How many degrees has aABC been rotated counterclockwise about the<br> origin?

Can someone please help me out! and please explain your answer, and how you got it right! thank you so much!

Contact [7]

It is

$24x - 30$

The equation for area of a trapezoid is

$\frac{1}{2} (a + b) \times h$

Substituting our values in

$\frac{1}{2} (3x + 7 + 5x - 3) \times 6$

We can then simplify the expression

$\frac{1}{2} (8x - 10) \times 6 \\ (4x - 5) \times 6 \\ 24x - 30$

8 0

3 years ago

Evan tosses a ball from the roof of a building. The path of the ball can be modelled

DiKsa [7]

Answer:

Please find attached sketch of the path of the ball, having plot area and plot points, created with MS Excel

Step-by-step explanation:

Question;

The equation representing the path of the ball obtained from a similar question posted online are;

h₁ = -4·(t + 1)·(t - 5), h₂ = -4·(t - 2)² + 36, h₃ = -4··t² + 16·t + 20

The above equations represent the same path

The equation, h₁ = -4·(t + 1)·(t - 5), gives the roots of the height function, h(t), used in determining the height of the ball after time <em>t</em>

At (t + 1) = 0 (t = -1) or at (t - 5) = 0 (t = 5), the ball is at ground level

The ball reaches the ground, is at ground level at t = 1, and at t = 5 seconds after being tossed, where h(t) = 0

The equation of the path of the ball in vertex form, y = a·(x - 2)² + k, is h₂ = -4·(t - 2)² + 36, where, by comparison, we have;

The vertex of the ball = The maximum height reached by the ball = (h, k) = (2, 36)

The coefficient of the quadratic term, t², is negative, therefore, the shape of the parabola is upside down, ∩, shape

The sketch of the path of the ball created with MS Excel, used in plotting the vertex, the initial value and the root points of the parabola, through which the ball passes and joining of the points with a 'smooth' curve is attached

5 0

2 years ago

Jan and Wayne went to the store to buy some groceries. Jan bought 2 cans of corn beef hash and 3 cans of creamed chipped beef fo

olasank [31]

You can solve this by using the system of equations.
Jan - 4.95 = 2H + 3C
Wayne - 5.45 = 3H + 2C

Use elimination.
-3(2H + 3C = 4.95)
2(3H + 2C = 5.45)

Solve. And you'll get:
-6H + (-9C) = -14.85
6H + 4C = 10.9

Cross out -6H and 6H because they cancel out. And you're left with:
-9C = -14.85
4C = 10.9

Add -9C with 4C, and -14.85 with 10.9.
-5C = -3.95

Divide each side with -5.
C = $0.79

Now to figure out what H is, just substitute the C in one of the equations with 0.79.
5.45 = 3H + 2(0.79)
5.45 = 3H + 1.58
-1.58 -1.58
3.87 = 3H
3.87/3 = 3/3(H)
1.29 = H

Finished!

7 0

3 years ago

Read 2 more answers

1.Show that the statement p: “If x is a real number such that x3 + 4x = 0, then x is 0” is true by

Genrish500 [490]

If x is a real number such that x3 + 4x = 0 then x is 0”.Let q: x is a real number such that x3 + 4x = 0 r: x is 0.i To show that statement p is true we assume that q is true and then show that r is true.Therefore let statement q be true.∴ x2 + 4x = 0 x x2 + 4 = 0⇒ x = 0 or x2+ 4 = 0However since x is real it is 0.Thus statement r is true.Therefore the given statement is true.ii To show statement p to be true by contradiction we assume that p is not true.Let x be a real number such that x3 + 4x = 0 and let x is not 0.Therefore x3 + 4x = 0 x x2+ 4 = 0 x = 0 or x2 + 4 = 0 x = 0 orx2 = – 4However x is real. Therefore x = 0 which is a contradiction since we have assumed that x is not 0.Thus the given statement p is true.iii To prove statement p to be true by contrapositive method we assume that r is false and prove that q must be false.Here r is false implies that it is required to consider the negation of statement r.This obtains the following statement.∼r: x is not 0.It can be seen that x2 + 4 will always be positive.x ≠ 0 implies that the product of any positive real number with x is not zero.Let us consider the product of x with x2 + 4.∴ x x2 + 4 ≠ 0⇒ x3 + 4x ≠ 0This shows that statement q is not true.Thus it has been proved that∼r ⇒∼qTherefore the given statement p is true.

8 0

2 years ago

for the school play adult tickets cost 4$ and children tickets cost 2$ natalie is working at the ticket counter and just sold 20

lilavasa [31]

Let us formulate the independent equation that represents the problem. We let x be the cost for adult tickets and y be the cost for children tickets. All of the sales should equal to $20. Since each adult costs $4 and each child costs $2, the equation should be

4x + 2y = 20

There are two unknown but only one independent equation. We cannot solve an exact solution for this. One way to solve this is to state all the possibilities. Let's start by assigning values of x. The least value of x possible is 0. This is when no adults but only children bought the tickets.

When x=0,
4(0) + 2y = 20
y = 10

When x=1,
4(1) + 2y = 20
y = 8

When x=2,
4(2) + 2y = 20
y = 6

When x=3,
4(3) + 2y= 20
y = 4

When x = 4,
4(4) + 2y = 20
y = 2

When x = 5,
4(5) + 2y = 20
y = 0

When x = 6,
4(6) + 2y = 20
y = -2

A negative value for y is impossible. Therefore, the list of possible combination ends at x =5. To summarize, the combinations of adults and children tickets sold is tabulated below:

Number of adult tickets Number of children tickets
0 10
1 8
2 6
3 4
4 2
5 0

6 0

3 years ago

How many degrees has aABC been rotated counterclockwise about the origin?