How do I solve n^2-5n-14=0 by factoring

Answers

Answer 1
Answer: (N-7)(n+2)=0 as you'd get n^2-7n+2n-14 then just simplify. Then it would be n=-2 or 7
Answer 2
Answer: n^2-5n-14=0 \n n^2-7n+2n-14=0\n n(n-7)+2(n-7)=0\n (n+2)(n-7)=0\n n=-2 \vee n=7

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Don completes the square for the equation x^2 + 6x + 3 = 0. Which of the following equations reveals the vertex of the parabola?

Answers

x² + 6x + 3 = 0

y = x² + 6x + 3
y - 3 = x² + 6x 

6x ⇒ 6x / 2x = 3 ⇒ 3² = 9

y - 3 + 9 = x² + 6x + 9
y + 6 = (x+3)² 
y = (x+3)² - 6

vertex of the parabola is (x+3)²

y = (x+3)(x+3)  - 6
y = x(x+3)+3(x+3) - 6
y = x² + 3x + 3x + 9 - 6
y = x² + 6x + 3

Prove 4t + t = 5t4t + t

t(4 + 1)

t(5)

5t

What property or properties were used to prove that the expressions are equivalent?
commutative and distributive properties
associative and distributive properties
associative and commutative properties
associative property

Answers

The proof used the distributive property and the associative property of multiplication.

Option B is the correct answer.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the liketerms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To be specific, the distributiveproperty was used to break down the expression 4t + t as:

4t + t = (4 + 1)t ________(1)

And then the associativeproperty was used to rearrange the terms as:

(4 + 1)t = 5t ________(2)

From (1) and (2)

We have shown that 4t + t is equivalent to 5t.

Thus,

The proof used the distributive property and the associative property of multiplication.

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Answer:

its A: commutative and distributive properties

Step-by-step explanation:

i got it right

John can service a television and a cable box in one hour. It took him four hours yesterday to service two televisions and ten cable boxes. How many minutes does John need to service a cable box?

Answers

For this item, we let x be the number of minutes he can service a television and y be the minutes he can service a cable box. Then, the system of linear equation that would best represent the given above is,
                                x + y = 60 
                                2x + 10 y = (4)(60)
The values of x and y from the equations are 45 and 15 minutes, respectively. Therefore, John needs 15 minutes to service a cable box. 

Alicia is a nurse.In 2016, she earned a monthly salary of £1750
In 2017, she was awarded a 2% pay increase on her monthly salary.
Given that in 2017 Alicia worked 45 hours per week for 48 weeks,
work out her average pay per hour for the year.

Answers

Final answer:

To calculate Alicia's average pay per hour for the year, we need to find her total earnings for the year and divide it by the total number of hours she worked.

Explanation:

To calculate Alicia's average pay per hour for the year, we need to find her total earnings for the year and divide it by the total number of hours she worked. In 2016, Alicia earned £1750 per month, so her annual salary would be £1750 x 12 = £21,000.

In 2017, she received a 2% pay increase, which means her monthly salary would be £1750 + 2% of £1750 = £1750 + (£1750 x 0.02) = £1750 + £35 = £1785.

Since Alicia worked 45 hours per week for 48 weeks in 2017, her total number of hours worked for the year would be 45 hours/week x 48 weeks = 2,160 hours. Now, we can calculate her average pay per hour by dividing her total earnings (£1785 x 12) by the total number of hours worked (2,160): £1785 x 12 / 2,160 = £10 per hour.

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AnswerAverage pay per hour 19.15

Step-by-step explanation:

1750 + 2% = 1785 pay increase

1785 x 12 months = 21420 a year

21420 divided by 52 weeks in a year averages to 411.92 weekly

Divide 411.92 by the 45 hours of work is 19.15 per hour

Brainliest please, if correct.

What is bigger 7/8 or 0.78

Answers

Solutions 

To solve the problem we first have to convert the fraction into a decimal. To convert a fraction into a decimal you have to divide the numerator by the denominator. 

7/8 
= 7 ÷ 8 
= 0.875 

0.875 is bigger then 0.78 therefore 7/8 is greater. 

How would you transform 5x + 2x into a single term? Substitute five different values into the expressions 5x + 2x and 7x - 1.

Answers

5x + 2x = 7x
 is it in a single term

Final answer:

The expression 5x + 2x simplifies into 7x. Substituting the values 1, 2, 3, 4, and 5 for x in both expressions yields the results 7, 14, 21, 28, and 35 for 5x + 2x, and 6, 13, 20, 27, and 34 for 7x - 1.

Explanation:

The expression 5x + 2x can be simplified into a single term by adding the coefficients of similar terms. This means you add the 5 and 2 together. The result is 7x.

For substituting different values into the expressions 5x + 2x and 7x - 1, let's use 1, 2, 3, 4, and 5 as the values for x.

  1. For x=1: 5(1) + 2(1) = 7 and 7(1)-1 = 6
  2. For x=2: 5(2) + 2(2) = 14 and 7(2)-1 = 13
  3. For x=3: 5(3) + 2(3) = 21 and 7(3)-1 = 20
  4. For x=4: 5(4) + 2(4) = 28 and 7(4)-1 = 27
  5. For x=5: 5(5) + 2(5) = 35 and 7(5)-1 = 34

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