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3 years ago

What expression gives the distance between the points 5,1 and 9,-6

Mathematics

1 answer:

notka56 [123]3 years ago

3 0

Answer:

Distance between the points 5,1 and 9,-6 is 8.0622

Explanation:

Given points = (5,1) and (9,-6)

The square root of this is the distance between the points Distance can be calculated

from the expression= $\sqrt{(x 2-x 1)^{2}+(y 2-y 1)^{2}}$

= $\sqrt{(9-5)^{2}+(-6-1)^{2}}$

= $\sqrt{(4)^{2}+(-7)^{2}}$

= $\sqrt{16+49}=\sqrt{65}=8.0622$

Distance (d) from given points = (5,1) and (9,-6) is 8.0622.

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3 years ago

Niles and Bob sailed at the same time for the same length of time. Niles' sailboat traveled 36 miles at a speed of 6 mph, while

kykrilka [37]

Answer:

Niles and Bob were traveling for 6 hours.

Step-by-step explanation:

The speed or rate at which an object is moving can be computed using the formula:

$s=\frac{d}{t}$

Here:

s = speed

d = distance traveled

t = time taken

It is provided that Niles and Bob sailed at the same time for the same length of time.

Speed of Niles sailboat is, s₁ = 6 mph.

Distance traveled by Niles' sailboat is, d₁ = 36 miles.

Speed of Bob's sailboat is, s₂ = 16 mph.

Distance traveled by Bob's sailboat is, d₂ = 96 miles.

It took both Niles and Bob the same time to travel the respective distance.

Compute the time it took Niles to travel 36 miles at 6 mph speed as follows:

$t_{1}=\frac{d_{1}}{s_{1}}$

$=\frac{36}{6}\\=6$

It took Niles 6 hours to travel 36 miles at 6 mph speed.

Compute the time it took Bob to travel 96 miles at 16 mph speed as follows:

$t_{2}=\frac{d_{2}}{s_{2}}$

$=\frac{96}{16}\\=6$

It took Bob 6 hours to travel 96 miles at 16 mph speed.

Thus, Niles and Bob were traveling for 6 hours.

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3 years ago

Here are the vertices of rectangle FROG: (-2,5),(-2,1),(6,5),(6,1). Find the perimeter of this rectangle. If you get stuck, try

ryzh [129]

Answer:

Part 1) The perimeter of rectangle is equal to 24 units

Part 2) The area of rectangle is equal to 32 square units

Step-by-step explanation:

Part 1) Find the perimeter of rectangle

we know that

The perimeter of rectangle is equal to

$P=2(L+W)$

where

L is the length of rectangle

W is the width of rectangle

we have

$F(-2,5),R(-2,1),O(6,1),G(6,5)$

Plot the figure to better understand the problem

using a graphing tool

see the attached figure

Remember that in a rectangle opposite sides are congruent and the measure of each interior angle is equal to 90 degrees

$FG=RO=L\\RF=OG=W$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance FG

$F(-2,5),G(6,5)$

substitute the values

$d=\sqrt{(5-5)^{2}+(6+2)^{2}}$

$d=\sqrt{(0)^{2}+(8)^{2}}$

$FG=8\ units$

step 2

Find the distance RF

$R(-2,1),F(-2,5)$

substitute the values

$d=\sqrt{(5-1)^{2}+(-2+2)^{2}}$

$d=\sqrt{(4)^{2}+(0)^{2}}$

$RF=4\ units$

step 3

Find the perimeter

$P=2(L+W)$

we have

$FG=RO=L=8\ units\\RF=OG=W=4\ units$

substitute

$P=2(8+4)=24\ units$

Part 2) Find the area of rectangle FROG

we know that

The area of rectangle is equal to

$A=LW$

we have

$FG=RO=L=8\ units\\RF=OG=W=4\ units$

substitute

$A=(8)(4)=32\ units^2$

8 0

3 years ago