How can I use summation notation to write the series 2, 4, 6, 8 for 10 terms?
To express the series 2, 4, 6, 8 in summation notation for the first 10 terms, we start by observing a pattern in the series. Each term can be represented as an arithmetic sequence where the first term (a) is 2 and the common difference (d) is also 2. The n-th term of an arithmetic […]
What is the radius of the circle whose equation is x² + y² = 9?
The equation of a circle is typically written in the form of (x – h)² + (y – k)² = r², where (h, k) is the center of the circle and r is the radius. In the equation provided, x² + y² = 9, we can see that it closely resembles the standard form. Here, […]
What is the value of a in the equation 3a + b = 54 when b = 9?
To find the value of a in the equation 3a + b = 54 when b = 9, we can start by substituting 9 for b in the equation: 3a + 9 = 54 Next, we need to isolate 3a. We do this by subtracting 9 from both sides of the equation: 3a = 54 […]
Choose the correct classification of 3×4, 9×3, 3×2, 6
To classify the numbers 3×4, 9×3, 3×2, and 6, we first need to calculate the results of the multiplications: 3×4 = 12 9×3 = 27 3×2 = 6 6 = 6 Now, we have the numbers: 12, 27, 6, and 6. Next, let’s classify these numbers based on their properties: Even and Odd: 12 and […]
Find the Surface Area of a Sphere with Radius 10 in Leave Your Answer in Terms of Pi
The formula for the surface area of a sphere is given by: Surface Area = 4πr² Where r is the radius of the sphere. In this case, the radius is 10 inches. Now, let’s substitute the value of the radius into the formula: Surface Area = 4π(10)² Calculating that: Surface Area = 4π(100) Surface Area […]
A car gets 35 miles per gallon how many gallons do you need to go 700 miles?
To determine how many gallons of gas you would need to drive 700 miles in a car that gets 35 miles per gallon, you can use a simple formula: Gallons Needed = Total Miles / Miles Per Gallon In this case, you will divide 700 miles by 35 miles per gallon: Gallons Needed = 700 […]
How do you know if two line segments are perpendicular?
To determine if two line segments are perpendicular, you need to check the relationship between their slopes. If the slopes of two line segments are negative reciprocals of each other, then the lines are perpendicular. For example, if the slope of the first segment is ‘m1’ and the slope of the second segment is ‘m2’, […]
Which is true about the polynomial y² + 3y + 12?
The polynomial y² + 3y + 12 is a quadratic expression. To analyze its properties, we can look at several aspects such as its roots, graph, and whether it factored or not. First, we can determine if the polynomial has real roots by calculating the discriminant (b² – 4ac). In this polynomial, a = 1, […]
An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. The second side of the triangle is 69 cm long. What can be determined?
In triangle ABC, let the angle bisector of angle A intersect side BC at point D, dividing BC into segments BD = 6 cm and DC = 5 cm. According to the angle bisector theorem, the ratio of the two segments on the opposite side is equal to the ratio of the other two sides […]
You jogged 11 kilometers at an average speed of 10 kilometers per hour. How long did you jog?
To find out how long you jogged, you can use the formula: Time = Distance / Speed In this case, you jogged a distance of 11 kilometers at an average speed of 10 kilometers per hour. Plugging in these values: Time = 11 km / 10 km/h = 1.1 hours This means you jogged for […]