Posted in Mathematics

5712 milligrams
0.005712 kilograms


Related Questions

Posted in Mathematics

Explain a thought process you might use when trying to find the additive or multiplicative inverse of a number or expression. …?

Definition of additive inverse.- If two numbers are added together and the sum is zero, they are the additive inverse of each other. 

………………………………….. IF A + B = 0 , they are the additive inverse of each other. 

Multiplicative Inverse.- If two numbers are multiplied together and the product is one. They are the multiplicative inverse of each other, also called reciprocal. 

………………………………….. A.B = 1 , they are the multiplicative inverse of each other. 

Example of: 

Additive inverses :……………. 5 + ( – 5 ) = 0 

Multiplicative inverses………..5 x 1/5 = 1 

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Rational expressions (for what value of x is the rational expression below undefined)? 3x-12/9-x …?

Answer:

For x = 9  the given rational expression frac{3x-12}{9-x}  is undefined.

Step-by-step explanation:

Given rational expression frac{3x-12}{9-x}

We have to find for what value of x is the given rational expression is undefined.

Consider the given rational expression frac{3x-12}{9-x}

For a fractional expression to be undefined the denominator has to be zero, so that frac{x}{0}=infty

Thus, for the given expression frac{3x-12}{9-x}

Denominator is 9-x

Thus, to make it not defined, Put 9 – x = 0

⇒ x = 9

Thus, for x = 9  the given rational expression frac{3x-12}{9-x}  is undefined.

Posted in Mathematics

If you save two pennies on January 1, four pennies on January 2, six pennies on January 3, and continue this pattern for one year (not a leap year), what will be the value of your entire savings, in dollars, at the end of that one year? Express your answer as a decimal without commas. …?

The answer is 
1J,  2J, 3J, ……………29D, 30D, 31D = 365 days
2     4     6 ………………………………….
 let be S  the value of entire savings
S= Sum 2K= 2 
Sum K      = 2 [365(365+1) / 2], 
      1<K<365    
 1<K<365
because  
Sum K = n(n+1) /2
               
1<K<n

finally S= 133590 pennies

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Find the complete solution of the linear system, or show that it is inconsistent. (If the system has infinitely many solutions, express your answer in terms of t, where x = x(t), y = y(t), and z = t. If there is no solution, enter NO SOLUTION.) x − y + 2z = 1 3x + y + 5z = 19 2x − y − 2z = −17 (x, y, z) = ( ________ ) …?

x − y + 2z = 1
3x + y + 5z = 19
2x − y − 2z = −17

-3x+3y-6z=-3

3x + y + 5z = 19

4y-z=16 (1)

-2x+2y-4z=-2
2x − y − 2z = −17

y-6z=-19  (2)

4y-z=16  (1)
y-6z=-19 (2)

4y-z=16 
-4y+24z=76

23z=92
z=4

y-6z=-19
y-6×4=-19
y-24=-19
y=24-19
y=5

x − y + 2z = 1
x-5+2×4=1
x-5+8=1
x+3=1
x=-2

(x,y,z)=(-2,5,4)

Posted in Mathematics

The expression below is a sum of cubes. 125×3 + 144 A.True B.False …?

An expression is a sum of cubes if it can be written in form of a³ + b³, where a and b can be any constant/variables.

So, this means the given expression 125x³ + 144 can only be sum of cubes if the both the terms i.e. 125x³ and 144 are perfect cubes.

125x³ = (5x)³ . This means 125x³ is a perfect cube. However, 144 is not a perfect cube.

Hence we can conclude that the expression 125x³ + 144 is not a sum of cubes. So the answer to this question if FALSE

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Posted in Mathematics

Which of the following expressions is this one equivalent to? (3x^3+15x^2+17x+3)/x+5 A. x^3-2x+5+(7/x+5) B. 3x-17+(88/x+5) C. 3x^2+17-(82/x+5) D. 3x^2-5x-8-(37/x+5) …?

Answer:

option (c) is correct,

3x^2+17-frac{82}{x+5} is the equivalent fraction to the given expression frac{3x^3+15x^2+17x+3}{x+5}

Step-by-step explanation:

Given expression ,  frac{3x^3+15x^2+17x+3}{x+5}

We have to choose an equivalent fraction from the given options.

Consider expression (c) ,

3x^2+17-frac{82}{x+5}

Taking LCM , Multiply 3x^2+17 by (x+5) , we get,

frac{3x^2(x+5)+17(x+5)-82}{x+5}

On solving , we get,

frac{3x^3+15x^2+17x+85-82}{x+5}

On simplifying, we get,

frac{3x^3+15x^2+17x+3}{x+5}

Which is equal to the given expression.

Thus, option (c) is correct,

3x^2+17-frac{82}{x+5} is the equivalent fraction to the given expression frac{3x^3+15x^2+17x+3}{x+5}

Posted in Mathematics

Express answer in exact form. Find the area of one segment formed by a square with sides of 6″ inscribed in a circle. (Hint: use the ratio of 1:1:√2 to find the radius of the circle.)

The answer is 5.13 in²

Step 1. Calculate the diameter of the circle (d).
Step 2. Calculate the radius of the circle (r).
Step 3. Calculate the area of the circle (A1).
Step 4. Calculate the area of the square (A2).
Step 5. Calculate the difference between two areas (A1 – A2) and divide it by 4 (because there are total 4 segments) to get the area of one segment formed by a square with sides of 6″ inscribed in a circle.

Step 1:
The diameter (d) of the circle is actually the diagonal (D) of the square inscribed in the circle. The diagonal (D) of the square with side a is:
D = a√2            (ratio of 1:1:√2 means side a : side a : diagonal D = 1 : 1 : √2)
If a = 6 in, then D = 6√2 in.
d = D = 6√2 in

Step 2.
The radius (r) of the circle is half of its diameter (d):
r = d/2 = 6√2 / 2 = 3√2 in

Step 3.
The area of the circle (A1) is:
A = π * r²
A = 3.14 * (3√2)² = 3.14 * 3² * (√2)² = 3.14 * 9 * 2 = 56.52 in²

Step 4.
The area of the square (A2) is:
A2 = a²
A2 = 6² = 36 in²

Step 5:
(A1 – A2)/4 = (56.52 – 36)/4 = 20.52/4 =  5.13 in²

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Posted in Mathematics

if the tax that you pay when you purchase an item is 12% of the sale price, write an expression that gives the tax on the item with a price p. write another expression that gives the total price ofthe item, including tax. – what operations are involved in th expression you wrote -determine the total price, including tax, of an item that costs 75. -explain how the order of operation helped you solve this problem.

Let be t the tax, 
so the tax on the item with a price p is:
t=(12 x p) /100
the total price of the item, including tax
let be T=
the total price, including tax
so T= t+p, where t=(12 x p) /100
so T = 112p/100

he total price, including tax, of an item that costs 75.
by using T = 112p/100, 
we can get T= 112 x 75 / 100, T=84

the problem is not difficult, so as fo me it is obvious

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