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Ierofanga [76]
3 years ago
5

Find the measure of an angle such that the difference between the measures of its supplement and four times its complement is 30

Mathematics
1 answer:
Katarina [22]3 years ago
7 0

Answer:

70 degrees

Step-by-step explanation:

x = angle

180 - x = it's supplement

90 - x = it's compliment

(180 - x) - 4(90 - x) = 30

180 - x - 360 + 4x = 30

reducing

3x = 210

x = 70

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Logarithms:
WITCHER [35]

Answer:

  • A) k = 18.75
  • B) R(0.8) = 161419
  • C) R(0.3) = 275

Step-by-step explanation:

<u>Given expression</u>

  • R(x) = 6*e^(kx)

A) <u>Given</u>

  • x = 0.04
  • R = 10

<u>Solving for k</u>

  • 10 = 6*e^(0.04k)
  • e^(0.04k) = 10/6
  • ln (e^0.04k) = ln (1.6666)
  • 0.04k = 0.51
  • k = 0.51/0.04
  • k = 12.75

B) <u>Given</u>

  • x = 0.8
  • R= ?

<u>The value of R(0.8) is:</u>

  • R(0.8) =
  • 6*e^(0.8*12.75) =
  • 6*e^(10.2) =
  • 161419  rounded

C) <u>Given</u>

  • x = 0.3
  • R = ?

<u>The value of R(0.3) is:</u>

  • R(0.3) =
  • 6*e^(0.3*12.75) =
  • 6*e^(3.825) =
  • 275 rounded
4 0
3 years ago
Which property does the following<br> equation represent?<br> 62? + 43 = 43+ 6x2
timurjin [86]

Answer:

commutative

Step-by-step explanation:

you are typing the same numbers but in different order

8 0
3 years ago
At a farm, there are two huge pits for storing hay. 90 tons of hay is stored in the first pit, 75 tons in the second pit. Then,
Travka [436]

Answer:

63 tons

Step-by-step explanation:

The problem statement asks for the tons of hay removed from the first pit. It is convenient to let a variable (x) represent that amount. This is said to be 3 times the amount removed from the second pit, so that amount must be x/3.

The amount remaining in the first pit is 90-x.

The amount remaining in the second pit is 75 -x/3.

Since the first pit remaining amount is half the second pit remaining amount, we can write the equation ...

... 90 -x = (1/2)(75 -x/3)

... 180 -2x = 75 -x/3 . . . . multiply by 2

... 105 - 2x = -x/3 . . . . . . subtract 75

... 315 -6x = -x . . . . . . . . multiply by 3

... 315 = 5x . . . . . . . . . . . add 6x

... 63 = x . . . . . . . . . . . . . divide by 5

63 tons of hay were taken from the first pit.

_____

<em>Check</em>

After removing 63 tons from the first pit, there are 27 tons remaining. After removing 63/3 = 21 tons from the second pit, there are 54 tons remaining. 27 is half of 54, so the answer checks OK.

6 0
3 years ago
HELP ASAP!! PLEASE SHOW STEPS!!!
Elden [556K]

I assume you just have to simplify the expression.

\dfrac{(4\times 10^{-5}) + (2 \times 10^{-5})}{3\times10^7} = \dfrac{6\times10^{-5}}{3\times10^7} = \boxed{2\times 10^2}

6 0
2 years ago
In the class 1 are 10 boys and 8 girls, in the class 2 are 12 boys and 8 girls. In the whole 7th grade are 22 boys and 16 girls.
Colt1911 [192]
In class one, the ratio is 10:8
in class two, the ratio is 12:8
in the 7th grade, the ratio is 22:16
4 0
3 years ago
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