What is the volume of this rectangular prism?

Answer:

  (4, 5)

Step-by-step explanation:

Dilation by factor d about point (a, b) effects the transformation ...

  (x, y) ⇒ d((x, y) -(a, b)) +(a, b)

  ⇒ (d(x-a) +a, d(y-b) +b)

  (x, y) ⇒ (dx +a(1-d), dy +b(1-d))

We have (x, y) = (3, 4) and (a, b) = (1, 2) and d=3/2. Filling in these numbers, we get ...

  (3, 4) ⇒ ((3/2)(3)+1(1-3/2), (3/2)(4)+2(1-3/2)) = (9/2 -1/2, 6 -1) = (4, 5)

Point E' is (4, 5).

_____

If you look at the graph, you realize that E is (2, 2) from (1, 2). Dilation by a factor of 3/2 moves it to (3/2)(2, 2) = (3, 3) from (1, 2). So ...

  E' = (3+1, 3+2)

  E' = (4, 5)

Answer:

= 8/6435

Step-by-step explanation:

Number of black balls = 8

Number of Brown balls = 5

Total number of balls = 8+5 = 13

Pr (8 balls picked at random are black ) =

Number of black balls / Total number of balls.

1st Pr ( 8 balls picked are black) = 8/13

Pr (2nd random pick) = 7/12

Pr (3rd random pick) = 6/ 11

Pr (4th random pick) = 5/10

Pr (5th random pick) = 4/9

Pr (6th random pick) = 3/7

Pr (7th random pick) = 2/6

Pr (8th random pick) = 1/5

Pr (8 balls picked at random are black ) = 8/13 * 7/12 * 6/11 * 5/10 * 4/9 * 3/7 * 2/6 * 1/5

= 8/13 * 7/12 * 6/11 * 1/2 * 4/9 * 3/7 * 1/3 * 1/5

= 8/6435

But pls note, I solved it such that there wasn't a replacement after each pick.

Math is fun

7 . X + 2y = 4 (move x beside 4, since it's positive it will be negative)

2y = 4 - X (divide terms to 2)

| 2y ÷ 2 = y | 4 ÷ 2 = 2 | -X ÷ 2 = -1/2 (There's always an imaginary 1 beside x, only just x).

y = 2 - 1/2x (rearrange terms)

y = -1/2x + 2

9. -2x + 3y = -6 (move -2x beside -6, since it's negative it will turn into a positive)

3y = -6 + 2x (divide by 3)

y = -2 + 2/3x (rearrange)

y = 2/3x -2

11. 5x - 2y = 14

-2y = 14 - 5x (-2 ÷ -5x is 5/2x, but since numerator and denominator are negative, fraction turns positive)

y = -7 + 5/2x

y= 5/2x - 7

13. 4x + 3y = 12

3y = 12- 4x

y = 4 -4/3x

y = -4/3x + 4

15. x + 3y = -3

3y = -3 -x

y = -1 -1/3x

y -1/3x - 1

There you go!

Just remember those steps and you should be fine :)

Answer:

Step-by-step explanation:

Mathematical expressions are expressions which are combinations of constants, variables and mathematical operations . A constant is a symbol in maths which has fixed numerical value for example 2 , 3, -6, are constants .A variable is a symbol in algebra which takes various numerical values and has no fixed value . Mathematical operations include .

By term word phase, we mean mathematical expression using constants and variables.

Given: 49 + m

Word Phase:

Sum of 49 and m

Here, 49 is a constant

m is a variable

+ is a mathematical operation.

Final answer:

The equation for the aircraft's flight is a quadratic equation representing the height of the aircraft at any given time. By rearranging the equation to isolate time and applying the quadratic formula, we can find the time at which the aircraft reaches its maximum height, which in this case is 3.79 minutes.

Explanation:

The flight of an aircraft from Toronto to Montreal is modeled by the equation h = -2.5t2 + 200t where t represents time in minutes and h represents height in meters. This is fundamentally a quadratic equation which is utilized in physics to characterize motion under constant acceleration. In this case, it models the height of the aircraft at any given time.

To find the time at which the airplane's maximum height is achieved, we must solve the equation for t. By rearranging the equation, we can isolate t, yielding a quadratic equation as follows: 0 m = 0 m + (10.0 m/s) t + (2.00 m/s2) t2. This simplifies to 200 = 10t + t2.

Applying the quadratic formula, we find two solutions for t, 3.79 s and 0.54 s. The time it takes the aircraft to reach its maximum height would be the longer solution, which is 3.79 minutes in this case.

Learn more about Quadratic Equations in Motion here:

brainly.com/question/37955752

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Final answer:

The question provides a quadratic equation to model the flight of an aircraft. This equation can be used to calculate the height of the aircraft at a specific time or to determine when the aircraft reaches its maximum height.

Explanation:

The question is asking about the trajectory of an aircraft as modelled by a quadratic equation, and specifically, how time influences height. The equation given is h = -2.5t²+200t. Quadratic equations are frequently used to describe the motion of objects when the acceleration is constant. This equation tells us that the height of the aircraft is dependent on the time squared and the time.

To solve for a specific time (t), we can plug the desired time into the equation to find the height of the aircraft at that time. For instance, if we want to find out the height of the aircraft 10 minutes into the flight, we would substitute t=10 into the equation, giving us h=-2.5 × (10)²+200 × (10). Simplifying this equation would provide the height of the aircraft 10 minutes into the flight.

Additionally, this equation could also be used to find the maximum height of the aircraft. The maximum height is reached when the derivative of the equation equals zero. Taking the derivative of h = -2.5t²+200t and setting it equal to zero will provide the time when the maximum height is reached.

Learn more about Quadratic Equations here:

brainly.com/question/30098550

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