Find the greatest common factor of 6m² and 7m².

would someone help me out with this question? I got it wrong the first time but I don't understand how.

OleMash [197]

Answers:

Choice 2) Angle ABC is bisected by ray BD.

Choice 3) BC = 1/2 AC

Choice 5) 2*(angle DBC) = angle ABC

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Explanation:

Since B is the midpoint of AC, this means that AC is cut in half to form the smaller equal pieces AB and BC

We can then say

AB+BC = AC

BC+BC = AC

2BC = AC

BC = (1/2)*AC

which shows why choice 3 is one of the answers

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Angle ABD is shown to be 90 degrees. Let's say we didn't know angle DBC is also 90. Lets call it x

(angle ABD) + (angle DBC) = 180

90 + x = 180

x = 180 - 90

x = 90

So angle DBC is also 90.

We can see that the 180 degree angle (ABC) is cut in half into two smaller 90 degree angles (ABD and DBC). Therefore, angle ABC has been cut in half and that's why choice 2 is another answer.

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Using the angle addition postulate, we know that,

(angle ABD) + (angle DBC) = angle ABC

(angle DBC) + (angle DBC) = angle ABC

2*(angle DBC) = angle ABC

Showing why choice 5 is the third answer.

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Choice 1 isn't true since ray BD helps form angle DBC.

Choice 4 isn't true because there isn't a tickmark on segment BD to indicate it's the same length as BC.

8 0

3 years ago

Suppose You walk from school and travel 3 blocks east then 6 blocks west then 11 blocks east again how far are and in which dire

Anuta_ua [19.1K]

You are 8 blocks east from the school

7 0

3 years ago

Let H be a subgroup of a group G. We call H characteristic in G if for any automorphism σ∈Aut(G) of G, we have σ(H)=H.

choli [55]

Answer:Problem 1. Let G be a group and let H, K be two subgroups of G. Dene the set HK = {hk : h ∈ H,k ∈ K}.

a) Prove that if both H and K are normal then H ∩ K is also a normal subgroup of G.

b) Prove that if H is normal then H ∩ K is a normal subgroup of K.

c) Prove that if H is normal then HK = KH and HK is a subgroup of G.

d) Prove that if both H and K are normal then HK is a normal subgroup of G.

e) What is HK when G = D16, H = {I,S}, K = {I,T2,T4,T6}? Can you give geometric description of HK?

Solution: a) We know that H ∩ K is a subgroup (Problem 3a) of homework 33). In order to prove that it is a normal subgroup let g ∈ G and h ∈ H ∩ K. Thus h ∈ H and h ∈ K. Since both H and K are normal, we have ghg−1 ∈ H and ghg−1 ∈ K. Consequently, ghg−1 ∈ H ∩ K, which proves that H ∩ K is a normal subgroup.

b) Suppose that H G. Let K ∈ k and h ∈ H ∩ K. Then khk−1 ∈ H (since H is normal in G) and khk−1 ∈ K (since both h and k are in K), so khk−1 ∈ H ∩ K. This proves that H ∩ K K.

c) Let x ∈ HK. Then x = hk for some h ∈ H and k ∈ K. Note that x = hk = k(k−1hk). Since k ∈ K and k−1hk ∈ H (here we use the assumption that H G), we see that x ∈ KH. This shows that HK ⊆ KH. To see the opposite inclusion, consider y ∈ KH, so y = kh for some h ∈ H and k ∈ K. Thus y = (khk−1)k ∈ HK, which proves that KH ⊆ HK and therefoere HK = KH. To prove that HK is a subgroup note that e = e · e ∈ HK. If a,b ∈ HK then a = hk and b = h1k1 for some h,h1 ∈ H and k,k1 ∈ K. Thus ab = hkh1k1. Since HK = KH and kh1 ∈ KH, we have kh1 = h2k2 for some k2 ∈ K, h2 ∈ H. Consequently,

ab = h(kh1)k1 = h(h2k2)k1 = (hh2)(k2k1) ∈ HK

(since hh2 ∈ H and k2k1 ∈ K). Thus HK is closed under multiplication. Finally,

Step-by-step explanation:

6 0

3 years ago

A large construction company wants to review the ages of its sales representatives. A sampling of the ages of 25 sales reps are

Shalnov [3]

A histogram with frequency on the x-axis and ages on the y-axis is shown below. Then the correct option is A.

<h3>What is a histogram?</h3>

A diagram is made up of rectangles whose size is related to a variable's frequency and whose width is comparable to the training sample.

A large construction company wants to review the ages of its sales representatives.

A sampling of the ages of 25 sales reps are given:

50, 42, 32, 35, 41, 44, 24, 46, 31, 47, 36, 32, 30, 44, 22, 47, 31, 56, 28, 37, 49, 28, 42, 38, 45.

Then the histogram with frequency table is given as

Range Frequency

20 to 24 2

25 to 29 2

30 to 34 5

35 to 39 4

40 to 44 5

45 to 49 5

50 to 54 1

55 to 59 1

Then the correct option is A.

The histogram is given below.

More about the histogram link is given below.

brainly.com/question/16819077

#SPJ1

6 0

2 years ago

The table shows the number of blue marbles and red marbles that four friends have collected.

anygoal [31]

Answer:

Gretchen

Step-by-step explanation

Jasmine: 12/10 : 1

Aaron: 3/2 : 1

Lucian: 1 : 1

Gretchen: 7 : 1

7 0

3 years ago

Read 2 more answers