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3 years ago

Which function has a domain of {x | x8}?

Mathematics

1 answer:

mylen [45]3 years ago

7 0

Answer:

b, f(x) - x+8 -1

Step-by-step explanation:

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When four times a number is decreased by 7, the result is 1. What is the number?

Shalnov [3]

Answer: The number is 1.

Step-by-step explanation:

create the formula from the problem

4x -7 = 1

move the seven to the other side by adding seven to both sides

4x (+7) -7 = 1 (+7)

4x = 8

then to get the x by itself, divide both sides by 4

4x/4 = 8/4

x = 2

You can check your work by plugging the x back into the original problem

4 (2) -7 = 1

8 -7 = 1

1 = 1 (this means it is correct)

6 0

3 years ago

Prove 2√(x) + 1/√(x + 1) <= 2√(x+1) for all x in [0,inf)

EleoNora [17]

Start by multiplying each side of the inequality by $\sqrt{x + 1}$ and simplifying:

$2 \sqrt x + \frac{1}{\sqrt{x+1}} \leq 2 \sqrt{x + 1}$
$(2 \sqrt x + \frac{1}{\sqrt{x+1}})(\sqrt{x + 1}) \leq (2 \sqrt{x + 1})(\sqrt{x + 1})$
$2 \sqrt{x(x + 1)} + 1 \leq 2(x + 1)$
$2 \sqrt{x^2 + x} + 1 \leq 2x + 2$
$2 \sqrt{x^2 + x} \leq 2x + 1$
$\sqrt{x^2 + x} \leq x + \frac{1}{2}$

From here, we can square both sides to get

$x^2 + x \leq (x + \frac{1}{2})^2$
$x^2 + x \leq x^2 + x + \frac{1}{4}$
$0 \leq \frac{1}{4}$ , which is always true.

3 0

3 years ago

If f(1) = 7 and f(n) = -3f(n − 1) then find the value of f(6).

ludmilkaskok [199]

Answer:

-1701

Step-by-step explanation:

The recursion relation tells you each term of the sequence is -3 times the previous term. Then the first 6 terms are ...

7, -21, 63, -189, 567, -1701

The value of f(6) is -1701.

_____

<em>Additional comment</em>

The explicit formula for a geometric sequence with first term 7 and common ratio -3 is ...

f(n) = 7×(-3)^(n-1)

Then f(6) is ...

f(6) = 7×(-3)^5 = 7×(-243) = -1701

8 0

2 years ago

On Friday it snowed 3 2/7 inches. On Saturday it snowed 2/7 inches. How much more did it snow on Friday then Saturday? A. 3 2/7

GalinKa [24]

Answer:

3 inches

Step-by-step explanation:

We need to take the snow on Friday - the snow on Saturday

3 2/7 - 2/7

3 +(2/7-2/7)

3 inches

3 0

4 years ago

Mrs. Kidd took her two children to a waterpark for summer fun. An adult ticket cost $32 and the total price of admission for Mrs

Leona [35]

32 + 2x = 84
2x = 52
x = 26
child's ticket is $26

4 0

3 years ago