A cylinder has a height of 11 inches. Its volume is 1,692.46 cubic inches. What is the radius of the cylinder?
Answers
The radius of the cylinder is approximately 5.17 inches
What is volume ?
Volume is a measure of the amount of space occupied by an object or a substance. It is usually expressed in cubic units, such as cubic meters, cubic centimeters, cubic inches, etc. The volume of a three-dimensional object, such as a cube, sphere, or cylinder, is calculated by measuring the length, width, and height or radius of the object and applying the appropriate formula. For example, the volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height of the cylinder.
According to the question:
The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
We are given that the height h = 11 inches and the volume V = 1,692.46 cubic inches.
Plugging in these values to the formula, we get 1,692.46 = πr²(11).
Solving for r, we can divide both sides by π(11) and then take the square root: r = √(1,692.46/(11π)).
Using a calculator, we get r ≈ 5.17 inches (rounded to two decimal places).
Therefore, the radius of the cylinder is approximately 5.17 inches.
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Related Questions
In a jar of blue and red marbles the ratio of blue marbles to red marbles is 5 to 3 there are 320 marbles in the jar how many red marbles are in the jar
Answers
Answer:
120 red marbles
Step-by-step explanation:
5 to 3 gives a total of 8
let x = # red marbles
3 = x
8 320
8x = 960
x = 120
For every $2 that Miguel saves his parents give him $4 if Miguel saves $60 how much money will his parents give him
Answers
Given the diagram shown below, determine the value of x.
Answers
math was fun until they added words and letters
Determine which of the following sets are countable. )
A) B = {b € R: 2
B) C = {c ER: 2
C) N×{1} = {(n, 1) : n € N }
D) Rx R = {(x, y): x, y € R}
Answers
These are the countable and uncountable a) The set of negative rationals (p) is countable. b) The set {r + √(2n) : r ∈ ℚ, n ∈ ℕ} is uncountable. c) The set {x ∈ ℝ : x is a solution to ax² + bx + c = 0 for some a, b, c ∈ ℚ} is countable.
a) The set of negative rationals (p) is countable. To see this, we can establish a one-to-one correspondence between the negative rationals and the set of negative integers. We can assign each negative rational number p to the negative integer -n, where p = -n/m for some positive integer m.
Since the negative integers are countable and each negative rational number has a unique corresponding negative integer, the set of negative rational is countable.
b) The set {r + √(2n) : r ∈ ℚ, n ∈ ℕ} is uncountable. This set consists of numbers obtained by adding a rational number r to the square root of an even natural number multiplied by √2. The set of rational numbers ℚ is countable, but the set of real numbers ℝ is uncountable. By adding the irrational number √2 to each element of ℚ,
we obtain an uncountable set. Therefore, the given set is also uncountable.
c) The set {x ∈ ℝ : x is a solution to ax² + bx + c = 0 for some a, b, c ∈ ℚ} is countable. For each quadratic equation with coefficients a, b, c ∈ ℚ, the number of solutions is either zero, one, or two. The set of quadratic equations with rational coefficients is countable since the set of rationals ℚ is countable.
Since each equation can have at most two solutions, the set of solutions to all quadratic equations with rational coefficients is countable as well.
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Find the generating function of the sequence {an}n≥0 determined by an = an−1 + 6an−1 with initial conditions a0 = 1, a1 = 3. You need to find the closed form of the generating function, but you don’t need find the closed form of the coefficients.
Answers
The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.
To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.
The given recurrence relation is: an = an-1 + 6an-2
We are also given the initial conditions: a0 = 1 and a1 = 3.
To find the generating function, we define the generating function A(x) as:
a(x) = a0 + a1x + a2x² + a3x³ + ...
Multiplying the recurrence relation by x^n and summing over all values of n, we get:
∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)
Now, let's express each summation in terms of the generating function a(x):
a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾
Simplifying and rearranging the terms, we have:
a(x)(1 - x - 6x²) = a0 + (a1 - a0)x
Using the given initial conditions, we have:
a(x)(1 - x - 6x²) = 1 + 2x
Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):
a(x) = (1 + 2x) / (1 - x - 6x²)
Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).
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Write sin(theta) in terms of cos(theta)
Answers
Answer:
\( \sin(theta) = \sqrt{ {1 - \cos^{2}(theta)} } \)
Step-by-step explanation:
From trignometery identities , we know that :-
\( { \sin^{2}(theta) } + { \cos^{2}(theta) = 1}\)
\( = { \sin^{2}(theta) } = 1 - { \cos^{2}(theta) } \)
Here further solving this , we get
\( \sin(theta) = \sqrt{ {1 - \cos^{2}(theta)} } \)
Quadrilateral WXYZ is a rectangle. Find each measure if m<1 = 30 . (Lesson 6-4 )
m<8
Answers
In a rectangle WXYZ, if the measure of angle 1 is 30 degrees, then the measure of angle 8 can be determined.
A rectangle is a quadrilateral with four right angles. In a rectangle, opposite angles are congruent, meaning they have the same measure. Since angle 1 is given as 30 degrees, angle 3, which is opposite to angle 1, also measures 30 degrees.
In a rectangle, opposite angles are congruent. Since angle 1 and angle 8 are opposite angles in quadrilateral WXYZ, and angle 1 measures 30 degrees, we can conclude that angle 8 also measures 30 degrees. This is because opposite angles in a rectangle are congruent.
Since angle 3 and angle 8 are adjacent angles sharing a side, their measures should add up to 180 degrees, as they form a straight line. Therefore, the measure of angle 8 is 180 degrees minus the measure of angle 3, which is 180 - 30 = 150 degrees.
So, if angle 1 in rectangle WXYZ is 30 degrees, then angle 8 measures 150 degrees.
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In a compton scattering experiment, an incident x-ray photon is traveling along the x direction. an electron, initially at rest, is struck by the photon and is accelerated straight ahead in the same direction as the incident x-ray photon. which way does the scattered photon move
Answers
In a Compton scattering experiment, the scattered photon moves in a direction different from the incident photon. It scatters at an angle relative to the incident direction.
In Compton scattering, the incident X-ray photon transfers energy and momentum to the electron it interacts with. As a result, both the electron and the scattered photon change their direction and energy.
When the incident X-ray photon strikes the initially at rest electron, it transfers some of its energy and momentum to the electron. This interaction causes the electron to gain energy and be accelerated in the same direction as the incident photon.
Simultaneously, the scattered photon, which retains some of its energy, moves in a direction different from the incident photon. The angle at which the scattered photon deviates from the incident direction is known as the scattering angle.
The scattered photon's direction depends on the interaction between the X-ray photon and the electron, and it can vary based on factors such as the energy of the incident photon and the scattering angle. The phenomenon of Compton scattering provides valuable insights into the behavior of X-rays and their interactions with matter.
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S||P FIND VALUE OF Z !
Answers
Answer:
Step-by-step explanation:
Please excuse my handwriting lol.
If 1200 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Answers
If 1200 square centimeters of material is available to make a box with a square base and an open top,
The largest possible volume of the box is V = 4000cm^3.
We have 1200 cm^2 worth of material. This represents the surface area of a box with a square base and an open top.
the dimensions of the box.
Square base implies the length and width are the same.
Let x = length/width.
The box has a height as well.
Let h = height
the surface area ; S.
S = (area of base) + (area of 4 walls)
The area of the base is x^2
The area of one of the walls is length times height, or xh. Since there are 4 of them, it would be 4 times xh, or 4xh.
S = x^2 + 4xh
And we know that S = 1200cm^2, so
x^2 + 4xh = 1200
Let's solve for h.
4xh = 1200 - x^2
h = (1200 - x^2) / (4x)
we require the volume formula.
V = (length) x (width) x (height)
And we know all of these.
V = (x)(x)(h)
V = (x^2) h
putting h = (1200 - x^2) / (4x) in the formula
V = (x^2) ( 1200 - x^2)/(4x)
We get a cancellation,
V = x(1200 - x^2)/4
V = (1/4)x (1200 - x^2)
This will be our volume function, V(x).
V(x) = (1/4)(x)(1200 - x^2)
To maximize V(x), we must first take the derivative and then make it 0. Using the product rule (and ignoring the constant 1/4), we have
V'(x) = (1/4) [ (1200 - x^2) + (x)(-2x) ]
Simplify,
V'(x) = (1/4) [ 1200 - x^2 - 2x^2 ]
V'(x) = (1/4) [ 1200 - 3x^2 ]
V'(x) = (1/4) [ 3(400 - x^2) ]
V'(x) = (3/4) [ 400 - x^2 ]
To maximize, make V'(x) = 0, and solve for x.
0 = (3/4) [ 400 - x^2 ]
0 = 400 - x^2
x^2 = 400
x = +/- 20
Therefore,
x = { 20, -20 }
However, since x represents a dimension, it can never be negative, and we must discard the negative solution. That means
x = 20.
This tells us that the maximum volume occurs when x = 20. However, the question is asking WHAT the largest volume of the box is. Solving this is as simple as plugging x = 20 into our volume function, V(x).
V(x) = (1/4)(x)(1200 - x^2)
Therefore,
V(20) = (1/4) (20) (1200 - 20^2)
V(20) = (1/4) (20) (1200 - 400)
V(20) = (1/4) (20) (800)
V(20) = (20/4)(800)
V(20) = 5(800)
V = 4000cm^3
Hence the answer is, the largest possible volume of the box is V = 4000cm^3.
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Find the quotient. 514÷15 A. 720 B. 7834 C. 267 D. 314
Answers
Answer:314
Step-by-step explanation:
Which of these equations are true when the value of y is 27?
I. - 9+ y = 18
II. - 18+ y = -45
III. 5y = 135
IV. 2y = 29
I and III
I and IV
C II and III
II and IV
Answers
Answer: i and lll
Step-by-step explanation:
please answer plssss plssss plsss NOTE: IF ANSWER IS GOOD +1 BRAINLIEST PART 3
Answers
Answer:
The median is the number in the middle. Line all the numbers up from least to greatest and find the one that's in the middle.
32 38 45 46 46 47 50 54 63
Since there are 9 numbers, then the 5th number is in the middle.
Therefore, 46 is the median.
Step-by-step explanation:
Answer:
46
Step-by-step explanation:
First, order everything from least to greatest...
32, 38, 45, 46, 46, 47, 50, 54, 63
Then, find the number that's in the middle.
32, 38, 45, 46, 46, 47, 50, 54, 63
Notice that there is an equal amount of numbers on each side.
Therefore, 46 would be the median of this data set.
-kiniwih426
Find the ordered pair that solves this by the elimination method. 1/5x +y = 6/5 and 1/10x + 1/3 y = 7/10
Answers
We already know that the solution is (9, -3/5), let's show that
\(\frac{1}{10}x+\frac{1}{3}y=\frac{7}{10}\)Let's plug our solution into the equation
\(\begin{gathered} \frac{1}{10}\cdot9+\frac{1}{3}\cdot(-\frac{3}{5})=\frac{7}{10} \\ \\ \frac{9}{10}-\frac{3}{15}=\frac{7}{10} \\ \\ \frac{9\cdot15-3\cdot10}{10\cdot15}=\frac{7}{10} \\ \\ \frac{135-30}{150}=\frac{7}{10} \\ \\ \frac{105}{150}=\frac{7}{10} \\ \\ \frac{21}{30}=\frac{7}{10} \\ \\ \boxed{\dfrac{7}{10} =\dfrac{7}{10} } \end{gathered}\)The second equation is true!
6 (4x6) x 9 (5x9) judjsjdjdjddjdnnddnfndndndndndndndndn
Answers
Answer:
48 600
Step-by-step explanation:
6(4×6) × 9(5×9)
Solve the numbers in brackets first
6(20) × 9(45)= 120 × 405
= 4 8 600
Answer:
6(20) × 9(45)= 120 × 405
= 4 8 600
the budget uses numerical data to predict short- and long-term needs of an organization. a. true b. false
Answers
True. A budget is a numerical representation of an organization's plan for the future.
It is employed to forecast the organization's anticipated earnings and costs for a given timeframe, typically a fiscal year.
This makes it easier for the business to calculate how much cash it will need to pay its bills and how much it may set aside for investments in the future.
The budget aids the business in making plans for unforeseen circumstances like a decline in sales or an increase in expenses.
The company may more effectively decide how to spend its resources and establish long- and short-term plans by using numerical data to forecast demands.
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1. let x and y be integers. we will assume that it is not true that x or y is even and will show that 3xy + 4 is odd.
Answers
Therefore, we have shown that \(3xy + 4 \)is odd when x and y are both odd integers.
To show that 3xy + 4 is odd, we will consider the fact that x and y are both odd integers since they are not even.
Let x = 2a + 1 and y = 2b + 1, where a and b are integers.
Now, we can substitute these expressions into the given equation:
\(3xy + 4 = 3(2a + 1)(2b + 1) + 4 \)
= \( 3(4ab + 2a + 2b + 1) + 4 \)
= \( 12ab + 6a + 6b + 3 + 4 \)
= \(2(6ab + 3a + 3b) + 7 \)
The term (6ab + 3a + 3b) is an integer, let's call it c. Thus, our equation becomes:
2c + 7
Since 2c is even, and 7 is odd, the sum (2c + 7) is odd.
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The following numbers appear in a table of random digits:38683 50279 38224 09844 13578 28251 12708 24684A scientist will be measuring the total amount of leaf litter in a random sample (n =5) of forest sites selected without replacement from a population of 45 sites. The sites are labeled 01, 02, . . . ,45 and she starts at the beginning of the line of random digits and takes consecutive pairs of digits. Which of the following is correct?A) Her sample is 38, 25, 02, 38, 22B) Her sample is 38, 68, 35, 02, 22C) Her sample is 38, 35, 27, 28, 08D) Her sample is 38, 65, 35, 02, 79E) Her sample is 38, 35, 02, 22, 40
Answers
The correct answer is B) Her sample is 38, 68, 35, 02, 22. This is because the scientist is selecting a random sample of 5 forest sites from a population of 45 without replacement. She is using consecutive pairs of digits from the table of random digits to select her sample.
Starting at the beginning of the line of random digits, the first pair is 38, which corresponds to forest site 38. The second pair is 68, which corresponds to forest site 68. The third pair is 35, which corresponds to forest site 35. The fourth pair is 02, which corresponds to forest site 02. And the fifth pair is 22, which corresponds to forest site 22.
Now, let's select a random sample of 5 forest sites without replacement:
1) 38
2) 35
3) 02
4) 22
5) 24
Thus, the correct answer is not listed in the given options. However, based on the consecutive pairs of digits and following the process mentioned, the sample should be 38, 35, 02, 22, and 24.
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Diego is collecting nickels. He has collected $7.05 so
far. The relationship between the number of nickels n
and the amount of money in dollars is represented by
which of the following equations?
A. 0.05 + n = 7.05
B. 0.05n = 7:05
C. 7.05 + n = 0.05
D. 7.05n = 0.05
Answers
If the total amount of money gathered by Diego in the jar is $7.05. The link between the number of nickels n and the quantity of money in dollars is expressed by the equation 0.05 + n = 7.05.
What is meant by equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Let $7.05 exists the total amount of money collected by Diego in the jar.
Where d is the number of dimes
n is the number of nickels
A) Let the equation be 0.05 + n = 7.05
Subtract 0.05 from both sides of the equation, we get
0.05 + n - 0.05 = 7.05 - 0.05
simplifying the above equation, we get
n = 7
B) Let the equation be 0.05 n = 7.05
Divide the equation by 0.05, we get
0.05 n / 0.05 = 7.05 / 0.05
n = 141
C) Let the equation be 7.05 + n = 0.05
Subtract 7.05 from both sides of the equation, we get
7.05 + n - 7.05 = 0.05 - 7.05
simplifying the above equation, we get
n = - 7
D) Let the equation be 7.05n = 0.05
Divide the equation by 7.05, we get
7.05 n / 7.05 = 7.05 / 0.05
n = 1 / 141.
If the total amount of money gathered by Diego in the jar is $7.05. The link between the number of nickels n and the quantity of money in dollars is expressed by the equation 0.05 + n = 7.05.
Therefore, the correct answer is option A) 0.05 + n = 7.05.
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Complete the equation so that it has solutions of –5 and 7. x2 x = 0
Answers
The equation it has solutions of –5 and 7 is x^2-2x-37=0
We have equation
solutions of equation are –5 and 7.
We have to find complete the equation.
We have given that solutions of the equation are -5, 7.
The standard form of a quadratic equation.
What is the factor of the quadratic equation?
\((x -\alpha) (x- \beta)\)
Where we have
\(p = -(\alpha+\beta) and q = (\alpha\times \beta)\)
So, roots are
\(( x- (-5)) (x-7)\)
\(p = -( -5+7)\) , \(q =(-5)(7).\)
\(p = -2 and q = -35.\)
On substituting p and q in equation
\(x^2+(-2)x-37=0\)
\(x^2-2x-37=0\)
Therefore,x^2-2x-37=0 is the equation of solution -5,7.
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Answer:
-2, -35
Step-by-step explanation:
Plz solve this question
Show the steps you need to take to solve it.
Answers
Answer:
V = 378y³
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsGeometry
Volume of a Rectangular Prism: V = lwh
l is lengthw is widthh is heightStep-by-step explanation:
Step 1: Define
Identify variables
l = 9y
w = 7y
h = 6y
Step 2: Find Volume
Substitute in variables [Volume of a Rectangular Prism]: V = (9y)(7y)(6y)Multiply: V = (63y²)(6y)Multiply: V = 378y³___________________________________
Problem:What is the volume of this rectangular prism?Formula for volume (v):\(\quad\quad\quad\quad \boxed{\tt{v = lwh}}\)
Given that:\(\quad\quad\quad\quad\tt{length (l)= 9y}\)
\(\quad\quad\quad\quad\tt{width(w)= 7y}\)
\(\quad\quad\quad\quad\tt{height(h)= 6y}\)
Solution:\(\quad\quad\quad\quad\tt{v = lwh}\)
\(\quad\quad\quad\quad\tt{v = (9y)(7y)(6y)}\)
\(\quad\quad\quad\quad\tt{v = (9y)(42 {y}^{2}) }\)
\(\quad\quad\quad\quad \underline{\tt{v = 378 {y}^{3} }}\)
Hence, the final answer is:\(\quad\quad\quad\quad \underline { \boxed{\tt{ \color{magenta}v = 378 {y}^{3} }}}\)
___________________________________
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How many polynomials can be formed with and 5 as zeroes?
Answers
The number of polynomials that can be formed with -2 and 5 as zeroes are more than 1.
What is a polynomial?
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.x² -3x - 7 is an illustration of a polynomial with a single indeterminate x.
Given that the zeros of a polynomial are -2 and 5.
The polynomial that has a and b as zeors is p(x) = k[x² + (a+b)x + ab].
where k is a real number.
The polynomial that has -2 and 5 zeros is
p(x) = k[x² + (-2 + 5)x + (-2)×5]
p(x) = k[x² + 3x - 10]
Where k is a real number.
The number of real numbers is infinity.
The number of polynomials is infinity.
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Please help this is timed!!
Answers
Answer:
can i see the rest of the problem...
Step-by-step explanation:
What would be the new coordinates of the following image after a dilation of 3?
Answers
Remember that the rule for a dilation by a factor of k about the origin is:
\((x,y)\rightarrow(kx,ky)\)Identify the coordinates of the points W, X and Z. Then, apply a dilation by a factor of 3 about the origin to find W', X' and Z', the new coordinates after the dilation.
\(\begin{gathered} W=(4,2) \\ X=(8,6) \\ Z=(8,2) \end{gathered}\)Apply a dilation by a factor of 3:
\(\begin{gathered} W(4,2)\rightarrow W^{\prime}(3\times4,3\times2)=W^{\prime}(12,6) \\ X(8,6)\rightarrow X^{\prime}(3\times8,3\times6)=X^{\prime}(24,18) \\ Z(8,2)\rightarrow Z^{\prime}(3\times8,3\times2)=Z^{\prime}(24,6) \end{gathered}\)Therefore, the new coordinates would be:
\(\begin{gathered} W^{\prime}=(12,6) \\ X^{\prime}=(24,18) \\ Z^{\prime}=(24,6) \end{gathered}\)The cross products of a proportion are never equal. true or false
Answers
I think it's FALSE I sure
false
Step-by-step explanation:
It could be equal because what if the proportions are something like 2/3=3/2
In this case the product of both sides is 6.
Is this graph a function?
Answers
Answer:
yes
Step-by-step explanation:
There were 40 dimes and quarters in the drawer. Peggy counted them and found that their total value was $4.75. How many coins of each type were there
Answers
Therefore, there are 35 dimes and 5 quarters in the drawer.
Let's use algebra to solve this problem. Let's assume the number of dimes is represented by the variable "D," and the number of quarters is represented by the variable "Q."
We are given two pieces of information:
There were a total of 40 dimes and quarters: D + Q = 40.
The total value of the coins was $4.75: 0.10D + 0.25Q = 4.75.
To solve this system of equations, we can use substitution or elimination.
Let's solve it using substitution: From the first equation, we can express D in terms of Q: D = 40 - Q.
Substituting this value into the second equation, we get:
0.10(40 - Q) + 0.25Q = 4.75
4 - 0.10Q + 0.25Q = 4.75
0.15Q = 0.75
Q = 0.75 / 0.15
Q = 5
Substituting this value back into the first equation, we find:
D + 5 = 40
D = 40 - 5
D = 35
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Can someone please help i don’t understand at all :/
Answers
Using the Segment Addition Postulate, considering the congruent segments and the trisection, the missing lengths of the segments are given by the following items:
CH = 4.HI = 4.ID = 4.CB = 12.AC = 6.AE = 12.A to F = 4.GE = 4.FB = 8.DG = 8.What is the segment addition postulate?The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.
For this problem, two other concepts are important, given by the bullet points below:
Congruence: Congruent segments have the same length.Trisection: A trisection of a segment divides the segment into three segments of equal lengths.CD = 12, hence, considering the trisection: (12/3) = 4.
CH = 4.HI = 4.ID = 4.CD is also congruent to CB, hence:
CB = 12.
CE = 6, and AE = 2CE, hence:
AC = 6.AE = 12.Due to the postulate, since DG = 8 and GE = 12, and the entire lengths are of 12, and considering the congruence:
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Which function is linear?
A. 9y+3=0
B. Y-4x=1
C. Y=2+6x⁴
D. X-2y=7
E. X/y+1=2
Answers
Answer:the answer is A
Step-by-step explanation:
Solve by dividing digits of
value and filling in zeros:
48000-800
Answers
The most appropriate choice for division will be given by -
48000 ÷ 800 = 60
What is division?
Division is used to obtain the value of single unit from a value of multiple unit. The number which is divided is called dividend and the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula in division
Divisor \(\times\) Quotient + Remainder = Dividend
Here
48000 ÷ 800
At first the numbers are being divided
48 ÷ 8 = 6
Now, From three zeroes, two zeroes will get cancelled
So one zero will remain.
So the correct answer is 60
48000 ÷ 800 = 60
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