These are 2 questions and 2 answers:
<span>1.
Question 1: The area of a rectangular carpet is given by the trinomial 5x^2 - 3x -
14. What are the possible dimensions of the carpet? Use factoring.
Answer: 5x^2 -3x -14
Explanation:
You might probe the different pairs of factors given in the answer choices to check wich product is equal to the oirginal polynomial or you can factor from zero.
I will show you how to factor that polynomial from zero:
1) given: 5x^2 - 3x - 14
2) multiply and divide by the leading coefficient =>
5 [5x^2 - 3x -14 ]
----------------------
5
3) Enter the the factor 5 inside the parenthesis:
5.5x^2 - 5.3x - 5.14
--------------------------
5
4) rearrange conviniently to show (5x) as a common factir of the first two terms
(5x)^2 - 3(5x) - 70
--------------------------
5
5) factor the numerator using 5x as common term of the two binomials:
(5x ) ( 5x ) <----> open the parenthesis
(5x - ) (5x + ) <-----> include the signs
(5x - 10) (5x + 7) <---> two numbers that add up - 3 and their product is - 70
=>
(5x - 10)(5x + 7)
---------------------
5
6) divide (5x - 10) by 5 => x - 2
7) factored expression
(x - 2) (5x + 7)
8) Conclusion: the answer is the option B. (5x + 7) and (x - 2)
2. Question 2. The area of a rectangular barnyard is given by the trinomial 6x^2 +
7x – 20. What are the possible dimensions of the barnyard? Use factoring
Answer: </span><span><span>option C. (2x + 5)(3x - 4)</span>
Explanation:
The procedure is the same of the question 1.
1) given: 6x^2 + 7x - 20
2) multiply numerator and denominator by 6 and rearrange to show (6x) as common factor ot the first two terms =>
(6x)^2 + 7(6x) - 120
--------------------------
6
3) factor the numerador using 6x as common factor ot two binomials, and simplify:
(6x + )(6x - )
(6x + )(6x - )
(6x + 15) (6x - 8)
=>
(6x + 15)(6x -8)
---------------------
6
(6x + 15)(6x - 8)
---------------------- =
3.2
(6x + 15) (6x - 8)
------------- . ------------ =
3 2
(2x + 5)(3x - 4)
4) answer: option C. (2x + 5)(3x - 4)</span>
The sum of the angles of a triangle is 180°. So you can do:
91° + (8x + 3)° + (10x - 4)° = 180° To find x, you need to isolate/get the variable "x" by itself in the equation. First combine like terms (terms that have the same variable and power/exponent]
91 + 3 - 4 + 8x + 10x = 180 (I rearranged for the like terms to be next to each other)
90 + 18x = 180 Subtract 90 on both sides
18x = 90 Divide 18 on both sides to get "x" by itself
x = 5
PROOF
91° + (8x + 3)° + (10x - 4)° = 180° Plug in 5 for "x"
91° + (8(5) + 3)° + (10(5) - 4)° = 180°
91° + (40 + 3)° + (50 - 4)° = 180°
91° + 43° + 46° = 180°
180° = 180°
Answer:
You should invest $2000 at 5% simple interest in order to earn $100 interest in 12 months.
Step-by-step explanation:
Using the formula
where
I = Interest earned
P = The principal (let say in $)
r = The Interest Rate
t = time
Given that
- P = The principal amount needed to invest (let say in $)
Thus,
100 = P × 5% × 1
100 = P × 5/100 × 1
100 × 100 = P × 5
10000 = P × 5
P = 10000/5
= 2000 (let say in $)
Thus, you should invest $2000 at 5% simple interest in order to earn $100 interest in 12 months.
Answer:
-3
Step-by-step explanation:
if x= -3
the denominator becomes 0 and the fraction becomes undefined.
