WORD PROBLEM

Which equation is equivalent to the given equation?<br><br>x^2 – 10x = 14

kumpel [21]

Answer:

(x - 5^2) = 39

Step-by-step explanation:

8 0

2 years ago

The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches, then the area of t

Yuliya22 [10]

The original are would be 48.

Since we know that the length and width are two consecutive even integers, we can model them as follows:

Width = x

Length = x + 2

This works because no matter what even number is put in for x, the length will also be even.

Now we know if we subtract 3 from the width, we have a new rectangle that gives us an area of 24 inches. Therefore, our new triangle has the following:

Width: x - 3

Length: x + 2

Area: 24

And we can plug this into the equation.

Length* Width = Area

(x + 2)(x - 3) = 24

x^2 - x - 6 = 24

x^2 - x - 30 = 0

This is not a quadratic that we can factor to show the following:

(x - 6)(x + 5) = 0

This gives us the answers of x = 6 and x = -5. Since a side can't be negative, we throw out the x = -5 and the answer is x = 6.

So if we go back to the original rectangle, we know:

Width = x = 6

Length = x + 2 = 8

Area = 6*8 = 48

7 0

3 years ago

What is 108.2x 10 to the 3rd power

xenn [34]

I think it’s 108200....

4 0

3 years ago

How do you solve this equation? <br>2x+8-22= -2

Schach [20]

Answer:

x=6

Step-by-step explanation:

First you have to subtract 8 from 22 and you get -14. Then you rewrite the equation, 2x-14=-2.

Since your subtracting 14 you would add 14 to both sides, so -14+14 and -2+14. -2+14 will turn out to be 12 and then you divide 2 from both sides, so 2x-2 and 12-2.

Your answer will be x=6

4 0

3 years ago

Read 2 more answers

A Hot air balloon can hold 90,000 cubic feet of air. It is being inflated at a rate of 6,000 cubic feet per minute . The total c

mojhsa [17]

$\bf \stackrel{\textit{cubic feet of air}}{\stackrel{\textit{dependent}}{a(t)}}\qquad \stackrel{\stackrel{\textit{time in minutes}}{independent}}{t}~\hspace{7em}a(t)=6000t$

the "t" variable is independent, namely it can change values "freely", and a(t) is dependent, because it depends on those values on "t" to get its own value.

if we make a table of values for minutes, we know the balloon is inflating at 6000 ft³ each passing minute.

1 minute......................... 6000(1) ft³

2 minutes......................6000(2) ft³

3 minutes......................6000(3) ft³

4 minutes......................6000(4) ft³

t minutes......................6000(t) ft³

before getting in the domain and range, let's find out how much air after 6 minutes.

a(6) = 6000(6)

a(6) = 36000 ft³.

now, what domain, namely values for "t" make sense?

well, we know the balloon can only hold up to 90000 ft³, and on every passing minute is filling up by 6000 ft³, after how many minutes will it be filled up?

90000/6000 = 15, after 15 minutes.

so at 0 minutes, t = 0, the balloon is empty, and 15 minutes later, t = 15, the balloon is filled up, [ 0 , 15 ].

what values for the range, namely a(t), makes sense?

well, we know when the balloon is empty is holding 0 ft³, and when is full it has 90000 ft³, [0 , 90000].

5 0

3 years ago