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2 years ago

A man claims that his lot is triangular, with one side 450 m long and the adjacent side 200 m long. The

Mathematics

1 answer:

harkovskaia [24]2 years ago

7 0

Answer:

545 m

Step-by-step explanation:

Set A = 28º, B as the angle between the 450 m and 200 m side, and C as the remaining angle. Then:

AB = 200 m

BC = 450 m

According to the law of sines:

$\frac{450}{sin(28)}=\frac{110}{sin(C)} \\sin(C) = \frac{110}{450}*0.469\\ C= 6.6^o$

The remaining angle is then:

$B= 180-28-6.6\\B=145.4^o$

Applying the law of sines again:

$\frac{450}{sin(28)}=\frac{AC}{sin(145.4)} \\AC= \frac{450}{0.469}*0.568\\ AC= 545\ m$

To the nearest meter, the other side is 545 meters long.

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Identify two numbers less than 20 with the most factors

Anastaziya [24]

<u>Answer</u>

18 and 12

<u>Explanation</u>

Factor is a number or algebraic expression that divides another number or expression evenly that is with no remainder.

Odd number have few factors so the can't be the answer.

WE are going to try the even numbers.

18 ⇒ 18, 9, 6, 3, 2, 1

16 ⇒ 16, 8, 4, 2, 1

12 ⇒ 12, 6, 4, 3, 2, 1

10 ⇒ 10, 5, 2, 1

Other number less than 10 has factors less than 5.

It can be seen from above that 18 and 12 have the most factors.

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2 years ago

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You save $5,000.00 and invest 60% of it in stocks while leaving the rest in a savings account earning a 4.9% APR. The stock incr

Angelina_Jolie [31]

Answer:

5,340

Step-by-step explanation:

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Amount invested in stock

=5000×0.6=3000

Amount invested in a saving account

5000-3000=2000

The stock increases 9% in the first year

3,000×(1+0.09)=3,270

and loses 4% of its value the second year

3,270×(1−0.04)=3,139.2

Amount of a saving account after two years

2,000×(1+0.049)^(2)=2,200.8

the total amount gained during the 2 years

3,139.2+2,200.8=5,340...answer

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2 years ago

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Avery wants to put a variety of muffins in a display case. The case is large enough to hold 60 muffins. types of muffins Blueber

IgorLugansk [536]

There are 54 muffins in the basket al you have to do is multiply the 60 by the added percentages which is .9 and you get the answer of 54

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2 years ago

Hank invested a total of $20,000, part at 7% and part at 10%. How much did he invest at each rate if the total interest earned i

jolli1 [7]

Answer:

The amount invested at 7% is $12,000 while the amount invested at 10% is $8,000

Step-by-step explanation:

The given parameters are;

The total amount Hank invested = $20,000

The interest earned in one year = $1640

Hank invested part of the $20,000 at 7% interest and part of the $20,000 at 10%

Let the part invested at 7% = X and the part invested at 10% = Y, we have;

7% of X + 10% of Y = $1640 which gives;

0.07×X + 0.1×Y = $1640.....................(1)

X + Y = $20,000.................................(2)

Multiply equation (1) by 10 and subtract equation (1) from equation (2) to get;

X + Y - 10×(0.07×X + 0.1×Y) = $20,000 - 10×$1640

X - 0.7·X - Y - Y = $20,000 - $16,400 = $3,600

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X = $3,600/0.3 = $12,000

X = $12,000

Y = $20,000 - X = $20,000 - $12,000 = $8,000

Y = $8,000

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2 years ago

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PtichkaEL [24]

Answer:

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1 year ago