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klemol [59]
2 years ago
11

Which proportion satisfies the geometric mean (altitude) theorem for the triangle?

Mathematics
2 answers:
Snezhnost [94]2 years ago
8 0

Answer:

D. \frac{2}{h}=\frac{h}{3}

Step-by-step explanation:

We have been given an image of a triangle. We are asked to choose the proportion that satisfies the geometric mean (altitude) theorem for the triangle.

The geometric mean (altitude) theorem states that altitude drawn from the right angle to hypotenuse divides the hypotenuse into two segments such that their product is equal to the altitude times altitude.

\frac{2}{h}=\frac{h}{3}

Therefore, option D is the correct choice.

Degger [83]2 years ago
3 0
D is the correct answer 
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What is the common ratio between successive terms in the sequence 1.5, 1.2, 0.96, 0.768
Pani-rosa [81]

Answer:

To determine the common ratio of a geometric sequence. You just need to divide any two consecutive terms on it. You can see below that all of them have the same quotient.

1.2 / 1.5 = 0.8

0.96 / 1.2 = 0.8

0.768 / 0.96 = 0.8

.

Decimal form = 0.8

Fraction form = 4/5

.

Check:

1.5 x 0.8 = 1.2

1.5 x 4/5 = 6/5 = 1 1/5 = 1.2

Therefore, the common ratio between successive terms in the sequence? 1.5, 1.2, 0.96, 0.768 is 0.8 or 4/5.

6 0
2 years ago
The average of a set of 18 consecutive integers is 22.5. what is the smallest integer in the set?
quester [9]
The sum of the 18 numbers is 22.5 x 18 = 405.
Let the numbers be x, x + 1, x + 2, . . ., x + 17

Sum of n term of an arithmetic sequence = n/2(a + l)
18/2(x + x + 17) = 405
9(2x + 17) = 405
2x + 17 = 405/9 = 45
2x = 45 - 17 = 28
x = 28/2 = 14

Therefore, the smallest integer is 14.
6 0
2 years ago
Given: The coordinates of triangle PQR are P(0, 0), Q(2a, 0), and R(2b, 2c).
masha68 [24]

Answer:

The line containing the midpoints of two sides of a triangle is parallel to the third side ⇒ proved down

Step-by-step explanation:

* Lets revise the rules of the midpoint and the slope to prove the

  problem

- The slope of a line whose endpoints are (x1 , y1) and (x2 , y2) is

  m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

- The mid-point of a line whose endpoints are (x1 , y1) and (x2 , y2) is

  (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})

* Lets solve the problem

- PQR is a triangle of vertices P (0 , 0) , Q (2a , 0) , R (2b , 2c)

- Lets find the mid-poits of PQ called A

∵ Point P is (x1 , y1) and point Q is (x2 , y2)

∴ x1 = 0 , x2 = 2a and y1 = 0 , y2 = 0

∵ A is the mid-point of PQ

∴ A=(\frac{0+2a}{2},\frac{0+0}{2})=(\frac{2a}{2},\frac{0}{2})=(a,0)

- Lets find the mid-poits of PR which called B

∵ Point P is (x1 , y1) and point R is (x2 , y2)

∴ x1 = 0 , x2 = 2b and y1 = 0 , y2 = 2c

∵ B is the mid-point of PR

∴ B=(\frac{0+2b}{2},\frac{0+2c}{2})=(\frac{2b}{2},\frac{2c}{2})=(b,c)

- The parallel line have equal slopes, so lets find the slopes of AB and

  QR to prove that they have same slopes then they are parallel

# Slope of AB

∵ Point A is (x1 , y1) and point B is (x2 , y2)

∵ Point A = (a , 0) and point B = (b , c)

∴ x1 = a , x2 = b and y1 = 0 and y2 = c

∴ The slope of AB is m=\frac{c-0}{b-a}=\frac{c}{b-a}

# Slope of QR

∵ Point Q is (x1 , y1) and point R is (x2 , y2)

∵ Point Q = (2a , 0) and point R = (2b , 2c)

∴ x1 = 2a , x2 = 2b and y1 = 0 and y2 = 2c

∴ The slope of AB is m=\frac{2c-0}{2b-2a}=\frac{2c}{2(b-c)}=\frac{c}{b-a}

∵ The slopes of AB and QR are equal

∴ AB // QR

∵ AB is the line containing the midpoints of PQ and PR of Δ PQR

∵ QR is the third side of the triangle

∴ The line containing the midpoints of two sides of a triangle is parallel

  to the third side

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