In a triangle the longest side is 3 inches longer than twice the shortest side. The third side is 2 inches less than twice the shortest side. If the perimeter of the triangle is 61 inches, which equation should be used to find the length of the shortest side, s?
Answers
The shortest side of the triangle is inches.
To solve this problem, let's use the information given about the triangle's sides. Let \(s\) represent the shortest side of the triangle in inches.
According to the problem, the longest side is \(3\) inches longer than twice the shortest side, so its length is \(2s + 3\) inches. The third side is \(2\) inches less than twice the shortest side, so its length is \(2s - 2\) inches.
The perimeter of the triangle is the sum of the lengths of its sides, which is given as \(61\) inches. Using this information, we can set up an equation:
\[s + (2s + 3) + (2s - 2) = 61\]
Now, combine like terms:
\[5s + 1 = 61\]
Subtract \(1\) from both sides:
\[5s = 60\]
Divide by \(5\):
\[s = 12\]
To check, the longest side would be \(2(12) + 3 = 27\) inches, and the third side would be \(2(12) - 2 = 22\) inches. Adding up these lengths (\(12 + 27 + 22\)) does indeed equal the given perimeter of \(61\) inches.
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a + b +c = 10a + b - c = 3 find the value of a + b + 3c
Answers
Answer:
18.8 feet, 59.1 feet to the nearest tenth
Step-by-step explanation:
The diameter is the line drawn that divides the circle into two while the circumference is the perimeter of the circle. Both are a measure of the radius of the circle.
The diameter D = 2r where r is the radius of the circle
The circumference = 2Πr = ΠD where Π = 22/7
Given that the circular fountain has a radius of 9.4 feet
Its diameter = 2 × 9.4 feet = 18.8 feet
The circumference = 22/7 × 18.8 feet
=59.09 feet
≈ 59.1 feet to the nearest tenth
9.4 * 2 = 18.8
diameter is 18.8 feet
circumference =
c = 3.14 * 18.8
c = 59.032
circumference is 59 feet.
y = and y =
y = and y =
y = and y =
Answers
Since the left side is a perfect square, it will just be reduced to:
4y - 3
For the constant on the right side, the positive and negative roots must be considered.
√72 = ±6√2
Equating the two:
4y - 3 = ±6√2
4y = 3 ± 6√2
y = (3 ± 6√2)/4
y = (3 + 6√2) / 4 = 2.87
and
y = (3 - 6√2) / 4 = -1.37
The solution of the quadratic equation (4y – 3)² = 72 are y = (6√2 + 3)/4 and y = (-6√2 + 3)/4
Solution to quadratic equations
Quadratic equations are equation that has a degree of 2. Given the quadratic equation as shown:
(4y – 3)² = 72
Take the square root of both sides
√(4y – 3)² = ±√72
4y -3 = ±√72
4y - 3 = ±6√2
4y = ±6√2 + 3
y = (6√2 + 3)/4 and y = (-6√2 + 3)/4
Hence the solution of the quadratic equation (4y – 3)² = 72 are y = (6√2 + 3)/4 and y = (-6√2 + 3)/4
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Show your work.
Answers
Answers
The state sales tax in Colorado is 2.9%.
We know that because we divide 2.32/80. We have to find out what percent the tax is of the amount paid. The answer comes to 0.029. Multiply it by 100, and you get 2.9%
A: Predicting the gender of a randomly chosen art teacher if 1 of 3 art teachers is female
B: Predicting the gender of a randomly chosen history teacher if 12 of 15 history teachers are female
C: Predicting the gender of a randomly chosen biology teacher if 8 of 12 biology teachers are female
D: Predicting the gender of a randomly chosen chemistry teacher if 4 of 9 chemistry teachers are female
E: Predicting the gender of a randomly chosen health teacher if 2 of 4 health teachers are female
Answers
Answer:
A: Predicting the gender of a randomly chosen art teacher if 1 of 3 art teachers is female.
C: Predicting the gender of a randomly chosen biology teacher if 8 of 12 biology teachers are female.
E: Predicting the gender of a randomly chosen health teacher if 2 of 4 health teachers are female.
Step-by-step explanation:
Notice that the spinner has 6 equal sections.
So, all situations that can be simulated with such spinner must be multiples, divisors of 6, or a number least than 6, that way, we could use the 6 equal-section spinner.
Option A uses 1 of 3, Option B uses 8 of 12, and Option E uses 2 of 4.
Therefore, the anwers are A, C and E.
Answer: A C E
Step-by-step explanation:
Answers
√2(5+√8)=5√2+√2*√8=4+5√2
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