Given 4 consecutive odd numbers with a sum of 224, we can create an equation to solve for the first number (x). After calculating x = 53, we find the largest number to be 59.
This is a problem about consecutive odd integers, which are odd integers that follow each other successively. Let's denote the first odd integer as x, the second as x+2, the third as x+4, and the fourth as x+6. These are all odd because adding 2 to an odd number always results in the next odd number.
The question states that the sum of these four consecutive odd numbers is 224, so we can create the following equation: x + (x+2) + (x+4) + (x+6) = 224.
Simplify this equation to obtain 4x + 12 = 224. Then, solve for x by first subtracting 12 from both sides to get 4x = 212 and then dividing by 4 to get x = 53. Our highest odd number would be x+6 which equals 59.
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The four consecutive odd integers whose sum is 224 are 53, 55, 57, and 59. The largest of these integers is 59.
To find four constructive odd integers whose sum is 224, you first need to understand that consecutive odd integers follow a certain sequence, each increasing by 2 from the previous one. Let's label the first consecutive odd integer as 'n'. So, the four consecutive numbers will be: n, n + 2, n + 4, n + 6.
According to the problem, the sum of these four numbers equals 224:
n + (n+2) + (n+4) + (n+6) = 224.
Solve this equation to find the value of 'n'. You'll get n = 52. Hence, the numbers are 52, 54, 56, 58.
Since we are looking for odd numbers, let's start with 53 (the first odd number greater than 52) and proceed: 53, 55, 57, 59. And these four numbers do sum up to 224. Therefore, the largest number in this series is 59, our final answer.
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h = the amount of hours
t = total
12h = t
Hope this helps
-AaronWiseIsBae
Answer:
12h
Step-by-step explanation:
took the quiz got a 100;)
Answer:
The values of x and y are x = 25 and y = 18
Step-by-step explanation:
The measure of an arc is equal to the measure of the central angle subtended by it
In circle W
∵ W is the center of the circle
∵ m∠QWS = 90°
∵ ∠QWS is subtended by arc QS
- Use the rule above
∴ m∠QWS = m arc QS
∴ m arc QS = 90°
∵ m arc QS = m arc QR + m arc RS
∵ m arc QR = (x + 11)°
∵ m arc RS = (3y)°
- Add them and equate the answer by 90
∴ (x + 11) + (3y) = 90
- Subtract 11 from both sides
∴ x + 3y = 79 ⇒ (1)
∵ VT passes through W
∴ VT is a diameter in circle W
- Diameter divides the circle into two equal arcs the measure
of its arc is 180° because the measure of the circle is 360°
∴ m arc VQRST is 180°
∵ m arc QRS = 90°
∵ m arc VQRST = m arc VQ + m arc QRS + m arc ST
- Substitute the measures of arc VQRST and QRS
∴ 180 = m arc VQ + 90 + m arc ST
- Subtract 90 from both sides
∴ 90 = m arc VQ + m arc ST
∵ m arc VQ = (y + 7)°
∵ m arc ST = 65°
∴ 90 = (y + 7) + 65
- Add like terms in the right hand side
∴ 90 = y + 72
- Subtract 72 from both sides
∴ 18 = y
Substitute the value of y in equation (1) to find x
∵ x + 3(18) = 79
∴ x + 54 = 79
- Subtract 54 from both sides
∴ x = 25
The values of x and y are x = 25 and y = 18