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antiseptic1488 [7]
4 years ago
12

Identify the following series as arithmetic, geometric, both, or neither. 2x + 2x² + 2x³ + . . . + 2xn

Mathematics
2 answers:
notsponge [240]4 years ago
8 0

Answer: It is a geometric series.

Step-by-step explanation:

Since we have given that

2x+2x^2+2x^3+.............+2x^n

Here, first term = 2x

Second term = 2x²

So, we can see that there is common ratio, i.e.

r=\dfrac{a_2}{a_1}=\dfrac{2x^2}{2x}=x

Hence, any sequence with common ratio would be geometric series.

Hence, It is a geometric series.

masha68 [24]4 years ago
3 0
The series is an geometric series, terms are generated by multiplying x.
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A player in a game must roll a fair six-sided number cube and then flip a coin. What is the probability of a player rolling 4 an
expeople1 [14]

Answer:

Step-by-step explanation:

P(4) = 1/6

P(h) = 1/2

P(both) = 1/2 * 1/6 = 1/12

7 0
3 years ago
What is f(x) = –4x2 + 24x + 13 written in vertex form? f(x) = –4(x – 6)2 + 23 f(x) = –4(x – 6)2 + 7 f(x) = –4(x – 3)2 + 4 f(x) =
nika2105 [10]
We have that
f(x) = –4x²<span> + 24x + 13
</span>
we know that

The vertex form for a parabola that opens up or down is:

f(x) = a(x - h)^2 + k

in the given equation, <span>a=-4</span><span>, therefore we add zero to the original equation in the form of </span><span>4h</span>²<span>−4h</span>²
f(x) = –4x² + 24x + 4h²−4h² +13
<span>Factor 4 out of the first 3 terms and group them 
</span>f(x) = –4*(x² -6x +h²) +4h² +13
<span>We can find the value of h by setting the middle term equal to -2hx
</span>−2hx=−6x
<span>h=3</span><span> and  </span><span>4h</span>²<span>=<span>36
</span></span>f(x) = –4*(x² -6x +9) +36 +13

we know that the term (x² -6x +9) is equals to------> (x-3)²
so
f(x) = –4*(x-3)² +49

the answer is
f(x) = –4*(x-3)² +49

 

4 0
4 years ago
What is the volume of a sphere with a radius of 18 units?
alekssr [168]

Answer:

A. 7776 pi units 3 .......

7 0
3 years ago
Water continuously moves between ____________ and _____________ parts of an ecosystem. Question 1 options: Biotic, Autotrophs Ab
borishaifa [10]

Answer:

Biotic, Abiotic

Step-by-step explanation:

Interconnected pathways through which water is recycled through the biotic and abiotic components of the biosphere.

The water cycle is driven by the Sun’s energy. The sun warms the ocean surface and other surface water, causing liquid water to evaporate and ice to sublime—turn directly from a solid to a gas. These sun-driven processes move water into the atmosphere in the form of water vapor.

Over time, water vapor in the atmosphere condenses into clouds and eventually falls as precipitation, rain or snow. When precipitation reaches Earth's surface, it has a few options: it may evaporate again, flow over the surface, or percolate—sink down—into the ground.

In land-based, or terrestrial, ecosystems in their natural state, rain usually hits the leaves and other surfaces of plants before it reaches the soil. Some water evaporates quickly from the surfaces of the plants. The water that's left reaches the soil and, in most cases, will begin to move down into it.

In general, water moves along the surface as runoff only when the soil is saturated with water, when rain is falling very hard, or when the surface can't absorb much water. A non-absorbent surface could be a rock in a natural ecosystem or asphalt or cement in an urban or suburban ecosystem.

Water evaporates to form the ocean surface and forms clouds by condensation. Water in clouds may fall as precipitation over either the land or the sea. Clouds formed over the sea may move over the land. When rain falls over the land, it may flow along the surface, infiltrate the soil—move into it from above ground—and percolate through the soil, moving downward to become groundwater. Groundwater in upper levels may flow into rivers, lakes, or oceans. Water near the soil surface may be taken up by plants and move out of their bodies through transpiration from the leaves. Snowmelt runoff and sublimation of snow and ice are other processes that contribute to the water cycle.

Water evaporates to form the ocean surface and forms clouds by condensation. Water in clouds may fall as precipitation over either the land or the sea. Clouds formed over the sea may move over the land. When rain falls over the land, it may flow along the surface, infiltrate the soil—move into it from above ground—and percolate through the soil, moving downward to become groundwater. Groundwater in upper levels may flow into rivers, lakes, or oceans. Water near the soil surface may be taken up by plants and move out of their bodies through transpiration from the leaves. Snowmelt runoff and sublimation of snow and ice are other processes that contribute to the water cycle.

Image credit: The water cycle by NOAA National Weather Service Jetstream, CC BY 2.0

Water in the upper levels of the soil can be taken up by plant roots. Plants use some of the water for their own metabolism, and water that's in plant tissues can find its way into animals’ bodies when the plants get eaten. However, most of the water that enters a plant's body will be lost back to the atmosphere in a process called transpiration.

4 0
3 years ago
The following equation has denominators that contain variables. For this equation write the value or values of the variable that
jarptica [38.1K]

Answer:

X = 3/5

Step-by-step explanation:

2/x=4/5x+2

Find the LCM of the denominator 5x and 1

2/x =4/5x + 2/1

2/x = (4 + 10x)/5x

Cross multiply the equation

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10x = 4x + 10x^2

Collect like term of the mixed number

10x - 4x = 10x^2

6x = 10x^2

Divide both side by 2x

6x/2x = {10x^2 } / 2x

3 = 5x

Divide both side by the coefficient of x

3/5 = 5x/5

X = 3/5

7 0
4 years ago
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