5.

Find the domain and range of f(x). Please explain your answer. f(x) = √(x^2+5x+6)

timama [110]

Answer:

Domain:— [ x ≥ -2, x ≤ -3 ]

Range:— [ y ≥ 0 ]

Step-by-step explanation:

You may use graphing calculator to draw a graph and examine the graph’s domain and range. However, I’ll explain further about the graph of quadratic in a surd.

First, factor the quadratic expression in the surd:—

$\displaystyle \large{f(x)=\sqrt{(x+3)(x+2)}}$

We can find the x-intercepts by letting f(x) = 0.

I’ll be separating in two parts — one for finding x-intercept and one for finding y-intercept.

__________________________________________________________

Finding x-intercepts

Let f(x) = 0.

$\displaystyle \large{0=\sqrt{(x+3)(x+2)}}$

Solve for x, square both sides:—

$\displaystyle \large{0^2 = (\sqrt{(x+3)(x+2)})^2}\\\displaystyle \large{0=(x+3)(x+2)}$

Simply solve a quadratic equation:—

$\displaystyle \large{x=-3,-2}$

Therefore, x-intercepts are:—

$\displaystyle \large{\boxed{x=-3,-2}}$

__________________________________________________________

Finding y-intercept

Let x = 0.

$\displaystyle \large{f(x)=\sqrt{(0+3)(0+2)}}\\\displaystyle \large{f(x)=\sqrt{3 \cdot 2}}\\\displaystyle \large{f(x)=\sqrt{6}}$

Therefore, y-intercept is:—

$\displaystyle \large{\boxed{\sqrt{6}}}$

__________________________________________________________

However, I want you to focus on x-intercepts instead. We know that the square root only gives you a positive value. That means the range of function can only be y ≥ 0.

For domain, first, we have to know how or what the graph looks like. You can input the function in a graphing calculator as you’ll see that when x ≥ -2, the graph heads to the right while/when x ≤ -3, the graph heads to the left. This means that the lesser value of x-intercept gets left and more value get right.

See, between -3 < x < -2, there is no curve, point or anything between the interval. Therefore, -3 < x < -2 does not exist in function.

Hence, the domain is:—

x ≥ -2, x ≤ -3

4 0

2 years ago

A restaurant averages ales of $120,000 when serving 20,000 guests. The restaurant's variable costs when 20,000 is $90,000. The c

Katarina [22]

Answer: Restaurant's monthly breakeven point in sales is $31333.

Step-by-step explanation:

Since we have given that

Number of guests = 20,000

Average sales = $120,000

Contribution margin per guest = $1.50

Let the number of sales be 'x'.

Cost per sales would be

$\dfrac{120000}{20000}\\\\=\$6$

Margin contributed by 2000 guests would be

$1.50\times 20000\\\\=\$3000$

So, Revenue function would be

$6x+3000$

Fixed monthly cost = $ 50,000

Variable cost for 20000 guests = $90000

So, Variable cost per sale would be

$\dfrac{90000}{20000}\\\\=\$4.5$

So, Cost function would be

$4.5x+50000$

Breakeven point would be

Cost function = Revenue function

$6x+3000=4.5x+50000\\\\6x-4.5x=50000-3000\\\\1.5x=47000\\\\x=\dfrac{47000}{1.5}\\\\x=\$31333.33\\\\x=\$31333$

Hence, Restaurant's monthly breakeven point in sales is $31333.

3 0

3 years ago

Catherine used the two points and the right triangle shown to find the slope of the line Catherine found the slope to be 1/10. I

blagie [28]

Answer:

Catherine is not correct (see the explanation)

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

the two points from the graph are

(4,40) and (7,70)

substitute the values in the formula

$m=\frac{70-40}{7-4}\\m=\frac{30}{3}\\m=10$

therefore

Catherine is not correct

4 0

3 years ago

An Airbus A380 has 1 first class section 1 business class section and 4 economy class sections

Juliette [100K]

Answer:

Yes, more than half are being used. (292 out of 546 used)

Step-by-step explanation:

The first part of this problem is to determine the total amount of seats on the plane so we can determine what half of the seats would be.

1st class has 14 seats.

Business-class has 64 seats.

And the 4 economy classes have 117 each, meaning 117 * 4 = 468

So the total amount of seats are 14 + 64 + 468 = 546

So half that amount would be 273.

Now we can determine the number of seats being used.

1st class has (6/7) * 14 = 12 seats used

Buisness-class has (7/16) * 64 = 28 seats being used

Economy has 4 * (7/13) * 117 = 4 * 63 = 252 seats being used

So the total amount of used seats would be 12 + 28 + 252 = 292.

Note that 292 is greater than 273, so there is indeed more than half the seats on the plane being used.

Cheers.

7 0

3 years ago

22.A large round pizza has a radius of r = 15 inches, and a small round pizza has a

lora16 [44]

Answer:

This is your answer If I'm right so.

Please mark me as brainliest. thanks!!

7 0

3 years ago