All categories

3 years ago

What is the justification for each step in the solution of the equation?

Mathematics

2 answers:

Alexandra [31]3 years ago

5 0

For this case we have the following equation:

$\frac{2}{3}x-\frac{1}{3}= 2 (x + 2)\\$

If we multiply both sides of the equation by 3 we get:

$2x-1 = 6 (x + 2)$ ---> Multiplication Property of Equality

Applying the distributive property we have:

$2x-1 = 6x + 12$ ---> Distributive Property

Adding 1 on both sides of equality we have:

$2x-1 + 1 = 6x + 12 + 1\\$

$2x = 6x + 13$ ---> Addition Property of Equality

Subtracting $6x$ on both sides we have:

$-6x + 2x = 6x-6x + 13\\$

$-4x = 13$ ---> Subtraction Property of Equality

Finally, dividing by -4 on both sides we have:

$\frac{-4x}{-4}= \frac{13}{-4}\\$

$x = -\frac{13}{4}$ ---> Division Property of Equality

adoni [48]3 years ago

3 0

Answer:

2/3x - 1/3 = 2(x + 2) Given

2x - 1 = 6(x + 2) Multiplication or Division Property of Equality

2x - 1 = 6x + 12 Distributive Property

2x = 6x + 13 Addition or Subtraction Property of Equality

-4x = 13 Addition or Subtraction Property of Equality

x = -13/4 Multiplication or Division Property of Equality

I took the test, you can trust these answer are correct.

You might be interested in

If w = 12 units, x = 7 units, and y = 8 units, what is the surface area of the figure? Figure is composed of a right square pyra

bearhunter [10]

Answer:

720 sq units.

Step-by-step explanation:

Length and width of square prism, w = 12 units

Height of square prism, x = 7 units

Height of square pyramid, y = 8 units

Please have a look at the attached image.

Here 2 Surfaces will not be exposed which are base of the square pyramid and the top of the square prism i.e. 2 square surfaces will not be exposed.

Here, surface area of the composite figure will be:

<em>Surface Area of Composite Figure = Lateral surface area of Square Pyramid + Surface Area of 5 surfaces of the square prism</em>

For finding the lateral surface area of pyramid, we need to find the slant height of the pyramid.

Let slant height be $l$ units.

Using pythagoras theorem, we can find out the value of $l$ .

As per theorem:

$Hypotenuse^{2} = Base^{2} + Height^{2}\\$

$\Rightarrow l^{2} = (\dfrac{w}{2})^{2} + y^{2}\\\Rightarrow l^{2} = (\dfrac{12}{2})^{2} + 8^{2}\\\Rightarrow l^{2} = {6}^{2} + 8^{2}\\\Rightarrow l^{2} = 36+64 = 100\\\Rightarrow l = 10\ units$

Lateral surface area of square prism = 4 $\times$ Area of triangular surface

$\Rightarrow 4 \times \dfrac{1}{2}\times Base \times Slant\ Height\\\Rightarrow 4 \times \dfrac{1}{2} \times 10 \times 12\\\Rightarrow 240\ sq\ units$

Surface Area of 5 surfaces of the square prism =

$4 \times x \times w + w^2\\\Rightarrow 4 \times 12 \times 7 + 12^2\\\Rightarrow 336 +144\\\Rightarrow 480\ sq\ units$

So, total surface area of composite figure:

240 + 480 = 720 sq units.

7 0

3 years ago

On a coordinate plane, point AS

nlexa [21]

Answer:

√1370 or about 37.01

Step-by-step explanation:

use distance formula

√(x2-x1)^2+(y2-y1)^2

sqrt(8-7)^2+(41-4)^2

sqrt(1)^2+(37)^2

sqrt 1+1369

sqrt 1370

= about 37. 01

3 0

3 years ago

How do you Translate shapes

VMariaS [17]

Answer:

translation means moving the shape without changing it.

hope this helps

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

A stone is thrown upward from ground level. With what minimum speed should the stone be thrown so as to reach a height of 81 fee

butalik [34]

Use the kinematics equation:
v1^2-v0^2=2as
since v1=0 (at height of 81 ft), and a=g=-32.2, substitute values:

0-v0^2=2*(-32.2)(81 ft)
Solve for v0
v0=sqrt(2*32.2*81)=72.2 m/s

3 0

4 years ago

Read 2 more answers

A circle has a radius of 4. An arc in this circle has a central angle of 288°.

Vikentia [17]

Answer:

6.4π units.

Step-by-step explanation:

Length of the arc = radius * the angle in radians

= 4 * 288 * π / 180

= 6.4π.

6 0

3 years ago