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mixas84 [53]
3 years ago
9

Which answer represents the series in sigma notation? −3+(−1)+1+3+5 A:∑j=15(2j−5)

Mathematics
1 answer:
insens350 [35]3 years ago
8 0

Answer:

A:∑j=15(2j−5)

Step-by-step explanation:

a = -3

d = -1 - (-3) = -1 + 3 = 2

j-th term: a + (j-1)d

-3 + (j - 1)(2)

-3 + 2j - 2

2j - 5

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The coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .
daser333 [38]

Answer: The correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

Explanation:

It is given that  coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

The distance formula for two points is given below,

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

DE=\sqrt{(2+2)^2+(4-5)^2}=\sqrt{17}

EF=\sqrt{(0-2)^2+(0-4)^2}=\sqrt{20}

FG=\sqrt{(-4-0)^2+(1-0)^2}=\sqrt{17}

DG=\sqrt{(-4+2)^2+(1-5)^2}=\sqrt{20}

Slope formula,

m=\frac{y_2-y_1}{x_2-x_1}

Slope of DE,

m_1=\frac{4-5}{2+2}= \frac{-1}{4}

Slope of EF,

m_2=\frac{0-4}{0-2}= 2

Slope of FG,

m_3=\frac{1-0}{-4-0}= \frac{-1}{4}

Slope of DG,

m_4=\frac{1-5}{-4+2}= 2

The slope of opposite sides are equal, it means the opposite sides are parallel.

All four sides do not have the same length. It means it is not a rhombus.

From the figure it is noticed that the opposite sides are parallel.

Therefore, the correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

3 0
3 years ago
Read 2 more answers
WILL GIVE BRAINLIEST!!! Find the length of DF
Leto [7]

Answer:

190.4

Step-by-step explanation:

Solve the following system:

{2 y - 3 x - 8 = 3 y + 4 x - 1 | (AB=DE)

4 y + 10 x + 3 = -2 y - 17 x + 9 | (BC=EF)

x = -16/5, y = 77/5

DF=AC=-27x+5y+27=190.4

There you go, have a great day

8 0
3 years ago
What is the volume of a cube with 1cm on each side
yKpoI14uk [10]
1 cm because 1 cm * 1 cm * 1 cm = 1 cm
3 0
3 years ago
Equation of the line that is perpendicular to y= 1/8x -2 and goes through the point <br> (-2,-3)
larisa [96]
The answer to this equation is y=-8x-19



I hope this helps!!!!!!!!
7 0
3 years ago
Read 2 more answers
Help on thisi please
SVETLANKA909090 [29]

Answer:

False for both

Step-by-step explanation:

Neither of these images are symmetrical vertically nor horizontally.

4 0
3 years ago
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