By using the induction, the equation 1+ 4 + 9 + ...........+n² = n(n-1)(2n-1)/6 where n ≥ 1 is proved.
The term induction in math is defined as a technique of proving a statement, theorem or formula which is thought to be true, for each and every natural number n.
In this case, we want to use induction to prove the equation:
=> 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1)/6 for all integers n ≥ 1.
To start the induction proof, we first prove that the statement is true for the base case n = 1.
The left side of the equation is 1, and the right side is
=> 1 * (1 + 1) * (2 * 1 + 1) / 6 = 1 * 2 * 3 / 6 = 1,
so the equation is true for n = 1.
Next, we assume that the equation is true for some integer k, where k ≥ 1. This means that:
=> 1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1)/6.
Now, we use this information to prove that the statement is true for k + 1. The left side of the equation for k + 1 is:
=> 1 + 4 + 9 + ... + k² + (k + 1)².
This is equal to k(k + 1)(2k + 1)/6 + (k + 1)² by the induction hypothesis.
The right side of the equation for k + 1 is:
=> (k + 1)(k + 2)(2k + 3) / 6.
We can simplify this to:
=> (k² + 3k + 3) * (k + 2) / 6 = (k² + 3k + 3)(k + 2) / 6.
Finally, we need to show that these two expressions are equal:
=>k(k + 1)(2k + 1)/6 + (k + 1)² = (k² + 3k + 3)(k + 2) / 6.
Expanding both sides and cancelling common terms, we find that:
=> k³ + 3k² + 2k + k² + 3k + 3 = 2k³ + 9k² + 12k + 6.
This shows that the equation is true for k + 1, and by induction, it is true for all integers n ≥ 1.
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Quetion: Billy collect action figure, but cannot remember how many he own. A) When he put them into group of 7, there would be 4 leftover. B) When he put them into group of 3, there would be 2 leftover. C) When he did group of 2, there wa 1 left out. D) Billy know that the number of action figure in hi collection i between 20 and 61. How many action figure doe he own?
Starting with condition D
What is action figure?
This is the most famous action figure of all-time, and with good reason. The G.I. Joe started it all as the very first action figure, debuting with many different styles and accessories. During its almost 50 year run, the toy line has expanded from just one “Real American Hero” to an entire team.To make a figure, download the Hasbro Pulse app, scan your face, customize the action figure and hairstyle, and wait until the postman brings you the coolest thing you've ever seen: Yourself, but tiny and in plastic. Your face can be added to characters from GI Joe, Ghostbusters, Power Rangers and others.1:12 is by far the most popular scale for action figures. It also creates the most confusion with 1:6 scale figures. 1:12 figures work under the assumption that 6 inches is 6 feet tall. So if you're looking for a 6-inch scale figure, you want 1:12, NOT 1:6.To learn more about action figure refers to:
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If sides of a triangle are a = 3, b = 6, and c = 7, then what is the altitude of the triangle?
The triangle is 2.98142 meters high.
Explain about the altitude of the triangle?The height of a triangle is the perpendicular tracing from one side to the other of the triangle. The height of the triangle is also referred to as the altitude, which joins the base to form a right-angle triangle.
The formula h = xy, where x and y are the bases of the two analogous triangles formed when the height of the right triangle is drawn from one vertex to its hypotenuse, can be used to determine the altitude of a right triangle.
A line segment connecting a triangle's vertex to its opposite side is known as the triangle's altitude. In relation to the base or the side it touches, it is perpendicular. It is possible to draw three altitudes in a triangle because it has three sides. The Orthocenter is the location where the three heights of a triangle intersect.
s = a + b +c\2
hb = √ -a4 +2(ab)² + 2 (ac)² - b4 +2 (bc)² - c4/2b
=√-3 4 +2 .(3.6)² +2.(3.7)² - 6 4 +2.(6.7)²-7 4 / 2.6
=2.98142
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suppose net income = $200 , depreciations = $10, and working capital went up by $70. what was cash from operations?
cash from operations is $140 when net income = $200 , depreciations = $10, and working capital went up by $70.
Cash from Operations = Net Income + Depreciation - Change in Working Capital
Plugging in the values:
Cash from Operations = $200 + $10 - $70
Cash from Operations = $140.
So, cash from operations is $140.
Cash from operations can be calculated by adding non-cash items such as depreciation and subtracting changes in working capital.
This means that the company generated $140 in cash from its operations during the given period. It is important to understand the cash from operations as it represents the cash generated from the day-to-day operations of the business and provides an indication of its ability to generate cash in the future.
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a number is a restriction on a rational expression if the number makes the denominator of the rational expression
A number is a restriction on a rational expression if the number makes the denominator of the rational expression equal to zero.
Hence, option (b) is correct choice.
Simply put, a rational expression is the product of two polynomials. Or to put it another way, it is a fraction using polynomials as the numerator and denominator.
A rational expression's denominator is undefined when it equals zero, hence it cannot be employed in the expression.
For that particular value of the number, the limitation renders the value of the rational statement undefinable.
To put it another way, the number is a limitation since it cannot be used as the input for the rational expression because the output would be an undefined value.
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The missing option may be:
(a) 1
(b) 0
(c) always positive
(d) Indefinite
Please help me with math problem!! Will give brainliest!! :)
The amount of feet saved is given as follows:
24 feet.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
Applying the Pythagorean Theorem, the diagonal length for this problem is given as follows:
d² = 35² + 50²
d = square root (35² + 50²)
d = 61 feet.
Without the diagonal, the distance would be of:
35 + 50 = 85 feet.
Hence the amount saved is given as follows:
85 - 61 = 24 feet.
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A family is filling up a circular pool. The pool has a depth of 6 feet and a diameter of 12 feet. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water will it take to fill up the pool completely? Use π = 3.14 and round to the nearest gallon.
5,073 gallons
1,691 gallons
678 gallons
91 gallons
To fill the entire pool we will 5,073 need gallons of water.
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.
Given, A family is filling up a circular pool. The pool has a depth of 6 feet and a diameter of 12 feet.
From the general formula of the volume of a cylinder,
Volume = pi * radius² * height
In our case,
radius = 12/2 = 6
Height = 6
Thus, Volume = 3.14 * 6 * 6 *6
The volume of the Pool = 678.24 Cubic foot
Since there are 7.48 gallons of water in a cubic foot
Thus,
The volume of the pool in gallons = 678.24 * 7.48
The volume of the pool in gallons = 5,073.23
Therefore, to fill the entire pool we will 5,073 need gallons of water.
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Answer:
5,073 gallons, the first person to answer was correct.
Step-by-step explanation:
I took the quiz so you don't have to! <3
Two teams need to raise $100 each for their end-of-the-year field trips. Team A wants to sell popcorn at the Spring Fling Carnival, and Team B wants to sell cotton candy. It costs $15 to rent a popcorn machine, whereas it costs $25 to rent a cotton candy maker. The cost of additional supplies for the popcorn is $0.05 per bag, and the additional cost for the cotton candy is $0.10 per stick. Team A will sell the bags of popcorn for $0.75 each. Team B will sell the cotton candy for $0.80 per stick.
What is the least number of items Team A needs to sell to avoid losing money?
Team A needs to sell 255 bags of popcorn to reach their goal of $100.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Team A will sell the bags of popcorn for $0.50 each.
Team B will sell the cotton candy for $0.75 per stick.
Let the number of bags of popcorn sold by Team A be "x".
So, the total cost for the popcorn machine rental and supplies is
= $15 + 0.05x.
To reach their goal of $100
$100 = 0.5x - ($15 + 0.05x)
$100 = 0.5x - $15 - 0.05x
$115 = 0.45x
x = $115 / 0.45
x = 255 bags of popcorn
Thus, Team A needs to sell 255 bags of popcorn.
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Question 4 (1 point) Quadrilateral DKLM is a rhombus. M A If DA = 4x and AL = 5x - 3, find DL. Blank 1:
The length DL of the rhombus is 24 units
How to determine the length DLThe figure that completes the question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
DA = 4x
AL = 5x - 3
This means that
DA = A:
So, we have
5x - 3 = 4x
Evaluate the like terms
x = 3
So, we have
DL = 2 * DA
This gives
DL = 2 * 4 * 3
Evaluate
DL = 24
Hence, the length is 24 units
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While walking her dog, Sylvia noticed that 32 houses had a pot of red flowers on their
front step and 24 had a pot of yellow flowers. Write the ratio of red to yellow pots of
flowers three different ways. There is part a part b and part c pls helppp
The ratio of red to yellow pots of flowers in three different ways are
16 : 12, 8 : 6, and 4 : 3
As per the given data Sylvia while walking with her dog, she noticed that the 32 houses had a pot of red flowers on their front step.
Also, 24 houses had a pot of red flowers on their front step.
Here we have to determine that the ratio of red pots of flowers to yellow pots of flowers in three different ways.
The three different ways will be part a part b and part c.
The ratio of red to yellow pots of flowers.
32 : 24
Simplify the above ratio.
16 : 12
Also, we have to simplify further.
We get:
8 : 6
Then:
4 : 3
Therefore the ratios are 16 : 12, 8 : 6, and 4 : 3
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How to convert 18 meters to feet?
18 meters = 59.0551 foot. Meter to Feet Conversion : One meter is approximately equal to 3.28084 feet. To convert meters to feet, multiply the given meter value by 3.28084 feet.
How do you convert meters to feet?One meter is roughly equivalent to 3.28084 feet. Multiply the given meter value by 3.28084 feet to convert meters to feet. 5 meters to feet, for example, is converted as follows: We know that multiplying 5 by 3.28084 converts 5 meters to feet.In most cases, all you need to know is that 1 meter = 3.28 feet, so simply divide a foot measurement by 3.28 to get the same length in meters.To convert meters to feet, we must first understand the difference in their lengths. According to the rule, one meter equals 3.28 feet and one foot equals 12 inches.To learn more about meters to feet conversion refer to:
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what is 0.9 is_______of 9?
Answer: 10
step by step explenation
a circle has a diameter with endpoints at (-2, 87) and (18, 91). what is the length of the diameter?
The length of the diameter of a circle with endpoints at points (-2, 87) and (18, 91) is 20.4 units
How to find length of lineThe length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
distance between points (-2, 87) and (18, 91) is calculated as follows
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
d =√{(-2 - 18)² + (87 - 91)²}
d =√{400 + 16}
d = √416
d = 20.4 units
The diameter has length 20.4 units
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What is the next term of the following sequence?
12, 6, 3,.
6 124 0
00
a
The next term in the sequence is 1.5
What is an arithmetic sequence?It is a series of numbers that increase or decrease by a constant amount called the ratio of the progression. It is increasing when the ratio is positive and decreasing when it is negative.
The sequence given is: 12,6,3
We have to find the ratio or constant amount to find the next term:
12/2 = 6
6/2 = 3
We can see the successive term is half of the preceding one, so the general formula will be:
A(n+1)=A(n)/2
For the next term we get:
A(4th)= A(n)/2
A(4th) = 3/2
A(4th) = 1.5
The sequence is: 12, 6 ,3 , 1.5
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Correctly written question:
What is the next term of the following sequence? 12, 6, 3, ...
what are the inputs to ttest ind method in the scipy module? select one. question 5 options: null and alternative hypothesis values dataframes of values from each sample and optional equal variance indicator z-score and the corresponding p-value test statistic and the p-value
The data frames containing the values from each sample, the optional equal variance indicator z-score, the related P-value test statistic, and the P-value null and alternative hypothesis are the inputs to the ttest ind method in the scipy module.
What are the modules of SciPy?
SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, signal and image processing, ODE solvers and other tasks common in science and engineering. Maybe the most used feature of SciPy is the stats module. In both NumPy and SciPy, we can generate multivariate Gaussian random numbers with non-zero correlation. This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values. This test assumes that the populations have identical variances by default.
The arrays must have the same shape, except in the dimension corresponding to axis (the first, by default)
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what is 46.327 rounded to the nearest tenth
Answer: 34.95 rounded to the nearest tenth is 35.0.
If
a
1
=
4
a
1
=4 and
a
n
+
1
=
−
5
a
n
+
5
a
n+1
=−5a
n
+5 then find the value of
a
4
a
4
I NEED THIS RN MY HW DUE
.
Answer:
I can't understand your question do comment the question.The area of a triangle varies directly with the width and the height of the triangle. If 6 is the area when width = 4 and height = 3, what is the area of the triangle if width is 6 and height is 4?
Answer:
9
Step-by-step explanation:
To find out, we use the formula for direct variation:
A = kwh
Where A is the area, k is the constant of proportionality, w is the width, and h is the height.
From the information given, we can find k:
6 = k (4)(3)
6 = 12k
k = 0.5
So, the area when width is 6 and height is 4 is:
A = kwh = 0.5 (6)(4) = 9
Answer:
Step-by-step explanation:
Let a = (0, 0), b = (7, 2), c = (3, 4), d = (3, 7), and e = (−1, 5). Cameron walks the polygonal path abcdea, writing down the number of degrees turned at each corner. What is the sum of these five numbers? notice that abcde is not a convex pentagon
Sum of angles at 5 corners of a polygonal path abcdea is 360 degrees (assuming convex polygon).
What is vector ?
Vector is a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.
The sum of the angles at the corners of a polygon is equal to (n-2) times 180 degrees, where n is the number of sides of the polygon. In this case, n = 5, so the sum of the angles at the corners is (5-2) * 180 = 360 degrees.
However, this assumes that the polygon is convex. Since abcde is not a convex pentagon, need to calculate the angles at each corner separately.
The angle between two lines can be calculated using the dot product formula:
cos(θ) = (u⋅v) / (||u|| * ||v||)
where u and v are the vectors representing the lines, and ||u|| and ||v|| are their magnitudes. The angle θ is between 0 and 180 degrees.
For example, to find the angle between the lines ab and bc,use the vectors b-a and c-b:
cos(θ) = (b-a⋅c-b) / (||b-a|| * ||c-b||)
Sum of angles at 5 corners of a polygonal path abcdea is 360 degrees (assuming convex polygon).
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The sum of these five numbers is 66.59 degrees.
To find the sum of the angles turned at each corner, we need to find the angle between each pair of adjacent sides.
First, we find the slope of the line segment between each pair of points:
AB: slope = (2-0)/(7-0) = 2
BC: slope = (4-2)/(3-7) = -2
CD: slope = (7-4)/(3-3) = 3
DE: slope = (5-(-1))/(-1-3) = -6
EA: slope = (0-5)/(0-(-1)) = 5
Next, we find the angle between each line segment using the inverse tangent function (atan).
AB: angle = atan(2) = 63.43 degrees
BC: angle = atan(-2) = -63.43 degrees
CD: angle = atan(3) = 71.57 degrees
DE: angle = atan(-6) = -84.97 degrees
EA: angle = atan(5) = 79.56 degrees
Adding up all the angles, we get:
63.43 + (-63.43) + 71.57 + (-84.97) + 79.56 = 66.59 degrees
So the sum of the five angles is 66.59 degrees.
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what is the complex conjugate of vector a ?
Answer: ℎ(())=(ℎ()),∀∈
Step-by-step explanation:
If
=()=1,…,,∈ℂA=(ai)i=1,…,n,ai∈C,
then
∗=(∗)=1,…,A∗=(ai∗)i=1,…,n,
where ∗ai∗ is the complex conjugate of respectively.
In a slightly more general setting than the functional analytic one (using inner product spaces or linear conjugate functions with alternate scale multiplication defined by multiplication by scale complex conjugate) where,
∈A∈V for some topological space, two maps :→f:V→V and :→g:V→V are (topologically) conjugate if ∃∃ a homeomorphism ℎh, such that; ℎ(())=(ℎ()),∀∈.
The complex conjugate of a vector "a" can be represented as the conjugate transpose of the vector "a".
What is the eigenvalue and eigenvector?
Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation, and the eigenvalue is the factor by which it is stretched.
A conjugate of a complex number is another complex number that has the same real part as the original complex number and the imaginary part has the same magnitude but opposite sign.
If we multiply a complex number with its conjugate, we get a real number.
The complex conjugate of a vector "a" can be represented as the conjugate transpose of the vector "a".
The conjugate transpose of a vector "a" is denoted as "a*".
The complex conjugate of a vector is important in the field of linear algebra, particularly in the study of eigenvalues and eigenvectors.
Hence, The complex conjugate of a vector "a" can be represented as the conjugate transpose of the vector "a".
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Factorize:
Pls answer
The factored form of 9a² - b² - 4c² + 4bc is
(3a + b - 2c) (3a - b + 2c)
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
9a² - b² - 4c² + 4bc
9a² - (b² + 4c² - 4bc)
Now,
(b² + 4c² - 4bc)
This can be written as,
= (b² - 4bc + 4c²)
= (b - 2c)²
Now,
9a² - (b - 2c)²
(3a)² - (b - 2c)²
This is in the form of a² - b².
a² - b² = (a + b) (a - b)
So,
(3a + b - 2c) (3a - b + 2c)
Thus,
(3a + b - 2c) (3a - b + 2c) is the factored form.
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What are the critical points and how are they found?
Answer:
A critical point of a continuous function f is a point at which the derivative is zero or undefined.
Step-by-step explanation:
Critical points are the points on the graph where the function's rate of change is altered—either a change from increasing to decreasing, in concavity, or in some unpredictable fashion.
Critical points are those which result in f'(x) = 0. They are found by using derivatives.
What is a critical point?
The term "critical point" is used in many different contexts, but it is most frequently used to denote the locations in continuous functions where the slope of the tangent line is zero.
Therefore, we define the critical points as those that result in f'(x) = 0.
The critical points are found by using derivatives.
For a function f(x), we first calculate its derivative i.e. f'(x) and equate it to zero in order to find the critical points.
Hence, this way we find the critical points.
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Suppose that a and b are nonzero vectors.
(a) Under what circumstances is compa b = compb a?
(b) Under what circumstances is proja b = projb a?
a) Compa a = compa b is occurs when the two vectors are proportional
b) Proja b = proja a is occurs when the two vectors are parallel.
A vector is a mathematical object with both magnitude and direction.
In the context of vectors, "comp" refers to the scalar (or dot) product and "proj" refers to the projection. The scalar product of two vectors is a scalar that measures the degree to which two vectors are pointing in the same direction. The projection of a vector is a vector that represents the component of the vector in a specific direction.
(a) The scalar product of two vectors is equal if and only if the two vectors are proportional. In other words, if a and b are nonzero vectors such that compa b = compb a, then the two vectors must be pointing in exactly the same direction.
(b) The projection of a vector is equal if and only if the two vectors are parallel. In other words, if a and b are nonzero vectors such that proja b = projb a, then the two vectors must be parallel, or pointing in exactly the same direction.
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Use The General Slicing Mothod To Find The Volume Of The Following Solid. The Solid With A Semicircular Base Of Radius 9 Whose Cross Section Is...
The volume of the solid can be found by using the general slicing method which involves slicing the solid into multiple thin slices, computing the volume of each slice.
The general slicing method can be used to find the volume of the solid with a semicircular base of radius 9 whose cross section is a triangle. This method involves slicing the solid into multiple thin slices, computing the volume of each slice, and then summing up the volumes of all the slices. To find the volume of each slice, we first need to determine the area of the cross-section for each slice. The area of the cross-section can be found by multiplying the base of the triangle by its height. For each slice, the base of the triangle is equal to 2πr/N, where r is the radius of the semicircle and N is the number of slices. The height of the triangle is equal to the thickness of each slice. Once the area of the cross-section is calculated, we can find the volume of each slice by multiplying the area by the thickness of the slice. Finally, the volume of the solid is equal to the sum of the volumes of all the slices.
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!!
a town wishes to enclose a plot of land with posts.
If the posts are spread 1m apart, there will be 150 posts too few.
If the posts are spread 3m apart, there will be 70 too many.
How many posts does the town have?
If the town wishes to enclose a plot of land with posts and the If the posts are spread 1m apart, there will be 150 posts too few. The number of posts the town have is: 260 posts.
How to find the number of posts?Let x represent the number of posts the town
If the posts are spread 1m apart, there will be x - 150 too few posts.
If the posts are spread 3m apart, there will be x - 70 too many posts.
Since the distance between posts is directly proportional to the number of posts.,
Let set up a proportion:
(1) / (x - 150) = (3) / (x - 70)
Cross multiplying:
(1) * (x - 70) = (3) * (x - 150)
Expand
x - 70 = 3x - 450
Solving for x:
2x = 520
Divide both side by 2x
x = 520/2
x = 260
Therefore the town has 260 posts.
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x | 2 9 16 23
y | 4 8 16 32
is the relationship linear, exponential, or neither?
The relationship on the table is an exponential function
How to determine the relationship typeFrom the question, we have the following parameters that can be used in our computation:
x | 2 9 16 23
y | 4 8 16 32
For a fucttion to be a linear function:
A change in the x value must correspond to a change in the y values
In the function
When x increases by 7, y doubles
So, it is not linear
Instead, it is an exponential function because is has a common ratio
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Simplify (¬n∨p)∧¬(n∧p) to ¬n
Using the distributive and double negation laws, the given statement can be simplified to ¬n.
The given expression can be simplified to ¬n using Boolean algebra. This can be shown by first using the distributive property to distribute the negation operator to the term (n ∧p). This will result in the expression ¬n ∨¬p. Then, using the commutative law of conjunction (∧), the expression can be reordered to (¬n ∧¬p) ∨p. Then, using the associative law of conjunction (∧), the expression can be reordered to ¬n ∧(¬p ∨p). Since the negation of a disjunction is the conjunction of the negations, then (¬p ∨p) simplifies to 1, which in turn simplifies the expression to ¬n ∧1, which is then simplified to ¬n. Therefore, the simplified expression is ¬n.
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7. the soccer team had a fundraiser. they sold pizzas for $5.00 each and sub sandwiches for $3.00 each. they sold 11 more subs than pizzas and earned a total of $233. write and solve a system of equations to represent this situation and determine how many pizzas they sold.
The soccer team sold 25 pizzas.
Let x be the number of pizzas sold. Then, the number of subs sold would be x + 11.
The total amount of money earned from pizzas is $5.00 * x and the total amount of money earned from subs is $3.00 * (x + 11).
We can represent this situation using the following system of equations:
5x + 3(x + 11) = 233
Expanding the second equation:
5x + 3x + 33 = 233
Combining like terms:
8x + 33 = 233
Subtracting 33 from both sides:
8x = 200
Dividing both sides by 8:
x = 25
So, the soccer team sold 25 pizzas.
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The soccer team sold 25 pizzas.
Let x be the number of pizzas sold. Then, the number of subs sold would be x + 11.
The total amount of money earned from pizzas is $5.00 * x and the total amount of money earned from subs is $3.00 * (x + 11).
We can represent this situation using the following system of equations:
5x + 3(x + 11) = 233
Expanding the second equation:
5x + 3x + 33 = 233
Combining like terms:
8x + 33 = 233
Subtracting 33 from both sides:
8x = 200
Dividing both sides by 8:
x = 25
So, the soccer team sold 25 pizzas.
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3. A girl is 12 years older than her daughter. 4 years ago when she gave birth to her daughter while in SHS 1, she was 4 times as old as her daughter. How old are they now?
Answer:
The mother is now 20 years old and the daughter is 8 years old. Let the mother's age be x and the daughter's age be y. We can write the equation x - 12 = y and x - 4 = 4y. Solving these equations simultaneously gives us x = 20 and y = 8.
Step-by-step explanation:
Find the area of the shaded regions below. Give
your answer as a completely simplified exact value
in terms of pi (no approximations).
Helppp pls
The area of the shaded regions in the given figure is 4.56 cm².
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
From the given figure,
Here, ΔLMN is isosceles triangle, ML=MN=4 cm
Now, area of a ΔLMN =1/2 ×Base×Height
= 1/2 ×4×4
= 8 cm²
By using Pythagora's theorem, we have
LN²=LM²+MN²
LN²=4²+4²
LN²=32
LN=4√2 cm
Area of semicircle = πr²/2
Here, radius =2√2 cm
Now, 3.14×(2√2)²/2
= 12.56 cm²
Area of shaded region = 12.56-8
= 4.56 cm²
Therefore, the area of the shaded regions in the given figure is 4.56 cm².
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what is 2 x 4 + 82 - 18 divide by 8 x 9?
Answer:
1 because,
(2*4+82-18)/8*9
(8+82-18)/72
(90-18)/72
72/72
1
Answer:
Step-by-step explanation:
2 x 4 + 82 - 18 / 8 x 9
We want to use the PEMDAS rule for working math problems with more than one operation.
P = Parentheses first
E = Exponents second
M/D = Multiplication and division third
A/S= Addition and subtraction last
There are no parentheses, so we look for exponents next and there are none.
The next operations are multiplication and division.
Step 1
2 x 4 = 8
8 + 82 - 18 / 8 x 9
Step 2
8 x 9 = 72
Step 3
8 + 82 - 18 / 72
Before we can divide by 72, we need to add and subtract the top numbers from left to right.
Step 4
8 + 82 - 18 = 72
72/72
Now divide 72 by 72
Step 5
72/72 = 1