The total number of ways five of them to sit in a row of chairs under the given condition is equal to 152 ways.
Use the principle of inclusion-exclusion to solve this problem.
Let us first consider the case where Alice sits next to Bob or Carla.
Now, treat Alice, Bob, and Carla as a block, which can be arranged in 3! = 6 ways.
Within this block, Alice can sit in two different positions,
And Bob and Carla can sit in the remaining two positions.
There are 6 x 2 = 12 ways for Alice to sit next to Bob or Carla.
Now,
Let us consider the case where Derek sits next to Eric.
Treat Derek and Eric as a block,
which can be arranged in 2! = 2 ways.
Within this block,
Derek can sit in two different positions,
And Eric can sit in the remaining position.
There are 2 x 2 = 4 ways for Derek to sit next to Eric.
However,
Double-counted the case where Alice sits next to Bob or Carla AND Derek sits next to Eric.
Treat Alice, Bob, Carla, Derek, and Eric as two blocks,
which can be arranged in 2! x 3! = 12 ways.
Within each block,
There are 2 ways to arrange the people.
There are 12 x 2 x 2 = 48 ways for both conditions to be satisfied.
Using the principle of inclusion-exclusion,
The total number of ways for the five of them to sit in a row of chairs under these conditions.
Total
= total number of ways - number of ways Alice sits next to Bob or Carla - number of ways Derek sits next to Eric + number of ways both conditions are satisfied
= 5! - 12 - 4 + 48
= 152
Therefore, there are 152 ways for the five of them to sit in a row of chairs under these conditions.
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Find the Area of the triangle below
Answer:20.25
Step-by-step explanation:
what enone product would you expect to obtain from intramolecular aldol condensation of 3-methylheptane dial?
The expected product from the intramolecular aldol condensation of 3-methylheptane dial is a cyclic α,β-unsaturated ketone with a seven-membered ring.
3-methylheptane dial is a 7-carbon compound with two carbonyl groups, one at each end of the molecule. Intramolecular aldol condensation occurs when one carbonyl group reacts with the other within the same molecule. The carbonyl group acts as an electrophile, while the enolate formed from the other carbonyl group acts as a nucleophile.
In the case of 3-methylheptane dial, intramolecular aldol condensation can occur between the carbonyl group at the 3-position and the enolate formed from the carbonyl group at the 6-position. The resulting intermediate undergoes dehydration to form a cyclic α,β-unsaturated ketone.
The product of the reaction will have a cyclic structure with a double bond between the α and β carbons. The exact structure of the product will depend on the stereochemistry of the starting material and the reaction conditions. However, the product is expected to have a seven-membered ring and to be an α,β-unsaturated ketone.
Therefore, the expected product from the intramolecular aldol condensation of 3-methylheptane dial is a cyclic α,β-unsaturated ketone with a seven-membered ring.
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if A shopkeeper sold a Radio at 336 rs and gain 5 persent profit find c. p
Answer:
If the shopkeeper sold the radio for 336 rs and gained a 5% profit, then the cost price (c.p.) of the radio can be calculated as follows:
Let x be the cost price of the radio. Since the shopkeeper gained a 5% profit, we can write the equation: x + 0.05x = 336 Solving for x, we get: x(1 + 0.05) = 336 x = 336/1.05 x = 320
So, the cost price (c.p.) of the radio is 320 rs.
Step-by-step explanation:
The two shorter sides of an right triangle measure 15 inches and 3 feet. What is the length of the longest side?
The two shorter sides of a right triangle measure 15 inches and 3 feet and the length of the longest side also known as the hypotenuse is 3.269557 feet.
It is given to us that the two shorter sides of a right triangle measure 15 inches and 3 feet.
Let us say that side a is 3 feet and side b is 15 inches and we need to find side c, that is the longest side also known as the hypotenuse,
A right-angled triangle is one in which only one angle is precisely 90 degrees. Since the total of all the angles in a triangle is always 180°, the other two angles will be obviously smaller than the right angle.
We define the sides of a right-angled triangle in a unique manner. The hypotenuse of a triangle is the edge that faces the right angle and is always the largest.
Pythagorean formula. Pythagoras' theorem says that: a² + b² = c². in a right triangle with cathetus a and b and with hypotenuse c.
Take the square root of both sides to find c = √(b²+a²). This Pythagorean theorem expansion can be thought of as a "hypotenuse formula."
Therefore, with this formula we can solve for hypotenuse:
side a = 15 inches = 1.3 feet
side b = 3 feet
a² + b² = c²
1.3² + 3² = c²
1.69 + 9 = c²
10.69 = c²
c = 3.269557 feet
Therefore, we can say that the two shorter sides of a right triangle measure 15 inches and 3 feet and the length of the longest side also known as the hypotenuse is 3.269557 feet.
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What property is being used in the following:
5/6 + 7/12 = 7/12 + 5/6
Answer:
Commutative property of addition
Step-by-step explanation:
The property being used in this equation is the commutative property of addition. This property states that when two numbers are added, the order in which they are added does not change the sum. So, in this case, we can rearrange the terms 5/6 and 7/12 and still get the same result.
List down three (3) equations that can be seen in the graph for each type of function and identify their
domamn and range.
constant funtion
Function,Domain,Range=
linear function
function,domain,range=
quadratic function
function,domain,range=
Three equations that can be seen in the graph for each type of function are x = -6, y = 1.5x -2.5 and y = x² + 6x + 10
How to calculate the identities and equations of the functionsFunction 1: Constant
A constant function is a mathematical function that always returns the same output value regardless of its input.
A constant function with the equation x = -6 exist on the graph with the following features: x = -6 as domain and [0, 4] as the range
Function 2: Linear
A linear function is a type of mathematical function where the output varies linearly with the input.
From the graph, we have the points
(4, 3.5) and (5, 5)
Using a graphing tool, the equation is
y = 1.5x -2.5
And the identities are [4, 5] as the domain and [3.5, 5] as the range
Function 3: Quadratic
This is a function of the form y = a(x - h)² + k or y = ax² + bx + c
From the graph, we have
(h, k) = (-3, 1) and (x, y) = (-2, 2)
Using a graphing tool, the equation is
y = x² + 6x + 10
And the identities are [-4, -2] as the domain and [1, 2] as the range
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PLEASE PLEASE HELP GIVE ME A WELL EXPLAINED ANSWER AND I WILL GIVE YOU 100 POINTS
Before a renovation, a movie theater had 140 seats. After the renovation, the theater has 171 seats. What is the approximate percentage increase of the number of seats in the theater? If necessary, round to the nearest tenth of a percent.
Answer:22.1%
Step-by-step explanation:
Calculate the surface area of the solid
I remember doing this but I don’t seem to remember sorry
Answer:
220-8pi
Step-by-step explanation:
the radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing (in mm3/s) when the diameter is 100 mm? (round your answer to two decimal places.)
The volume of the sphere is increasing at a rate of 209,439.51 mm³/s when the diameter is 100 mm
The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 100 mm? (Round your answer to two decimal places).Formula to calculate the volume of a sphere = (4/3) × π × r³where r = radius of the sphere, π = pi = 3.14, d = diameter of the sphere. The diameter of the sphere, d = 100 mm.So, the radius of the sphere, r = d/2 = 100/2 = 50 mm.
Now, we need to find the rate of change of the volume of the sphere when the radius of the sphere is increasing at a rate of 4 mm/s.We know that the volume of the sphere is given by V = (4/3) × π × r³.We have to differentiate the above formula with respect to time (t).dV/dt = d/dt [(4/3) × π × r³]dV/dt = (4/3) × π × 3r² × dr/dt, substitute r = 50 mm and dr/dt = 4 mm/s in the above equation to find dV/dt.dV/dt = (4/3) × π × 3(50)² × 4dV/dt = 209,439.51 mm³/sTherefore, the volume of the sphere is increasing at a rate of 209,439.51 mm³/s .
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I have been stuck on this/ that
The coordinates of the graph when reflected over x-axis is given as A' (7, -8) and B' (2, -3).
What are transformations?The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.
The mapping of reflection over the x-axis is depicted as follows:
(x, y) to (x, -y)
The coordinates of A and B are:
A (7, 8)
B (2, 3)
After the reflection over x-axis the coordinates are transformed as follows:
A' = (7, -8)
B' = (2, -3)
Hence, the coordinates of the graph when reflected over x-axis is given as A' (7, -8) and B' (2, -3).
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N + 2/5 = 4/5
What is “N”?
Answer:
2/5
Step-by-step explanation:
same denominator so ignore it.
2 + 2 = 4
2/5 + 2/5 = 4/5
simple way.
Write -1.1 as a mixed number.
Answer:
- 1 1/10--------------------------------
A mixed number is the number in the format a b/c, where a - whole number and b/c - the fraction part.
Show the given as a mixed number:
- 1.1 = - (1 and 0.1) = - (1 and 1/10) = - 1 1/10The hour hand of a clock is 4.5 cm long while the minute hand of clock is 5.5 cm long (Take # 3.14) What distance does the tip of the hour hand cover in twelve hours (b) What distance does the tip of the minute hand cover in one (c) Which tip covers a longer distance in (a) and (b) above and by how much
(a) The distance that the tip of the hour hand covers in twelve hours is 28.29 cm.
(b)The distance that the tip of the minute hand covers in one hour is 34.57 cm.
(c) The tip of the minute hand covers a longer distance than the tip of the hour hand by 6.28 cm.
How to find the distance the tip of the hour hand cover in twelve hours?(a) To find the distance that the tip of the hour hand covers in twelve hours, we need to calculate the circumference of the circle that the tip of the hour hand traces in twelve hours. The circumference is given by:
C = 2πr
where r is the length of the hour hand
C = 2 x 22/7 x 4.5
C = 28.29 cm
(b) Also, the distance that the tip of the minute hand covers in one hour is:
C = 2 x 22/7 x 5.5
C = 34.57 cm
(c) We can see that the distance covered by the minute hand in one hour (34.57 cm) is greater than the distance covered by the hour hand in twelve hours (28.29 cm).
difference = 34.57 cm - 28.29 cm = 6.28 cm
Thus, the tip of the minute hand covers a longer distance than the tip of the hour hand by 6.28 cm.
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Last month, the price of one pound of carrots was $2 1/12 and Joe
sold 12 1/12 pounds of carrots. This month, the price has increased
by $1 1/10and Farmer Joe only sold 5 1/8 pounds of carrots. What is
the price of a pound of carrots this month?
The price of a pound of carrots this month is $3.183.
What is the price of a pound of carrots in the month?The price of one pound of carrots last month was $2 1/12. To add $1 1/10 to this price, we need to convert both prices to twelfths of a dollar to make the addition easier.
$2 1/12 = 25/12
$1 1/10 = 11/10
Adding these two prices together gives us:
= 25/12 + 11/10
= 3.18333333333
= $3.183.
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A rope is swinging in such a way that the length of the arc is decreasing geometrically. If the the first arc is 18 feet long and the third arc is 8 feet long, what is the length of the second arc?
Explain step by step.
Geometric Sequence:
In mathematics, a sequence in which each number is multiplied by its previous term is called a geometric sequence.
The standard form of the geometric sequence is:
an=a1×rn−1Where, r = Common ratio a1= First term an=n th term
The length of the second arc is 8 feet.
The rope is swinging in such a way that the length of the arc is decreasing geometrically.
If the first arc is 18 feet long and the third arc is 8 feet long,
The length of the second arc :
In order to find the second arc length, we need to use the formula of the geometric sequence.
We have to understand what is given and what is required.
Given : First arc = 18 feet
Third arc = 8 feet.
To Find : Length of the second arc.
The formula of the geometric sequence is :
[tex]a_n[/tex] = [tex]a_1[/tex] × rn − 1
where, r = Common ratio [tex]a_1[/tex] = First term [tex]a_n[/tex] = [tex]n^{th}[/tex] term
Here, the length of the first arc is [tex]a_1[/tex] = 18.
The length of the third arc is [tex]a_3[/tex] = 8.
We have to find the length of the second arc, which is [tex]a_2[/tex]
Using the formula of the geometric sequence, we can find the [tex]a_1[/tex]: r= [tex]a_3[/tex] / [tex]a_2[/tex]
We know that [tex]a_1[/tex]= 18 and [tex]a_3[/tex]= 8
Substitute the values: r= 8 / [tex]a_2[/tex]
Now, we can rewrite the formula of the geometric sequence: an=[tex]a_1[/tex]×rn−1an= [tex]a_1[/tex] x r(n-1)
The length of the first arc is [tex]a_1[/tex] = 18 feet.
Substituting the value of r, we get:
8 / [tex]a_2[/tex] = r18 x r(n-1) = [tex]a_2[/tex]
We are given that the length of the third arc is 8 feet,
thus : 8 = 18 x r(3-1)8
= 18 x [tex]r_2[/tex][tex]r_2[/tex]
= 8 / 18[tex]r_2[/tex]
= 4 / 9r
= √(4/9)
Using this value of r, we can find the length of the second arc :
[tex]a_2[/tex] = 18 x (4/9) (2-1) [tex]a_2[/tex]
= 18 x (4/9)[tex]a_2[/tex]
= 8
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Suppose that the functions q and r are defined as follows. Find the following
The value of the function q and r are as follows (q ° r )(7) = 22 and (r ° q)(7) = 8.
What are composite functions?The process of integrating two or more functions into one function is known as composition of functions. A function is an example of labour. Take making bread as an example. Let x be the flour, let g(x) be the function that the food processor performs to prepare the dough using the flour, and let f(x) be the function that the oven does to bake the bread. The output of g(x) should be sent into the function f(x) to make bread (i.e., the prepared dough should be placed in the oven). The outcome is represented by the symbol f(g(x)), and it is made up of the functions f(x) and g. (x).
The function q and r are as follows:
q(x) = x² + 6
r(x) = √(x + 9)
The value of:
(q ° r )(x) = q(r(x))
Here, substitute the value of x in q(x) with the value of r(x):
q(r(x)) = (√(x + 9))² + 6
q(r(x)) = x + 9 + 6
Substitute x = 7:
q(r(7)) = 7 + 9 + 6 = 22
Now, (r ° q) = r(q(x))
r(q(x)) = √(x² + 6 + 9)
= √(x² + 15)
Substitute x = 7:
r(q(7)) = √(7² + 15) = √(49 + 15) = √64 = 8
Hence, the value of the function q and r are as follows (q ° r )(7) = 22 and (r ° q)(7) = 8.
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Un vêtements qui coutait initialement 100€ a vu son prix diminuer de 30% une première fois puis une deuxième fois de 20%.Quel pourcentage de réduction correspond à ces deux baisses successives?
Step-by-step explanation:
La première baisse de prix est de 30%, ce qui signifie que le prix du vêtement est maintenant de 70% de son prix initial :
Prix après la première baisse = 100€ - (30% x 100€) = 70€
Ensuite, le prix est réduit à nouveau de 20%. Cela signifie que le prix final est de 80% du prix après la première baisse :
Prix après la deuxième baisse = 70€ - (20% x 70€) = 56€
Le pourcentage de réduction totale correspond donc à la différence entre le prix initial et le prix final, exprimé en pourcentage du prix initial :
Pourcentage de réduction totale = ((100€ - 56€) / 100€) x 100% = 44%
Le vêtement a donc subi une réduction de 44% au total après les deux baisses successives de prix.
Drag the expressions into the boxes to correctly complete the table, 25 points
These are the polynomial equations:
A = x^ (1/4) - ∛x + 4√x - 8x + 16
B = 3x² - 5x⁴ + 2x - 12
C = x³ - 7x² + 9x - 5x⁴ - 20
D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1
These are the non-polynomial equations:
E = 4/x⁴ + 3/x³ - 2/x² - 1
F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1
Describe a polynomial?Polynomials are mathematical expressions that only use addition, subtraction, multiplication, and non-negative exponentiation of the variables, along with coefficients (constants that multiply with the variables), coefficients, and constants.
Some of the elements of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. An equation must always begin with the "=" sign and have terms on both sides.
Let the polynomial equations be represented by the following letters: A, B, C, D, E, and F.
In the equation, we can solve for other values to obtain:
Moreover, a polynomial equation is not an algebraic equation that has a negative exponent or an exponent that is fractional. Thus, negative exponent expressions are not polynomials.
A = x^ (1/4) - ∛x + 4√x - 8x + 16
This polynomial exists.
B = 3x² - 5x⁴ + 2x - 12
This polynomial exists.
C = x³ - 7x² + 9x - 5x⁴ - 20
This polynomial exists.
D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1
It is a polynomial.
E = 4/x⁴ + 3/x³ - 2/x² - 1
It is not a polynomial.
F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1
A polynomial is not what it is.
The polynomials are thus resolved.
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I need some help with this question!
You are building a square table. You put a diagonal support on the underside of the tabletop. The diagonal support is 3 meters long. What is a side length of the square table? Round to the nearest tenth, if necessary.
Answer:
2.1
Step-by-step explanation:all side lengths are the same (duh) use 4 and 3 (4 bc there is 4 sides). 4 as the diagonal support
4²=16
3²=9
16-9=7 then use square root for 7 the square root of 7 is 2.6457513111 or 2.1
how many extra calories would a person burn if they slowly walked (1.7 miles per hour) rather than sit for one hour?
On average, a person weighing 150 pounds can burn approximately 80 to 90 extra calories by slowly walking at a pace of 1.7 miles per hour for one hour instead of sitting.
The number of extra calories a person would burn by slowly walking instead of sitting for one hour depends on various factors, such as the person's weight, height, age, and gender. However, on average, a person weighing 150 pounds can burn approximately 80 to 90 calories by walking at a slow pace of 1.7 miles per hour for an hour.
This number may vary slightly based on individual differences and other factors, such as incline or terrain. Walking is a low-impact form of exercise that can help increase calorie burn and improve overall health, making it a great option for those looking to lead a more active lifestyle.
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Which is the cheapest + workings out, PLEASE HELP!!
The cheaper price for the 12 orchid is the 8.60 pounds for 4 orchid.
How to find the cheaper price for the 12 orchid?The cheaper price for the 12 orchid can be calculated as follows;
Therefore, for the first Orchid:
4 orchid = 8.60 pounds
12 orchid = ?
cross multiply
cost for 12 orchid = 8.60 × 12 / 4
cost for 12 orchid = 103.2 / 4
cost for 12 orchid = 25.8 pounds
For the second orchid:
5.40 pounds for each.
Now, 1 / 3 off,
Therefore,
1 / 3 ×5.40 = 1.8
Therefore,
5.40 - 1.8 = 3.6 pounds for each
Therefore,
12 orchid = 12 × 3.6 = 43.2 pounds
Therefore, the cheaper price is 8.60 pounds for 4 orchid.
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An object 60m long is drawn using a scale of 1cm to 10m. What is the length on drawing?
Using strategy 1 (in your head), divide 60m by 10m to get 6, then multiply that number by one to get 6cm. the length on drawing is 6cm
Procedure 2 (proportions)
Create a proportion first.
We know that 1 cm equals 10 metres, so we place them on a fraction (the operation is unaffected by the denominator or numerator). However, we don't know how many cm equal 10m, so we make that into a variable, in this case x.
1cm x cm
——— ———
100m 60m
Go diagonally to where the variables have already been put in to solve a proportion. You are unable to calculate 60 metres and x centimetres because you are unsure of x. Yet you can travel 60m. Start by multiplying 1 by 30 to reach the number 60. The result of multiplying 60 by 10m is x. This will equal 6.
Thus, your response is 6.
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Monica needs 12 lemons per liter of water, to make lemonade for 4 people. What amount of lemons and water does Monica need to prepare lemonade for 30 friends?
Step-by-step explanation:
12 lemons / 4 people * 30 people = 90 lemons
1 liter/ 12 lemons * 90 lemons = 7.5 liters of water
Here are four different crescent moons shapes.
1. What do Moons A,B, and C all have in common that Moon D doesn't?
2. Use numbers to describe how moons A,B, and C are different from Moon D.
The number of horizontal square of D over the number of vertical
squares = 3 : 2
What is square in math?
A planar shape with four equal sides and four right (90°) angles is referred to as a square in geometry. An equilateral rectangle is a specific sort of square, while a parallelogram is a special kind of square (an equilateral and equiangular one). All four of the sides and all four of the angles make up the regular quadrilateral known as the square. The square's angles are 90 degrees apart from each other or at right angles. The square's diagonals are also equal and split at an angle of 90 degrees.
the number of horizontal squares of A, B , and C over the number of vertical square = 2 : 3
the number of horizontal square of D over the number of vertical
squares = 3 : 2
6 : 4 = 3 : 2
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A worker at an animal shelter recorded data about the adoption of cats in the table shown below.
TIME UNTIL ADOPTION FOR CATS AT SHELTER
Time to Adopt
Age
0000
0
Based on the table, which of these statements are true? Choose all that are correct.
a
Younger than 6 Months
6 Months to 1 Year
1 Year and Older
1 to 7 Days 8 Days to 1 Month More than 1 Month
12
9
4
5
2
6
e
3
6
11
Of all the cats adopted, 34.9% are between 6 months and 1 year old
Of the cats 1 year or older, about 58% took more than 1 month to be adopted.
Of all the cats adopted, about 66% were adopted in a month or less.
C
d Of the cats that took more than a month to adopt, 12.5% were younger than 6 months
Of the cats who took 1 to 7 days to be adopted, 25% were between 6 months and 1 year old.
Based on the table provided, the statement that is true is of all the cats adopted, about 66% were adopted in a month or less.
How to calculate a percentage?To calculate a percentage, you need to divide a part by the whole and then multiply the result by 100. The formula for calculating a percentage is:
Percentage = (Part / Whole) x 100
Alternatively, if you have the percentage and the whole, you can use the following formula to find the part:
Part = (Percentage / 100) x Whole
Based on this, let's prove the true statement:
Total of animals: 58 cats
Total of cats adopted in a month or less: 38
Percentage = 38/ 58 x 100 = 65.5% which can be rounded as 66%
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Determine whether the polygons with the given vertices are congruent. Use transformations to explain your reasoning. 7. A(8, -6), B(1, -3), C(1, -9), and D(-7, 1), E(0, -2), F(0, 4) 8. J(-4, 1), K(-10, 3), L(-10, 9), M(-4, 7) and N(4, 2) O(2, -8), P(-4, -8), Q(-2, 2)
(7) The two polygons are congruent since we can obtain a congruent image of DEF by applying a translation or a rotation.
(8) The two polygons are congruent since we can obtain a congruent image of JKLM by applying a translation or a rotation.
What is the translation or a rotation of the polygons?
To determine whether the two polygons are congruent, we can apply a series of transformations to one of them to see if it can be mapped onto the other.
(7) Let's first label the polygons: ABCD is the first polygon and DEF is the second polygon.
Translation: We can translate DEF four units to the right and two units down to obtain the image of DEF, which is congruent to ABCD.
Rotation: We can rotate DEF about the point (0, 1) by 180 degrees to obtain the image of DEF, which is congruent to ABCD.
Since we can obtain a congruent image of DEF by applying a translation or a rotation, we can conclude that the two polygons are congruent.
(8) Let's label the two polygons: JKLM is the first polygon and NOPQ is the second polygon.
Translation: We can translate JKLM six units to the right and three units down to obtain the image of JKLM, which is congruent to NOPQ.
Rotation: We can rotate JKLM about the point (-4, 4) by 180 degrees to obtain the image of JKLM, which is congruent to NOPQ.
Since we can obtain a congruent image of JKLM by applying a translation or a rotation, we can conclude that the two polygons are congruent.
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Bo and Erica are yoga instructors. Between the two of them, they teach 43 yoga classes each week. If Erica teaches 11 fewer than twice as many as Bo, how many classes does each instructor teach per week?
Answer:
Erica teaches 32.33 or 32 classes
Bo teaches 10.67 or 10 classes
Step-by-step explanation:
B + E = 43
E - 11 = 2B
B + E = 43
E = 43 - B
E - 11 = 2B
(43 - B) - 11 = 2B
B = 10.67 = 10
B + E = 43
(10.67) + E = 43
E = 32.33 = 32
The diagonal of a square is 10 inches long. What is the length, in inches, of each side of the square? Write the answer in simplified radical form.
The length of each side of the square is 5√2 inches
The diagonal of a square divides it into two 45-45-90 right triangles. In such triangles, the hypotenuse (which is the diagonal of the square) is √2 times as long as each leg. Let x be the length of each side of the square. Then we have
x√2 = 10
Solving for x, we get
x = 10 /√2
To simplify this expression, we can multiply both the numerator and denominator by √2
x = 10 /√2 × √2 /√2
Multiply the numbers
= 10√2 / 2
Divide the numbers
= 5√2 inches
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A banner is centered between two poles by four ropes of equal length. The dimensions of the banner ground and poles are shown what is the length of one of the ropes x to the nearest foot
The length of one of the ropes is approximately 10.77 feet when rounded to the nearest foot.
Let's call the distance between the poles "d" and the height of the poles "h". We can use the Pythagorean theorem to find the length of the ropes:
If we draw a diagram, we can see that the four ropes form the hypotenuses of four right triangles. Each right triangle has a base of d/2 and a height of h - (banner height)/2.
Therefore, we have:
[tex]x^2[/tex] = [tex](d/2)^2[/tex] + [tex](h - (banner height)/2)^2[/tex]
Substituting the given values, we get:
[tex]x^{2}[/tex] = [tex](20/2)^2[/tex]+ [tex](16 - (8/2))/2)^2[/tex]
[tex]x^{2}[/tex]= 100 + [tex](8/2)^2[/tex]
[tex]x^{2}[/tex] = 100 + 16
[tex]x^{2}[/tex] = 116
Taking the square root of both sides, we get:
x = [tex]\sqrt{116}[/tex]
x ≈ 10.77
Therefore, the length of one of the ropes is approximately 10.77 feet when rounded to the nearest foot.
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would this relationship best be described as proportional or non proportional? justify your answer
the relationship between the diameter of the pizza and its cost per square inch is non-proportional.
The relationship between the diameter of the pizza and its cost per square inch is non-proportional.
If the relationship were proportional, then the cost per square inch of the pizza would remain constant as the diameter changes. However, in this case, we see that as the diameter of the pizza increases, the cost per square inch decreases. This is because the area of a circle increases more rapidly than its diameter, so the cost must be spread out over a larger area, resulting in a lower cost per square inch.
Therefore, the relationship between the diameter of the pizza and its cost per square inch is non-proportional.
the complete question is :
would relationship between the dilation factor k and the resulting volume of a solid best be described as proportional or non proportional? justify your answer
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