Answer:
arithmetic sequence: 24, 42, 66, 90, 114; y = 24x - 30
geometric sequence: -54, 162, -486, 1458, -4374; y = -6(-3)^(x - 1)
Step-by-step explanation:
Arithmetic sequence:
-6, 18, ...
18 - (-6) = 24
18 + 24 = 42
42 + 24 = 66
66 + 24 = 90
90 + 24 = 114
y = -6 + 24(x - 1)
y = -6 + 24x - 24
y = 24x - 30
Geometric sequence:
-6, 18, ...
18/(-6) = -3
18 * (-3) = -54
-54 * (-3) = 162
162 * (-3) = -486
-486 * (-3) = 1458
1458 * (-3) = -4374
y = -6(-3)^(x - 1)
Answer:
Minimum number of units sold to make profit is equal to 20
Step-by-step explanation:
Revenue earned by the company as a function of number of units sold as x:
R(x) = 0.55x
Cost for selling units as a function of number of units sold as x:
C(x) = 10 + 0.05x
<em>Net profit earned by the company = (Revenue earned by the company) - (Cost of selling units)</em>
P(x) = (0.55x) - (10 + 0.05x)
P(x) = 0.55x - 10 - 0.05x
P(x) = 0.5x - 10
To earn profit the following condition should satisfy: P(x) ≥ 0
0.5x - 10 ≥ 0
0.5x ≥ 10
x ≥ 
x ≥ 20
7) Certainly there is a typo in the statement, just see that the expression of item (ii) is different from that of item (i). Probably the correct expression is:

. With this consideration, we can continue.
(i) Let E the expression that we are analyzing:

Since (x-1)² is a perfect square, it is a positive number. So, E is a result of a sum of two positive numbers, 2(x-1)² and 3. Hence, E is a positive number, too.
(ii) Manipulating the expression:

So, it's the case when E=0. However, E is always a positive number. Then, there is no real number x that satisfies the expression.
8) Let E the expression that we want to calculate:

Multiplying by (2-1) in the both sides:

Repeating the process, we obtain:
Rational expressions are those that have fractional terms. We state restrictions because it may cause the equation to be undefined in some values of x. The most common restriction for rational expressions is N/0. This means any number divided by zero is undefined.
<h3>What is rational expressions and examples?</h3>
A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials. Here are some examples of rational expressions.
To find the restrictions on a rational function, find the values of the variable that make the denominator equal 0.
Learn more about rational expressions here:
brainly.com/question/9353162
Answer:
14.2cm
Step-by-step explanation:
Complete question:
<em>In circle O, the length of radius OL is 6 cm and the length of arc LM is 6.3 cm. The measure of angle MON is 75°. </em>
<em>Rounded to the nearest tenth of a centimeter, what is the length of arc LMN? </em>
<em></em>
Find the diagram attached
arc LN= arc LM + arc MN
First we need to get the arc MN
length of an arc = theta/360 * 2πr
length of arc MN = 75/360 * 2(3.14)(6)
length of arc MN = 0.20833*37.68
length of arc MN = 7.85
Hence;
arc LN = 6.3 + 7.85
arc LN = 14.15cm
Hence the length of arc LN is 14.2cm