What fraction of each gallon of purple paint is red paint?

Which are the solutions of the quadratic equation x2 =-5-3

alexdok [17]

Answer: x = 2 • ± √2 = ± 2.8284

Step-by-step explanation:

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 8 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step 1 :

x2 - 8 = 0

Step 2 :

Solving a Single Variable Equation :

2.1 Solve : x2-8 = 0

Add 8 to both sides of the equation :

x2 = 8

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 8

Can √ 8 be simplified ?

Yes! The prime factorization of 8 is

2•2•2

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 8 = √ 2•2•2 =

± 2 • √ 2

The equation has two real solutions

These solutions are x = 2 • ± √2 = ± 2.8284

Two solutions were found :

x = 2 • ± √2 = ± 2.8284

Not sure what you need help with, but I hope I helped you somehow.

5 0

3 years ago

How do you find the surface area of a regular triangular prism

Dmitry [639]

So a triangular prisim is like a triangle stacked on top of x number of identical triangles making a height, like a piece of paper made into a stack

so
basically find the area of each side and add

look at diagram/attachment
find area of triangle
1/2 b times h= area of 1 triangular face

multiply by 2 because 2 sides so 1/2 times 2 b times h=b times h

then 3 other sides
find area of each side and add
areas=(H times B)+(H times c)+(H times a)

so SA=(b times H)+(H times B)+(H times c)+(H times a)

8 0

3 years ago

Help with both questions offering 10 points

Alexandra [31]

Answer:

$\:\mathrm{First\: problem:\:}-2,\\\:\mathrm{Second\: problem:\: }-3$

Step-by-step explanation:

The slope of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

Plugging in any two points in the table we have:

First problem:

$m=\frac{1-5}{2-0}=\frac{-4}{2}=\fbox{$-2$}$

Second problem:

$m=\frac{-1-5}{2-0}=\frac{-6}{2}=\fbox{$-3$}$

8 0

3 years ago

Read 2 more answers

The Campbell family has a disposable income of $60,000 annually. Assume that their marginal propensity to consume is 0.8 (the Ca

posledela

Given the Keynesian equation C=A+MD, we find 10000 + (0.8 x 60000) = $58000. M is the Marginal propensity to consume, the A is the Autonomous consumption, and D is disposable income, giving Annual consumer spending as C.

7 0

3 years ago

Help Please!!!!!!!!!!!

Ira Lisetskai [31]

What is the question?

8 0

3 years ago