Since the sum of the angles of a triangle = 180°
Then <span>80º + (2x + 2)º + 5xº = 180</span>°
82° + (7x)° = 180°
(7x)° = 180° - 82°
x = 98° ÷ 7
∴ x = 14
The answer is 2/11 in simplest form
9514 1404 393
Answer:
2 1/2 cups
Step-by-step explanation:
A proportion says the ratio of one thing to another is the same for different amounts. Here, we want cups, so we can use the proportion ...
cups/people = 2/12 = x/15 . . . . . where x is the number we want to find
Multiplying by 15 gives ...
x = 15(2/12) = 5/2 = 2 1/2
You will need 2 1/2 cups of zucchini to feed 15 people with the same recipe.
Answer:
AB and CD are parallel lines
Step-by-step explanation:
• Parallel lines have equal slopes
• The slopes of perpendicular lines are negative reciprocals
Calculate the slope m using the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
let (x₁, y₁ ) = A(1, 4) and (x₂, y₂ ) = B(3, 8)
m = = = 2
let (x₁, y₁ ) = C(- 1, 6) and (x₂, y₂ ) = D(3, 14)
m = = = 2
Since slope of AB and CD are equal then lines are parallel
PART A:
The given quadratic equation is 2x²-10x-8=0
The radicand is given by b²-4ac where a, b, and c are the constants in a quadratic form ax²+bx+c
From the given equation, we have
a = 2
b = -10
c = -8
Radicand b²-4ac = (-10)² - 4(2)(-8) = 100 + 64 = 164
The radicand is >0 hence the quadratic equation has two distinct roots
PART B:
4x²-12x+5 = 0
We can use the factorization method to solve the equation
Firstly, we multiply 4 by 5 to get 20
Then we find the pair of numbers that multiply gives 20 and sum gives -12
The pair of number is -2 and -10
Rewriting the equation
4x²-2x-10x+5 = 0
2x(2x-1)-5(2x-1) = 0
(2x-1)(2x-5) = 0
2x-1 = 0 and 2x-5 = 0
x = 1/2 and x = 5/2