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3 years ago

8

a computer sales associate makes $74 each day that he works and makes approximately $20 in commission for each computer that he

sells. if he wants to make at least $254 in one day, at least how many computers does he need to sell?

1 answer:

podryga [215]3 years ago

8 0

Answer: 120

Step-by-step explanation:

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I) Find the first 4 terms in the expansion of

Katyanochek1 [597]

Answer:

(i) $64+192 x^2+240 x^4+160x^6$

(ii) 1072

Step-by-step explanation:

<u>Part (i)</u>

Using Binomial series formula:

$(2+x^2)^6=2^6+6C1 \cdot 2^{6-1}\cdot x^2+6C2 \cdot 2^{6-2}\cdot(x^2)^2+6C3 \cdot 2^{6-3}\cdot(x^2)^3$

$=64+6 \cdot 32\cdot x^2+15 \cdot 16\cdot x^4+20 \cdot 8 \cdot x^6$

$=64+192 x^2+240 x^4+160x^6$

<u>Part (ii)</u>

<u /> $(1-\frac{3}{x^2})^2=(1-\frac{3}{x^2})(1-\frac{3}{x^2})$

$=1-\dfrac{6}{x^2}+\dfrac{9}{x^4}$

$(2+x^2)^6(1-\frac{3}{x^2})^2=(64+192 x^2+240 x^4+160x^6)\left(1-\dfrac{6}{x^2}+\dfrac{9}{x^4} \right)$

$=64-\dfrac{384}{x^2}+\dfrac{576}{x^4}+192x^2-1152+\dfrac{1728}{x^2}+240x^4-1440x^2+2160+...$

There is no need to keep expanding since the remaining will include the variable.

Therefore, the term independent of x = 64 - 1152 + 2160 = 1072

6 0

3 years ago

The sum of the squares of two consecutive positive even integers is 52.Find the integers

ankoles [38]

Answer:

The two consecutive positive integers are $4$ and $6$ .

Step-by-step explanation:

Let $x$ be an even integer, then the next even integer is $(x+2)$ .

The sum of the squares of these even integers is $52$ .

We can write the following equation and solve for $x$ .

$x^2+(x+2)^2=52$ .

We expand to get,

$x^2+x^2+4x+4=52$ .

We simplify to get,

$2x^2+4x+4-52=0$ .

This gives us,

$2x^2+4x-48=0$

We divide through by 2 to get,

$x^2+2x-24=0$ .

This is now a quadratic trinomial

We split the middle term to get,

$x^2+6x-4x-24=0$ .

We factor to obtain,

$x(x+6)-4(x+6)=0$

$\Rightarrow (x+6)(x-4)=0$

$\Rightarrow (x+6)=0 or (x-4)=0$

$\Rightarrow x=-6 or x=4$

We discard $x=-6$ since it is not a positive integer.

$\therefore x=4$

Hence the two consecutive positive even integers are,

$4$

and

$4+2=6$

5 0

4 years ago

Read 2 more answers

Max has cashews that sell for $4.75 a pound and peanuts that sell for $2.75 a pound. How much must he mix to get 80 pounds of a

dolphi86 [110]

Answer:

10 lb of cashews and 70 lb of peanuts

Step-by-step explanation:

Let x = the pounds of cashews.

Then 80 – x = the pounds of peanuts

Value of cashews + value of peanuts = volume of mixture

x×4.75 + (80 – x)×2.75 = 80×3 Remove parentheses

4.75x + 220 - 2.75x = 240 Combine like terms

2.00x + 220 = 240 Subtract 220 from each side

2.00x = 20 Divide each side by 2.00

x = 10 lb

80 - x = 80 – 10

80 - x = 70 lb

Max will mix 10 lb of cashews with 70 lb of peanuts.

=====

<em>Check: </em>

10×4.75 + 70×2.75 = 80×3.00

47.50 + 192.50 = 240.00

240.00 = 240.00

6 0

3 years ago

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Which is the adjectival phrase in the sentence? Those old patio chairs on the deck are beginning to rust.

LUCKY_DIMON [66]

Those old (letter a).

7 0

3 years ago

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What are the factors of 3x2 + 10x + 3? (3x − 1)(x − 3) (3x − 3)(x − 1) (3x + 1)(x + 3) (3x + 3)(x + 1)

natka813 [3]

The factors of 3x^2+10x+3 are (3x+1)(x+3)

4 0

4 years ago

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