Factor
x
2
+
15
x
+
44
x
2
+
15
x
+
44
using the AC method.
(
x
+
4
)
(
x
+
11
)
Answer:
The solutions of the equation are 0 , π
Step-by-step explanation:
* Lets revise some trigonometric identities
- sin² Ф + cos² Ф = 1
- tan² Ф + 1 = sec² Ф
* Lets solve the equation
∵ tan² x sec² x + 2 sec² x - tan² x = 2
- Replace sec² x by tan² x + 1 in the equation
∴ tan² x (tan² x + 1) + 2(tan² x + 1) - tan² x = 2
∴ tan^4 x + tan² x + 2 tan² x + 2 - tan² x = 2 ⇒ add the like terms
∴ tan^4 x + 2 tan² x + 2 = 2 ⇒ subtract 2 from both sides
∴ tan^4 x + 2 tan² x = 0
- Factorize the binomial by taking tan² x as a common factor
∴ tan² x (tan² x + 2) = 0
∴ tan² x = 0
<em>OR</em>
∴ tan² x + 2 = 0
∵ 0 ≤ x < 2π
∵ tan² x = 0 ⇒ take √ for both sides
∴ tan x = 0
∵ tan 0 = 0 , tan π = 0
∴ x = 0
∴ x = π
<em>OR</em>
∵ tan² x + 2 = 0 ⇒ subtract 2 from both sides
∴ tan² x = -2 ⇒ no square root for negative value
∴ tan² x = -2 is refused
∴ The solutions of the equation are 0 , π
Rational numbers are the numbers that can be written as the fraction of two integers and absolute value is the distance a number is away from 0. If we look at a number line, the absolute value is the distance any number on the number line is away from 0. Distance is always positive, so our absolute value is always 0.
Answer:
<h3>If the taste tester takes 10 minutes to eat a cheeseburger, then it would take him is
minutes
Eating round the clock, it would take him is
</h3>
Step-by-step explanation:
Given that "In order to develop a more appealing cheeseburger, a franchise used taste tests with 13 different buns, 5 different cheeses, 2 type of lettuce, and 3 types of tomatoes"
From the given we can write
13 buns
8 cheese
4 lettuces
3 tomatoes
∴ There would be different cheeseburger combinations is given by
Given that if the taste tester takes 10 minutes to eat a cheeseburger, then it would take him
minutes
Eating round the clock, it would take him
hours
1 Subtract 22 from both sides
13x=4x+38-213x=4x+38−2
2 Simplify 4x+38-24x+38−2 to 4x+364x+36
13x=4x+3613x=4x+36
3 Subtract 4x4x from both sides
13x-4x=3613x−4x=36
4 Simplify 13x-4x13x−4x to 9x9x
9x=369x=36
5 Divide both sides by 99
x=\frac{36}{9}x=
9
36
6 Simplify \frac{36}{9}
9
36
to 44
x=4x=4
