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3 years ago

15

Simplify fully

title="\frac{4x^{2} +4x}{2x^{2} -2}" alt="\frac{4x^{2} +4x}{2x^{2} -2}" align="absmiddle" class="latex-formula">

1 answer:

Tatiana [17]3 years ago

5 0

Answer:

$\frac{2x}{x-1}$

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A salesman receives a commission of $4 for every pair of dress shoes he sells. He is paid $3 for every pair of athletic shoes he

Crank

Answer: he sold 9 pairs of dress shoes.

he sold 4 pairs of athletic shoes.

Step-by-step explanation:

Let x represent the number of pairs of dress shoes that he sells.

Let y represent the number of pairs of athletic shoes that he sells.

The total number of pairs of shoes that he sold in a day is 13. It means that

x + y = 13

The salesman receives a commission of $4 for every pair of dress shoes he sells. He is paid $3 for every pair of athletic shoes he sells. The commission that he got on that day was $48. It means that

4x + 3y = 48- - - - - - - - - - 1

Substituting x = 13 - y into equation 1, it becomes

4(13 - y) + 3y = 48

52 - 4y + 3y = 48

- 4y + 3y = 48 - 52

- y = - 4

y = 4

x = 13 - y = 13 - 4

x = 9

4 0

3 years ago

Several terms of a sequence {an}n=1 infinity are given. A. Find the next two terms of the sequence. B. Find a recurrence relatio

s344n2d4d5 [400]

Answer:

A) $\frac{1}{1024},\frac{1}{4096}$

B) $\left\{\begin{matrix}a(1)=1 & \\ a(n)=a(n-1)*\frac{1}{4} &\:for\:n=1,2,3,4,... \end{matrix}\right.$

C) $\\a_{n}=nq^{n-1} \:for\:n=1,2,3,4,...$

Step-by-step explanation:

1) Incomplete question. So completing the several terms: $\left \{a_{n}\right \}_{n=1}^{\infty}=\left \{ 1,\frac{1}{4},\frac{1}{16},\frac{1}{64},\frac{1}{256},... \right \}$

We can realize this a Geometric sequence, with the ratio equal to:

$q=\frac{1}{4}$

A) To find the next two terms of this sequence, simply follow multiplying the 5th term by the ratio (q):

$\frac{1}{256}*\mathbf{\frac{1}{4}}=\frac{1}{1024}\\\\\frac{1}{1024}*\mathbf{\frac{1}{4}}=\frac{1}{4096}\\\\\left \{ 1,\frac{1}{4},\frac{1}{16},\frac{1}{64},\frac{1}{256},\mathbf{\frac{1}{1024},\frac{1}{4096}}\right \}$

B) To find a recurrence a relation, is to write it a function based on the last value. So that, the function relates to the last value.

$\left\{\begin{matrix}a(1)=1 & \\ a(n)=a(n-1)*\frac{1}{4} &\:for\:n=1,2,3,4,... \end{matrix}\right.$

C) The explicit formula, is one valid for any value since we have the first one to find any term of the Geometric Sequence, therefore:

$\\a_{n}=nq^{n-1} \:for\:n=1,2,3,4,...$

6 0

3 years ago

Factor completely. x2 −3x−40 Enter your answer in the box.

Aleks [24]

Answer:

(x - 8) (x + 5)

Step-by-step explanation:

You want to start with breaking down -40 to find the integers that will go into that, which are 8 and 5. Then you take the knowledge of 8 and 5 and turn your attention to -3x.

8 and 5 must be added together to equal -3x. 8 is the larger number so it must be the negative in the equation and be must be the positive. Thus it would be -8x + 5x = -3x

Knowing that, is it simple to break x^2 because it is simply x * x = x^2

5 0

4 years ago

Read 2 more answers

22.Island A is 160 miles from island B. A ship captain travels 170 miles from island A and then finds that he is off course and

bixtya [17]

we know that

Applying the law of cosines:

c² = a² + b² - 2abcos(C)

where:

a,b and c are sides of the triangle and C is the angle opposite side c

let

a=170 mi

b=200 mi

c=160 mi

that is

160² = 170² + 200² - 2(170)(200)cos(C)

solve for C

25,600 = 28,900 + 40,000 - 68,000cos(C)

25,600 - 28,900 - 40,000 = -68,000cos(C)

-43,300=-68,000cos (C)

cos (C)=0.6367

C=arc cos(0.6367)--------> C=50.45°

hence,

he should turn in the direction of island b by

180 - 50.45 = 129.55 degrees

the answer is

129.55 degrees

6 0

4 years ago

A farmer owns 24 acres of land. He plans to use 6 acres for an entrance into the farm and partition the remaining land into 1/3

alex41 [277]

Answer:

he will have 54 1/3 acres of land

Step-by-step explanation:

8 0

3 years ago