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butalik [34]
3 years ago
10

50 points!!! Need It ASAP

Mathematics
2 answers:
stira [4]3 years ago
7 0

Answer:

Last option

Step-by-step explanation:

Alex17521 [72]3 years ago
6 0

The last option :) Ask if explanation needed

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The coordinates of quadrilateral PQRS are P(–3, 0), Q(0, 4), R(4, 1), and S(1, –3). What best describes the quadrilateral?
denis-greek [22]

Answer:

Square

Step-by-step explanation:

Plot the vertices of the quadrilateral PQRS on the coordinate plane (see attached diagram). The diagram shows that this is a square. Let's prove it.

1. Find all sides lengths:

PQ=\sqrt{(-3-0)^2+(0-4)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\ \\QR=\sqrt{(0-4)^2+(4-1)^2}=\sqrt{(-4)^2+(3)^2}=\sqrt{16+9}=\sqrt{25}=5\\ \\RS=\sqrt{(4-1)^2+(1-(-3))^2}=\sqrt{(3)^2+(4)^2}=\sqrt{9+16}=\sqrt{25}=5\\ \\SP=\sqrt{(1-(-3))^2+(-3-0)^2}=\sqrt{(4)^2+(-3)^2}=\sqrt{16+9}=\sqrt{25}=5

All sides have the same lengths.

2. Find the slopes of all lines:

PQ:\ \dfrac{4-0}{0-(-3)}=\dfrac{4}{3}\\ \\QR:\ \dfrac{1-4}{4-0}=-\dfrac{3}{4}\\ \\RS:\ \dfrac{-3-1}{1-4}=\dfrac{4}{3}\\ \\SP:\ \dfrac{0-(-3)}{-3-1}=-\dfrac{3}{4}

Since the slopes of PQ and RS are the same, lines PQ and RS are parallel. Since the slopes of QR and SP are the same, lines QR and SP are parallel.

The slopes \frac{4}{3} and -\frac{3}{4} have the product of

-\dfrac{3}{4}\cdot \dfrac{4}{3}=-1,

then lines are pairwise perpendicular.

This means PQRS is a square.

4 0
3 years ago
Cuánto costará cercar una finca cuadrada de 14 metros de lado a razón de $150 el metro lineal de alambrada
disa [49]

Answer:

$ 2100

Step-by-step explanation:

De la pregunta anterior:

1 metro de cerca de alambre = $ 150

14 metros = x

Cruz multiplicar

x = 14 × $ 150

x = $ 2100

Por lo tanto, costaría $ 2100 por una cerca de 14 metros

6 0
3 years ago
Which equation represents a proportional relationship? A) y = x 8 B) y = 8 x C) y = x 8 + 8 D) y = 8 x + 8
Liula [17]

Answer:

B y=8x

Step-by-step explanation:

A proportional relationship must go through the point x=0, y=0 and be in the form y=kx  where x is a constant

A) y = x^8

B) y = 8 x

C) y = x^8 + 8

D) y = 8 x + 8

The only points that is in the form y= kx is option B

C and D do not go through x=0, y=0  and A is not in the form y=kx where k is a constant

6 0
3 years ago
Determine how far the vehicle travels in 3 hours.
tresset_1 [31]

Answer:

90 miles

Step-by-step explanation:

1 1/2 is half of 3 so just multiply 45 by two

8 0
2 years ago
Point Q' is the image of Q(5, -3) after a translation down 2 units and right 4 units. What are the coordinates of Q'?
ra1l [238]

Answer:

A. (9,-5)

Step-by-step explanation:

Translation down is -2 to the y coordinate, which is (5,-5). Then you translate it right 4 units, which is +4 to the x coordinate, so the final coordinate is (9,-5).

5 0
3 years ago
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