MATHEMATICS
MIDDLE SCHOOL

Answer:

Answer:

Proportion states that the two ratio or fractions are equal.

Given the statement: One grain of sand approximately weighs 7 * 10^{-5} g.

To find how many grains of sand are there in 6300 kg of sand.

Let x be the number of grains of sand in 6300 kg of sand.

Using conversion :

1 kg = 1000 g

6300 kg = 6300000 g

Then, by using proportion method, we have;

By cross multiply we get;

or

[using ]

Divide both sides by 7 we get;

Standard form is a way of of writing down very large or very small numbers easily.

Therefore, grains of sand are there in 6300 kg of sand.

MIDDLE SCHOOL

2 rectangular prism have a combined volume of 432 cubic feet. Prism a has half the volume of prism b. what is the volume of prism a? prism b

Let the volume of prism A be X. Then the volume of prism B is 2X. The combined volume could be described like this:

432 = X + 2X

Solving the equation,

432 = 3X

432/3=X

144=X

The volume of A is 144 cubic feet, while the volume of B is 288 cubic feet.

432 = X + 2X

Solving the equation,

432 = 3X

432/3=X

144=X

The volume of A is 144 cubic feet, while the volume of B is 288 cubic feet.

COLLEGE

One number is 3 more than another. The difference between their square is 63. What are the numbers?

X = y + 3

x^2 - y^2 = 63

(y + 3)^2 - y^2 = 63

(y + 3)(y + 3) - y^2 = 63

y^2 + 6y + 9 - y^2 = 63

6y + 9 = 63

6y = 54

y = 54/6

y = 9

x = y + 3

x = 9 + 3

x = 12

check...

x^2 - y^2 = 63 x = y + 3

12^2 - 9^2 = 63 12 = 9 + 3

144 - 81 = 63 12 = 12 (correct)

63 = 63 (correct)

ur 2 numbers are 9 and 12

x^2 - y^2 = 63

(y + 3)^2 - y^2 = 63

(y + 3)(y + 3) - y^2 = 63

y^2 + 6y + 9 - y^2 = 63

6y + 9 = 63

6y = 54

y = 54/6

y = 9

x = y + 3

x = 9 + 3

x = 12

check...

x^2 - y^2 = 63 x = y + 3

12^2 - 9^2 = 63 12 = 9 + 3

144 - 81 = 63 12 = 12 (correct)

63 = 63 (correct)

ur 2 numbers are 9 and 12

MIDDLE SCHOOL

Which equation has no solution?

(-x-3)=5

(2x-1)=0

(5-3x)=-8

(-x+9)=0

Answer:

All the given equations have solutions.

Step-by-step explanation:

To find the solution for (-x-3)=5

(-x-3)=5

-x + 3 = 5

x - 3 = -5

x = -5 + 3 = -2

x = -2

To find the solution for (2x-1)=0

(2x - 1) = 0

2x - 1 = 0

2x = 1

x = 1/2

To find the solution for (5-3x)=-8

(5 - 3x) = -8

5 - 3x = -8

-3x = -8 -5

-3x = -13

x = -13/-3

x = 13/3

To find the Solution for (-x+9)=0

(-x + 9) = 0

-x + 9 = 0

x = 9

HIGH SCHOOL

Complete the first step in writing the equation of a circle in graphing form. EQUATION: x^2 -2x+y^2+6y-6=0 STEP 1: x^2-2x+y^2+6y=[1]

X^2 - 2x + y^2 + 6y = 6 is the first step