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lidiya [134]
3 years ago
11

Given $f(x) = \frac{\sqrt{2x-6}}{x-3}$, what is the smallest possible integer value for $x$ such that $f(x)$ has a real number v

alue? please show steps. Thank you!
Mathematics
1 answer:
Gelneren [198K]3 years ago
4 0

Given:

The function is:

f(x)=\dfrac{\sqrt{2x-6}}{x-3}

To find:

The smallest possible integer value for $x$ such that $f(x)$ has a real number value.

Solution:

We have,

f(x)=\dfrac{\sqrt{2x-6}}{x-3}

This function is defined if the radicand is greater than or equal to 0, i.e., 2x-6\geq 0 and the denominator is non-zero, i.e., x-3\neq 0.

2x-6\geq 0

2x\geq 6

\dfrac{2x}{2}\geq \dfrac{6}{2}

x\geq 3             ...(i)

And,

x-3\neq 0

Adding 3 on both sides, we get

x-3+3\neq 0+3

x\neq 3             ...(ii)

Using (i) and (ii), it is clear that the function is defined for all real values which are greater than 3 but not 3.

Therefore, the smallest possible integer value for x is 4.

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Ad libitum [116K]

Answer: 177.4999849 , or 56.5pi

Step-by-step explanation:

You simply divide the diameter by 2 to get the radius (28.25) and then plug into the circumference equation, 2*pi*r = Circumfrence.

3 0
2 years ago
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Cidnee is weighing combinations of geometric solids. She found that 4 cylinders and 5 prisms weigh 32 ounces and that 1 cylinder
vitfil [10]

Answer:

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

Step-by-step explanation:

Let be x and y the masses of a cylinder and a prism, measured in ounces, respectively. After a careful reading of the statement we get the following linear equations by interpretation:

i) <em>She found that 4 cylinders and 5 prisms weigh 32 ounces:</em>

4\cdot x +5\cdot y = 32\,oz (Eq. 1)

ii) <em>And that 1 cylinder and 8 prisms weigh 35 ounces:</em>

x + 8\cdot y = 35\,oz (Eq. 2)

Now we solve the system of linear equations algebraically:

From (Eq. 2):

x = 35 - 8\cdot y

(Eq. 2) is (Eq. 1):

4\cdot (35-8\cdot y) + 5\cdot y = 32

140-32\cdot y +5\cdot y = 32

32\cdot y - 5\cdot y = 140-32

27\cdot y = 108

y = 4\,oz

From (Eq. 2):

x = 35 - 8\cdot (4)

x = 35 - 32

x = 3\,oz

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

4 0
3 years ago
Which functions are symmetric with respect to the y axis<br>​
Inessa05 [86]

Answer:

A, B, and D

Step-by-step explanation:

Only the functions that have x by itself between the absolute value signs (A, B, and D) are symmetric with respect to the y-axis .

Placing a constant outside the absolute value signs moves the function up or down the y-axis but retains the symmetry.

Adding a constant inside the absolute value signs (as in C and E) moves the axis of symmetry to the left or right of the y-axis.

In the diagram, both A and B are symmetric with respect to the y-axis, but C has been shifted three units to the left.

4 0
3 years ago
6÷2(1+2)= _____ whats the answer to this
GalinKa [24]

Answer:

9

Step-by-step explanation:

You do parenthesis first so 1+2=3

Then you do division 6 divided by 2=3

Then you will multiply 3 by 3 so 9

This is known as pemdas

P=parenthesis

E=exponents

MD=multiplication and division you do it left to right so if division is in front of multiplication then you do division

As=Addition and subtraction is also left to right

8 0
2 years ago
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Exhibit 12-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Li
snow_lady [41]

Answer:

b. multinomial population

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So this is an example of a multinomial population.

The correct answer is:

b. multinomial population

7 0
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