All categories

2 years ago

Use the given information to write an equation and solve the problem. (28-31 in the picture)

Mathematics

2 answers:

DanielleElmas [232]2 years ago

6 0

Answers :
28/ 120 degrees
29/ 30 degrees
30/ 56 & 124 degrees
31/ 72, 108, 18 degrees

tia_tia [17]2 years ago

3 0

Answer:

28. 120 degrees

29. 30 degrees

30. 56 degrees & 124 degrees

31. 72 degrees, 108 degrees, and 18 degrees

Step-by-step explanation:

We assign variable x for the answer we are looking for (28-29).

28.

Supplement means x + y = 180 degrees. We also know x = 2y. Substitution gives us 3y = 180 degrees, so y = 60 degrees and x = 120 degrees.

29.

Complement means x + y = 90 degrees. We are given 2x = y. Substitution brings us 3x = 90 degrees, x = 30 degrees.

30.

Supplement means x + y = 180 degrees. We are told that y = 2x + 12, so we substitute. This gives 3x + 12 = 180 degrees, x = 56 degrees. Substituting that back into the equation for y, we get 124 degrees.

31.

Supplement means x + y = 180 degrees. Complement means x + z = 90 degrees. Using our given info, we know y = 6z. We can substitute that in to get x + 6z = 180. Subtracting our second and third equations, we get 5z = 90, z = 18 degrees. Therefore, x = 72 degrees, y = 108 degrees.

You might be interested in

What is the smallest integer k>2000 such that both 17k/66 and 13k/105} are terminating decimals?

Dvinal [7]

17k/66 and 13k/105 must reduce to fractions with a denominator that only consists of powers of 2 or 5.

For example, some fractions with terminating decimals are

1/2 = 0.5

1/4 = 1/2² = 0.25

1/5 = 0.2

1/8 = 1/2³ = 0.125

1/10 = 1/(2•5) = 0.1

1/16 = 1/2⁴ = 0.0625

and so on, while some fractions with non-terminating decimals have denominators that include factors other than 2 or 5, like

1/3 = 0.333…

1/6 = 1/(2•3) = 0.1666…

1/7 = 0.142857…

1/9 = 1/3² = 0.111…

1/11 = 0.09…

1/12 = 1/(2²•3) = 0.8333…

etc.

Since 66 = 2•3•11, we need 17k to have a factorization that eliminates both 3 and 11.

Similarly, since 105 = 3•5•7, we need 13k to eliminate the factors of 3 and 7.

In other words, 17k must be divisible by both 3 and 11, and 13k must be divisible by both 3 and 7. But 13 and 17 are both prime, so it's just k that must be divisible by 3, 7, and 11. These three numbers are relatively prime, so the least positive k that meets the conditions is LCM(2, 7, 11) = 231, and thus k can be any multiple of 231.

If you're familiar with modular arithmetic, this is the same as solving for k such that

13k ≡ 0 (mod 3)

17k ≡ 0 (mod 3)

17k ≡ 0 (mod 7)

13k ≡ 0 (mod 11)

and the Chinese remainder theorem says that k = 231n solves the system of congruences, where n is any integer.

Now it's just a matter of finding the smallest multiple of 231 that's larger than 2000, which easily done by observing

2000 = 8•231 + 152

and so k = 9•231 = 2079.

3 0

2 years ago

I need 4 numbers that equal 50 added together<br> no links

Svet_ta [14]

Answer:

1 + 49

2 + 48

3 + 47

4 + 46

5 + 45

6 + 44

7 + 43

8 + 42

9 + 41

10 + 40

11 + 39

12 + 38

13 + 37

14 + 36

15 + 35

16 + 34

17 + 33

18 + 32

19 + 31

20 + 30

21 + 29

22 + 28

23 + 27

24 + 26

25 + 25

26 + 24

27 + 23

28 + 22

29 + 21

30 + 20

31 + 19

32 + 18

33 + 17

34 + 16

35 + 15

36 + 14

37 + 13

38 + 12

39 + 11

40 + 10

41 + 9

42 + 8

43 + 7

44 + 6

45 + 5

46 + 4

47 + 3

48 + 2

49 + 1

50 + 0

8 0

3 years ago

Solve three and two fifths plus three and four sixths

Rasek [7]

Answer:

7 1/15

Step-by-step explanation:

3 2/5 + 3 4/6 = 7 1/15

4 0

2 years ago

Read 2 more answers

Which graph represents the solution set to this system of equations? –x + 2y = 6 and 4x + y = 3 On a coordinate plane, a line go

erastova [34]

Answer:

On a coordinate plane, a line goes through (0, 3) and (2, 4) and another line goes through (0, 3) and (0.75, 0).

This answer almost coincide with option C. I suppose there was a mistype.

Step-by-step explanation:

The system of equations is formed by:

–x + 2y = 6

4x + y = 3

In the picture attached, the solution set is shown.

The first equation goes through (0, 3) and (2, 4), as can be checked by:

–(0) + 2(3) = 6

–(2) + 2(4) = 6

The second goes through (0, 3) and (0.75, 0), as can be checked by:

4(0) + (3) = 3

4(0.75) + (0) = 3

6 1

3 years ago

Read 2 more answers

A report by the US Geological Survey indicates that glaciers in Glacier National Park, Montana, are shrinking. Recent estimates

postnew [5]

Answer

a) C

b) B

c) C, E

d) 15.5

e) 0.7

f) 67.7

Step-by-step explanation

a) A linear equation can be written as $y=mx+c$ where $m$ is the slope and $c$ is the intercept on the $y$ -axis. The slope describes how $y$ changes when $x$ changes. A negative value means the it is a decreasing change. In our case, $y$ is $A$ and $x$ is $t$ . Thus, the slope of the equation is $m=-0.062$ . This means that the area of glacier is decreasing by $0.062 \text{km}{}^2 = 62000 \text{m}{}^2$ every year since 2000.

b) The $A$ -intercept (= 16.2 $\text{km}{}^2$ ) represents the area covered when $t=0$ . But $t=0$ starting from year 2000. This intercept then represents the area covered by glacier in the year 2000. Therefore, the area covered by glacier in 2000 was 16.2 $\text{km}{}^2$ .

c) $A=f(t)$ means the area covered after year 2000. Setting it to 12 means the area covered after $t$ years is 12 $\text{km}{}^2$ ). $t$ is therefore the number of years since 2000 that the total area covered will be 12 $\text{km}{}^2$ ).

d) $f(12)=16.2−0.062\times12 =16.2-0.744 = =15.456 15.5 \text{km}{}^2$ to 1 decimal place.

e) The term involving $t$ represents the disappearing area. In 12 years, the disappeared area is $0.062\times12=0.744 =0.7 \text{km}{}^2$ to 1 decimal place.

f) $f(t)=16.2−0.062t =12$

$0.062t = 16.2-12 = 4.2$

$t = \dfrac{4.2}{0.062}=67.7419\ldots =67.7$ years to 1 decimal place.

8 0

3 years ago