Answer:
An equation whose variables are polar coordinates is called a polar equation.
Step-by-step explanation:
Polar Equation--
A polar equation is a equation that describe the relationship between r and θ, where r is the distance from the pole to a point on a curve and θ is the angle subtended by that point with respect to the x-axis.
Hence, here r,θ acts as a variable of the equation.
So, we can change any rectangular equation in terms of variable x and y into the polar equation in terms of variable r and θ by using the transformation:
x=r cosθ and y=r sinθ.
Answer:
A, D
Step-by-step explanation:
A: I goes down 2 and right 5
B: It does not go down 3 and right 2
C: It does not go up 2 and right 5
D: It goes down 5 and right 2
B)7.5+5s>4500
C)7.5+5s<_(less or equal)4500
D)7.5a+5s>_(greater or equal)4500
The director's goal is ticket sales of at least $4500. So, the inequality representing the director's goal is:
7.5a + 5s ≥ 4500
The correct option is:
D) 7.5a + 5s ≥ 4500
Let, set up the inequality based on the given information.
Let "a" represent the number of adult tickets sold and "s" represent the number of student tickets sold.
The revenue from adult tickets is given by: 7.5a (as each adult ticket costs $7.50)
The revenue from student tickets is given by: 5s (as each student ticket costs $5.00)
To find the total ticket sales, we add the revenue from adult and student tickets:
Total ticket sales = 7.5a + 5s
Now, the director's goal is ticket sales of at least $4500. So, the inequality representing the director's goal is:
7.5a + 5s ≥ 4500
The correct option is:
D) 7.5a + 5s ≥ 4500
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- 8x + 10
Write your answer as two ordered pairs:
(x1, y1), (×2, y2)
Separate the values with a comma.
Round, if
necessary, to the nearest hundredth.
Answer:
To find the x-intercepts of the parabola defined by the equation y = 2x² - 8x + 10, you need to set y equal to zero (because x-intercepts occur when y is zero) and solve for x.
So, you have:
0 = 2x² - 8x + 10
Now, you can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation, a = 2, b = -8, and c = 10. Plug these values into the formula:
x = (-(-8) ± √((-8)² - 4 * 2 * 10)) / (2 * 2)
x = (8 ± √(64 - 80)) / 4
x = (8 ± √(-16)) / 4
Since the discriminant (the value inside the square root) is negative, there are no real solutions, which means this parabola does not have x-intercepts in the real number system.
So, there are no ordered pairs (x1, y1) and (x2, y2) for x-intercepts because there are no x-intercepts for this parabola in the real number system.
Step-by-step explanation:
Certainly, let's find the x-intercepts step by step for the equation:
y = 2x² - 8x + 10
Step 1: Set y to zero because x-intercepts occur when y equals zero:
0 = 2x² - 8x + 10
Step 2: Now, we want to solve this equation for x. We can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this formula:
a is the coefficient of the x² term (which is 2 in this case).
b is the coefficient of the x term (which is -8).
c is the constant term (which is 10).
Step 3: Plug the values of a, b, and c into the formula:
x = (-(-8) ± √((-8)² - 4 * 2 * 10)) / (2 * 2)
Step 4: Simplify the equation inside the square root:
x = (8 ± √(64 - 80)) / 4
x = (8 ± √(-16)) / 4
Step 5: Now, notice that we have a square root of a negative number (√(-16)). In the real number system, we can't take the square root of a negative number. This means there are no real solutions for x.
Step 6: Since there are no real solutions, there are no x-intercepts for this parabola in the real number system. Therefore, there are no ordered pairs (x1, y1) and (x2, y2) for x-intercepts in this case.
Answer:
The answer is below
Step-by-step explanation:
The scale for the drawing is 1 inch = 40 feet.
The right angled triangle has legs of 3 inches and 4 inches. Using the scale, the length of the legs is:
3 inches = 3 inch * 40 feet / inch = 120 feet and 40 inches = 4 inch * 40 feet / inch = 160 feet.
The area of a right angled triangle is half the product of the two legs. Hence:
Area of right angled triangle = 1/2 * 120 feet * 160 feet = 9600 ft²
The rectangle with dimensions of 1.5 inches and 2.5 inches. Using the scale, the length of the sides is:
1.5 inches = 1.5 inch * 40 feet / inch = 60 feet and 2.5 inches = 2.5 inch * 40 feet / inch = 90 feet.
The area of a rectangle is the product of the two sides. Hence:
Area of rectangle = 60 feet * 90 feet = 5400 ft²