A computer costing Rs. 34,000 is sold at Rs. 38080 including VAT. Find the amount of VAT and its percentage.​

Answer:

= −135.47x

Step-by-step explanation:

^^^^^^^^^^^^^^^

Answer:

D

Step-by-step explanation:

The line of best fit is a line that represents the “average” between all of the points. It’s typically in the middle of all of the points. In this case, I’d go with D because 4 points lie on the line of best fit and the line trends sharply upwards, following the general direction of the points.

The factored form of 3y - 18 using the G.C.F. is 3 * (y - 6).

What is the factor?

Factor is a mathematical expression or a number that divides another expression or number evenly. The factor of an expression is a number that divides the expression evenly, leaving no remainder.

The expression 3y - 18 can be factored using the greatest common factor (G.C.F.) of 3.

The G.C.F. of 3 and 3y is 3.

So, 3y - 18 can be factored as:

3 * (y - 6)

Hence, The factored form of 3y - 18 using the G.C.F. is 3 * (y - 6).

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Answer:

5:1

Step-by-step explanation:

10 divided by 2 is 5

2 divided by 2 is one.

Hope you get a good Grade!

Answer:

5:1

Hope this helps!

Answer:

1

Step-by-step explanation:

The exponent is the number of times you multiply the base aka i in this case.

i = -1

Substitute -1 for i.

-1^2

-1 x -1 = 1

because when you multiply two negatives they make a positive.

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Answer:

d) More than 3.

Step-by-step explanation:

The polynomial (x - 5)(x + 2)  ( = x^2  - 3x + 10) has zeros of -2 and 5 but so have the polynomials formed by multiplying this by any integer:

- for example 2(x - 5)(x + 2) , 4(x - 5)(x + 2) and so on.

Answer:

38.97 kilograms

Step-by-step explanation:

38 ones and 97 hundredths

38                  0.97

38.97

Answer:

The length of the short side was 12 and the length of the long side was 32

Step-by-step explanation:

We will say that the length is the shorter side, and be using l as the variable, and that width is the longer side, and be using w as the variable. The first two equations we have are:

w = l + 20

And

2(2l + 3w) = 240

We will start with the second equation, then substitute in the first equation for w. We have:

4l + 6w = 240

Divide both sides by 2:

2l + 3w = 120

Then, we substitute in l + 20 for w, giving us:

2l + 3l + 60 = 120

Subtract 60 from both sides and combine like terms:

5l = 60

l = 12

So, the original length was 12, now substituting this into our first equation gives us:

w = 12 + 20 = 32

So the original width was 32. So, the length of the short side was 12 and the length of the long side was 32.

Hope this helped!

Answer:

It is -108

Step-by-step explanation:

Hope it helps!

Answer:

r = ± \(\sqrt{S+2t}\)

Step-by-step explanation:

S = r² - 2t ( add 2t to both sides )

S + 2t = r² ( take square root of both sides )

± \(\sqrt{S+2t}\) = r

Answer:

-3/5

Step-by-step explanation:

-2/5+-1/5= -3/5

I used a calculator to ensure this answer was correct

The coordinates of the image if this pre-image is reflected across the x-axis is simply the same x-coordinates and their opposite y-coordinates.

When reflecting an image across the x-axis, the x-coordinates remain the same, while the y-coordinates become their opposite. In other words, to reflect a point across the x-axis,

we simply change the sign of the y-coordinate of the point.For example, suppose we have a point P with coordinates (2, 4). If we reflect P across the x-axis,

the resulting image point, P', would have coordinates (2, -4). This is because the x-coordinate of P, which is 2, remains the same, while the y-coordinate, which is 4, becomes -4

when we change its sign.Another example would be reflecting point A(-3, 2) across the x-axis. The x-coordinate of A remains -3 and the y-coordinate becomes its opposite so the coordinate of the image point A' would be (-3, -2)

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Every number between 3 and 5 is included in the Union where x∈R of [3− x^2,5+ x^2], and no number outside of that range is included. The union is equal to [3,5].

To prove that the Union where x∈R of [3− x^2,5+ x^2] = [3,5], we need to show that every number between 3 and 5 is included in the union, and no number outside of that range is included. First, let's consider any number between 3 and 5. Since x can be any real number, we can choose a value of x such that 3− x^2 is equal to the chosen number. For example, if we choose the number 4, we can solve for x by subtracting 3 from both sides and then taking the square root: 4-3 = 1, so x = ±1. Similarly, we can choose a value of x such that 5+ x^2 is equal to the chosen number. If we choose the number 4 again, we can solve for x by subtracting 5 from both sides and then taking the square root: 4-5 = -1, so x = ±i. Therefore, any number between 3 and 5 can be expressed as either 3- x^2 or 5+ x^2 for some value of x. Since the union includes all such intervals for every possible value of x, it must include every number between 3 and 5. Now, let's consider any number outside of the range 3 to 5. If a number is less than 3, then 3- x^2 will always be greater than the number, since x^2 is always non-negative. If a number is greater than 5, then 5+ x^2 will always be greater than the number, again because x^2 is always non-negative. Therefore, no number outside of the range 3 to 5 can be included in the union. In conclusion, we have shown that every number between 3 and 5 is included in the Union where x∈R of [3− x^2,5+ x^2], and no number outside of that range is included. Therefore, the union is equal to [3,5].

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Thus, the general solution of the given differential equation `2y′ y = 5t²` is `y = Ke^(5t³/6)` where `K` is a constant of integration.

The general solution of the given differential equation `2y′ y = 5t²` and using it to determine how solutions behave as t is discussed below:Solving the differential equation:

Separating the variables of the differential equation `2y′ y = 5t²` we get:dy/y = (5/2)t² dtIntegrating both sides, we have:ln|y| = (5/6) t³ + C1

Taking the exponential of both sides, we get:y = Ke^(5t³/6) , where K = ± e^(C1) is a constant of integration.

The general solution of the given differential equation is given by `y = Ke^(5t³/6)` where `K` is a constant of integration.

How solutions behave as `t`:When `t → ∞` (i.e., as t grows large), `e^(5t³/6) → ∞`. So solutions of the given differential equation `y′ y = 5t²` grow exponentially as `t → ∞`.

When `t → -∞` (i.e., as t gets very negative), `e^(5t³/6) → 0`. So solutions of the given differential equation `y′ y = 5t²` approach `y = 0` as `t → -∞`.

Thus, the general solution of the given differential equation `2y′ y = 5t²` is `y = Ke^(5t³/6)` where `K` is a constant of integration.

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Answer:

  D(3.4, 20.8)

Step-by-step explanation:

Given points B(-2, 10) and C(8,7), you want the coordinates of point D such that BD has a slope of 2 and CD has a slope of -3.

The equation for the slope between two points is ...

  m = (y2 -y1)/(x2 -x1)

Using this formula and the given points, we can find D(x, y) to satisfy ...

  2 = (y -10)/(x +2)

  -3 = (y -7)/(x -8)

Putting each of these equations in general form, we have ...

  2(x +2) -(y -10) = 0

  2x -y +14 = 0

and

  -3(x -8) -(y -7) = 0

  3x +y -31 = 0

Adding the two equations eliminates the y-variable:

  (2x -y +14) +(3x +y -31) = 0

  5x -17 = 0 . . . . . . simplify

  x -3.4 = 0 . . . . . . divide by 5

  x = 3.4 . . . . . . . . . add 3.4

Substituting for x in the first equation gives ...

  2(3.4) -y +14 = 0

  y = 6.8 +14 = 20.8 . . . . add y

The point D has coordinates (3.4, 20.8).

__

Additional comment

The graph shows the equations of the lines written in point-slope form.

The circles can be proven to be similar by applying a dilation transformation with a scale factor of 3/2 and a translation transformation of 1 unit downwards.

To prove that two circles are similar, we need to show that they have the same shape but possibly different sizes. In this case, Circle 1 and Circle 2 can be proven to be similar by applying certain transformations.

First, we can apply a dilation transformation to Circle 1. The dilation will enlarge or shrink the circle while maintaining its shape. The scale factor of the dilation can be found by comparing the radii of the two circles. The ratio of the radii is 15/9 = 5/3. Therefore, Circle 1 can be dilated by a scale factor of 5/3 to match the size of Circle 2.

Next, we can apply a translation transformation to Circle 1. The translation will move the circle while preserving its size and shape. In this case, Circle 1 can be translated 1 unit downwards to align its center with the center of Circle 2.

By applying a dilation transformation with a scale factor of 5/3 and a translation transformation of 1 unit downwards to Circle 1, we can prove that the circles are similar.

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Answer:

A.

Step-by-step explanation:

The answer would be 324 because: 12+12+12= 36, 36+36+36= 108 so thus 108+108+108 equals 324.

Hope my answer helped you and if it did I'd really appreciate it if you can mark it the brainliest :)

Answer:

>

Step-by-step explanation:

lets make 52/9 a mixed number, 5 7/9

so >

11> 5 7/9

Answer:

3/7 times 2/3 is 2/7

Step-by-step explanation:

I used a calculator ! Please let me know if i am incorrect.

Answer:

0.28571428571

basically 0.28

Step-by-step explanation:

gooogle calculator

Answer:

x^2+11x+30

Step-by-step explanation:

Answer:

x = -2, y = -4

Step-by-step explanation:

Take the first equation-   -2y = 2 - 3x
Arrange it first-
-3x + 2y = -2

Multiply is by 5 on both sides
5(-3x + 2y) = 5(-2)
-15x + 10y = -10

Take the second equation-    -5y = 10 - 5x
Arrange it-
-5x + 5y = -10

Multiply is by 2 on both sides
2(-5x + 5y) = 2(-10)
-10x + 10y = -20

Subtract second equation from the first one-

  -15x + 10y = -10
-  -10x + 10y = -20
= -5x = 10

-5x = 10
x = 10/(-5)
x = -2

Substitute the value of x in Equation 1
-2y = 2 - 3(-2)
-2y = 2 + 6
-2y = 8
y = 8/(-2)
y = -4

Hope it helps ;)

Answer:

28

Step-by-step explanation:

Answer:

9 divided by 3= 6. You can buy 6 packages of blueberries for $9 dollars.

Step-by-step explanation:

The derivative of the function r = ∫(5 - x^4)sin(x) dx is dr/dx = (5 - x^4)sin(x).

The derivative of the function r = ∫(5 - x^4)sin(x) dx is given by dr/dx.

To find dr/dx, we need to apply the chain rule. Let's break down the expression step by step:

r = ∫(5 - x^4)sin(x) dx

Differentiating both sides with respect to x

dr/dx = d/dx [∫(5 - x^4)sin(x) dx]

Since we have an integral inside the derivative, we can apply the Fundamental Theorem of Calculus:

dr/dx = (5 - x^4)sin(x)

Therefore, the derivative of the function r = ∫(5 - x^4)sin(x) dx is dr/dx = (5 - x^4)sin(x).

The derivative represents the rate of change of r with respect to x. In this case, it shows how the function r changes as x varies. The resulting derivative is a product of two functions, (5 - x^4) and sin(x), which captures the combined effect of both factors on the rate of change.

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The global extreme values of f(x, y) subject to the constraints:

f_min ≈ 0.426

f_max = 14/5 ≈ 2.8

Lagrange multipliers are a mathematical method used to find the extreme values (maximum or minimum) of a function subject to one or more constraints.

Given function is;

f(x, y) = 4x³ + 4x²y + 5y²;    where, x, y ≥ 0, x + y ≤ 1

First, we need to set up the Lagrangian function:

L(x, y, λ) = 4x³ + 4x²y + 5y² - λ(x + y - 1)

Taking partial derivatives with respect to x, y, and λ and setting them equal to zero, we get:

∂L/∂x = 12x² + 8xy - λ = 0

∂L/∂y = 4x² + 10y - λ = 0

∂L/∂λ = x + y - 1 = 0

Solving these equations simultaneously,

x = 2/5, y = 3/5, λ = 26/25

We also need to check the boundary of the feasible region, which is the line x + y = 1. We can set y = 1 - x and substitute into the function f(x, y):

g(x) = f(x, 1-x) = 4x³ + 4x²(1-x) + 5(1-x)² = 4x³ - x² + 6x - 5

Taking the derivative of g(x) with respect to x and setting it equal to zero,

g'(x) = 12x² - 2x + 6 = 0

Solving for x,

x = (1 ± √7)/6

Therefore, the global maximum of f(x, y) subject to the constraints is:

f_max = f(2/5, 3/5) = 4(2/5)³ + 4(2/5)²(3/5) + 5(3/5)² = 14/5

f_min = f((1 - √7)/6, (5 + √7)/6) = 4((1 - √7)/6)³ + 4((1 - √7)/6)²((5 + √7)/6) + 5((5 + √7)/6)² ≈ 0.426

Therefore, the global extreme values of f(x, y) subject to the constraints:

f_min ≈ 0.426

f_max = 14/5 ≈ 2.8

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A figure with two circular bases that are congruent and parallel is a cylinder.

The correct answer is an option (c)

We know that cylinder a three dimensional geometric figure which has two  parallel circular bases at a distnace.

In cylinder, the two circular bases are joined by a curved surface which is at a fixed distance from the center.

The axis of cylinder is nothing but the line segment joining the center of two circular bases.

Also, the distance between the two circular bases is the height of the cylinder.

If the bases of the cylinder are not exactly over each other but sideways, then it is an oblique cylinder.

And if the axis of the cylinder forms a right angle with its two parallel bases then it is called a right cylinder.

Therefore, the required figure would be a cylinder.

The correct answer is an option (c)

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The complete question is:

A geometric figure with two circular bases that are congruent and parallel.What do you call a figure with two circular bases that are congruent and parallel?

a. Rectangular prism

b. Cone

c. cylinder

d. sphere

The number of observations strictly less than 24 is 7.

The five-number summary consists of the minimum value (13), the first quartile (Q1) or 25th percentile (24), the median or second quartile (Q2) or 50th percentile (38), the third quartile (Q3) or 75th percentile (51), and the maximum value (69).

Since Q1 represents the value below which 25% of the observations lie, and the five-number summary indicates that Q1 is 24, it means that 25% of the observations are less than or equal to 24.

Therefore, the number of observations strictly less than 24 is 25% of 33, which equals 7.

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