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3 years ago

Answer the two questions in the image above for brainliest!!

Mathematics

1 answer:

Elena-2011 [213]3 years ago

4 0

Answer:

Complementary, 65

106+x=180

Step-by-step explanation:

Complementary angles add to 90, Supplementary angles add to 180

These are complementary angles

x+25 = 90

Subtract 25 from each side

x+25-25 =90-25

x = 65

The next questions they are supplementary angles because they add to 180

106+x=180

Subtract 106 from each side

106-106+x=180-106

x=74

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catering service offers 8 appetizers, 11 main courses, and 7 desserts. A banquet committee is to select 7 appetizers, 8 main

guapka [62]

Answer: The required number of ways is 46200.

Step-by-step explanation: Given that a catering service offers 8 appetizers, 11 main courses, and 7 desserts.

A banquet committee is to select 7 appetizers, 8 main courses, and 4 desserts.

We are to find the number of ways in which this can be done.

We know that

From n different things, we can choose r things at a time in $^nC_r$ ways.

So,

the number of ways in which 7 appetizers can be chosen from 8 appetizers is

$n_1=^8C_7=\dfrac{8!}{7!(8-7)!}=\dfrac{8\times7!}{7!\times1}=8,$

the number of ways in which 8 main courses can be chosen from 11 main courses is

$n_2=^{11}C_8=\dfrac{11!}{8!(11-8)!}=\dfrac{11\times10\times9\times8!}{8!\times3\times2\times1}=165$

and the number of ways in which 4 desserts can be chosen from 7 desserts is

$n_3=^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!\times3\times2\times1}=35.$

Therefore, the number of ways in which the banquet committee is to select 7 appetizers, 8 main courses, and 4 desserts is given by

$n=n_1\times n_2\times n_3=8\times165\times35=46200.$

Thus, the required number of ways is 46200.

7 0

4 years ago

Find the digit that makes (_1,258) divisible by 9

ZanzabumX [31]

21258/9 =2362, so the answer would be 2

5 0

3 years ago

Alan has twice as many dimes as he has quarters and 10 more nickels than dimes. The remaining 35 coins are pennies. How many of

zaharov [31]

Answer:

He has 3 quarters , 6 dimes and 16 nickles

Step-by-step explanation:

∵ Dimes is d , Quarter is q , nickels is n and pennies is p

∵ Quarter = 25 cents

∵ Dime = 10 cents

∵ Nickle = 5 cents

∵ Penny = 1 cent

∵ The remaining 35 coins are pennies ⇒ 35 cents

∵ He has $2.50 = 2.50 × 100 = 250 cents

∴ The value of quarters , dimes and nickels = 250 - 35 = 215 cents

∴ 25q + 10d + 5n = 215 ⇒ (1)

∵ d = 2q

∴ q = 1/2d ⇒ (2)

∵ n = 10 + d ⇒ (3)

Substitute (2) and (3) in (1)

∴ 25(1/2 d) + 10d + 5(10 + d) = 215

∴ 12.5d + 10d + 50 + 5d = 215

∴ 27.5d = 215 - 50

∴ 27.5d = 165

∴ d = 165 ÷ 27.5

∴ d = 6

∴ q = 1/2 (6) = 3

∴ n = 10 + 6 = 16

∴ He has 3 quarters , 6 dimes and 16 nickles

7 0

3 years ago

Read 2 more answers

What is 39/69 in simplest form?

wariber [46]

39/69 = 13/23 is in simplest form

First you do 39 divide by 3 = 13 and do 69 divid by 3 = 23

8 0

4 years ago

What is 9.3 x 10 to the 7 power in standard notation

Semmy [17]

Move the decimal point 7 spaces to the right and it gives you 93,000,000

7 0

4 years ago