1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mars2501 [29]
4 years ago
12

Two horses are ready to return to their barn after a long workout session at the track. The horses are at coordinates H(1,10) an

d Z(10,1). Their barns are located in the same building, which is at coordinates B(-3,-9). Each unit/grid on the coordinate plane represents 100 meters. Which horse is closer to the barn? Justify your answer.
Mathematics
2 answers:
bulgar [2K]4 years ago
7 0
H(1,10)   Z(10,1) B(-3,-9)
1st Calculate the distance H(horse) H to B(barn)
2nd Calculate the distance Z(horse) H to B(barn)
3rd Compare 


1st distance H(horse) H to B(barn) 
HB = √[(x₂-x₂)²+(y₂-y₁)₂] → √[-3-1)² + (-9-10)²]=√377 = 19.42

2nd distance ZB = √[(-3-10)²+(-9-1)²] = √269 = 16.4

HB in meter =19.42 x 100  = 1,942 m
ZB in  meter = 16.4 x 100  =  1,640 m

Obviously HB > ZB  and Z is closer to  the Barn

alexgriva [62]4 years ago
4 0
\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&H({{ 1}}\quad ,&{{ 10}})\quad 
%  (c,d)
&B({{ -3}}\quad ,&{{ -9}})
\end{array}\quad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
HB=\sqrt{(-3-1)^2+(-9-10)^2}\implies HB=\sqrt{(-4)^2+(-19)^2}
\\\\\\
HB=\sqrt{377}\implies HB\approx 19.4\cdot \stackrel{meters}{100}\implies HB\approx 1940~m\\\\
-------------------------------\\\\

\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&Z({{ 10}}\quad ,&{{ 1}})\quad 
%  (c,d)
&B({{ -3}}\quad ,&{{ -9}})
\end{array}\quad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
ZB=\sqrt{(-3-10)^2+(-9-1)^2}\implies HB=\sqrt{(-13)^2+(-10)^2}
\\\\\\
ZB=\sqrt{269}\implies ZB\approx 16.4\cdot \stackrel{meters}{100}\implies ZB\approx 1640~m
You might be interested in
Write an equation of the line that passes through (18, 2) and is parallel to the line 3y - x = -12
GarryVolchara [31]
First you need to find the slope.
You do this by adding x to both sides to get 3y=x-12
Then, you divide by three on both sides to get y=1/3x -4
to find the new y intercept you insert the point and the slope in the equation
2=1/3(18)+b 
You multiply 1/3 and 18 to get 2=6+b
Finally you subtract 6 on both sides to get -4=b.
This means that the equation of the line is the same as the given line
3 0
3 years ago
In a crayon box there are 5 dark colors for every 8 light colors. If there are 20 dark colors, how many light colors are there?
PilotLPTM [1.2K]
5x4=20 so 8x4=32 32 light colors in the box
5 0
3 years ago
Read 2 more answers
What is the input value of f(x)=−2
Korolek [52]

Answer:

2

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
martin mixes 1 cup lemonade with 4 cups cranberry juice to make his favorite drink how much cranberry juice does he need if he u
mars1129 [50]
He will need 20 cups of cranberry juice.
3 0
3 years ago
Read 2 more answers
Look at the graph: What is the slope?
Arisa [49]

Answer:

The slope is 2/3

Step-by-step explanation:

The line crosses through the blue grid lines leaving gaps on each. Find two points which cross at an intersection such as (0,30) and (30,50). Find the slope by substituting these points into the slope formula:

m = \frac{y_2-y_1}{x_2-x_1} = \frac{50-30}{30-0} =\frac{20}{30} =\frac{2}{3}

5 0
3 years ago
Other questions:
  • Harper has $15 to spend at the grocery store. She is going to buy bags of fruit that cost $4.75 and one box of crackers that coa
    10·1 answer
  • A square has an area of A square centimeters. For which value of A does a square have a side length that is a rational number?
    12·1 answer
  • HELP REALLY QUICK 15 POINTS!
    6·2 answers
  • If your annual salary is $64,710, what is your semimonthly salary?
    8·2 answers
  • 27 + 5 x 6 = what is the answer
    6·2 answers
  • My dad has 5 apples, I give him 2, how many apples does he have?
    5·2 answers
  • HELPPPPP PLEASEEEEE
    8·1 answer
  • The speed of a falling object increases at a constant rate as time increases since the object was dropped. Which graph could rep
    12·1 answer
  • [ BRAINLIEST TO CORRECT. ANSWER QUICK. PLEASE. MATH ]
    12·2 answers
  • D. (x + y, 3x-2y) = (7,11)​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!