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Tcecarenko [31]
3 years ago
13

Two right triangles are graphed on a coordinate plane. One triangle has a vertical side of 2 and a horizontal side of 6. The oth

er triangle has a vertical side of 10 and a horizontal side of 30.
Could the hypotenuses of these two triangles lie along the same line?

(A) No, because they are not similar triangles
(B) No, because one is larger than the other
(C) Yes, because they are both right triangles
(D) Yes, because they are similar triangles
Mathematics
1 answer:
LuckyWell [14K]3 years ago
4 0

Answer:

Consider two right triangles: 1. ΔABC with vertices A(0,0), B(0,2), C(6,0). Then AB is perpendicular to AC and AB=2 units (vertical leg), AC=6 units (horizontal leg).2. ΔXYZ with vertices X(6,-10), Y(6,0), Z(36,-10). Then XY is perpendicular to XZ and XY=10 units (vrrtical leg), XZ=30 units (horizontal leg).The equation of the line BC is Check whether points Y and Z lie on this line:Y(6,0):  - true;Z(36,-10):  - true.Answer:  the hypotenuses of these two triangles could lie along the same line

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PLease help me with this!
astraxan [27]

Answer:

1. x2 - 9 > 0

x^2-3^2>0

(x+3)(x-3)>0

(x+3)>0 and (x-3)>0

x>-3       and  x>3

2. x2 - 8x + 12 > 0

   x^2 - 8x  +12>0

   x^2 -2x -6x +12 >0   (-8x is replaced by (-2x) + (-6x) )

   x(x-2) -6(x-2) >0

    (x-6)(x-2)>0

(x-6)>0    and (x-2)>0

    x>6     and     x>2

3. -x2 - 12x - 32 > 0

    -x^2 -12x -32 >0

     x^2 +12x +32 <0

      x^2 +4x +8x +32<0

      x(x+4) +8(x+4)<0

      (x+8)(x+4)<0

(x+8)<0   and  (x+4)<0

x<-8      and    x<-4

4. x2 + 3x - 20 >= 3x + 5

   x^2 +3x -20 >= 3x +5

   x^2 +3x -20 -3x >= 3x +5 -3x

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     x^2 >=25

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      (x-5)(x+5)>=0

(x-5)>=0  and (x+5)>=0

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6 0
2 years ago
What is the sum of an 8-term geometric series if the first term is -11, the last term 180,224, and the common ratio is -4? answe
Blababa [14]
The general formula for the sum of the n terms of a geometric progression is:

Sn = A1 (1 - r^n) / (1 - r)

In this case, n = 8; A1 = - 11, r = -4

S8 = -11 (1 - (-4)^8) / (1 -(-4)) = 144,177

Answer: option c.
 
4 0
3 years ago
Algebra 1 please help!
Leona [35]

Answer:

a. geometric

b. a<em>n</em> =  2(2)^n-1 or a<em>n</em> = 2^n

c. a<em>n+1</em> <em>= </em>a<em>n</em> x 2

Step-by-step explanation:

The sequence, 2, 4, 8, 16, 32,...

a. The sequence is geometric because there is a common ratio in the numbers of the sequence. Each number is made by multiplying the common ratio and the previous number.

b. The explicit formula that can be used to find any term is a<em>n</em> =  2(2)^n-1 or a<em>n</em> = 2^n

Note: the variable n and number 1 is written in italics to show that it should be in subscript

a<em>n</em> = a<em>1 </em>(r)n-1

With the common ratio of n being 2 and first number being 2, we have:

a<em>n</em> =  2(2)^n-1

or

a<em>n</em> = 2^n

c. The recursive formula for the sequence is a<em>n+1</em> <em>= </em>a<em>n</em> x 2

a<em>n+1</em> = a<em>n </em>x r

Plugging in the values, we have

a<em>n+1</em> <em>= </em>a<em>n</em> x 2

Your welcome, and comment if you have any questions! If you could mark this answer as brainliest, I would appreciate it very much!

5 0
2 years ago
There are 32 point guards and 50 posts In Leo's basketball league. Leo must include all players on a team and wants each team to
Fantom [35]

The greatest number of teams Leo can create is 2

<em><u>Solution:</u></em>

Given that,

There are 32 point guards and 50 posts In Leo's basketball league

From given,

Number of point guards = 32

Number of posts = 50

Leo must include all players on a team and wants each team to have the same number of point guards and the same number of posts

To find the greatest number of teams Leo can create, we should find the greatest common factor of 32 and 50

When we find all the factors of two or more numbers, and some factors are the same, then the largest of those common factors is the Greatest Common Factor

<em><u>Greatest Common Factor of 32 and 50:</u></em>

The factors of 32 are: 1, 2, 4, 8, 16, 32

The factors of 50 are: 1, 2, 5, 10, 25, 50

Then the greatest common factor is 2

Thus the greatest number of teams Leo can create is 2

5 0
3 years ago
What's the common difference in −1,−4,−7,−10
kondor19780726 [428]

Answer:

-3

Step-by-step explanation:

7 0
2 years ago
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