A triangle has two sides of length 18 and 17. What is the smallest possible whole-number length for the third side?
Answers
a, b, c - sides of a triangle
a + b > c
a + c > b
b + c > a
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We have a = 18 and b = 17. Substitute:
18 + 17 > c
35 > c → c < 35
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18 + c > 17 subtract 18 from both sides
c > -1
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17 + c > 18 subtract 17 from both sides
c > 1
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c < 35 and c > -1 and c > 1.
Therefore 1 < c < 35
Answer: The smallest possible whole number length of third side is 2.
Final answer:
The smallest possible whole-number length for the third side of a triangle with the other two sides being 18 and 17 is 2, based on the rule that each side of a triangle must be less than the sum and more than the absolute difference of the other two sides.
Explanation:
In the realm of geometry, there is a rule for a triangle that states the length of any side of a triangle must be less than the sum of the lengths of the other two sides, but greater than the absolute difference of those two sides. Given a triangle with two sides of lengths 18 and 17, we apply this rule.
To find the smallest possible whole number length for the third side, we calculate the absolute difference of the existing two sides: |18 - 17| = 1.
But, since we are looking for a whole number, the smallest possible length for the third side cannot be 1, it must be more than 1. Therefore, the smallest possible whole-number length for the third side is 2.
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the domain of the function f(x) = 3x3 is {2, 5}. what is the function’s range? the range of the function f(x) = 3x3 when its domain is {2, 5} is
Answers
Answer:
awnser one is 7 and question 2 is -10
Step-by-step explanation:
−12−2−−55=? question one
In the first fraction, the negative numerator and negative denominator cancel each other.
Since the the second fraction is negative and you are subtracting, remove the negative sign and switch the operation to addition.
The equivalent equation is
122+55=?
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(12/2, 5/5) = 10
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
(122×55)+(55×22)=?
Complete the multiplication and the equation becomes
6010+1010=?
The two fractions now have like denominators so you can subtract the numerators.
Then:
60+1010=7010
Since 70 divided by 10 equals 7 then,
7010=7
Therefore:
−12−2−−55=7
Question 2
−81+6−3=?
In the second fraction, move the negative sign from the denominator to the numerator and the value remains the same.
The equivalent equation is
−81+−63=?
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(-8/1, -6/3) = 3
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
(−81×33)+(−63×11)=?
Complete the multiplication and the equation becomes
−243+−63=?
The two fractions now have like denominators so you can add the numerators.
Then:
−24+−63=−303
Since -30 divided by 3 equals -10 then,
−303=−10
Therefore:
−81+6−3=−10
Solution by Formulas
Apply the fractions formula for addition, to
−81+6−3
and solve
(−8×−3)+(6×1)1×−3
=24+6−3
=30−3
=−10
Answers
Answers
Answers
(5,40) (10,80)
80-40=40
10-5=5
40/5=8
Answers
Fraction: 3 / 4 it's already reduced to lowest terms
Fraction: 11 / 14 it's already reduced to lowest terms
Step 2: Calculate LCM (lowest common multiple) of the reduced fractions' denominators, it will be the common denominator of the compared fractions:
Denominator 4, factored = 22
Denominator 14, factored = 2 * 7
LCM (4, 14) = 22 * 7 = 28
Step 3: Calculate each fraction's expanding number (LCM divided by each fraction's denominator):
For fraction: 3 / 4 is 28 : 4 = (22 * 7) : 4 = 7
For fraction: 11 / 14 is 28 : 14 = (22 * 7) : 14 = 2
Step 4: Expand fractions to bring them to the common denominator (LCM):
3 / 4 = (7 * 3) / (7 * 4) = 21 / 28
11 / 14 = (2 * 11) / (2 * 14) = 22 / 28
Answers
Answer:
1/2
Step-by-step explanation:
When reducing fractions, you're trying to answer the question, "do the numerator and denominator have any common factors that can be canceled?" Knowing your multiplication tables helps answer this question.
Answer:
1/2
Step-by-step explanation:
7
7/14 is identical to ---------
2(7)
This can be reduced to 1/2 by cancelling out the 7s.