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3 years ago

Find the missing measurements of the right triangle. Round your answers to the

Mathematics

1 answer:

nadya68 [22]3 years ago

4 0

Answer:

m∠B = 63°

AB = 26.4

AC = 23.6

Step-by-step explanation:

m∠B = 90 - 27 = 63°

Sin 27 = 12/AB

AB (sin 27) = 12

AB = 12/sin 27 = 26.4

Tan 27 = 12/AC

AC (tan 27) = 12

AC = 12/tan 27 = 23.6

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mr. ken's class is collecting empty water bottles. they started with 17 water bottles on day 1. on day 3, they had 30 water bott

Oxana [17]

They had 23 and 38 water bottles on day 2 and day 4 respectively. Also, there will be 68 water bottles on day 7.

Explanation

Suppose, the equation representing the number of bottles is $y= ax^2 +bx+c$ , where $x$ is the number of days.

There are 17 water bottles on day 1, 30 water bottles on day 3 and 47 water bottles on day 5

So, the three points in the form of (x, y) are: (1, 17) , (3, 30) and (5, 47)

Plugging these three points into the above equation, we will get .....

$17=a(1)^2 + b(1) +c\\ a+b+c=17 ............................ (1)\\ \\ 30=a(3)^2+b(3)+c\\ 9a+3b+c=30 ......................... (2) \\ \\ 47=a(5)^2+b(5)+c\\ 25a+5b+c=47 ......................... (3)$

Subtracting equation (1) from equation (2) , we will get .....

$8a+2b=13 ..................... (4)$

Subtracting equation (2) from equation (3) , we will get .....

$16a+2b=17 ...................... (5)$

Now, subtracting equation (4) from equation (5) , we will get ......

$16a -8a = 17-13\\ \\ 8a= 4\\ \\ a=\frac{4}{8}= 0.5$

Substituting this $a= 0.5$ into equation (4) ........

$8(0.5)+2b=13\\ \\ 4+2b=13\\ \\ 2b=9\\ \\ b=\frac{9}{2}=4.5$

Again, substituting $a=0.5$ and $b=4.5$ into equation (1) , we will get ......

$0.5+4.5+c=17\\ \\ 5+c=17\\ \\ c=17-5 =12$

So, the equation will be now: $y= 0.5x^2 +4.5x+12$

For finding the number of bottles on day 2 , day 4 and day 7 , we need to plug $x=2 , 4, 7$ respectively into the above equation.

For $x= 2$ , $y= 0.5(2)^2 +4.5(2)+12 = 2+9+12= 23$

For $x= 4$ , $y= 0.5(4)^2 +4.5(4)+12 = 8+18+12= 38$

For $x= 7$ , $y= 0.5(7)^2 +4.5(7)+12 = 24.5+31.5+12= 68$

So, they had 23 water bottles on day 2 and 38 water bottles on day 4

Also, there will be 68 water bottles on day 7

6 0

3 years ago

Houses cost £150 000 one year ago they now cost £_____this is a 25% increase

Tanya [424]

187,500
150000x1.25
Hope this helps

5 0

3 years ago

Read 2 more answers

Pepper Jackie has 5.8 kg of rainbow sprinkles. If she divides them equally into 8 star containers, how much will be in each star

Karolina [17]

Answer:

725 grams

Step-by-step explanation:

You divide 5.8 kg by 8 (the star containers)

and the final answer is 0.725 kg or 725 grams

4 0

4 years ago

The sum of three numbers is 105 . The third number is 3 times the first. The second number is 5 more than the first. What are th

Ivahew [28]

The answer is 17+9+79

3 0

4 years ago

An artist is painting flower pots that each require 1/32 gallon of paint. What is the maximum number of flower pots the artist c

Alex787 [66]

Answer:

24 flower pots

Step-by-step explanation:

Fraction of paint required per flower pot = 1/32

Number of pots that can be painted with 3/4 galoons of paint :

Total Fraction of paint had / fraction of paint required per flower pot

3/4 ÷ 1/32

3/4 * 32 / 1

(3*32) / 4

96 /4

= 24 flower pots

7 0

3 years ago