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nikdorinn [45]
3 years ago
13

The Smith family was driving to visit

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
7 0

Answer:

10

Step-by-step explanation:

24 - 14 = 10

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Work out the area of the trapezium ABDE.<br> B<br> 9 cm<br> 6 cm<br> 8 cm<br> →D<br> E
Evgen [1.6K]

Answer:

Area of the trapezium ABDE = 30 cm²

Step-by-step explanation:

Area of a trapezium = \frac{1}{2}(b_1+b_2)h

Here, b_1 and b_2 are the parallel sides of the trapezium

h = Distance between the parallel sides

From the picture attached,

ΔCAE and ΔCBD are the similar triangles.

So by the property of similarity their sides will be proportional.

\frac{AE}{BD}= \frac{CE}{CD}

\frac{9}{6}=\frac{CE}{8}

CE = \frac{9\times 8}{6}

CE = 12 cm

Therefore, DE = CE - CD

DE = 12 - 8 = 4 cm

Now area of trapezium ABDE = \frac{1}{2}(AE+BD)(DE)

                                                  = \frac{1}{2}(6+9)4

                                                  = 30 cm²

Therefore, area of the trapezium ABDE = 30 cm²

8 0
2 years ago
I need help with 25.
noname [10]

Sum of linear pair of angles = 180°

so

<EFG + <GFH = 180°

2n + 21 + 4n + 15 = 180°

6n + 36 = 180°

6n = 144

n = 24

<EFG = 2(24) + 21 = 69°

<GFH = 4n + 15 = 4(24) + 15 = 111°

6 0
3 years ago
Find the values of the missing angles<br><br> HELP PLEASE DO ANY! I’ll give you brilliance
yan [13]

Answer:

1) x = 42 ; y = 42

2) x = 72 ; y = 48 ; z = 60

Step-by-step explanation:

1)

x + 42 + 96 = 180

x + 138 = 180

x = 42

y + 42 + 96 = 180

y + 138 = 180

y = 42

2)

x + 108 = 180

x = 72

y + 132 = 180

y = 48

z + x + y = 180

z + 72 + 48 = 180

z + 120 = 180

z = 60

3 0
2 years ago
What is Permutations and Combinations?
marissa [1.9K]

Answer:

See below

Step-by-step explanation:

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

Permutation can be expressed in math as:

\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }

where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.

Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:

Since there are 3 letters total and 3 selected letters to arrange then:

\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}

Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:

ABC - 1

ACB - 2

BAC - 3

BCA - 4

CAB - 5

CBA - 6

Notice that if you do visually, you'll get the same answer as the calculation of permutation!

----

Combination can be expressed mathematically as:

\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }

The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.

Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:

Since there are 3 letters total and 3 selected letters:

\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}

Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.

5 0
2 years ago
Identify the factors in the expression 6 (×+5)
Setler [38]
The factors are 6 and x + 5
5 0
3 years ago
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