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muminat
2 years ago
15

Given points A (0,0), B (4,0), C (0,2), D (0,0), E (2,0), and F (0,1), which of the following proves that

Mathematics
1 answer:
damaskus [11]2 years ago
3 0

Similar triangles may or may not have equal side lengths

Triangles ABC and DEF are similar by SSS theorem

<h3>How to determine the similarity statement</h3>

The coordinates of the two triangles are:

A (0,0), B (4,0), C (0,2), D (0,0), E (2,0), and F (0,1)

Calculate the lengths of both triangles using the following distance formula

d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}

For triangle ABC, we have:

AB = \sqrt{(0 -4)^2 + (0 -0)^2} = 4

BC = \sqrt{(4 -0)^2 + (0 -2)^2} = 2\sqrt 5

CA = \sqrt{(0 -0)^2 + (0 -2)^2} = 2

For triangle DEF, we have:

DE = \sqrt{(0 -2)^2 + (0 -0)^2} = 2

EF = \sqrt{(2 -0)^2 + (0 -1)^2} = \sqrt 5

FD = \sqrt{(0 -0)^2 + (1 -0)^2} = 1

Divide corresponding sides of the triangles to calculate the scale factor k

k = \frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}

This gives

k = \frac{4}{2} = \frac{2\sqrt 5}{\sqrt 5} = \frac{2}{1}

Evaluate the quotients

k = 2 = 2 = 2

Since the quotients are equal, then the triangles are similar

Hence, triangles ABC and DEF are similar by SSS theorem

Read more about similar triangles at:

brainly.com/question/14285697

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A. 8/17<br> B. 15/17<br> C. 15/8<br> D. 8/15
Vlada [557]

Answer:

A)  8/17

Step-by-step explanation:

cos = adj/hyp

In this problem the unknown angle has a hypotenuse pf 17, 15 as opposite, and 8 as adjacent

8 0
2 years ago
Esma and Hunter were trying to solve the equation:
Leni [432]

Answer:

both

Step-by-step explanation:

When would these strategies work?

Esma wants to solve by completing the square. If our equation looks like

a

x

2

+

b

x

+

c

=

k

ax

2

+bx+c=ka, x, squared, plus, b, x, plus, c, equals, k, this strategy would work. If

a

=

1

a=1a, equals, 1, we can square half of

b

bb to find what number completes the square. If

a

>

1

a>1a, is greater than, 1, we need to factor before we complete the square.

Hunter wants to solve using the zero product property. If we have a factored expression that equals zero, this strategy would work.

Whose strategy would work to solve

x

2

+

8

x

=

2

x

−

8

x

2

+8x=2x−8x, squared, plus, 8, x, equals, 2, x, minus, 8?

Hint #22 / 4

Esma's strategy

Esma is correct that adding

1

11 to both sides completes the square. She can factor

x

2

+

6

x

+

9

x

2

+6x+9x, squared, plus, 6, x, plus, 9 and rewrite the equation as

(

x

+

3

)

2

=

1

(x+3)

2

=1left parenthesis, x, plus, 3, right parenthesis, squared, equals, 1. Then she can solve using square roots.

So Esma's strategy would work.

[Show me this strategy worked out.]

Hint #33 / 4

Hunter's strategy

Hunter is correct that he can factor

x

2

+

6

x

+

8

x

2

+6x+8x, squared, plus, 6, x, plus, 8 as

(

x

+

2

)

(

x

+

4

)

(x+2)(x+4)left parenthesis, x, plus, 2, right parenthesis, left parenthesis, x, plus, 4, right parenthesis.

He can then solve

(

x

+

2

)

(

x

+

4

)

=

0

(x+2)(x+4)=0left parenthesis, x, plus, 2, right parenthesis, left parenthesis, x, plus, 4, right parenthesis, equals, 0 using the zero product property since he has a factored expression equal to zero.

So Hunter's strategy would work.

[Show me this strategy worked out.]

Hint #44 / 4

Answer

Both of Esma's and Hunter's strategies would work.

7 0
2 years ago
At a baseball game, 3 drinks and 4 hotdogs cost $15.00. At the same game, 3 drinks and 1 hotdog cost $10.50. Find the cost for a
Serhud [2]

Answer:

$3

Step-by-step explanation:

Given data

Let the cost of drinks be x

and the cost of hotdogs be y

so

3x+4y=15-------1

also

3x+y= 10.5------2

solve 1 and 2

 3x+4y=15

-3x+y= 10.5

     3y= 4.5

divide both sides by 3

y= 4.5/3

y= $1.5

Put y= 1.5 in 1

3x+4(1.5)=15

3x+6= 15

3x=15-6

3x= 9

x= 9/3

x= $3

Hence the cost of a drink is $3

8 0
3 years ago
Helppp more points 20 math
Serjik [45]

Answer:

root(250)

answer choice C

Step-by-step explanation:

explanation in the pic above.

7 0
3 years ago
PLZ HELP HELP PLZZ 5/5 × 2 and 3/4 will be greater than less than or equal to 2 and 3/4??​
il63 [147K]
1)2
2) less than
I think
7 0
3 years ago
Read 2 more answers
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