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Vera_Pavlovna [14]
3 years ago
10

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

_____

<em>Alternate solution</em>

<em>Pick's Theorem</em> 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

__

<em>Additional comment</em>

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

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Y=2x+1 when x increases by 5,y increases by​
Dmitriy789 [7]

Answer:

10

Step-by-step explanation:

say x=0

then y would be 1

increasing x by 5 makes x=5

and then 5 x 2 + 1=11

so y went from 1-11(difference of 10) with the variation

so the answer is 10

3 0
1 year ago
Two lines intersect at a point. The vertical angles formed are supplementary.
Nastasia [14]

we know that

<u>Vertical angles</u> are a pair of opposite and congruent angles formed by intersecting lines.

so

Let

x1---------> angle vertical 1

x2---------> angle vertical 2

x1=x2 ------> equation 1

in this problem

if the vertical angles formed are supplementary

that means that

x1+x2=180 ------> equation 2

substitute equation 1 in equation 2

x1+x1=180

2x1=180

x1=180/2

x1=90 degrees

therefore

<u>the answer is</u>

The vertical angles are right angles



8 0
3 years ago
solve for each please i really need help if u want to help me with my test and i get an a or a b i will give u 500 dollars
Len [333]

Answer:

The relation is not a function

The domain is {1, 2, 3}

The range is {3, 4, 5}

Step-by-step explanation:

A relation of a set of ordered pairs x and y is a function if

  • Every x has only one value of y
  • x appears once in ordered pairs

<u><em>Examples:</em></u>

  • The relation {(1, 2), (-2, 3), (4, 5)} is a function because every x has only one value of y (x = 1 has y = 2, x = -2 has y = 3, x = 4 has y = 5)
  • The relation {(1, 2), (-2, 3), (1, 5)} is not a function because one x has two values of y (x = 1 has values of y = 2 and 5)
  • The domain is the set of values of x
  • The range is the set of values of y

Let us solve the question

∵ The relation = {(1, 3), (2, 3), (3, 4), (2, 5)}

∵ x = 1 has y = 3

∵ x = 2 has y = 3

∵ x = 3 has y = 4

∵ x = 2 has y = 5

→ One x appears twice in the ordered pairs

∵ x = 2 has y = 3 and 5

∴ The relation is not a function because one x has two values of y

∵ The domain is the set of values of x

∴ The domain = {1, 2, 3}

∵ The range is the set of values of y

∴ The range = {3, 4, 5}

3 0
2 years ago
Find the equation of the line that is perpendicular to x - y = -5 and passes through (4, 7).
Ivanshal [37]
X - y = -5
-y = -x - 5
y = x + 5...slope here is 1. A perpendicular line will have a negative reciprocal slope. All that means is flip ur slope and change the sign. So our perpendicular line will have a slope of -1.

y = mx + b
slope(m) = -1
(4,7)...x = 4 and y = 7
now we sub and find b, the y int
7 = -1(4) + b
7 = -4 + b
7 + 4 = b
11 = b

so ur perpendicular equation is : y = -x + 11 <==
8 0
3 years ago
What is the surface area of the triangular prism
Harrizon [31]

Answer:

surface \: a = 9 \times 5 \\  =  45ft \times 2 \\  =   {90}^{2} ft\\ surface \: b =  \frac{1}{2} bh \\  =  \frac{1}{2 }  \times 6 \times 4 \\  = 3 \times 4 \\  = 12 \times 2 \\  =  {144}^{2} ft \\  =  90 + 144 \\  =  {234}^{2} ft

3 0
2 years ago
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