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2 years ago

If f(x)=x-3, which inequality can be used to find the domain of f(x)?

Mathematics

1 answer:

Scrat [10]2 years ago

3 0

Given that,

$f(x) = \sqrt{x-3}$

To find,

The domain of f(x).

Solution,

We have, $f(x) = \sqrt{x-3}$

To find domain,

The term under the square root must be positive or null as follows :

$x-3\ge 0$

Adding 3 both sides

$x-3+3\ge 0+3\\\\x\ge 3$

So, the domain is x-3>0 .

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You are running a fuel economy study. One of the cars you find is blue. can travel 35 1/2 miles on 1 1/4 gallons of gasoline. An

IgorLugansk [536]

Answer:

1) 28.4 miles per gallon

2) 34 miles per gallon

3) the red car

Step-by-step explanation:

We have the following information:

Blue car:

Travels 35 1/2 miles on 1 1/4 gallons of gasoline

Red car:

Travels 27 1/5 miles on 4/5 gallons of gasoline

We want to know the unit rate for miles per hour, and to do it we have to divide the miles they travel by the gallons each car uses:

Blue car:

(35 1/2) / (1 1/4) = 28.4 miles per gallon

Red car:

(27 1/5) / (4/5) = 34 miles per gallon

The red car travels greater distance with 1 gallon of gasoline

8 0

3 years ago

Read 2 more answers

A shopper paid $2.52 for 4.5 pounds of potatoes,$7.75 for 2.5 pounds of broccoli,and $2.45 for 2.5 pounds of pears.What is the u

Sidana [21]

Answer:

Step-by-step explanation:

A shopper paid $2.52 for 4.5 pounds of potatoes. This means that the unit price for each potato would be

2.52/4.5 = 0.55556

Approximately $0.6 per pound.

The shopper paid $7.75 for 2.5 pounds of broccoli. This means that the unit price for each broccoli would be

7.75/2.5 = $3.1 per pound.

The shopper paid $2.45 for 2.5 pounds of pears. This means that the unit price for each pear would be

2.45/2.5 = $0.98 per pound

6 0

3 years ago

How do you work out this equation

Gnom [1K]

Answer:

x is equal to negative one, and y is equal to negative four.

Step-by-step explanation:

You can do this by solving one of the equations by either x or y, then substituting it into the other. Let's solve the second one for y:

$2y = 3x - 5\\y = \frac{3x - 5}{2}$

Now we'll substitute that into the first equation:

$9x - 2y = -1\\9x - 2(\frac{3x - 5}{2}) = -1\\9x - 3x + 5 = -1\\6x + 5 = -1\\6x = -6\\x = -1$

So we now know that x is equal to -1. We can simply substitute that into one of the original equations to find y:

$2y = 3x - 5\\2y = 3(-1) - 5\\2y = -3 - 5\\2y = -8\\y = -4$

We now know that x is equal to -1, and y is equal to -4. We can also check our answer by plugging that -4 into the other equation, and see if we still get -1:

$9x - 2y = -1\\9x - 2(-4) = -1\\9x + 8 = -1\\9x = -1 - 8\\9x = -9\\x = -1$

So we know that our answer is correct.

3 0

3 years ago

Let f(x)=(4x^2-11)^3 and g(x)=4x^2-11. given that f(x)=(h^o g)(x), find h(x).

lozanna [386]

So, f(x) is a composite function. This means that g(x) is inside of h(x); in other words, you would substitute g(x) for x in h(x).

Something happened to g(x) (in the form of h(x)) to turn it into f(x). You should notice that f(x) is simply g(x) raised to the third power.

Therefore, h(x) = x^3

You can check this by working it backwards.

Start with: h(x) = x^3
Substitute: x = g(x) = 4x^2-11
Now you have: h(x) = (g(x))^3 = (4x^2-11)^3

Hope this helps!

7 0

3 years ago

The length of a rectangle is 4 inches more than the width.The perimeter is 136 inches

nataly862011 [7]

lets start by labeling the rectangle. let w = width so length(l) = w+4 (i.e 4 more than the width)

Perimeter of a rectangle= sum of all the sides= l+ w+l+w=2l +2w

now we know that p = 2l + 2w = 100

but we know that l=w+ 4

2(w+4) +2w=100

2w +8 +2w = 100

4w+8 =100

4w= 92

w=23

and if we substitute into 2l+2w= 100

we will get l =27.

4 0

2 years ago