests?
12. Use the circle graph below to determine how many of the 140 students made an A or a B.
(see picture of circle graph attached below)
13. The bar graph shows the number of cups of coffee, in hundreds of cups, that a professor had in a given year.
a) Estimate the number of cups in 2004.
b) What year shows the greatest decrease in cups?
(see picture of bar graph below)
14. The line graph shows the average class size of a first grade class at a grade school for years 2001 through 2005. (see picture line graph below)
In which years did the average class size increase from the previous year?
How much did the average size increase from 2001 to 2003?
The premise is that both of my next-door neighbors and I have brick homes. So, all of the homes in our area are brick construction. A good illustration of inductive reasoning is this.
How to use equations to answer the rest?2. Given that the pattern appears to be multiplying by 3, then 6, then 9, then 12, and so on, the next multiplication fact is probably 37 x 15 = 555.
3.
(A) The number 101 comes next in the list.
(b) The following digit in the series is -10.
4. According to the formula n(n+1)/2, the first n positive integers are added together. Hence, 48(48+1)/2 = 1176 is the sum of the first 48 positive integers.
5.
(A) The formula n(3n-1)/2 yields the nth pentagonal number. Thus, 6(3x6-1)/2 = 91 is the sixth pentagonal number.
(b) The expression n(n+1)/2 yields the nth triangular number. Hence, 8(8+1)/2 = 36 is the eighth triangular number.
6. There are ten ways to use the four nickels, three dimes, and two quarters to make a 30-cent purchase from the vending machine.
7. The first week, Ronnie had $12 to his name.
8.a.The ones digit in the number 24000 is 6.
(b) 341's units digit is 3.
9. 19 rungs make up the ladder.
10. Catwoman owns 42 felines.
11. 58 nests would require 8 birdhouses, plus 2 additional nests.
12. A total of 60 pupils received an A or a B.
13.
(a) 550 cups are anticipated to be consumed in 2004.
(b) The year 2003 exhibits the biggest decline in cups.
14. Since 2001, the typical class size has risen.
15. During 2001 and 2002, as well as between 2004 and 2005, the average class size increased. From 2001 to 2003, the average class size grew by two pupils.
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Solve for s.
3s + 1 = 10
S=
Submit
Answer:
S ========================= 9
because 9+ 1= 10
simple
Answer:
s=3
Step-by-step explanation:
3s+1 = 10
To solve for s in this two step equation, we must first subtract 1 from each side.
3s+1-1 = 10-1
3s = 9
Then divide by 3 on each side.
3s/3 = 9/3
s=3
Calculate the difference between the offensive and defensive
Offensive is 81.8 and defensive is 31.57
Answer:
50.23
Step-by-step explanation:
To calculate the difference between the offensive and defensive values, we simply subtract the defensive value from the offensive value:
81.8 - 31.57 = 50.23
The difference between the offensive and defensive values is 50.23.
Does this table graph identify a linear, quadratic, or an Exponential function
X: -3, -2, -1, 0, 1
Y: 2, 8, 2, 1/2, 1/8
The table graph X: -3, -2, -1, 0, 1; Y: 2, 8, 2, 1/2, 1/8 identify an exponential function.
To determine if the function represented by this table is linear, quadratic, or exponential, we can look for a pattern in the ratios of consecutive y-values to consecutive x-values.
Ratio of (8-2)/(-2-(-3)) = 6/1 = 6Ratio of (2-8)/(-1-(-2)) = -6/1 = -6Ratio of (1/2-2)/(0-(-1)) = -3/2 = -1.5Ratio of (1/8-1/2)/(1-0) = -3/8The ratios of the consecutive y-values to consecutive x-values do not remain constant, indicating that the function is neither linear nor quadratic.Furthermore, the ratios decrease or increase depending on the direction of the movement, suggesting that the function is an exponential function.
Hence, we can conclude that the function represented by this table is an exponential function.
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Question 1 of 5
You're putting together a student poetry book and want to create it as an EPUB book that you
can read in the Books app. How can you make an EPUB book and open it in the Books app?
Identify the correct order of the following steps.
1 Create a new document using a book template.
2 Choose Copy to Books.
3 Enter EPUB information, then tap Export.
4 Tap Export, then choose EPUB.
5 Add text to the book, then tap the More button in the upper-right corner
Choose Download as ePub or Download as PDF from the Personal Books screen's export icon. The Apple Ibooks icon will say Transfer to Books when you select Open in.
What, in plain terms, are books?A book is a device for storing data in the form either writing or images. Books are often made up of several pages that are bound together and covered in reeds, parchment, vellum, or paper.
Why are books essential to our lives?Books are important in life, especially for young people. Reading books helps pupils learn more, improves their intelligence, and raises their awareness of the diverse nations and civilizations throughout the world.
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The correct order of the steps is:
1. Create a new document using a book template.
2. Add text to the book, then tap the More button in the upper-right corner.
3. Enter EPUB information, then tap Export.
4. Tap Export, then choose EPUB.
5. Choose Copy to Books to open the EPUB book in the Books app
.Your answer: To create an EPUB book and open it in the Books app, follow these steps in the correct order: 1. Create a new document using a book template. 2. Add text to the book, then tap the More button in the upper-right corner. 3. Tap Export, then choose EPUB. 4. Enter EPUB information, then tap Export. 5. Choose Copy to Books.
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Jake and carry 6 and 1/4 lb of wood in from the barn his father can carry one and five seven times as much as Jake how many pounds can Jake's father carry
Answer:
Jake's father can carry 10 and 5/7 lb of wood.
Step-by-step explanation:
Jake carried 6 and 1/4 lb of wood.
Let's convert this to an improper fraction:
6 and 1/4 = (4 * 6 + 1)/4 = 25/4
So, Jake carried 25/4 lb of wood.
Jake's father can carry 1 and 5/7 times as much as Jake.
Let's convert this to a fraction:
1 and 5/7 = (7 * 1 + 5)/7 = 12/7
So, Jake's father can carry 12/7 times as much as Jake.
To find out how many pounds Jake's father can carry, we need to multiply Jake's weight by 12/7:
Jake's father can carry = (25/4) * (12/7)
= (25 * 12) / (4 * 7)
= 300/28
= 10 and 5/7 lb (when simplified to a mixed number)
HELP ME PLEASEEE!!!!
Find the coordinates of the circumcenter of the triangle with the given vertices. R(-2,5), S(-6,5), T(-2,-1).
Answer:
the circumcenter of triangle RST is (-4, 3).
Step-by-step explanation:
To find the circumcenter of a triangle, we need to find the intersection of the perpendicular bisectors of its sides.
Let's first find the midpoints of the sides RS, ST, and RT.
Midpoint of RS:
x-coordinate = (-2 + (-6))/2 = -4
y-coordinate = (5 + 5)/2 = 5
Midpoint of RS is (-4, 5).
Midpoint of ST:
x-coordinate = (-6 + (-2))/2 = -4
y-coordinate = (5 + (-1))/2 = 2
Midpoint of ST is (-4, 2).
Midpoint of RT:
x-coordinate = (-2 + (-2))/2 = -2
y-coordinate = (5 + (-1))/2 = 2
Midpoint of RT is (-2, 2).
Now, let's find the equations of the perpendicular bisectors of RS and ST, and then find their point of intersection.
Perpendicular bisector of RS:
The slope of RS is (5 - 5)/(-6 - (-2)) = 0.
The midpoint of RS is (-4, 5).
So, the equation of the perpendicular bisector of RS is x = -4.
Perpendicular bisector of ST:
The slope of ST is (5 - (-1))/(-6 - (-2)) = -3/2.
The midpoint of ST is (-4, 2).
So, the equation of the perpendicular bisector of ST is y = (-3/2)(x + 4) + 2, which simplifies to y = (-3/2)x - 1.
Now, let's find the point of intersection of these two lines.
x = -4 for the perpendicular bisector of RS, so we substitute that into the equation of the perpendicular bisector of ST:
y = (-3/2)(-4) - 1 = 4 - 1 = 3.
Therefore, the circumcenter of triangle RST is (-4, 3).
A manufacturer sells its products to a wholesaler for $73 each. The
wholesaler then marks up those products and sells them to retailers
for $80.43. What is the wholesaler's markup rate? Round to the
nearest hundredth.
The wholesaler's markup is the difference between the selling price and the cost price, which is $80.43 - $73 = $7.43.
The markup rate can be found by dividing the markup by the cost price and multiplying by 100 to get a percentage:
markup rate = (markup / cost price) x 100%
markup rate = ($7.43 / $73) x 100%
markup rate = 10.17%
Therefore, the wholesaler's markup rate is 10.17%, rounded to the nearest hundredth.
Select the correct answer from each drop-down menu.
AABC is similar to ADEF. The ratio of the perimeter of AABC to the perimeter of ADEF is 1:10. The longest side of ADEF measures 4
The length of the longest side of AABC is
2
4
16
30
units. The ratio of the area of AABC to the area of ADEF is 1:100 v
Reset
Next
The length of the longest side of AABC is 4 units, and the area of AABC is equal to the area of ADEF.
What is angle ?An angle is the figure formed by two rays or lines that share a common endpoint, called the vertex of the angle. The measure of an angle is usually given in degrees or radians and is determined by the amount of rotation between the two rays or lines. Angles are used in geometry and trigonometry to study shapes, distances, and other properties of objects.
According to the given information:Since AABC is similar to ADEF, the corresponding sides of the two triangles are proportional. Let the longest side of AABC be x. Then:
x/4 = 1/10 (since the ratio of the perimeters is 1:10)
Solving for x, we get:
x = 4/10 * 10 = 4
Therefore, the length of the longest side of AABC is 4 units.
Since the ratio of the areas of AABC to ADEF is 1:100, and we know that the longest side of ADEF measures 4, we can use the fact that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths:
Area of AABC / Area of ADEF =[tex](x/4)^2 = 1/100[/tex]
Substituting x = 4, we get:
Area of AABC / Area of ADEF[tex]= (4/4)^2 = 1[/tex]
So, the area of AABC is equal to the area of ADEF.
Therefore, The length of the longest side of AABC is 4 units, and the area of AABC is equal to the area of ADEF.
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