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3 years ago

Help, please????????

Mathematics

1 answer:

xz_007 [3.2K]3 years ago

5 0

9514 1404 393

Answer:

E) 25.5 units²

Step-by-step explanation:

The figure is not carefully drawn, so it is difficult to tell that it is a trapezoid. The "height" of it is BC, the diagonal of a rectangle that is 1 unit by 4 units. The Pythagorean theorem tells you that length is ...

BC = √(1² +4²) = √17

We notice that the "bases" of the trapezoid (CD and AB) are 1 and 2 times this length. The trapezoid area formula tells us the area is ...

A = 1/2(b1 +b2)h

A = 1/2((√17)(1 +2))(√17) = 3/2(17) = 25.5 . . . . square units

_____

Alternate solution

Pick's Theorem is a theorem that can help you find the area of a polygon when its vertices are all on grid points. It tells you the area is ...

A = i + b/2 -1

where i is the number of grid points interior to the figure, and b is the number of grid points on the boundary. Here, the boundary grid points are those that are labeled plus the one at (-2, 1). Counting the interior grid points gives a total of 24, so the area by Pick's theorem is ...

A = 24 + 5/2 -1 = 25.5 . . . square units

Additional comment

Once you're familiar with Pick's theorem (and/or any of a few other methods of computing area from coordinates), you see that the area of any polygon whose vertices are grid points will be an integer multiple of 1/2. The only such answer choice here is choice E.

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Which expression is equivalent to (-3y - x) - (5y - 8x)?

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Answer:

Step-by-step explanation:

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3 years ago

Kyle held a balloon 8 feet off the ground, straight above his head. Ava is standing 15 feet directly to the right of Kyle.

Mazyrski [523]

Complete Question:

Kyle held a balloon 8 feet off the ground, straight above his head. Ava is standing 15 feet directly to the right of Kyle.

Write an equation using the Pythagorean Theorem to find the value of x.

How far are Ava's feet from the balloon?

Answer:

Ava's feet is 17ft away from the balloon

Step-by-step explanation:

Given

$height = 8ft$

$distance = 15ft$

The attached image represents the scenario

Using Pythagoras theorem (from the attachment), we have:

$x^2 = 8^2 + 15^2$

$x^2 = 64 + 225$

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$x = \sqrt{289$

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6 0

3 years ago

A quadratic function is defined by

ella [17]

Answer:

1. The vertex of the graph of the function is (-4, 7)

2. The vertex represents a minimum value

3. The equation represented by the new graph is g(x) = (x + 4)² + 1

Step-by-step explanation:

The given quadratic function is given in vertex form, y = a·(x - h)² + k, as follows;

g(x) = (x + 4)² + 7

1. By comparing the given quadratic function and the vertex form of a quadratic equation, we have;

a = 1, h = -4, and k = 7

The vertex of the graph of the function, (h, k) = (-4, 7)

2. Given that a = 1 > 0, the graph of the quadratic function opens upwards and the vertex represents a minimum value

3. Shifting the graph 6 units down from where it is now will give;

The vertex = (h, k - 6) = (-4, 7 - 6) = (-4, 1)

h = -b/(2·a), k = (-b²/(4·a) + c = -a·h² + c

c = k + a·h²

Therefore, initial value of the constant term, c = -1×(-4)² + 7 = 23

After the shifting the graph 6 units down, c = 23 - 6 = 17

∴ k = 1 = -a·(-4)² + 17

∴ -16/16 = -1 = -a

a = 1

Therefore, the equation represented by the new graph is g(x) = (x + 4)² + 1.

5 0

3 years ago

Tia performed an experiment where she flipped a coin 200 times. The coin landed heads up 92 times and tails up 108 times. Which

ra1l [238]

Total number of times she flipped a coin =200.

Total number of heads in the experiment=92

Total number of tails in the experiment=108

Therefore probability of the coun landing heads up in this experiment is 0.5

In the above experiment, the probability of the coin landing heads up is

P(H)= 92/200 = 0.46

In the above experiment, the probability of the coin landing tails up is P(T) = 108/200 = 0.54

The ratio obj represent the experimental probability of the coin landing heads up in this experiment

Therefore the correct option is 1.

3 0

3 years ago

Read 2 more answers

What is c/22 + 668 = 684 I NEED HELP!!!!!!!!!!!!!!

scoundrel [369]

Answer:

352

Step-by-step explanation:

So first you need to subtract 668 from both sides.

c/22 + 668 = 684

-668 -668

---------------------------

c/22 = 16

Then multiply both sides by 22.

c/22 * 22 = 16*22

c = 352

Check-

352/22=16

16+668=684

6 0

3 years ago