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2 years ago

A line segment has endpoints of (-2,6) and

Mathematics

1 answer:

lys-0071 [83]2 years ago

8 0

Answer:

(-3, -1.5)

Step-by-step explanation:

Given:

Endpoint₁: (-2, 6)
Endpoint₂: (-4, -9)

$\boxed{\text{Midpoint of a line segment:} \ \huge\text(\dfrac{x_1 + x_2}{2} ,\dfrac{y_1 + y_2}{2} \text)}$

Substitute the endpoints of the line segment in the midpoint:

$\implies \huge\text[\dfrac{-2 + (-4)}{2} ,\dfrac{6 + (-9)}{2} \text]$

Simplify the coordinates in the midpoint:

$\implies \huge\text[\dfrac{-2 - 4}{2} ,\dfrac{6 - 9}{2} \text] \implies \huge\text[\dfrac{-6}{2} ,\dfrac{-3}{2} \text]\implies \huge\text[-3 ,-1.5 \text]$

Thus, the coordinate of the midpoint is (-3, -1.5)

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A hemispherical tank is filled with water and has a diameter of 22 feet. If water

taurus [48]

Given :-

Diameter of tank = 20 feet

Radius of tank, r = 20/2 = 10 feet

To Find :-

Volume of the hemisphere

Formula to be used :-

Volume of the hemisphere = 2/3 × π × r³

Solution :-

Putting the values, we get

Volume of the hemisphere = 2/3 × π × r³

⇒ Volume of the hemisphere = 2/3 × 22/7 × 10 × 10 × 10

⇒ Volume of the hemisphere = 44000/21

⇒ Volume of the hemisphere = 2095. 23 feet³

Now, Total weight of the water

⇒ Total weight of the water = 62.4 × 2095.23

⇒ Total weight of the water = 130742.35 pounds

Hence, the Total weight of the water is 130742.35 pounds

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Cynthia is in the process of constructing two tangent line segments from a point outside circle O to circle O as shown. Which li

Allisa [31]

Answer:

(B) Segments MA and MB

Step-by-step explanation:

The tangent to the circle at a point is perpendicular to the radius of the circle drawn to the point of tangency.

Tangent at a point is unique.

Since there can be no two tangents at a point on circle, the options (b) and (c) are ruled out.

Now, if OA is perpendicular to MA, MA is the tangent else if OA is perpendicular to PA, PA is the tangent. Same is the case with point B.

Tangents from the same external point has same length.

MA = MB since they are the radii of the same circle with center M.

Hence, MA and MB meet all the requirements of the tangents.

8 0

4 years ago

Read 2 more answers

PLEASE HELPPPPPP. I NEED IT DONEEEEE.

agasfer [191]

Answer:

1. Couples tickets: $8

Individual tickets: $4

2. Song download cost: $2

Movie download cost: $15

Step-by-step explanation:

You can solve both of these questions by doing system of equations.

Let's start with question 1.

There are 2 variables in this equation:

- Couples tickets price: let's represent these with the letter C

- Individual tickets price: let's represent these with the letter K

Writing the two equations would look this these:

5c + 2k = 48

3c + 2k = 32

Next, isolate a variable. I am going to isolate K in the first equation.

$2k = -5c + 48 \\k = -\frac{5}{2}c + 24$

Now that we isolated a variable we can plug that back in to the second equation:

$3c + 2(-\frac{5}{2}c + 24) = 32\\3c - \frac{10}{2}c + 48 = 32\\3c -5c + 48 = 32\\-2c + 48 = 32\\-2c = -16\\c = 8$

We found that c is equal to 8 so we can put that back in to an equation to solve for k.

5(8) + 2k = 48

40 + 2k = 48

2k = 8

k = 4

Therefore, the price for couples tickets is $8 and the price for individual tickets is $4.

Check #1:

5(8) + 2(4) = 48

40 + 8 = 48

48 = 48

3(8) + 2(4) = 32

24 + 8 = 32

32 + 32

Now, let's go on to question 2.

There are 2 variables in this equation:

- Price of songs downloaded: let's represent these with S

- Price of movies downloaded: let's represent these with M

Writing the two equations would look like this:

15s + 11m = 195

15s + 8m = 150

There is a simple way to answer this system, however.

If you change the bottom equations signs to negative you can minus the second equation from the first equation like this:

15s + 11m = 195

-(15s +8m = 150)

Minus them to get this equation:

3m = 45

Solve

m = 15

We have found that each movie download costs $15, now let's plug this back into an equation:

15s + 11(15) = 195

15s + 165 = 195

15s = 30

s = 2

Each song costs $2 to download.

Check #2:

15(2) + 11(15) = 195

30 + 165 = 195

195 = 195

15(2) + 8(15) = 150

30 + 120 = 150

150 = 150

I hope this helps!!

- Kay :)

6 0

3 years ago

Points A and B are on opposite sides of a lake. A point C is 105.6 meters from A. The measure of ∠BAC is 70.5°, and the measure

nignag [31]

Answer:

= 70 Meters

Step-by-step explanation:

We can use the sine rule as follows:

Angle ABC=180-(70.5+38.833)

=70.667°

Using the sine rule and sides AB, AC and angles ABC and ACB:

b/Sin B=c/Sin C

Replacing with the values above we get:

AC/Sin ABC= AB/Sin ACB

105.6/Sin 70.667=AB/Sin 38.833

AB=(105.6 Sin 38.833)/Sin 70.667

=70.17 meters

The distance between the two points to the nearest meter is 70 meters

8 0

3 years ago

A university student center sells 1,600 cups of coffee per day at a price of $2.40. a market survey shows that for every $0.05 r

Lena [83]

2.00 would be the best price to maximize revenue in the situation you gave me to answer

5 0

3 years ago