All categories

4 years ago

Which equation demonstrates the identity property?

1 answer:

3 0

Identity property states that any number operated with the identity gives back the number.
From the stated option -17 x 1 = -17 demonstrates the identity property.

You might be interested in

For each equation, determine whether it has no solutions, exactly one solution, or is true for all values of x (and has infinite

nignag [31]

Answer:

Equation 1 has exactly one solution.
Equation 2 has infinitely many solutions.
Equation 3 has no solution.

Step-by-step explanation:

We are given three equations to solve. First, let's solve the equations for x.

Equation 1

$\displaystyle{6x+8=7x+13}\\\\7x + 13 = 6x + 8\\\\x + 13 = 8\\\\\bold{x = -5}$

Therefore, we determined that for the first equation, x = -5. We can check our solution by substituting it back into the original equation.

$\displaystyle{6(-5)+8=7(-5)+13}\\\\-30 + 8 = -35 + 13\\\\-22 = -22 \ \checkmark$

Since we got a true statement, there are no other values of x for which we get a true statement. Let's test this with the opposite value: positive 5.

$6(5)+8=7(5)+13\\\\30 + 8 = 35 + 13\\\\38 = 48 \ \text{X}$

Therefore, for Equation 1, there is exactly one solution.

Equation 2

$6 x + 8 = 2 ( 3 x + 4 )\\\\6x + 8 = 6x + 8\\\\0 + 8 = 8\\\\8 = 8 \ \checkmark$

We get a true statement by solving for x (which ends up canceling out of the equation entirely). Therefore, we can check any value in place of x to see if we get a true statement. For this instance, I will use -3.

$6(-3) + 8 = 2 ( 3(-3) + 4 )\\\\-18 + 8 = 2(-9+4)\\\\-18 + 8 = 2(-5)\\\\-18 + 8 = -10\\\\-18 = -18 \ \checkmark$

We still get a true statement, so Equation 2 has infinitely many solutions.

Equation 3

$6 x + 8 = 6 x + 13\\\\0 + 8 = 13\\\\8 \neq 13$

We get a false statement. Therefore, Equation 3 has no solution.

3 0

3 years ago

Read 2 more answers

Help please asap

padilas [110]

These are 2 questions and 2 answers:

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: option C. (2x + 5)(3x - 4)

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)

6 0

3 years ago

Express 7½ as a fraction in its lowest form

N76 [4]

Answer:

15/14

Step-by-step explanation:

5 0

3 years ago

1) Jacob had $4.30 and spent $2.90 on snacks. How much did he have left

gregori [183]

Answer:

Your answer is Jacob had $1.40 left

8 0

3 years ago

Read 2 more answers

How are neuroscience and medical science alike?

pishuonlain [190]

Answer:

They're both science

Step-by-step explanation:

5 0

3 years ago