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katen-ka-za [31]
3 years ago
9

F(x)=1/2×+6 plz helpppppppppp​

Mathematics
1 answer:
FromTheMoon [43]3 years ago
3 0

Answer:

The solution set can be given as:

\{x|x\ \epsilon\ R,x\neq -3\}

Step-by-step explanation:

Given function:

f(x)=\frac{1}{2x+6}

To find the domain of the function in set notation.

Solution:

For the function f(x) to exist the denominator must be ≠ 0

We have the denominator (2x+6) which  cannot be = 0.

Thus, we can find the domain of the function using the above relation.

The function f(x) will not exist when:

2x+6=0

Solving for x

Subtracting both sides by 6.

2x+6-6=0-6

2x=-6

Dividing both sides by 2.

\frac{2x}{2}=\frac{-6}{2}

∴ x=-3

Thus, the function will not exist at x=-3. This means it has all real number solutions except -3.

The solution set can be given as:

\{x|x\ \epsilon\ R,x\neq -3\}

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3 years ago
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A university is building a new student center that is two- thirds the distance from the arts center to the residential complex.
Natasha2012 [34]

Answer:

C = (\frac{21}{5},\frac{33}{5})

Step-by-step explanation:

Given

Points: (1, 9) and (9, 3)

Ratio = 2/3

Required

Determine the coordinate of the center

Represent the ratio as ratio

Ratio = 2:3

The new coordinate can be calculated using

C = (\frac{mx_2 + nx_1}{n + m},\frac{my_2 + ny_1}{n + m})

Where

(x_1,y_1) = (1, 9)

(x_2, y_2) = (9, 3)

m:n = 2:3

Substitute these values in the equation above

C = (\frac{2 * 9 + 3 * 1}{3 + 2},\frac{2 * 3 + 3 * 9}{2 + 3})

C = (\frac{18 + 3}{5},\frac{6 + 27}{5})

C = (\frac{21}{5},\frac{33}{5})

Hence;

<em>The coordinates of the new center is </em>C = (\frac{21}{5},\frac{33}{5})<em></em>

7 0
3 years ago
12.
g100num [7]

Answer:

Step-by-step explanation:

tan^{-1} (\frac{\sqrt{3} }{3} )=x\\tan x=\frac{\sqrt{3} }{3} =tan (\frac{\pi}{6} )\\x=\frac{\pi}{6}

7 0
3 years ago
Can someone solve this? and tell me how?
maksim [4K]

Answer:

1/3

Step-by-step explanation:

When working with balanced expressions (stuff on both sides of the equal sign), "what you do to one side, you do to the other", which keeps it balanced.

The first thing we notice is the exponent 1/4, which is one both sides, so we can get rid of it on both sides by using the <u>reverse operation</u>.

The reverse of exponents is <u>square root</u>.

(4x + 10)^{\frac{1}{4}} = (9 + 7x)^{\frac{1}{4}}\\\sqrt[\frac{1}{4}]{(4x + 10)^{\frac{1}{4}}} = \sqrt[\frac{1}{4}]{(9 + 7x)^{\frac{1}{4}}}\\\\4x + 10 = 9 + 7x

Isolate x to solve. Separate the variables and non-variables.

4x + 10 = 9 + 7x

4x - 4x + 10 = 9 + 7x - 4x          Subtract 4x from both sides

10 = 9 + 3x                

10 - 9 = 9 - 9 + 3x            Subtract 9 from both sides

1 = 3x            Divide both sides by 3 to isolate x

x = 1/3           Answer

8 0
3 years ago
Solve by graphing -3x + y = 4 y = -2x - 1
Dafna11 [192]

Answer:

(-1,1)

Step-by-step explanation:

6 0
2 years ago
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