Circle O has a circumference of approximately 44 in. What is the approximate length of the diameter, d? 7 in. 14 in. 22 in. 44 i
2 answers:
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Answer:
3x³+3x²+3x+8+
Step-by-step explanation:
You can use synthetic division for this problem since the divisor is in (x-a) form. The fraction is the remainder over the divisor.
To find the area of a prism, you calculate the area of the cross-section and multiply that number by the length. The cross-section of this prism is a trapezium, and the formula for this is 
.
Insert your given numbers to find out the area of this prism's cross-section:
Now, multiply 90 by the length, 10cm, to find out the volume of the prism;
90×10=900cm³
Therefore, your answer id the third option.
Insert your given numbers to find out the area of this prism's cross-section:
Now, multiply 90 by the length, 10cm, to find out the volume of the prism;
90×10=900cm³
Therefore, your answer id the third option.
Answer:
1. 43, 45, and 47
2. 50, 52, and 54
3. 47 years old
4. 106 degrees
5. 66 degrees
Step-by-step explanation:
1. Let's assume that the first number in the three consecutive odd numbers is x.
We can write an equation to express this now. .
Combining like terms, we get . Subtracting by (x+2) on each side, we get
. Since the smallest number is 43, we can find the two larger numbers as well, since they are 2 more than one another. Therefore, the numbers are 43, 45, and 47.
2. Let's assume that the first number in the three consecutive even integers is x.
We can write an equation to express this now.
Combining like terms, we get . Subtracting by (x+2) on each side, we get
. Since the smallest number is 50, we can find the two larger numbers as well, since they are 2 more than one another. Therefore, the numbers are 50, 52, and 54
3. We can write his current age in years as x. Next year, his age will be x+1. We know that the sum of his current age and his age next year is 73, so we can write an equation to express this.
. Therefore, 2x + 1 = 73, or 2x = 72. This means that x = 36, or his current age is 36. In 11 years, his age will be 36 + 11 = 47 years old.
4. . Combining like terms, we get
Subtracting by 5 on both sides, we get
This means that
. Now, we can find the degree measures of both angles and find the larger one. The degree measure of the angle on the left is 21(5) + 1 = 106 degrees, and the degree measure of the angle on the right is 14(5) + 4 = 74 degrees. Therefore, the degree measure of the larger angle is 106 degrees.
5. We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can sum the angles up and equate them to 180 degrees.
(x-24) + (2x-108) + (1/3x+12) = 10/3x - 120 = 180. Adding 120 to both sides, we get 10/3x = 300. Multiplying both sides by 3/10, we get x = 900/10 = 90. Therefore, plugging in x = 90, we get 66 degrees.