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snow_lady [41]
3 years ago
15

Which of the following is the correct solution to the linear inequality shown below?

Mathematics
1 answer:
Georgia [21]3 years ago
5 0
Correct answer is C.

Line y=\frac{1}{3}x-2 intersects y-axis at -2 and passes through the point (3,-1).

Line must be dashed, because the inequality sign is ">".

Point (0,0) must lie in the solution set because it satisfies inequality y>\frac{1}{3}x-2.

0\ \textgreater \  \frac{1}{3}\times 0-2
\\
\\0\ \textgreater \ -2
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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
Vanessa has scored 45, 32, and 37 on her three math quizzes. She will take one more quiz and she wants a quiz average of at leas
zhenek [66]

45 + 32 + 37 = 114

114÷3 = 38

4 total quizzes,


 for a 40 average on 4 quizzes she needs 40*4 = 160 total points




for 3 quizzes she has 45 +32 +37 = 114 points


160-114 = 46, she needs at least a 46 on the 4th quiz


6 0
3 years ago
Read 2 more answers
Which are names of points drawn in the figure?
fenix001 [56]
I believe that the answer is B and D
7 0
3 years ago
A box of oranges weighs 4kg. if one orange weighs 80 g how many oranges are in the box?
wlad13 [49]

Answer:

50 Oranges is your answer.

Step-by-step explanation:

Lets see..

4 kg = 4000 grams mainly because 1kg = 1000 grams in total.

4000 grams divided by 80 grams will give you the number of oranges that the box has since each orange weighs 80 grams.

4000/80 = 50.

hope this helps!

5 0
3 years ago
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Devin has started a lawn care service. He will charge a mowing fee of $7 plus $2 per square yard of lawn. He also offers trimmin
Maru [420]

Answer:7+2xy

Step-by-step explanation:apex

4 0
3 years ago
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