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ycow [4]
3 years ago
14

What is the sum of the first 14 terms of the sequence an = 6n -12

Mathematics
1 answer:
mina [271]3 years ago
6 0
When n = 1  first term  = -6 
n = 2  second term =  0
n = 3 third term = 6

n = 4 4th term = 12

so we have an Arithmetic sequence  first term = -6 and common difference = 6

Sum 14 terms  =  (14/2)[2*-6 + (14-1)*6]

 =  462  answer
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The length of a rectangle is a inches. Its width is 5 inches less then the length. Find the area and perimeter of the rectangle
Travka [436]

Answer:

Area = (a² -5a) in²

Perimeter = (4a -10) in

Step-by-step explanation:

Let the length of the rectangle be a.

Given that, its width is 5 in less than the length.

So,

length ⇒ a

width ⇒ (a - 5)

First, let's find the area of the rectangle.

Area = length × width

Area = a ( a - 5 )

<em>Solve the brackets.</em>

Area = <u>(a² -5a) in²</u>

<u />

Now, let us find the perimeter of the rectangle.

Perimeter = 2 ( l + w )

Perimeter = 2 ( a + a - 5 )

Perimeter = 2 ( 2a - 5 )

Perimeter = <u>(4a -10) in</u>

3 0
2 years ago
Convert 5.82% to an equivalent decimal​
lisov135 [29]

5.82% = 0.0582 in decimal form.

7 0
3 years ago
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I need help with the question attached
uranmaximum [27]

Answer:

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7 0
3 years ago
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Find the derivative
zalisa [80]

First use the chain rule; take y=\dfrac{x+5}{x^2+3}. Then

\dfrac{\mathrm df}{\mathrm dx}=\dfrac{\mathrm df}{\mathrm dy}\cdot\dfrac{\mathrm dy}{\mathrm dx}

By the power rule,

f(x)=y^2\implies\dfrac{\mathrm df}{\mathrm dy}=2y=\dfrac{2(x+5)}{x^2+3}

By the quotient rule,

y=\dfrac{x+5}{x^2+3}\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{(x^2+3)\frac{\mathrm d(x+5)}{\mathrm dx}-(x+5)\frac{\mathrm d(x^2+3)}{\mathrm dx}}{(x^2+3)^2}

\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{(x^2+3)-(x+5)(2x)}{(x^2+3)^2}

\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{3-10x-x^2}{(x^2+3)^2}

So

\dfrac{\mathrm df}{\mathrm dx}=\dfrac{2(x+5)}{x^2+3}\cdot\dfrac{3-10x-x^2}{(x^2+3)^2}

\implies\dfrac{\mathrm df}{\mathrm dx}=\dfrac{2(x+5)(3-10x-x^2)}{(x^2+3)^3}

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3 years ago
Which is an equation of the line with a slope of 2 that passes through (3,−5)?
Naya [18.7K]

Answer:

equation of a line= y-y¹=m(x-x¹)

y--5=2(x-3)

y+5=2x-6

y=2x-6+5

y=2x-1

7 0
3 years ago
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