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2 years ago

Find the positive value of x in the geometric sequence 7x-2,4x+4,3x

1 answer:

5 0

Hello,

Let's assume k the ratio.

$
 \left \{ {{3x=k*(4x+4)} \atop {4x+4=k*(7x-2)}} \right. \\\\
 \left \{ {{3x-4kx=4k} \atop {4x-7kx=-2k-4}} \right. \\\\
 \left \{ {{x(3-4k)=4k} \atop {x(4-7k)=-2k-4}} \right. \\\\
 \left \{ {{x=\dfrac{4k}{3-4k} \atop {x=\dfrac{-2k-4}{4-7k} \right. \\\\

\dfrac{4k}{3-4k}=\dfrac{-2k-4}{4-7k}\\\\

36k^2-6k-12=0\\
6k^2-k-2=0\\

\boxed{k= \dfrac{2}{3} \ or\ k= -\dfrac{1}{2}}\\\\

x=\dfrac{4*\dfrac{2}{3} }{3-4*\dfrac{2}{3} }=8\\
x=\dfrac{4*\dfrac{-1}{2} }{3-4*\dfrac{-1}{2} }=-\dfrac{2}{5}\\





$

$\boxed{x= 8 \ or\ x= -\dfrac{2}{5}}\\\\$

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Answer:

L= 0.83 in

Step-by-step explanation:

Width= 1.2 in when length = 1 in

Required

Determine the length when width = 1 in

First, we need to determine the ratio

Ratio = $\frac{Width}{Length}$

Ratio = $\frac{1.2}{1}$

Ratio = 1.2 ---(1)

Let the required length be represented with L

So:

Ratio = $\frac{Width}{Length}$

Ratio = $\frac{1}{L}$ ---(2)

Equate (1) and (2)

$\frac{1}{L}$ = 1.2

Multiply through by 1.2

L * $\frac{1}{L}$ = 1.2 * L

1 = 1.2 * L

Divide through by 1.2

L = $\frac{1}{1.2}$

L = 0.83 in (Approximated)

6 0

3 years ago

A company's profit (in millions of dollars) can be represented by x^2-6x+12, where x is the number of years since the company st

Sergeu [11.5K]

The function that models the profit of the company in million of dollars is:

$P= x^{2} -6x+12$

where x represents the number of years since the company started. We want to find when the profit of the company was $4 million. Setting P as 4 in above equation, we can find the value of x when the profit was $4 million.

$4= x^{2} -6x+12 \\ \\ 
 x^{2} -6x+8=0 \\ \\ 
 x^{2} -2x-4x+8=0 \\ \\ 
x(x-2)-4(x-2)=0 \\ \\ 
(x-2)(x-4)=0 \\ \\ 
x=2, x=4$

Thus, we can conclude that the profit of the company was $4 million in 2nd and 4th year

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2 years ago

John types 265 words in 5 minutes. At this rate, how many words does he type per minute

Arisa [49]

Answer:

John can type 53 words per minute

Step-by-step explanation:

You would divide 265 by 5 to get the result of 53.

7 0

1 year ago

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Yakvenalex [24]

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2 years ago

Maddie and her friends are making s'mores over the campfire. they have a bag of 48 marshmallows, 2 packs of graham crackers cont

VladimirAG [237]

The answer would be 16 S'mores and the limiting reactant would be the grahams.

(This is assuming that S'mores would need 2 grahams, 1 marshmallow and 1 chocolate piece.)

Limiting reactant would be the reactant that runs out first.

Let's take your problem into account and see what we have:

48 marshallows

32 grahams (2 x 16 per pack)

45 chocolate pieces (5 x 15 pieces per bar)

Since need 2 of the grahams per S'more then the maximum yield of the grahams is 16 S'mores.

The maximum yield of marshmallows is 48.

The maximum yield of chocolate is 45.

Since you cannot make S'mores without the grahams, then you can only make 16 S'mores before the grahams run out.

8 0

3 years ago