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3 years ago

Given line segment AB, the coordinates of A are (3,-5) and the coordinates midpoint are (5,-1), what are the coordinates for B?

Mathematics

1 answer:

dsp733 years ago

6 0

Answer:

Step-by-step explanation:

Point P(5, -1) being the midpoint of AB means that $x_P-x_A=x_B-x_P$

$5-3=x_B-5\\\\2+5=x_B\\\\x_B=7$

and $y_P-y_A=y_B-y_P$

$-1-(-5)=y_B-(-1)\\\\-1+5=y_B+1\\\\y_B=3$

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Can u help me figure this out lol

Evgesh-ka [11]

Answer:

Cost of a T-shirt is £4
Cost of a Hat is £1

Step-by-step explanation:

Let T be the cost of each T-shirt and H the cost of each hat

We get two equations based on the cost description

3T + 2H = 14 ...... (1)
2T + 7H = 15 ...... (2)

Multiply (1) by 2 and (2) by 3 so that the T terms are the same
(1) x 2 ==> 6T + 4H = 28 ... (3)
(2) x 3 ==> 6T + 21H = 45 ... (4)

Subtract (3) from (4) to eliminate the T terms
21H - 4H = 45 - 28 or 17H = 17 ==> H = 1

Substituting the value of H in either (1) or (2) will give us a value for T
Substitute in (1)
3T + 2*1 = 14 ==> 3T = 12, T = 4

Check
In (1) 3 *4 + 2 *1 = 14
In (2) 2*4 + 7*1 = 15
So satisfies both equations

4 0

2 years ago

A city has a population of 310,000 people. Suppose that each year the population grows by 9%. What will the population be after

Leno4ka [110]

Answer: 644,800

Step-by-step explanation:

This can also be solved using the terms of Arithmetic Progressions.

Let the 13 years be number of terms of the sequences (n)

Therefore ;

T₁₃ = a + ( n - 1 )d , where a = 310,000 and d = 9% of 310,000

9% of 310,000 = 9/100 x 310,000

= 27,900

so the common difference (d)

d = 27,900

Now substitute for the values in the formula above and calculate

T₁₃ = 310,000 + ( 13 - 1 ) x 27,900

= 310,000 + 12 x 27,900

= 310,000 + 334,800

= 644,800.

The population after 13 years = 644,800.

3 0

2 years ago

It takes a train 60 seconds to completely drive through a bridge of 1260 m, and 90 seconds to completely drive through a tunnel

Olegator [25]

The length of train is 120 meters

The speed of train is 25 meter per second

Solution:

The speed is given by formula:

$speed = \frac{distance}{time}$

Given that,

It takes a train 60 seconds to completely drive through a bridge of 1260 m

And 90 seconds to completely drive through a tunnel of 2010 m

Let the length of the train be "x"

The total distance travelled by the train across the bridge is given by:

total distance = x + 1260 + x = 2x + 1260

[ here we use x + x to represent that train completely drives through bridge ]

The time taken is given as 60 seconds

Therefore, the speed is given as:

$speed = \frac{2x+ 1260}{60}$

The total distance travelled by the train through the tunnel is given by:

total distance = x + 2010 + x = 2x + 2010

The time taken is given as 90 seconds

Therefore, the speed is given as:

$speed = \frac{2x+ 2010}{90}$

The speed of the train was the same in both cases.

Equate both speeds

$\frac{2x+ 1260}{60} = \frac{2x+ 2010}{90}$

$\frac{x+630}{30} = \frac{x+1005}{45}$

$45(x+630) = 30(x+1005)\\\\45x + 28350 = 30x + 30150\\\\45x - 30x = 30150 - 28350\\\\15x = 1800\\\\x = 120$

Thus length of train is 120 meters

Find the speed of train:

$speed = \frac{2x+ 1260}{60}\\\\speed = \frac{2(120) + 1260)}{60}\\\\speed = 25$

Thus speed of train is 25 meter per second

5 0

3 years ago

Use the order of operations to find the value of the expression: 20 - 12 + 8 x 5

Nezavi [6.7K]

Here’s what I got

Have nice day

6 0

3 years ago

- Inessa ran 3 laps in 10 minutes. How long

Anni [7]

Answer: 16 minutes and 40 seconds

Step-by-step explanation:

1.) Divide 10 minutes by 3 laps in order to find out how long it takes her to run a single lap. (it ends up being 3 minutes and 20 seconds per lap)

2.) Multiply this number by 5, you get 16 minutes and 40 seconds.

NOTE: remember that you’re using intervals of 60 (seconds in a minute) rather than intervals of 100.

8 0

2 years ago