All categories

4 years ago

What is the domain of the function on the graph?

Mathematics

1 answer:

Dennis_Churaev [7]4 years ago

5 0

Answer:

All real numbers greater than or equal to -3

Step-by-step explanation:

First look at graph where the line points to which direction of the graph

And look for any closed or open circles in the graph

Since in the graph has a close circle at (-3,-2) meaning it includes that x-value for its domain.

With the graph going to positive infinity it states that the domain is all real numbers.

So in conclusion it has a domain of all real numbers greater than or equal to -3

You might be interested in

n △ABC, point P∈ AB is so that AP:BP=1:3 and point M is the midpoint of segment CP. Find the area of △ABC if the area of △BMP is

monitta

Answer: The area of ABC is 56 m².

Explanation:

It is given that in △ABC, point P∈ AB is so that AP:BP=1:3 and point M is the midpoint of segment CP.

Since point P divides the line AB in 1:3, therefore the area of triangle APC and BPC is also in ratio 1:3. To prove this draw a perpendicular h on AB from C.

$\frac{\text{Area of } \triangle BCP}{\text{Area of } \triangle ABC} =\frac{\frac{1}{2}\times BP\times CH}{\frac{1}{2}\times AB\times CH} =\frac{BP}{AB}= \frac{3}{4}$

Since the area of BPC is $\frac{3}{4}$ th part of total area, therefore area of APC is $\frac{1}{4}$ th part of total area.

The point M is the midpoint of CP, therefore the area of BMP and BMC is equal by midpoint theorem.

$\text{Area of } \triangle BMP=\text{Area of } \triangle BMC$

$21=\text{Area of } \triangle BMC$

Area of BPC is,

$\text{Area of } \triangle BPC=\text{Area of } \triangle BMP+\text{Area of } \triangle BMC$

$\text{Area of } \triangle BPC=21+21$

$\text{Area of } \triangle BPC=42$

Area of APC is,

$\text{Area of } \triangle APC=\frac{1}{3}\times \text{Area of } \triangle BPC$

$\text{Area of } \triangle APC=\frac{1}{3}\times 42$

$\text{Area of } \triangle APC=14$

Area of ABC is,

$\text{Area of } \triangle ABC=\text{Area of } \triangle APC+\text{Area of } \triangle BPC$

$\text{Area of } \triangle ABC=14+42=56$

Therefore, the area of ABC is 56 m².

5 0

3 years ago

A car salesperson sells a car for $21,000. She receives a 5.25% commission on the sale of the car.

valkas [14]

She receives $1,102.50 for commission. All you need to do to solve this problem is multiply the amount given by the percentage as a decimal.

5 0

3 years ago

Read 2 more answers

Which choice is equivalent to the expression below? √-216

myrzilka [38]

The answer is b.6i/6

8 0

3 years ago

Write the equation in slope-intercept form. -10x+2y=12 -please help

Goryan [66]

Answer:

y=5x+6

hope this helps

have a good day :)

Step-by-step explanation:

3 0

3 years ago

A bacteria culture starts with 12,000 bacteria and the number doubles every 50 minutes.

Vlada [557]

Answer:

a) $y=12000(2)^{\frac{t}{50}}$

b) Approx. 27,569 bacteria

c) About 103 minutes

Step-by-step explanation:

This will follow exponential modelling with form of equation shown below:

$y=Ab^{\frac{t}{n}}$

Where

A is the initial amount (here, 12000)

b is the growth factor (double, so growth factor is "2")

n is the number of minutes in which it doubles, so n = 50

Substituting, we get our formula:

$y=Ab^{\frac{t}{n}}\\y=12000(2)^{\frac{t}{50}}$

To get number of bacteria after 1 hour, we have to plug in the time into "t" of the formula we wrote earlier.

Remember, t is in minutes, so

1 hour = 60 minutes

t = 60

Substituting, we get:

$y=12000(2)^{\frac{t}{50}}\\y=12000(2)^{\frac{60}{50}}\\y=12000(2)^{\frac{6}{5}}\\y=27,568.76$

The number of bacteria after 1 hour would approximate be 27,569 bacteria

To get TIME to go to 50,000 bacteria, we will substitute 50,000 into "y" of the equation and solve the equation using natural logarithms to get t. Shown below:

$y=12000(2)^{\frac{t}{50}}\\50,000=12,000(2)^{\frac{t}{50}}\\4.17=2^{\frac{t}{50}}\\Ln(4.17)=Ln(2^{\frac{t}{50}})\\Ln(4.17)=\frac{t}{50}*Ln(2)\\\frac{t}{50}=\frac{Ln(4.17)}{Ln(2)}\\\frac{t}{50}=2.06\\t=103$

After about 103 minutes, there will be 50,000 bacteria

4 0

3 years ago