Answer: 345 - 9x = 12 is the equation. Each book cost $37.
Step-by-step explanation: 345 - 12 = 333. This reveals that she spent $333 on books. We divide this by nine to find how much each cost. 333 / 9 = 37. In the equation, x = 37.
Answer:
Options A, D
Step-by-step explanation:
The way that we will be checking if these 3 numbers can represent a triangle is by checking if a + b ≥ c. That means that the first two sides have to be greater than or equal to the third side.
Step 1: Determine if Option A is a triangle
10 + 16 = 26 <- 26 is less than 27 that means that it cannot form a triangle.
Step 2: Determine if Option B is a triangle
14 + 28 = 42 <- 42 is greater than 39 which means that these three numbers can form a triangle.
Step 3: Determine if Option C is a triangle
12 + 27 = 39 <- 39 is equal to 39 which means that these three numbers can form a right triangle.
Step 4: Determine if Option D is a triangle
8 + 22 = 30 <- 30 is less than 31 meaning that these three numbers can't form a triangle.
Answer: Options A, D
To determine if a set of numbers can represent the sides of a triangle, we need to check if the sum of the lengths of any two sides is greater than the length of the third side. Two sets of numbers that could not represent the sides of a triangle are 1, 2, 3 and 4, 5, 9.
In order for three numbers to represent the sides of a triangle, the sum of the lengths of any two sides must be greater than the length of the third side, which is known as triangle inequality. Let's consider the options:
Therefore, the sets of numbers that could not represent the sides of a triangle are 1, 2, 3 and 4, 5, 9.
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3x + 3y = 45
Answer:
y=15-x
Step-by-step explanation:
3y=45-3x
y=15-x
If you want to solve for y, you need another one equation
Answer:
y = -x + 15
Step-by-step explanation:
Subtract 3x from each side (left and right side of the equal sign) which will leave you with 3y = -3x + 45. Then divide everything by 3 which gets you
y = -x +15
Answer:
Step-by-step explanation:
The parametrical components of the curve are:
and
After some trigonometrical and algebraic handling, the parametrical variable is eliminated in the resulting expression:
To eliminate the parameter and find the Cartesian equation of the curve x = 7sinθ,y = cos2θ, we can express x in terms of θ, rearrange the equation, and substitute it into the other equation to eliminate the parameter θ. The resulting equation 2(x/7)² + y - 1 = 0 represents the Cartesian equation of the curve.
To eliminate the parameter and find the Cartesian equation of the curve, we can express x in terms of θ using the given equation x = 7sinθ. Rearranging this equation, we get sinθ = x/7. Similarly, we can express y in terms of θ using the given equation y = cos2θ, which can be rewritten as cos(2θ) = y.
Now we can use the trigonometric identity cos(2θ) = 1 - 2sin²θ to eliminate θ from the equations. Substituting this identity into the second equation, we get 1 - 2(sinθ)² = y.
Simplifying this equation, we have 2(sinθ)² + y - 1 = 0. Finally, we can express sinθ in terms of x using the equation sinθ = x/7, and substitute it into the simplified equation to eliminate θ. This gives us 2(x/7)² + y - 1 = 0, which represents the Cartesian equation of the given curve.
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