A boy's mother was 32 years old when he was born. Let a represent the boy's age and m represent the mother's age.

Dave and Sandy Hartranft are frequent flyers with a particular airline. They often fly from City A to City B, a distance of 756

horsena [70]

Answer:

Plane = 441 mi/h; wind = 63 mi/h

Step-by-step explanation:

distance = rate × time

Let p = the plane's speed in still air

and w = the wind speed . Then,

p + w = speed with wind

p - w = speed against wind

We have two conditions:

(1) 756 = (p - w) × 2

(2) 756 = (p + w) × 1.5

Distribute the constants (3) 756 = 2p - 2w

(4) 756 = 1.5p + 1.5 w

Multiply Equation (3) by 3 (5) 2268 = 6p - 6w

Multiply Equation (4) by 4 (6) 3024 = 6p + 6w

Add Equations (5) and (6) 5292 = 12p

Divide each side by 12 (7) p = 441 mi/h

Substitute (7) into Equation(3) 756 = 882 - 2w

Add 2w to each side 2w + 756 = 882

Subtract 756 from each side 2w = 126

Divide each side by 2 w = 63 mph

The plane's speed in still air is 441 mi/h.

The wind speed is 63 mph.

Check:

(1) 756 = (441 - 63) × 2 (2) 756 = (441 + 63) × 1.5

756 = 378 × 2 756 = 504 × 1.5

756 = 756 756 = 756

8 0

3 years ago

Wendy throws a dart at this square shaped target: Part A: is the probability of hitting the black circle inside the target close

KonstantinChe [14]

Since the area of the circle is only 3.14. that means 3.14 out of one hundred units can be hit. so you have a 3.14% chance of hitting the circle in the middle. SO the probability is very close to 0.

100 - 3.14 = 96.86, so we have a 97 percent chance (approximately) of landing in the white space, This is very close to one.

3 0

3 years ago

Estimate how many 12inches rulers will be about the same length as the flag

MAVERICK [17]

You would need 13/14 12in rulers to make it the size of the flag

8 0

3 years ago

-6x-14y=-20<br> -3x-7y=-10

Alex Ar [27]

ANSWER:

x = 10 / 3

y = 0

STEP-BY-STEP EXPLANATION:

We will be using simultaneous equations to solve this problem. Let's first establish the two equations which we will be using.

Equation No. 1 -

- 6x - 14y = - 20

Equation No. 2 -

- 3x - 7y = - 10

First, we will make ( x ) the subject in the first equation and simplify accordingly.

Equation No. 1 -

- 6x - 14y = - 20

- 6x = - 20 + 14y

x = ( - 20 + 14y ) / - 6

x = ( - 10 + 7y ) / - 3

From this, we will make ( y ) the subject in the second equation and substitute the value of ( x ) from the first equation into the second equation to solve for ( y ) accordingly.

Equation No. 2 -

- 3x - 7y = - 10

- 7y = - 10 + 3x

- 7y = - 10 + 3 [ ( - 10 + 7y ) / - 3 ]

- 7y = - 10 + [ ( - 30 + 21y ) / - 3 ]

- 7y = - 10 + ( 10 - 7y )

- 7y = - 7y

- 7y + 7y = 0

0y = 0

y = 0

Using this, we will substitute the value of ( y ) from the second equation into the first equation to solve for ( x ) accordingly.

x = ( - 10 + 7y ) / - 3

x = [ - 10 + 7 ( 0 ) ] / - 3

x = [ - 10 + 0 ] / - 3

x = - 10 / - 3

x = 10 / 3

6 0

3 years ago

If you were to solve the following system by substitution, what would be the best variable to solve for and from what equation?2

aivan3 [116]

The second equation because they all have a common factor of 3. You can get x by itself. However, with the first one, you'll end up with fractions instead.

8 0

3 years ago