I need help on this worksheet!

Which functions domain consists of all real numbers except -2?

Eddi Din [679]

Answer:

option (a) f(x)= 1/x+2

Step-by-step explanation:

(a) f(x) = 1/ x+2

To find the restriction for domain , we set the denominator =0 and solve for x

x+2 =0, so x=-2

When x=-2 then denominator becomes 0 that is undefined.

So, domain is all real numbers except -2

(b) f(x)= 2x

In this function, there is no denominator or square root or log function

so there is no restriction for x, hence domain is all real numbers

(c) f(x) = 2x-2

In this function, there is no denominator or square root or log function

so there is no restriction for x, hence domain is all real numbers

f(x) = 1/ sqrt(x+2)

if we have square root in the denominator then we set the denominator >0 and solve for x. because square root of negative values are undefined

x+2>0, x>-2

Hence domain is all real numbers that are greater than -2

8 0

3 years ago

Sam evaluated the expression x2y for x = 7 and y = 9. He got a value of 49. which of the follwing statements is correct

Marrrta [24]

<span>B. sam forgot to multiply.
The correct answer is
</span> x^2*y=(7^<span>2)*(9)=49*9=441 </span>

7 0

3 years ago

Please Help me! Algebra 1

dem82 [27]

Option a: The number of bacteria at time x is 0.

Option b: An exponential function that represents the population is $y=200(1.5)^x$

Option c: The population after 10 minutes is 11534(app)

Explanation:

It is given that the coordinates of the graph are (0,200), (1,300) and (2, 450)

Option a: To determine the number of bacteria x when y = 200

From the graph, we can see that the line meets y = 200 when x = 0

Thus, the coordinates are (0,200)

Hence, the number of bacteria at time x is 0 when y = 200.

Option b: Now, we shall determine the exponential function of the population.

The general formula for exponential function is $y=a \cdot b^{x}$

Where a is the starting point and $a=200$

b is the common difference.

To determine the common difference, let us divide,

$\frac{300}{200} =1.5$

Also, $\frac{450}{300} =1.5$

Hence, the common difference is $b=1.5$

Thus, substituting the values $a=200$ and $b=1.5$ in the formula $y=a \cdot b^{x}$ ,

we have, $y=200(1.5)^x$

Hence, An exponential function that represents the population is $y=200(1.5)^x$

Option c: To determine the population after 10 minutes, let us substitute $x=10$ in $y=200(1.5)^x$ , since the x represents the population of the bacteria in minutes.

Thus, we have,

$\begin{aligned}y &=200(1.5)^{x} \\&=200(1.5)^{10} \\&=200(57.67) \\&=11534\end{aligned}$

Hence, the population after 10 minutes is 11534(app)

7 0

3 years ago

How much it will take for a bag to travel 5 meters across the floor of it is traveling at 1 m/s

tester [92]

Time = $\frac{distance}{speed}$

The distance the bag will travel is 5 meters, and the speed it is traveling at is 1 m/s. Plug these into the formula for time.

$\frac{5 m}{1 m/s}$ = 5 s
5/1 = 5 and the m (meters) cancel out, so you are left with s, seconds.

It will take the bag 5 seconds to travel across the floor.

5 0

2 years ago

The number of guppies that a fish tank can safely hold depends on its volume. A fish tank should have a volume of 576 cubic inch

andre [41]

The answer is 24 guppies. First find the volume of the tank, then divide that volume by 576 (you should get 8), then you multiply 3 guppies by 8 to get 2e

3 0

2 years ago