Olivia has 127 in her saving account. She will deposit 5 into the account each week given x>0

Sum of cubes: (a b)(a2 – ab b2) = a3 b3 Difference of cubes: (a – b)(a2 ab b2) = a3 – b3 Which products result in a sum or diffe

valentina_108 [34]

By comparing all the options with the formula of sum of cubes and difference of cubes we get that $(x+4)\left(x^{2}-4 x+16\right)$ is sum of cubes

<h3>What is formula of sum of cubes and difference of cubes?</h3>

Formula of sum of cubes and difference of cubes are following

$(a+b)(a^2 -ab +b^2) = a^3+ b^3 \\\\\\(a - b)(a^2+ ab+ b^2) = a^3 - b^3$

(a)

$(x-4) \left(x^{2}+4 x-16\right)\\=(x-4) \left(x^{2}+4 x-4^2\right)\\\\$

by comparison with formula we can say that this is neither sum or nor difference of cubes.

(b)

$(x-1)\left(x^{2}-x+1\right)\\=(x-1)\left(x^{2}-x+1^2\right)$

by comparison with formula we can say that this is neither sum nor difference of cubes.

(c)

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

we can say that this is neither sum nor difference of cube as it's difference of squares.

(d)

$(x+4)\left(x^{2}-4 x+16\right)\\\\(x+4)\left(x^{2}-4 x+4^2\right)$

by comparison with formula this is equal to

$x^{3}+4^{3}\\$

Hence this is sum of cubes

(e)

$(x+4)\left(x^{2}+4 x+16\right)\\(x+4)\left(x^{2}+4 x+4^2\right)$

by comparison with formula we can say that this is neither sum nor difference of cubes.

By comparing all the options with the formula of sum of cubes and difference of cubes we get that $(x+4)\left(x^{2}-4 x+16\right)$ is sum of cubes

To know more about cubes visit: brainly.com/question/107100

8 0

2 years ago

Jim is showing his work in simplifying (−8.5 + 6.1) − 1.3.

dexar [7]

9514 1404 393

Answer:

In step 4, Jim's answer is incorrect.

Step-by-step explanation:

In step 1, Jim swaps the order of addends using the commutative property of addition.

In step 2, Jim uses the distributive property to factor -1 from the final two terms. (The associative property lets Jim move parentheses.)

6.1 +(-8.5 -1.3) . . . associative property

6.1 +(-1)(8.5 +1.3) . . . distributive property

In step 3, Jim has used the properties of real numbers to form the sum of two of them.

In step 4, Jim wrote an answer of 1.1, when the answer should have been -3.7. Jim's answer is incorrect.

__

The descriptive statements about steps 2 and 4 are both true.

8 0

3 years ago

Solve the system.<br> x = y +2 <br> 3x = 6 (y + 2)

Zielflug [23.3K]

Answer:

(x , y)=(0 , -2)

Step-by-step explanation:

5 0

2 years ago

A map has a scale of 1:5000000000 .

erastova [34]

Considering the definition of scale, you obtain:

the real length of the road is 500,000 km.
the real area of the farm is 300 hectares.

<h3>Definition of map</h3>

A map is the conventional graphical representation of a portion of the earth or another celestial body that shows the size and position of elements of the landscape according to the selected scale and projection. That is, a map is a representation of a place, at a size smaller than the actual size.

<h3>Definition of scale</h3>

The scale of a cartographic representation, or map scale (m), is the relationship of similarity between the real dimensions of the geographical space represented and those of its image on the map. In general, it is also defined as the ratio of the lengths of a linear element in the plane and its representation on the terrestrial reference surface.

That is, the scale of the map is defined as the proportionality relationship that exists between a distance measured on the ground and its corresponding measurement on the map.

<h3>Real length of the road</h3>

A map has a scale of 1:5000000000. This indicates that 1 unit on the map is equivalent to 5,000,000,000 in reality.

You know that the road on the map is 10 cm or 0.0001 km long (knowing that 1 km= 100,000 cm).

Then you can apply the following rule of three: if by definition of scale 1 km on the map is equivalent to 5,000,000,000 km in reality, 0.0001 km on the map is equivalent to how much distance in reality?

$real length of the road=\frac{0.0001 kmx 5,000,000,000 km }{1 km}$

<u><em>real length of the road= 500,000 km</em></u>

Finally, the real length of the road is 500,000 km.

You know that the area of a farm of the map is 6 cm square, 0.0006 m sr 0.00000006 hectares (knowing that 1 cm square= 0.0001 m square and 10,000 m square= 1 hectare).

Then you can apply the following rule of three: if by definition of scale 1 hectare on the map is equivalent to 5,000,000,000 hectares in reality, 0.00000006 hectares on the map is equivalent to how much area in reality?

$real area of the farm=\frac{0.00000006 hectaresx 5,000,000,000 hectares }{1 hectare}$