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Lelu [443]
3 years ago
6

1. Two angles are supplements. The larger is 10 more than 4 times the smaller. Find both angles,

Mathematics
1 answer:
scZoUnD [109]3 years ago
5 0

Step-by-step explanation:

Supplementary angles equal 180°

1. Let the two angles be x and y

then y = 4x + 10

x + y = 180

x + (4x + 10) = 180

5x + 10 = 180

5x = 180 - 10

5x = 170

x = 170 / 5

x = 34

x = 34y = 146

2. if the two angles are equal then divide 180 by 2 to get 90

3. 180 - x = 3(90 - x)

180 - x = 270 - 3x

2x = 90

x = 45

4. 180 - x = 2x - 12

180 - 12 = 2x + x

168 = 3x

x = 56

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A flagpole is located at the edge of a sheer y = 70-ft cliff at the bank of a river of width x = 40 ft. See the figure below. An
Gnom [1K]
I would solve this using tangents.  Let h be height of flagpole.
Set up 2 right triangles, each with a base of 40.
The larger triangle has height of "h+70"
Smaller triangle has height of 70.

Now write the tangent ratios:
tan A = \frac{h+70}{40}  , tan B = \frac{70}{40}

Note: A-B = 9
To solve for h we need to use the "Difference Angle" formula for Tangent
tan (A-B) = \frac{tanA - tanB}{1+tan A  tan B}
Plug in what we know:
tan(9) = \frac{ \frac{h+70}{40} -  \frac{70}{40}}{1+ (\frac{h+70}{40})(\frac{7}{4})}
tan (9) = \frac{ \frac{h}{40}}{ \frac{7h +650}{160}} = \frac{4h}{7h+650}
h = \frac{650 tan(9)}{4-7 tan(9)}
h = 35.6
7 0
3 years ago
P(A)* P(B)≠ p(AnB)<br><br> Why does it contain a not equal to sign
RoseWind [281]

Answer:

P(A|D) and P(D|A) from the table above are not equal because P(A|D) =  and P(D|A) =

Step-by-step explanation:

Conditional probability is the probability of one event occurring  with some relationship to one or more other events

.

P(A|D) is called the "Conditional Probability" of A given D

P(D|A) is called the "Conditional Probability" of D given A

The formula for conditional probability of P(A|D) = P(D∩A)/P(D)

The formula for conditional probability of P(D|A) = P(A∩D)/P(A)

The table

              ↓         ↓       ↓

           :  C     :   D    : Total

→ A      :  6     :    2    :   8

→ B      :  1      :    8    :   9

→Total :  7     :    10  :  17

∵ P(A|D) = P(D∩A)/P(D)

∵ P(D∩A) = 2 ⇒ the common of D and A

- P(D) means total of column D

∵ P(D) = 10

∴ P(A|D) =

∵ P(D|A) = P(A∩D)/P(A)

∵ P(A∩D) = 2 ⇒ the common of A and D

- P(A) means total of row A

∵ P(A) = 8

∴ P(D|A) =

∵ P(A|D) =

∵ P(D|A) =

∵   ≠  

∴ P(A|D) and P(D|A) from the table above are not equal

Step-by-step explanation:

4 0
3 years ago
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Sedbober [7]

Step-by-step explanation:

\frac{8}{6}  =  \frac{x}{3}  \\ x =  \frac{3 \times 8}{6}  = 4

7 0
2 years ago
Can someone please help me with This real quick and thank you so much ❣✊
dolphi86 [110]
7.5, 50.6 minus 5.8 =44.8, divide this by 6, 7.44 recuring 7

5 0
3 years ago
What is (11 5/8 - 2 1/16) - 4 3/4 ? ​
Vitek1552 [10]

Answer:

4.8125 or 4 13/16

Step-by-step explanation:

(11 10/16 - 2 1/16) - 4 12/16

(9 9/16) - 4 12/16

4 .8125 or 4 13/16

3 0
3 years ago
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