The common base that can be used to rewrite each side of the equation is 2.
How to find the common base used to rewrite each equation?The common base that can be used to rewrite each side of the equation is as follows:
2ˣ⁺³ - 3 = 5
add 3 to both sides
2ˣ⁺³ - 3 + 3 = 5 + 3
2ˣ⁺³ = 8
Hence,
2ˣ⁺³ = 2³
Therefore, the common base that can be used to rewrite each side of the equation is 2.
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Round your answer to four decimal places. Look up, say hello.The sine ratio is B1 when the reference angle is 50 degrees
The sine of an angle is the ratio of height to the hypotenuse. The value of sin 50° = 0.7660.
What is an angle?
An angle is a figure in Plane Geometry generated by two rays or lines that share a common endpoint. The term "angle" is derived from the Latin word "angulus," which meaning "corner". The two rays are referred to as the sides of an angle, while the common terminus is referred to as the vertex.
The sine of an angle is the ratio of height to the hypotenuse of a right triangle.
The reference angle is 50.
Now sin 50 = 0.766044.
The 5 digits after the decimal point is 4. 4 is less than 5 thus the 4 digits after the decimal point remain the same.
sin 50 = 0.7660
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Considere los polinomios pi(t) = 1 + 1, p2(t) = 1-1, P3(1) =
4, p4(1) = 1 + 7, y Ps(1) = 1 + 2t + 7, y sea H el subespacio
Ps generado por el conjunto S = (Pi P2. P3 P4. Ps). Utilice el
método descrito en la demostración del teorema del conjunto generador (sección 4.3) para producir una base de H. (Expli-que cómo seleccionar los elementos apropiados de S.)
Therefore, We can use the Gaussian elimination method to find the basis of H.
Define Gaussian elimination method.In linear and multilinear algebra, the procedure of Gauss elimination involves first solving one of the simultaneous linear equations for one variable (in terms of all the others) and then substituting this expression into the other equations to discover the answers.
Define linear equation.A linear equation is an algebraic equation in which each term has an exponent of 1, which, when plotted on a graph, always yields a straight line. One example with one variable is where ax+b = 0, where a and b are fundamental values and x is the variable.
Selecting the polynomials Pi(t) = 1 + t and P2(t) = 1 - t from the set S. These are linearly independent since they cannot be written as a linear combination of the other polynomials in the set and checking if the span of Pi(t) and P2(t) is equal to H. Then expressing the remaining
polynomials P3(t), P4(t), and Ps(t) in terms of Pi(t) and P2(t) and checking if they can be written as a linear combination of Pi(t) and P2(t) or not.
P3(t) = 4 can be written as 4 * Pi(t) - 4 * P2(t)
P4(t) = 1 + 7t can be written as Pi(t) + 7 * P2(t)
Ps(t) = 1 + 2t + 7t^2 can be written as Pi(t) + 2t * P2(t) + 7 * P2(t)^2
From this, we can see that all the polynomials in S can be written as a linear combination of Pi(t) and P2(t). So, the span of Pi(t) and P2(t) equals H. Hence, { Pi(t), P2(t) } is a basis for the subspace H.
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Find the slope of the line passing through the points −3, 7 and −7, 5.
7x+6y=16 4x-2y=1 using elimation
For the given equations 7x+6y=16 and 4x-2y=1 the value of x is 1 and y is 3 / 2.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the two equations are 7x+6y=16 and 4x-2y=1. The solution of the equations by elimination method is calculated as,
7x + 6y = 16
4x -2y = 1
Cross-multiply the two equations by the coefficients of variable y.
-14x -12y = -32
-24x + 12y = -6
____________
-38x = -38
x =1
The value of y will be calculated as,
4x - 2y = 1
4 -2 y = 1
y = 3 / 2
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solve for c. Solve the following formula for the indicated variable
Answer:
c=2a/h-b
Step-by-step explanation:
I need a answer asap
Use the number line below, where RS=6y+3 , ST=4y+8 , and RT=61.
a. What is the value of y?
b. Find RS and ST.
Solving the provided question, we can say that from given number line, value of y is 5 and RS is 33 ST is 28.
what is number line?A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.
RS + ST = RT
10y+ 11 = 61
loy = 50
putting values
RS 5 33
ST 4 * 5 + = 28
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In the statement, a property of real numbers has been incorrectly applied.
Correct the right side of the statement.
3(x + 8) = 3x + 8
What is the value of 2(x divided by y)3 yo the third power+z. If X=72, Y=23, Z=12
Therefore , the solution of the given problem of expression comes out to be 589418163090.78.
Expression : what is it?Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.
Here,
Given :
=> 2 x/y [tex]3^{z}[/tex]
At x = 72 , y=23 , z=23
So,
Putting values
=> 2*72/23 * 3²³
=> 589418163090.78
Therefore , the solution of the given problem of expression comes out to be 589418163090.78.
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Match the numbers on the left with all appropriate number sets on the right. A number on the left may match with more than one number set on the right
Each of the numbers on the left should be matched with all appropriate number sets on the right as follows:
√5 ⇒ Irrational.6 ⇒ Natural, Whole, Integer, Rational.1/2 ⇒ Rational.-2 ⇒ Integers, Rational.What are the types of numbers?In Mathematics, there are six (6) common types of numbers and these include the following:
Irrational numbers.IntegersNatural (counting) numbers.Real numbersRational numbers.Whole numbers.What is a rational number?In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 6, 12, 1/2, 0.5, √16, -2, etc.
Additionally, -2 can be classified as both a rational number and an integer.
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What is the greatest common factor of 6 and 10? 2 4 6 10
The correct answer is (option A)
How did we figure this out?
We are trying to find the greatest common factor of 6 and 10 so we need to divide 10 and 6:
→ 10/6
→ = 1.6
→ = 2
How does it equal 2?Now we are rounding the number 1.6. 6 is close to 10 so it would equal 10 = 2
Therefore, the correct answer is (option A)
What are the domain and range of the function f(x) =-x+3-2
Therefore , the solution of the given problem of domain comes out to be
Domain =[-∞,∞) and Range: (-∞,∞].
What is a domain?A function's domain is the range of possible arguments that it may accept. These integers indicate the cin of a polynomial like f. (x). The range of potential values that can be used with a function is known as its domain. The number that the method returns after inserting the x value belongs to this set. The formula for a function with y as the predictor variables and x as the regression coefficient is y = f. (x). When a single value of y can be successfully produced from a value of x, that x values is said to fall within the domain of the function.
Given : f(x) = -x+3-2
after being streamlined, y = -x + 1
To Locate: What are the function's domain and range?
Solution:
In relation to the Domain:
=> -x + 1 < 0
=> -x < -1
Domain =[-∞,∞) thus.
for the range
=> -x + 1 < 0
=> -x < -1
=>f(x)= -x -1 Consequently, Range: (-∞,∞]
Therefore , the solution of the given problem of domain comes out to be
Domain =[-∞,∞) and Range: (-∞,∞].
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Which statements are true about a histogram? Select all that apply.
Group of answer choices
The bars in a histogram don't touch.
You can find the exact value of the median if you are given only the histogram.
The bars in a histogram represent frequency.
A histogram must go up by the same interval on the horizontal axis.
A histogram can have a horizontal axis with different intervals.
In the question given, only option a, c and e are correct because the bars in a histogram do not touch, the bars also represent the frequency and the histogram can have a horizontal axis with different intervals
What is a HistogramA histogram is a graphical representation of data that uses bars of different heights to show the frequency of a particular variable. It is used to show the distribution of numerical data.
In the given question, we can simply select the right choices and eliminate the wrong ones.
In option A, the bars in a histogram don't touch. This is true because in histogram, the bars do not touch.
In option B, this is false because we can't find the exact value of the median with only the histogram.
In option C, this is true because the bars represents the frequency of the data.
In option d, this is false as the histogram must not go up the same interval along the horizontal axis.
In option e, this is true because the histogram can have a horizontal axis with different intervals.
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Find the average rate of change of g(x)=3x^2-5x from x=4 to x=8 simplify your answer as much as possible
The average rate of change of g(x)=3x^2-5x from x=4 to x=8 is 90
How to determine the average rate of changeFrom the information given, we have that;
g(x) = 3x² - 5x
To determine the rate from x = 4 to x = 8
First, substitute the value of x as 4, we get;
g(4) = 3(4)² - 5(4)
expand the bracket, we get;
g(4) = 48 - 20
Subtract the values
g(4) = 28
For g(8), we get;
g(8) = 3(8)² - 5(8)
expand the bracket
g(8) = 192 -- 40
subtract the values
g(8) = 152
The average rate is;
= 152 + 28/2
= 90
Hence, the value is 90
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What is the proof of the non-existence of a solution of a Diophantine equation?
Answer:
Let a, b and c be integers with a≠0 and b≠0, and let d=gcd(a,b). If d does not divide c, then the linear Diophantine equation ax+by=c has no solution.
What Is the Domain Graph
A. 3 < y < 5
B. < x < 5
C. 2 < x < 5
D. 3 < y < 5
HELLLPPP PLEASEEEEEE ASAPP
Answer: C. the domain is 2 to 5 because it's the x axis
Step-by-step explanation:
2 questions, giving 28 points!
write two numbers that multiply to the value on top and add to the value
-30
+
+4
7
The numbers that result in the top and bottom numbers are: -3.83 and 7.83
What is System of Linear Equations?System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
x y= -30............ (1)
and, x + y= 4 ...................(2)
So, x + (-30/x)= 4
x² - 30 = 4x
x² -4x -30 = 0
Solving the Quadratic Equation
x= (4 ±√4² - 4(1)(-30) / 2)
x= (4 ± √136)/ 2
x= (4 ± 11.66)/2
x= (4+ 11.66)/2 or x= (4- 11.66)/2
x= 15.66/2 or x= -7.66/2
x = 7. 83 or x= -3.83
So, For y=7.83
x+ y = 4
x= -3.83
For y=-3.83
x+y=-4
x+(-3.83)= 4
x= 7.83
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✔) The tectonic plates of the ocean floor are constantly spreading. The Mid-Atlantic Ridge is
spreading slowly at about 5 x 10 kilometers per year. The East-Pacific Rise is spreading
faster at about 1.5 x 10 kilometers per year.
)) Use these numbers to complete the sentence below. Write your answer in standard form,
without using exponents.
The East-Pacific Rise is spreading about
times as fast as the Mid-Atlantic Ridge.
Ver en
As a result, the East Pacific Rise rate of change extends by around 6 to 16 centimeters annually, compared to the Mid-Atlantic Ridge's 2 to 5 cm.
What factors appear to determine a mathematical change rate?The relation of one quantity's changes to someone else's change is known as the rate of change. The rate of change in linear relationships is constant. Here are a few instances with varying rates: Every week, forty rats are added to the rat population. When an automobile is moving at 68 km, its distance traveled grows by 68 mph over time. When calculating the change in distance for a car employing 27 miles per gallon, the duration is multiplied x 27 mile for each gallon.
Here,
Using the data in the inquiry
Conclusion: As a result, we may say also that East Pacific Rise is expanding more quickly than the Mid-Atlantic Ridge.
The East Pacific Rise expands roughly 6 to 16 centimeters year, whereas the Mid-Atlantic Ridge distributes about 2 to 5 centimeters annually.
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find the gradient vector field of f. f(x, y) = tan(3x − 4y)
The gradient vector field of f(x, y) = tan(3x − 4y) is ∇f = (3 [tex]sec^2[/tex](3x − 4y) , −4 [tex]sec^2[/tex](3x − 4y)).
The gradient vector field of f(x, y) = tan(3x − 4y) is given by ∇f = (3 [tex]sec^2[/tex](3x − 4y) , −4 [tex]sec^2[/tex](3x − 4y))
The gradient vector field, also known as the gradient of a scalar function, is a vector-valued function that describes the direction of the steepest increase of a scalar function at a given point. It is represented by the symbol ∇ and is defined as the vector of partial derivatives of the function with respect to each variable.
To find the gradient vector field of f(x, y) = tan(3x − 4y), we take the partial derivatives with respect to x and y:
∂f/∂x = 3 [tex]sec^2[/tex](3x − 4y)
∂f/∂y = −4 [tex]sec^2[/tex](3x − 4y)
The gradient vector field is a useful tool in vector calculus and can be used to find the direction of the maximum increase of a scalar function, the direction of a vector field, the direction of a level curve, the equation of a tangent plane, and many other applications.
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A sphere has a volume of 400cm3 find the volume of sphere N whose radius is half radius of m
Answer:
The volume of sphere N is 400cm3/8 = 50cm3
Step-by-step explanation:
The volume of a sphere is given by the formula: V = 4/3 * π * r^3
where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.
Given that the volume of sphere M is 400cm3 and the radius of sphere N is half the radius of sphere M, we can write an equation to find the volume of sphere N:
Vm = 4/3 * π * rm^3 = 400cm3
We know that radius of sphere N is half of sphere M so
rn = rm/2
So the volume of sphere N can be found by substituting the value of radius of sphere N in the sphere volume formula:
Vn = 4/3 * π * (rm/2)^3
Vn = 4/3 * π * (rm^3)/8
Vn = (Vm)/8
So, the volume of sphere N is 1/8th of the volume of sphere M, which is 400cm3.
The volume of sphere N is 400cm3/8 = 50cm3
Select the correct answer from each drop-down menu.
Find the asymptote and determine the end behavior of the function from the graph.
-5
-3 -2
-1
y
5
3
2
1
2
3
4
X
5
The asymptote of the graph is given as 3
How to find the asymptote of a graph?As one or both of the x or y coordinates go to infinity, a line is said to be an asymptote of a curve in analytic geometry when the distance between the curve and the line approaches zero.
The value of x from the graph here is given as 3. The curve cuts across the x axis at 3. This is the value as x moves towards positive infinity
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5+5= Calculate the mean and the median of the frequency distribution given below : Class Limit 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 5 10 25 30 20 10
Therefore ,the mean of given data is 36, Simply dividing the total number of values by the sum of all the values in the data set yields it.
What in math is a mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Here,
Given :
=> Mean=summation of fxi
=> Mean = 3600 /100 = 36
Therefore , the solution of the given problem of mean is comes out to be
Mean = 36.
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Evelyn bought some belts online for $70. She used a coupon code to get a 10% discount. The website also applied a 5% processing fee to the price after the discount. How much did Evelyn pay, in the end? Round to the nearest cent.
Answer:
66.15
Step-by-step explanation:
70 dollars - discount + fee
discount = 10% of total = 10% of 70 = 0.1 * 70 = 7
fee = 5% of discounted price
discounted price = original - discount = 70 -7 = 63
fee = 5% of 65 = 0.05 * 65 = 3.15
70 - 7 + 3.25 = 66.15
What is the radius of a globe that has a volume of 904.78 in³?
The radius of the globe with a volume of 904.78 in³ is 6 in.
What is the volume of a sphere?The amount of space occupied within a sphere is referred to as its volume. Every point on the surface of the sphere is equally spaced from its centre, making it a three-dimensional round solid figure.
The fixed point and fixed distance are referred to as the sphere's centre and radius, respectively.
Given that the volume of the sphere is 904.78 in³. The radius of the sphere is calculated as,
Volume = ( 4 / 3 )πr³
r³ = ( 3 x volume ) / 4π
r³ = ( 3 x 904.78 ) / 4π
r³ = 2714.34 / 4π
r³ = 216
r = 6 in
Hence, the radius of the globe is 6 in.
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In ACDE, m/C = 67° and m/D = 52°. Which statement about the sides of ACDE
must be true?
If one angle is 67° and the other is 52°, the other two angles are equal and the angle has a value of 120°.
what is angle ?A place where two lines converge creates an angle. They are quantified in degrees and are denoted by the symbol °. Four essential types are reflex, acute, right, and obtuse angles. A circle has 360 degrees. One terminal exists when two rays (half-lines) are merged form an angle. The rays are referred to as the angle's sides, occasionally as its legs, and occasionally as its arms, while the latter is referred to as the angle's vertex. The place where all points of an angle converge is known as the vertex.
given
total interior angles = 360°
m/C = 67° , m/D = 52°
67° + 52° + 2x = 360 °
119 + 2x = 360 °
2x = 360 ° - 119°
x = 120°
if one angle is 67° and the other is 52°, the other two angles are equal and the angle has a value of 120°.
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The complete question is :-In ACDE, mzC = 67° and mzD = 52°. Which statement about the sides of ACDE must be true?
DE > CD > EC
DE > EC > CD
EC > CD > DE
EC > DE > CD
CD > DE > EC
CD > EC > DE
Lorraine prepared a 4.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.5 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars can Lorraine fill?
3 jars
9 jars
10 jars
12 jars
12
Step-by-step explanation:
bc i did the math
Answer: The answer is 12.
Step-by-step explanation:
The answer is twelve because if you divide 1.5 by 4, it equals 0.375, and then you divide 4.5 by 0.375, you get 12! hope this helps!
Answers for 5,6,7 please I need help
Description Interval notation Set builder notation
5. (-∞, -4] {x | x ≤ -4 |
6. (-∞, ∞) { x | x all real numbers }
7. (-11/3, 17/3] { x | x -11/3 < x ≤ 17/3 }
What is interval notation?Continuous sets of real numbers can be represented using interval notation by the numbers that bound them. When written, intervals resemble ordered pairs in several ways.
In interval notation ( ) means open interval, [ ] represents closed interval
Numbers on the square brackets are included in the notation while numbers of the braces (open interval) are not included
Set builder notation is a type of mathematical notation used to describe sets by naming its components or highlighting the requirements that each member of the set must meet.
Set builder notation used curtly brackets to carry out the information.
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Find the mass and center of mass of the lamina that occupies the region D and has the given density function ?.
D is bounded by y = (1 ? x^2) and y = 0;
?(x, y) = 7ky
m =
(x bar, y bar)=
To find the mass of the lamina, we need to integrate the density function over region D. The density function is given by? (x, y) = 7ky, where k is a constant. The region D is bounded by y = [tex](1 ? x^2)[/tex] and y = 0, and the limits of integration are [tex]0 < = y < = (1 - x^2)[/tex] .
So, the mass of the lamina is:
[tex]m = ∫∫?(x, y) dx dy = ∫∫ 7ky dx dy\\= 7k ∫∫ y dx dy = 7k * ∫ (1 - x^2) dy dx\\= 7k * ∫(0 to 1 - x^2) y dy\\= 7k * (1/2 * ∫(0 to 1 - x^2) y^2 dy)\\= 7k * (1/2 * [y^3/3] evaluated at y = (1-x^2) and y=0)\\= 7k * (1/2 * [((1-x^2)^3/3] - 0))= 7k * (1/2 * (1/3 - x^6))[/tex]
To find the center of mass (x bar, y bar) of the lamina, we need to find the x and y coordinates of the center of mass.
The x-coordinate is given by
[tex](x bar) = 1/m * ∫∫ x ?(x, y) dx dy = 1/m * ∫∫ x * 7ky dx dy \\= 7k * ∫ (x * y) dx dy\\= 7k * (x * 1/2 * ∫(0 to 1 - x^2) y^2 dy)\\= 7k * (x * 1/2 * [y^3/3] evaluated at y = (1-x^2) and y=0)\\= 7k * (x * (1/2 * (1/3 - x^6))\\The y-coordinate is given by\\(y bar) = 1/m * ∫∫ y ?(x, y) dx dy = 1/m * ∫∫ y * 7ky dx dy= 7k * ∫ (y^2) dx dy\\= 7k * (1/3 * ∫(0 to 1 - x^2) y^3 dy)\\= 7k * (1/3 * [y^4/4] evaluated at y = (1-x^2) and y=0)\\= 7k * (1/3 * (1/4 - x^6/2))[/tex]
It's worth noting that the mass and center of mass of the lamina depend on the constant k, which is not specified in the problem.
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The stadium capacity allows for players,
radio and newspaper reporters, and stadium
workers in addition to spectators. How many
of these people could be at a game?
A right Riemann sum has the formula A=∑ni=1Δxf(xi) A = ∑ i = 1 n Δ x f ( x i ) where x is the width of each of the n rectangles and f(xi) is the height.
what is is Riemann sum?A specific method of approximating an integral with a finite sum in mathematics is known as a Riemann sum. Riemann is the name of a German mathematician who lived in the 19th century. Approximating the area of functions or lines in graphs, as well as the length of curves and other approximations, is a highly typical application. The picked points in each subinterval of the partition are all in the upper Riemann sum, given an interval partition. The interval is often separated into subintervals of equal size.
Riemann sum formula is A=∑f(xi)Δx A = ∑ f ( x i ) Δ x ,
where A is the curve's area under the evaluable interval,
f(xi) f ( x i ) is each rectangle's height (or the average of the two heights in the case of a trapezoid)
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On solving the provided question, we can say that By addition, people could be at a game = 42,500 - 275 = 42225
what is addition?The other three fundamental operations are subtraction, multiplication, and division. Addition is one of the four basic operations. The sum or total of these combined values is obtained by adding two integers. The process of merging two or more numbers is known as addition in mathematics. Numbers are added together to form addends, and the outcome of this operation, or the final response, is referred to as the sum. This is one of the crucial mathematical operations we employ on a regular basis. You would add numbers in a variety of circumstances. Combining two or more numbers is the foundation of addition. You can learn the fundamentals of addition if you can count.
By addition,
Stadium capacity = 42,500
General admission seating = 31,750
Reserved seating = 10,475
42,500-( 31,750 + 10,475 ) =42,500- 42225 = 275
people could be at a game = 42,500 - 275 = 42225
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I. need help please…