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3 years ago

8

You are given the numbers {32+n,n/8,n+225}. Find the smallest value of n so that all of the numbers in the set are natural numbe

rs.

1 answer:

gogolik [260]3 years ago

6 0

N=0,8,16,24,...; because when n=8k $(k\in \mathbb{N})$ then n/8 is natural number.
So the smallest value of n is 0.

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Please dont ignore, Need help!!! Use the law of sines/cosines to find..

Ket [755]

Answer:

16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

<h3>16</h3>

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

$\sin{A} = \sin{103\textdegree{}}$ ,
The opposite side of angle A $a = BC = 26$ ,
The angle C is to be found, and
The length of the side opposite to angle C $c = AB = 6$ .

$\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}$ .

$\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}$ .

$\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}$ .

Note that the inverse sine function here $\sin^{-1}()$ is also known as arcsin.

<h3>17</h3>

By the law of cosine,

$c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}$ ,

where

$a$ , $b$ , and $c$ are the lengths of sides of triangle ABC, and
$\cos{C}$ is the cosine of angle C.

For triangle ABC:

$b = 21$ ,
$c = 30$ ,
The length of $a$ (segment BC) is to be found, and
The cosine of angle A is $\cos{123\textdegree}$ .

Therefore, replace C in the equation with A, and the law of cosine will become:

$a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}$ .

$\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}$ .

<h3>18</h3>

For triangle ABC:

$a = 14$ ,
$b = 9$ ,
$c = 6$ , and
Angle B is to be found.

Start by finding the cosine of angle B. Apply the law of cosine.

$b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}$ .

$\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}$ .

$\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree$ .

<h3>15</h3>

For triangle DEF:

The length of segment DF is to be found,
The length of segment EF is 9,
The sine of angle E is $\sin{64\textdegree}}$ , and
The sine of angle D is $\sin{39\textdegree}$ .

Apply the law of sine:

$\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}$

$\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9$ .

7 0

3 years ago

Vx-w=2 <br> rearrange it and make x the subject

Anit [1.1K]

Answer:

$vx - w = 2 \\ vx = 2 + w \\ x = \frac{2 + w}{v}$

8 0

2 years ago

Simplify:<br> 4(2a+3)+5(a+3)

EleoNora [17]

Answer:

13a+27

Step-by-step explanation:

8a+12+5a+15= 13a+27

5 0

3 years ago

Read 2 more answers

Tara bought s sheets of stickers. There are 5 stickers on each sheet. Write an expression that

olya-2409 [2.1K]

Answer:

y= 5s

Step-by-step explanation:

Since 5 stickers are in every sheet depending on the number of sheets you get and times it with 5 you get the number of stickers Tara bought.

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3 years ago

Will give brainliest!!!

Igoryamba

y = 80x - 60

Answer is B. y = 80x - 60

Double check:

When x = 1, y = 80(1) - 20 = 80 -60 = 20

When x = 2, y = 80(2) - 20 = 160 -60 = 100

When x = 3, y = 80(3) - 20 = 240 -60 = 180

When x = 4, y = 80(4) - 20 = 320 -60 = 260

When x = 5, y = 80(5) - 20 = 400 -60 = 340

6 0

3 years ago