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kap26 [50]
3 years ago
5

I'd greatly appreciate the help-

Mathematics
1 answer:
dem82 [27]3 years ago
7 0

Answer:

The 3rd option

Step-by-step explanation:

To prove that 2 triangles are similar, we need to prove that 2 pairs of their angle measurements are congruent.

This is because all triangles have 180 degrees, so if 2 pairs are congruent, the remaining angles will also be congruent

We know that m<D=m<E

We also know that m<DCA=m<ECB because they are vertical angles.

Vertical angles are always congruent.

Therefore, the triangles are similar.

The correct similarity statement would be 1, since <D corresponds with <E.

Now let's look at the 3rd Statement. To prove that two lines are similar, we would have to prove that their alternate interior angles are congruent.

A pair of alternate interior angles would be <D and B or or <E  and <A

There is no way to prove this, since we do not know any of the angle  or that measurements or if the triangles are isosceles triangles.

Hence, the correct choice would be 1 only.

You might be interested in
In 1999 Daniel was 146 cm tall. He grew to be 176 cm by the year 2006. What was Daniel's rate of growth over this period of his
andreyandreev [35.5K]

Answer:

he grows by 5 cm every year between 1999 and 2006

Step-by-step explanation:

This is a arithmetic progression problem with the formula;

T_n = a + (n - 1)d

We are told that In 1999 Daniel was 146 cm tall. He grew to be 176 cm by the year 2006.

Thus;

a = 146

d = 2006 - 1999 = 7

Thus;

176 = 146 + (7 - 1)d

176 - 146 = 6d

30 = 6d

d = 30/6

d = 5 cm

Thus, he grows by 5 cm every year between 1999 and 2006

3 0
3 years ago
The two rectangles shown have equal areas. Find the value of x
Tema [17]

Answer:

x=18

Step-by-step explanation:

We need to find the areas of the rectangles

1st rectangle

A= l*w

A = (2x+4)*9

   = 18x+36



2nd rectangle

A = l*w

   = 15*(3x-30)

    = 45x-450


Since the area of the rectangles are equal, we set these two equations equal

18x+36 = 45x-450

Subtract 18x from each side

18x-18x+36 = 45x-18x-450

36 = 27x-450

Add 450 to each side

36+450 =27x

486 = 27x

Divide by 27 on each side

486/27 = 27x/27

18=x


7 0
3 years ago
Brandy has a new part-time job. On Monday, she worked 8 hours. On Wednesday, she worked three-fourths as long as she did on Mond
Setler79 [48]

Answer:

both of them are odd (because both of them are even, the reverse would be true)

Step-by-step explanation:

if she worked 8 on Monday, and on Wednesday worked for 3/4ths that amount of time she would've worked 6 hours. So an UNTRUE statement about this would be that they're both odd.

8 0
3 years ago
Find an equation of the line: through the point (2, −4) with a y-intercept of −2. PLEASE HELP ONLY HAVE 20 MINUTES
Ber [7]

Answer:

Y=-x-2 or Y=-1x-2

Step-by-step explanation:

5 0
3 years ago
HELP!!<br>Find the third term of (x^2+3y)^3
lana66690 [7]

Answer:

T_{3}=27{x}^{2}y^2

Step-by-step explanation:

The given binomial expression is:

( {x}^{2} + 3y)^{3}

When we compare to:

{(a +b)}^{n}

We have

a =  {x}^{2}

b = 3y \\ n = 3

The nth term is given by;

T_{r+1}=^nC_ra^{n-r}b^r

To find the 3rd term, we put:

r + 1 = 3 \\ r = 2

We substitute into the formula to get:

T_{3}=^3C_2( {x}^{2} )^{3-2}(3y)^2

We simply:

T_{3}=3( {x}^{2} )^{1} \times 9y^2

T_{3}=27{x}^{2}y^2

3 0
3 years ago
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