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Naya [18.7K]
2 years ago
11

Simplify the expression. c^-6 d^4/c^-16 d^14

Mathematics
1 answer:
pochemuha2 years ago
6 0

Answer:

\red{\frac{ {c}^{10}}{{d}^{10} } }

Step-by-step explanation:

\huge \: \frac{ {c}^{ - 6}  {d}^{4}}{ {c}^{ - 16}  {d}^{14} }  \\  \\  =  \huge \: \frac{ {c}^{16 - 6}}{{d}^{14 - 4} } \\  \\  =  \huge \:  \red{\frac{ {c}^{10}}{{d}^{10} } }

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What is the equation of the line that contains the point (-1, 4) and has a slope of 3?
sertanlavr [38]

Let's write the equation with formula:-

\boxed{ \sf \: formula : y -y_{1} =  m(x -  x_{1})}

Where,

  • x1 is -1 and y1 is 4 and m is 3

\tt \: y - 4= 3(x - ( - 1))

\tt \: y  - 4 = 3(x + 1)

\tt \: y  - 4 = 3x + 3

\tt \: y = 3x + 3 + 4

\tt \: y = 3x + 7

<em>Thus, The correct choice is option C!!~</em>

4 0
2 years ago
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The mayor of Gemelos, CA strongly believes that drinking coffee stunts growth. In an attempt to getcoffee banned from Gemelos, t
Otrada [13]

Answer:

Yes, it is a matched pairs design.

Step-by-step explanation:

Assuming that the twins used in the experiment are identical, this can be treated as a matched pairs designed. Although there are two individuals receiving different treatments, they are genetically similar enough for this to be considered a matched pairs design (One individual subjected to two different treatments).

3 0
3 years ago
The ubiquitous 12oz aluminum cans used to distribute drinks in this country have a diameter of approximately 2.75 inches and a h
gayaneshka [121]

Answer:

3.5%

Step-by-step explanation:

The volume of a cylinder = \pi r^2h

<em>r</em> = radius of cylinder,

<em>h</em> = height of cylinder

For the non-optimal can,

<em>r</em> = 2.75/2 = 1.375

<em>h</em> = 5.0

V = \pi(1.375^2)\times 5.0 = 9.453125\pi

<em />

For the optimal can,

<em>d</em>/<em>h</em> = 1,

<em>d</em> = <em>h</em>

2<em>r </em>=<em> h</em>

<em>r</em> = h/2

V = \pi\left(\dfrac{h}{2}\right)^2\times h = \pi\left(\dfrac{h^3}{4}\right)

They have the same volume.

<em />\pi\dfrac{h^3}{4} = 9.453125\pi<em />

h^3 = 37.8125

h=3.36 (This is the height of the optimal can)

r = \dfrac{3.36}{2} = 1.68 (This is the radius of the optimal can)

The area of a cylinder is

<em />A = 2\pi r(r+h)<em />

For the non-optimal can,

A = 2\pi\times\dfrac{2.75}{2}\left(\dfrac{2.75}{2}+5.0\right) = 17.53125\pi

For the optimal can,

A = 2\pi\times1.68\left(1.68+3.36\right) = 16.9344\pi

Amount of aluminum saved, as a percentage of the amount used to make the optimal cans = \dfrac{17.53125\pi - 16.9344\pi}{16.9344\pi}\times 100\% = 3.5\%

5 0
3 years ago
The graph of an exponential function has a y-intercept of 8 and contains the point (3,64). Find the exponential function that de
Brums [2.3K]

Given:

Y-intercept of exponential function is 8.

It contains the point (3,64).

To find:

The exponential function that describes the graph.

Solution:

The general form of an exponential function is

y=ab^x      ...(i)

where, a is initial value or y-intercept and b is growth factor.

Since, y-intercept is 8, therefore, a=8.

Put a=8 in (i).

y=8b^x         ...(ii)

It contains the point (3,64). Put x=3 and y=64.

64=8b^3

Divide both sides by 8.

\dfrac{64}{8}=b^3

8=b^3

2^3=b^3

On comparing both sides, we get

b=2

Put b=2 in (ii).

y=8(2)^x

The functions form of this equation is

f(x)=8(2)^x

Therefore, the required function is f(x)=8(2)^x.

6 0
3 years ago
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I Bought 10 apples three days ago. 3 of them were rotten, I ate 2 and gave 5 away. How many apples do I have left?
Nutka1998 [239]

Answer: 0

Step-by-step explanation: if you gave 5 away your left with 5 if 3 were rotten your left with 2 but you ate 2 meaning you have no apples left.

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