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2 years ago

Find the distance between (1, 3) and (-2, -6) and put it in simplest radical form

Mathematics

2 answers:

julia-pushkina [17]2 years ago

5 0

Answer:

$D=\sqrt{90}\ or\ D=9.49$

Step-by-step explanation:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\D=\sqrt{(-2-1)^2+(-6-3)^2}\\\\D=\sqrt{(-2-1)^2+(-6-3)^2} \\\\D=\sqrt{(-3)^2+(-9)^2} \\\\D=\sqrt{9+81} \\\\D=\sqrt{90}\\\\D=9.49$

Hope this helps!

GarryVolchara [31]2 years ago

3 0

Answer:

$\tt 9.48$

Step-by-step explanation:

(1,3) and (-2,-6)

$\tt Distance= \sqrt{(-6-3)^2+(-2-1)^2}$

$\tt =\sqrt{9^2+3^2}$

$\tt =\sqrt{81+9} =\sqrt{90}$

$\tt Distance=\sqrt{90} =9.48$

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PART A: A landmark on the first map is a triangle with side lengths of 3 cm, 4 cm, and 5 cm. What are the side lengths of the tr

Greeley [361]

Complete Question:

Johnny printed two maps of a walking trail near his home. The length of the walking trail on the first map is 8 cm.

(a) Choose a length between 5 cm and 15 cm for the walking trail on the second map: ________cm.

(b) Determine the scale factor from the first map to the second map.

(c) A landmark on the first map is a triangle with side lengths of 3 cm, 4 cm, and 5 cm. What are the side lengths of the triangle landmark on the second map?

(d) Draw one of the triangles from part C. Label the side lengths and vertices accordingly. You may use this drawing tool or draw your triangle on paper:

Answer:

(a) Length = 4cm

(b) Scale factor = 0.5

(d) See attachment for triangle

Step-by-step explanation:

(a) Choose a length between 5 cm and 15 cm

$Length =4cm$ <em>--- This is solely up to you (you can make use of any length between 5 cm and 15 cm)</em>

(b) The scale factor

The scale factor (k) is calculated as:

$k = \frac{New\ Length}{Old\ Length}$

$k = \frac{4cm}{8cm}\\$

$k = 0.5$

(c) What are side lengths of 3 cm, 4 cm, and 5 cm on the second landmark

Using:

$k = \frac{New\ Length}{Old\ Length}$

The old lengths, in this case are: 3cm, 4cm and 5cm

Make New length the subject

$New\ Length = k * Old\ Length$

When $Length = 3cm$

$New\ Length = 0.5 * 3cm = 1.5cm$

When $Length = 4cm$

$New\ Length = 0.5 * 4cm = 2cm$

When $Length = 5cm$

$New\ Length = 0.5 * 5cm = 2.5cm$

So: 3cm, 4cm and 5cm are represented by 1.5cm, 2cm and 2.5cm respectively, on the second scale

(d) See attachment for triangle

7 0

3 years ago

The system of equations is graphed on the coordinate plane.

ehidna [41]

Answer: The solution is (3, -2)

This means that x = 3 and y = -2 pair up together.

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Explanation:

The solution is where the two lines cross. Note if we started at the origin (0,0) and moved to the right 3 units, and then down 2 units, we would arrive at the location (3, -2).

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

As a way to check, we can plug x = 3 into each equation. We should get y = -2 as a result for each equation

y = (-5/3)x + 3

y = (-5/3)*3 + 3

y = -5+3

y = -2

The first equation is confirmed. Let's check the second equation

y = (1/3)x - 3

y = (1/3)*3 - 3

y = 1 - 3

y = -2

Both equations have the y value equal -2 when x = 3. Therefore, the overall solution is confirmed.