Write an equation for the quadratic function whose vertex is (âˆ’2,10) and passes through (1,28)

The water pressure on Mustafa as he dives is increasing at a rate of 0.9920.9920, point, 992 atmospheres (\text{atm})(atm)left p

Paha777 [63]

This problem is a simple dimensional analysis. We are simply tasked to express the rate 0.992 atm/m to atm/km.

Dimensional analysis, in simpler terms, is just the process of expressing an answer in another unit by multiplying conversion factors.

For this problem, we'll need to perform the following:

$\frac{0.992 atm}{m}= \frac{1000m}{1km} = \frac{992atm}{km}$

Notice that we used the conversion factor 1000 meters = 1 kilometer to convert the units from atm/m to atm/km. Thus, we arrive at the final answer 992 atm/km.

8 0

2 years ago

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If a polygon is a regular pentagon, then it has 5 sides.

mina [271]

If a polygon has 5 sides, then it is a regular pentagon
False: regular pentagon = equiangular. There are pentagons that have 5 sides that are not equiangular

3 0

2 years ago

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A curious student asks his math teacher: "I heard you have three daughters. How old are they?" The math teacher says: "Well, the

scZoUnD [109]

Answer:

There are 7 solutions.

The possible answers are:

The oldest daughter is 72 and the others are 1 and 1 and the room number is 74.

The oldest daughter is 36 and the others are 1 and 2 and the room number is 39.

The oldest daughter is 24 and the others are 1 and 3 and the room number is 28.

The oldest daughter is 18 and the others are 1 and 4 and the room number is 23.

The oldest daughter is 12 and the others are 2 and 3 and the room number is 17.

The oldest daughter is 12 and the others are 1 and 6 and the room number is 19.

The oldest daughter is 9 and the others are 1 and 8 and the room number is 18.

The first few solutions are laughable and unlikely, but all are possible.

OR..

The clue that the sums of the daughters' ages is the room number is the sleeper. The student's first response is that two possible age combinations meet the necessary conditions. The teacher's reference to the "oldest daughter" resolves the ambiguity, so one of the solutions must consist of a set of ages in which at least two of the oldest daughters are the same age.

The prime factors of 72 are 2^3 *3^2. Because one of the solutions requires the two oldest daughters to be the same age, only combination 6, 6, 2 would be admissible. There are insufficient factors for any other combination in which the duplicate ages represent the oldest daughter. The ages of these daughters sum to 14, which is the room number. The other combination must therefore add to 14 and have an unique oldest age. The combination 8, 3, 3 meets all conditions and is the answer.

4 0

2 years ago

If triangle LMN has an obtuse angle at vertex M, which statements could be true? Check all that apply.

nirvana33 [79]

Answer: Triangle LMN is an obtuse triangle.

The angle at vertex L is acute.

The angle at vertex N is acute.

Step-by-step explanation:

Here, triangle LMN has an obtuse angle at vertex M,

Thus, by the definition of obtuse angle triangle LMN is an obtuse triangle,

Now, Angle M is obtuse,

⇒ 90° < m∠ M < 180°

Since, by the property of a triangle,

m∠ L + m∠ M + m∠ N = 180°

⇒ m∠ M = 180° - ( m∠ L+ m∠ N )

⇒ 90° < 180° - ( m∠ L+ m∠ N ) < 180°

⇒ 90° - 180° < - ( m∠ L+ m∠ N ) < 0

⇒ -90° < - ( m∠ L+ m∠ N ) < 0

⇒ 90° > ( m∠ L+ m∠ N ) > 0 ( Since, a < b ⇒ - a > - b)

⇒ 90° > m∠ L and 90° > m∠ N

⇒ Both angle L and angle N are acute.

5 0

2 years ago

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The congruent sides of an isosceles triangle are each 1 unit longer than the length of the shortest side of the triangle. The pe

DochEvi [55]

Answer:

10 units

Step-by-step explanation:

Represent the length of the shortest side of the triangle by x. Then the sum of the lengths of the other two sides is 2(x + 1), and the perimeter of the triangle is thus x + 2(x + 1), or 3x + 2.

Represent the side length of the square by x - 2. Then the perimeter of the square is 2(x - 2) + 2(x - 2) = 4(x - 2) = 4x - 8, and this perimeter matches that of the triangle:

4x - 8 = 3x + 2, or

x = 10

The length of the shortest side of the triangle is 10 units.

7 0

2 years ago

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