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3 years ago

If average of m numbers is n^2 and average of n numbers is m^2 then average of m+n numbers is

1 answer:

4 0

The sum of the m numbers divided by m (which is the average) equals n^2. Then, the sum of the m numbers equals mn^2.
The sum of the n numbers divided by n (which is the average) equals m^2. Then, the sum of the n numbers equals nm^2.
The average of m+n numbers which is the sum of the m numbers plus the sum of the n numbers divided by (m+n) equals (mn^2+nm^2)/(m+n). This is mn(n+m)/(m+n). Then the factor (m+n) can be ruled out and the result is mn.

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I need help please.

Ivan

1. It is given that f(x) is 16 times the square root of x.

Putting that in mathematical terms we have,

f(x) = 16 * $\sqrt{x}$

also, y = f(x)

So, we have the function

y= 16 $\sqrt{x}$

4. We need to solve the inequality equation : 4x + 2y ≤ 6

Let us take the equation,

4x+2y ≤ 6

2y ≤ 6-4x

y ≤ $\frac{6-4x}{2}$

y ≤ 3-2x

So, any point (x,y) lies on the given inequality region, where y≤ 3-2x

5. Solving system of equations using addition method

Given:

-5x-y =38 ------> a

-6x-3y =60 -------> b

Divide the equation b by no. 3

(-6x-3y)/3 = 60/3

-2x-y = 20 -------> c

Subtracting equation c from a we have,

-5x-y - (-2x-y) = 38 - 20

-5x-y+2x+y = 18

-3x = 18

x = -6

Now, substituting the value of x in equation a, we get

-5(-6) - y =38

30-y =38

y= 30-38 = -8

y=-8

∴ x = -6 and y = -8

6. Finding composition of functions

Given : f(x) =15x + 7 ; g(x) = x² - 5x

To find : (f+g)(x)

(f+g) (x) = f(g(x))

So, replace the value of x in f(x) by g(x), where g(x)= x² - 5x

(f+g)(x) = 15(x²-5x) +7 =15x²-75x+7

∴ (f + g)(x) = 15x²-75x+7

7. System of 3 equations must be solved to find the solution

-8x-8y-5z=-6

7x-8y-9z =17

9x+2y+6z =-1

Solving by substitution method.

Isolate x from first equation :

x= (-6+8y+5z)/(-8)

Substitute this value of x in 2nd and 3rd equations.

$7 (- \frac{-6+8y+5z}{8})-8y -9z = 17$

$9(- \frac{-6+8y+5z}{8}) + 2y + 6z = -1$

Now, isolating y from the 2nd equation rewritten above, we have

y= - $\frac{107 z + 94}{120}$

Now substituting this value of y in the 3rd equation rewritten above, we have

$9(- \frac{-6+8(-\frac{107 z + 94}{120})+5z}{8}) + 2(-\frac{107 z + 94}{120}) + 6z = -1$

Isolating z from above equation, we have

z = -2

Substitute z= -2 in the equation of y, we have

y= - $\frac{107 (-2) + 94}{120}$ = 1

y = 1

Substituting the value of y and z, in the equation of x, we have

x= (-6+8(1)+5(-2))/(-8) = 1

x = 1

∴ x=1 ; y = 1 ; z = -2

8. 5x ≤ 7

Solving the above equation, we have

x ≤ 7/5

Please see attachment for the graph.

9. The given function is : g(y) = $\sqrt{y}$ -6

The domain is the set of values of y for which there can be a value of g(y).

Here g(y) can be real only if y is greater than or equal to 0.

∴ The domain of the given function is [0,∞) .

10. Given : y is a function of x.

Definition of function : A function is a relation that associates each element in the domain to one element of another set, the co-domain of the function.

∴ For each element x, in the domain, there is only one value of y in the range.

4 0

2 years ago

Please help with the question!

MAVERICK [17]

Answer:

68.2275604137

Step-by-step explanation:

you can round down

I hope this helps

8 0

2 years ago

What is the volume of the cone? Use 3.14 for π. Round your answer to the nearest hundredth.

Tasya [4]

Answer:178.71696m^3

Step-by-step explanation:

To find the volume of cone=1/3πr2h

To find the height using pythagoras theorem and the theorem state that the square on the hypotenuse of a right-angled triangle is the same or equal in area to the sum of the squares on the other two sides.

7^2=h^2+3^2

h^2=49-9

h=√40

h=6.32m

V=1/3×3.142×3m×3m×6.32m

Therefore our answer is;

V=178.71696m^3

7 0

3 years ago

Which expression is equal to (6x−4)(3x−1)?

Natali5045456 [20]

Answer:

$(6x-4)(3x-1) = 18x^2 - 18x + 4$ is the required simplification.

Step-by-step explanation:

Here, the given expression is (6x−4)(3x−1).

By DISTRIBUTIVE PROPERTY of numbers:

A ( B + C ) = AB + AC

Simplifying the given expression, we get:

$(6x-4)(3x-1) = 6x(3x-1)-4(3x-1)\\= 6x(3x) -1(6x) -4(3x) +4\\=18x^2 - 6x - 12x + 4\\18x^2 - 18x + 4$

or, $(6x-4)(3x-1) = 18x^2 - 18x + 4$

Hence the given expression is simplified.

3 0

3 years ago

Simplify a5 ÷ a4, a ≠ 0.<br> A) 5a<br> B) a<br> C) 4a<br> D) 1

wel

I assume you mean a^5 divided by a^4. This is a rule that applies to all exponents in that when you divide exponents, you subtract the top from the bottom. So, 5-4 is 1 and that would the answer is b

8 0

2 years ago