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3 years ago

Consider the functions f(x) = 8x + 16 and g(x) = x^2 + 2x + 5.

Mathematics

1 answer:

motikmotik3 years ago

7 0

Answer:

x =8

Step-by-step explanation:

To answer this question you must find the point at which $g(x)\geq f(x)$

So, we have:

$x^2 + 2x + 5 \geq 8x + 16$

$x^2 + 2x -8x + 5 -16\geq0\\\\x^2 -6x -11\geq 0$

To solve the quadratic function we use the quadratic formula

$\frac{-b \± \sqrt{b^2- 4ac}}{2a}$

Where:

$a = 1\\b =-6\\c = -11$

Then:

$\frac{-(-6) \± \sqrt{(-6)^2- 4(1)(-11)}}{2(1)}\\\\x = 7.47\\x = -1.472$

The line cuts the parabola by 2 points, x = -1.472 and x = 7.47.

You can verify that between x = -1.472 and x = 7.47. the line is greater than the parabola, but from x = 7.47, the parabola is always greater than the graph of the line.

Therefore the point sought is:

x = 7.47≈ 8

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I need help writing the first 5 terms of the sequence!

Angelina_Jolie [31]

The first five terms of the sequence are 1, 4, 7, 10, 13.

Solution:

Given data:

$a_{1}=1$

$a_{n}=a_{n-1}+3$

General term of the arithmetic sequence.

$a_{n}=a_{n-1}+d$ , where d is the common difference.

d = 3

$a_{n}=a_{n-1}+3$

Put n = 2 in $a_{n}=a_{n-1}+3$ , we get

$a_{2}=a_1+3$

$a_{2}=1+3$

$a_2=4$

Put n = 3 in $a_{n}=a_{n-1}+3$ , we get

$a_{3}=a_2+3$

$a_{3}=4+3$

$a_3=7$

Put n = 4 in $a_{n}=a_{n-1}+3$ , we get

$a_{4}=a_3+3$

$a_{4}=7+3$

$a_4=10$

Put n = 5 in $a_{n}=a_{n-1}+3$ , we get

$a_{5}=a_4+3$

$a_{5}=10+3$

$a_5=13$

The first five terms of the sequence are 1, 4, 7, 10, 13.

3 0

3 years ago

Tim Hortons is hiring and offers $200 every week plus $5 per hour. McDonalds offers $300 every week plus $2 per hour. State the

Bogdan [553]

Answer: After working for 33 $\frac{1}{3}$ hours a week

Step-by-step explanation:

Let us write equations to represent these two places. Let x be hours worked and y be money earned.

Tim Hortons:

$200 + $5x = y

McDonalds:

$300 + $2x = y

Now, to find the conditions of which Tim Hortons is the better employer (on the basis of money earned) we must find the interval that Tim Hortons pays more. This can be found by setting up another equation, or by graphing. I have shown both. See attached for the graph.

$200 + $5x > $300 + $2x

$5x > $100 + $2x

$3x > $100

x > $\frac{100}{3}$