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3 years ago

If angle M is represented by x + 16 and angle G is represented by

Mathematics

1 answer:

Evgen [1.6K]3 years ago

8 0

Answer:

the measure of angle M is 73 degrees

Step-by-step explanation:

the sum of complementary angles is 90 degrees. so set up the equation as:

x+16+x-40=90

combine like terms and you get:

2x-24=90

add 24 on both sides and you get:

2x=114

divide by 2 on both sides to isolate x and you get:

x=57

since the equation for angle M is x+16, you substitute 57 for x and you get:

M=57+16

M=73

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swimming downstream you can swim 2 miles in 40 minutes, and upstream you can swim 2 miles in 60 minutes...how long will it take

Akimi4 [234]

Answer:

Vp = 1 / 24 miles/min the speed in still water

Step-by-step explanation:

Lets call Vp speed of swimmer and Vw speed of water then:

Downstream Vp + Vw

Swimmer does 2 miles in 40 minutes then he does

1 mile in 20 minutes

Upstream Vp - Vw

Swimmer does 2 miles in 60 minutes then he does

1 mile in 30 minutes

We get the following system:

(Vp + Vw )* 20 = 1 (1) and

( Vp - Vw )* 30 = 1 (2)

Solving the system

From equation (1)

20*Vp + 20* Vw = 1 ⇒ Vw = ( 1 - 20*Vp ) /20

Plugging that value in the second equation

(Vp - Vw )* 30 = 1 ⇒ [ Vp - ( 1 - 20*Vp )/20 ] * 30 = 1

[20*Vp - 1 + 20*Vp ] * 30/20 = 1 ⇒ [ 40*Vp - 1 ] *30 = 20 or

[ 40*Vp - 1 ] *3 = 2

120* Vp - 3 = 2 ⇒ 120*Vp = 5 and Vw = 1 /120 miles/min

Vp = 5 / 120 miles/min or

Vp = 1 / 24 miles/min

and speed of water Vw = 1 / 120

8 0

3 years ago

Joseph has 3,134 pieces of paper in his classroom.emily has 5,229 pieces of paper in her classroom.how many pieces of paper do t

AysviL [449]

2095 is the correct answer

7 0

4 years ago

Read 2 more answers

The sum of two numbers is 44. The second number is 4 less than three times the first number. Let x represent the first number an

MakcuM [25]

Answer:

$y = 4minus3 \times$

$let x = 44 \\ \\ lety = 4 \\ \\ x + y = 44 \\ \\ 12 \times 4 - 4 = 44$

3 0

3 years ago

Find the measure of each angle in degrees and radians.<br>

Paul [167]

Problem 9

This is not correct. It would be correct if the longer arc mark was not there. However, because it is there, you have to travel 360-30 = 330 degrees in the negative direction. So the angle shown along that arc is -330 degrees which converts to -11pi/6 radians.

====================================

Problem 10

The spiral arc almost wraps itself around 2 times over, effectively almost making two full revolutions.

1 revolution = 2pi radians

2 revolutions = 4pi radians (multiply both sides by 2)

Subtract off pi/3

4pi - pi/3 = 12pi/3 - pi/3 = 11pi/3

11pi/3 represents the radian measure of the spiral arc

Convert to degrees

11pi/3 radians = (11pi/3)*(180/pi)

11pi/3 radians = (11/3)*180

11pi/3 radians = 11*180/3

11pi/3 radians = 11*60

11pi/3 radians = 660 degrees

====================================

Problem 11

Add pi/2 radians to the angle measure shown

pi/2 + 7pi/18 = 9pi/18 + 7pi/18

pi/2 + 7pi/18 = 16pi/18

pi/2 + 7pi/18 = 8pi/9

The full angle in radians is 8pi/9 radians

Now convert to degrees

8pi/9 radians = (8pi/9)*(180/pi)

8pi/9 radians = (8/9)*180

8pi/9 radians = 8*180/9

8pi/9 radians = 8*20

8pi/9 radians = 160 degrees

====================================

Problem 12

Add pi/2 radians (aka 90 degrees) to pi/9 to get

pi/2 + pi/9 = 9pi/18 + 2pi/18

pi/2 + pi/9 = 11pi/18

This represents the red angle shown in the diagram below.

Subtract this found angle from 4pi, which represents 2 full revolutions

4pi - 11pi/18 = 72pi/18 - 11pi/18

4pi - 11pi/18 = 61pi/18

The spiral mark shown in the diagram is 61pi/18 radians

Convert to degrees

61pi/18 radians = (61pi/18)*(180/pi)

61pi/18 radians = (61/18)*180

61pi/18 radians = 61*180/18

61pi/18 radians = 61*10

61pi/18 radians = 610 degrees

8 0

3 years ago

⚠️⚠️ HELP me find the M the B and equation (Y=Mx+B) ⚠️⚠️

ziro4ka [17]

Y = 30x

the b (y intercept) is 0

M = 30

B = 0

7 0

3 years ago