Asap! 20 points! 5 questions! 1. the sum of 8 and 5 times a number is 43. which equation below can be used to find the unknown number? a) (8 + 5)n = 43 b) 8 + 5n = 43 c) (8 + n) = 43 d) 8(5n) = 43 2. marcos drove twice as far a candice. together, they drove 66 miles. which equation can be used to find the number of miles candice drove? a) 3x = 66 b) 2x + 1/2x = 66 c) 3x = 66 + x d) 3x = 66 - x 3. a 180 ft long board is cut into 3 pieces. the second piece of board is twice as long as the first. the third piece of board is six times as long as the first. what is the length of the first piece of the board? a) 20 ft b) 40 ft c) 60 ft d) 120 ft 4. the difference of 5 times a number and 8 is 27, which equation below can be used to find the unknown number? a) (8 - 5) - n = 27 b) 8 - 5n = 27 c) 5n - 8 = 27 d) 8 + 5 - n = 27 5. a secretary at the police department makes $8 less per hour than the dispatcher. the combined hourly wage of the secretary and the dispatcher is $40. which equation could be used to find the hourly wage of the dispatcher? a) 2x + 8 = 40 b) 2x - 8 = 40 c) 8 = 2x = 40 d) (8 - 2)x = 40

1. Let the unknown number be x

The phrase “8 and” means addition so that’s 8 +

5 times a number is multiplication so that’s 5 times x, or simply, 5x

So the correct equation would be 8 + 5x = 43

And the correct value for variable x is 7

8 + 35 = 43

2. A

3. Here we can see that there has to be a single unknown variable and using that variable we have to create an equation. That equation will ultimately help us to find the exact value of the variable. This way we can easily reach the answer that is asked in the question.

Let us assume the length of the first piece = x

Length of the second piece = 2x

Length of the third piece = 6x

Now we can get to the equation

x + 2x + 6x = 180

9x = 180

x = 180/9

 = 20

So the length of the first piece of the board is 20 feet.I hope i have explained the problem to your satisfaction and understanding

4. C

5. B

Step-by-step explanation:

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)