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3 years ago

Consider the rational expression x2+6x−2/6x−5 .

Mathematics

2 answers:

pychu [463]3 years ago

8 0

Answer:

Correct choices are C, D and E

Step-by-step explanation:

Consider expression $\dfrac{x^2+6x-2}{6x-5}.$

Note that numerator $x^2+6x-2$ consists of three terms: $x^2,\ 6x,\ -2$ and the denominator $6x-5$ consists of two terms: $6x,\ -5.$

A. False option.

The term in the numerator and in the denominator can be divided out, if both numerator and denominator are factored. Since $6x$ is a term in numerator and denominator and is not a factor, then it cannot be divided out.

B. False option.

The numerator is quadratic trinomial. Each quadratic trinomial has at most 2 factors. Since 3>2, then the numerator cannot have three factors.

C. True option, because three terms of the numerator are $x^2,\ 6x,\ -2.$

D. True option, because two terms of the denominator are $6x,\ -5.$

E. True option. The linear polynomial is always single factor.

DaniilM [7]3 years ago

3 0

Answer:

The last three terms are true.

Step-by-step explanation:

The last three statements are true. Yes, the numerator has 3 terms: x^2 + 6x - 2. Yes, the denominator has 2 terms: 6x - 5. Yes, that denominator is a single factor.

No, the numerator does not have three factors. It does, however, have three terms. No, 6x in the numerator does not cancel out the 6x in the denominator.

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A website is selling barbecue grills for $783. The site got the barbecue grills at a cost of $580. What is the mark-up, as a per

olasank [31]

Answer:

35%

Step-by-step explanation:

The price it cost the site to buy the grills was $580 but they were selling them for $783. So for each grill, they get a profit of $203. (783-580=203).

35% of $580 is 203 which adds up to $783

So therefore the markup rate is 35% I hope this helps!

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2 years ago

Which graph represents the function f(x) =-lx-2l-1

zimovet [89]

It’s the second one from the right

Since there’s a - behind x it means it has to be facing down so it’s either 2 or 4

Now it’s x-2 and we know that x moves the opposite so it needs to move 2 to the right so the answer is 2

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3 years ago

The function D(t) defines a traveler's distance from home, in miles, as a function of time, in hours. D(t) = StartLayout enlarge

nalin [4]

- At 2 hours, the traveler is 725 miles from home.

- At 3 hours, the distance is constant, at 880 miles. --> TRUE.

- The total distance from home after 6 hours is 1,062.5 miles --> TRUE.

Step-by-step explanation:

The function D(t) is defined as follows:

$D(t) = 300t+125$ for $t< 2.5$

$D(t) = 880$ for $2.5 \leq 3.5$

$D(t) = 75t+612.5$ for $t\leq 6$

Where

t is the time in hours

D(t) is the distance covered, in miles, after t hours

Now let's analyze the different statements:

- The starting distance, at 0 hours, is 300 miles. --> FALSE. In fact, if we substitute t = 0 into the 1st equation, we get

$D(0) = (300)(0)+125 = 125$

So, the distance at t = 0 is 125 miles.

- At 2 hours, the traveler is 725 miles from home. --> TRUE. In fact, if we substitute t = 2 into the 1st equation,

$D(2) = (300)(2)+125 = 725$

- At 2.5 hours, the traveler is 875 miles from home. --> FALSE. In fact, for t=2.5 we have to use the 2nd equation, which states that the distance is:

D(t) = 880

So, not 875 miles.

- At 3 hours, the distance is constant, at 880 miles. --> TRUE. This is clearly visible from the 2nd equation: for t between 2.5 and 3.5 (so, in this case), the distance is

D(t) = 880

- The total distance from home after 6 hours is 1,062.5 miles --> TRUE. In fact, if we replace t = 6 into the last equation,

$D(6)) = 75(6)+612.5=1062.5$