What is the domain (in interval notation) of the following functions?1. g(x)=3/(5x-4)
2. h(x)=√(x)/(x-5)
3. f(x)=√(x)/(x^2-5x)
4. g(x)=(√(x)+5)/(x^2-x-20)
5. h(x)=3/(x^2+1)
6. f(x)=(√(x-2))/(x+1)
7. g(x)= x^2/(3x^2-x-2
8. h(x)=3(x-4)^2-7
Number sets in parenthesis are either on top of or beneath the fraction bar and ^2 here represents a number squared.

Answers

Answer 1

Answer: $1.\ng(x)=(3)/(5x-4)\n\nD:5x-4\neq0\to5x\neq4\ \ \ /:5\to x\neq(4)/(5)\to x\in\mathbb{R}\ \backslash\ \{(4)/(5)\}\n\n2.\nh(x)=(√(x))/(x-5)\n\nD:x\geq0\ \wedge\ x-5\neq0\to x\geq0\ \wedge\ x\neq5\to x\in\left<0;\ \infty\right)\ \backslash\ \{5\}$

$3.\nf(x)=(√(x))/(x^2-5x)\n\nD:x\geq0\ \wedge\ x^2-5x\neq0\to x\geq0\ \wedge\ x(x-5)\neq0\n\n\to x\geq0\ \wedge\ x\neq0\ \wedge\ x\neq5\to x\in\mathbb{R^+}\ \backslash\ \{5\}\n\n4.\ng(x)=(√(x)+5)/(x^2-x-20)\n\nD:x\geq0\ \wedge\ x^2-x-20\neq0\to x\geq0\ \wedge\ (x+4)(x-5)\neq0\n\n\to x\geq0\ \wedge\ x\neq-4\ \wedge\ x\neq5\to x\in\left<0;\ \infty\right)\ \backslash\ \{-4;\ 5\}$

$5.\nh(x)=(3)/(x^2+1)\n\nD:x^2+1\neq0\to x^2\neq-1\to x\in\mathbb{R}\n\n6.\nf(x)=(√(x-2))/(x+1)\n\nD:x-2\geq0\ \wedge\ x+1\neq0\to x\geq2\ \wedge\ x\neq-1\to x\in\left<2;\ \infty\right)$

$7.\ng(x)=(x^2)/(3x^2-x-2)\n\nD:3x^2-x-2\neq0\to (3x+2)(x-1)\neq0\to x\neq-(2)/(3)\ \wedge\ x\neq1\n\n\to x\in\mathbb{R}\ \backslash\ \{-(2)/(3);\ 1\}\n\n8.\nh(x)=3(x-4)^2-7\n\nD:x\in\mathbb{R}$

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Answers

Answer:

37,400

Step-by-step explanation:

Whatever the number 10 is being squared by, you just move the decimal right if it is a positive number. In this case, it is 10 to the 4th power.

If you move the decimal in 3.74 four times to the right, you will get 37,400.

Answer:

37400

Step-by-step explanation:

move the decimal place over 4 to the right

What is the first term in the pattern with formula 20 · 5n – 1?A.0

B.20

C.25

D.100

Answers

What is the first term in the pattern with formula 20 · 5n – 1?

The first term in the pattern is B.20.

In a sequence, the format would be:
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If 5x+4y=23 and 4x+5y=22, then what is the value of (x + y)

Answers

Answer:

x=3 and y=2

Step-by-step explanation:

I plugged in a lot of numbers until it worked out.

5(3) + 4(2) = 15+8 which equals 23

then 4(3) + 5(2) = 12+10 which equals 22.

hope that helps!

x=3 and y=2

3+2=5

yay

X =

10
8
9
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Answers

Answer:

x = 8.

Step-by-step explanation:

Using the chords of a circle intersection theorem:

5x = 4 * 10

x = 40 /5

x = 8.

Answer:

X=8

Step-by-step explanation:

The table shows ordered pairs of the function y=8-2x, when x=8,the value of y is

Answers

y just happens to be -8

If n is the average of three numbers x, 12, and 15, what is the value of x?

Answers

9- because it looks like 12 and 15 were multiplied by 3,
3x5= 15
3x4= 12
3x3= 9

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