Answer:
a. (-3, 6)
b. 268.3 m
Step-by-step explanation:
a. Determine the coordinates of the tennis court.
Let (x,y) be the coordinates of the tennis court. Since we have equal distances from the tennis court to each residence, we have using the equation for distance between two points (x₁,y₁) and (x₂,y₂), d = √[(y₂ - y₁)² + (x₂ - x₁)²]. Using the first two residences, (-6, 12) and (0,0) as (x₂,y₂) and (x, y) = (x₁,y₁), So,
d = √[(12 - y)² + (-6 - x)²]
d = √[(12 - y)² + (6 + x)²]
d = √[(144 - 24y + y² + 36 + 12x + x²]
d = √x² + y² + 12x - 24y + 180
d² = x² + y² + 12x - 24y + 180 (1)
Also, with (x₂, y₂) = (0,0) we have
d = √[(0 - y)² + (0 - x)²]
d = √[( - y)² + (- x)²]
d = √[y² + x²]
d = √[x² + y²]
d² = x² + y² (2)
Also, with (x₂, y₂) = (3,9) we have
d = √[(9 - y)² + (3 - x)²]
d = √[(81 - 18y + y² + 9 - 6x + x²]
d = √(x² + y² - 6x - 18y + 90)
d² = x² + y² - 6x - 18y + 90 (3)
Substituting (2) into (1), we have
d² = x² + y² + 12x - 24y + 180 (1)
d² = d² + 12x - 24y + 180 (1)
d² - d² = 12x - 24y + 180
12x - 24y + 180 = 0
12x - 24y = -180
dividing through by 12, we have
x - 2y = -15 (4)
Substituting (2) into (3), we have
d² = x² + y² - 6x - 18y + 90 (3)
d² = d² - 6x - 18y + 90 (3)
d² - d² = - 6x - 18y + 90
- 6x - 18y + 90 = 0
- 6x - 18y = -90
dividing through by -6, we have
x + 3y = 15 (5)
Subtracting (5) from (4), we have
x - 2y = -15 (4)
-
x + 3y = 15 (5)
-5y = -30
y = -30/-5
y = 6
substituting y = 6 into (4), we have
x - 2y = -15
x - 2(6) = -15
x - 12 = -15
x = 12 - 15
x = -3
So, the coordinates of the tennis court is (-3, 6)
b. What is the distance from a residence to the court to the nearest 10th of a metre? (1unit=40m).
Using equation (2),
d² = x² + y² (2) where x and y are the coordinates of the tennis court, and x = -3 and y = 6
So,
d² = x² + y²
d² = (-3)² + (6)²
d² = 9 + 36
d² = 45
d = √45 units
Since 1 unit = 40 m,
d = √45 × 40 m
d = 6.708 × 40 m
d = 268.33 m
d ≅ 268.3 m to the nearest tenth of a metre
An animal starts from rest and accelerates to its top speed in 7 seconds. It continues at this speed for 9 seconds and then slows to a stop in a further 4 seconds. Calculate the total distance that the animal travelled
Answer:
hggffffxdfffdsddfdohgfffdedss
(-5/2) to the power of 2
Answer:
The answer of (-5/2) to the power of 2 is 6.25.
Can anyone help ? :) thanks
no se ingles xd asi que la verdad sorry aun que dime si es potensiacion
Find the volume of the prism. 5 cm 13 cm 13 cm
The lines represented by the equations y- 6x = -7 and 24y - 4x = 192 are
Answer:
negative signs
Step-by-step explanation:
What is the area of the triangle below?
3 18
A. 27 sq. units
B. 18 sq. units
C. 21 sq. units
D. 54 sq. units
Helppppp ASAP please
Answer:
A. 27 sq. units
Step-by-step explanation:
A = 1/2 · b · h
A = 1/2 · 3 · 18
A = 1/2 · 54
A = 27 sq. units
Answer:A-27
Step-by-step explanation:
A=1/2 18*3=27
The answers are
A.9
B.25
C.18
D.15
PLEASE HELPPPP
Answer:
9
Step-by-step explanation:
Because I don't know but I think I'm correct.
Help plzz
Question given below
How does 3/4 and 9/12are alike and different?
Evaluate expressions- if r=45 and t=9 what is the value of the following expression?
A.36
B.75
C.80
D.66
Answer:
[tex]d. \: \: 66[/tex]
Step-by-step explanation:
[tex]r + 63 \div t \times 3[/tex]
[tex]45+63÷9 \times 3[/tex]
[tex]45+7 \times 3[/tex]
[tex]45 + 21[/tex]
[tex]66[/tex]
Hope it is helpful...Find the range of 45, 38, 47, 42, 40, 47
At a show, there are 19 adults, 45 teenagers, and 36 children.
What is the probability that a person chosen at random from the audience is not a teenager?
Answer:
55% or 0.55 or 11/20
Step-by-step explanation:
probability the person chosen is an adult or child out of all
so 19+36/19+36+45
55/100
The probability that the selected person is not a teenager is [tex]\frac{11}{20}[/tex].
What is probability?
Probability is a measure of happening or non happening of the outcomes of the random experiment.
Probability formulaP(E) = Total number favorable of outcomes/ Total number of outcomes
Where,
P(E) is the probability of an event.
According to the given question.
Total number of adults in the audience = 19
Total number of teenagers in the audience = 45
Total number of children in the audience = 36
Total audience = 19 + 45 + 36 = 100
Now, the probability that the selected person is teenager = [tex]\frac{45}{100} = \frac{9}{20}[/tex]
Therefore,
The probability that a selected person is not a teenager
= [tex]1 -\frac{9}{20}[/tex]
= [tex]\frac{11}{20}[/tex]
Hence, the probability that the selected person is not a teenager is [tex]\frac{11}{20}[/tex].
Find out more information about probability here:
https://brainly.com/question/11234923
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Michals basketball team practiced for 2hours 40 minutes yesterday and 3 hours 15 minutes today how much longer did the team practice today than yesterday
Answer:
35 minutes
Step-by-step explanation:
The is calculated using the Subtraction operation
The number of minutes longer the team practiced today than yesterday =
Number of minutes they practiced today - Number of minutes they practiced yesterday
Number of minutes they practiced today = 3 hours 15 minutes
Number of minutes they practiced yesterday = 2hours 40 minutes
The number of minutes longer the team practiced today than yesterday =
3 hours 15 minutes - 2hours 40 minutes
= 35 minutes
Therefore, the team practiced 35 minutes longer today than yesterday
Question 3 Look at the diagram below. If XY = 7 and XZ = 30, what is the value of t? 7 2t - 1 X Y Z
Answer:
Step-by-step explanation:
go to brainly.com
Divide *° -3x– 10x+ 24 by X-2
Answer:
[tex] - 13 - \frac{2}{x - 2} [/tex]
Step-by-step explanation:
[tex] \frac{ - 3x - 10x + 24}{x - 2} [/tex][tex] \frac{ - 13x + 24}{x - 2} [/tex][tex] - 13 - \frac{2}{x - 2} [/tex]
Hope it is helpful...In the figure, m is parallel to n and mZ4 = 122°. Find the measures of the other
angles.
n
m
t
65
m26=0°
m22-1°
mZ8 = 1
m25-1°
m23=0°
m27=°
m21=°
Enter your answer in each of the answer boxes.
Review progress
Question 6
of 20
Answer:
Step-by-step explanation:
m=3x +4xm
What is the value of n?
Answer:
n = 28 degree
Step-by-step explanation:
2n + 17 + 2n - 5 + 2n = 180 degree (sum of interior angles of a triangle)
6n +12 = 180
6n = 180 - 12
n = 168/6
n = 28 degree
Which expression is equivalent to the expression shown (5^3) ^9 divided 5^12
Answer:5 exponent of 15
Step-by-step explanation:trust
Give the Solution to the System of
Equations shown below
YA
6
5
4
3
2
1
-4
-3
-2
10
1
2
3
-1
2
Answer:
Step-by-step explanation:
-10 g
Select elther relation (If the set is a relation but not a function), function (If the set is both a relation and a function), or
neither (If the set is not a relation).
F=[(x, y) |x+y=10)
A. neither
B. Function
C. Relation
Answer:
B
Step-by-step explanation:
The given set F=[(x, y) |x+y=10) is a function.
What is a function?A relation is a function if it has only One y-value for each x-value.
The set F represents a relation since it contains ordered pairs of elements. Specifically, it contains all pairs (x, y) such that x+y=10.
For example, (2, 8) and (5, 5) are elements of F since 2+8=10 and 5+5=10.
However, it is not necessarily a function since it is possible for two different x values to have the same y value, which would violate the vertical line test for functions.
For example, both (2, 8) and (8, 2) are in F since 2+8=10 and 8+2=10.
Hence, the given set F=[(x, y) |x+y=10) is a function.
To learn more on Functions click:
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if each square on the grid represents 400mi square how many miles will jacob's family travel?
Answer:
80miles
Step-by-step explanation:
Area of a square grid = L²
L is the side length of the grid
Given that Area of the square = 400mi square
400 = L²
L =√400
L = 20miles
To get the number of miles travelled, we will find its perimeter
P = 4L
P = 4(20)
P = 80miles
Hence Jacob's family travels 80miles
p(Febuary 31) Calculate the probability of the event
Answer:
You can't find the probibilty of the event because it doesn't exist
Step-by-step explanation:
Please help me with this one …..
Answer:
is the clean area the desired one (I assume, yes)?
then y <= 3x + 5
if the dotted area is the desired area, then
y >= 3x + 5
Step-by-step explanation:
the factor of x is the slope of the line expressed as y/x ratio.
clearly, the line shows that for x changing by 1 unit y changes by 3 units. so, the slope is 3/1.
that leaves us only with the 2 middle options.
for "y <=" the desired values of y for a given x must be on the line (equal) or below (smaller than the value of the line equation). that is true, if the desired area is the clear one (no dots).
so, "y >=" is true, if the dotted area is desired.
For two positive real numbers a and b, which may be equal, determine the smallest possible value of a/b + b/a
Given that tanθ almost equal to≈ 2.773 where 0<θ<π2, find the values of sinθ and cosθ. Show work.
Step-by-step explanation:
the given data is
tanθ = 2.773 and 0<θ<π/2
this implies θ = tan inverse(2.773)
⇒ θ = 70.16°
Therefore, sinθ = sin70.16° = 0.9406
similarly,cosθ = cos70.16° = 0.3393
therefore, values of sinθ and cosθ are 0.9406 and 0.3393 respectively.
help again gives brainlist
Answer:
rhombii
Step-by-step explanation:
they all look equilateral without all having right angles
John starts on the ground floor of a building. He runs up five flights of stairs, then runs
up 6 flights of stairs, then runs down 8 flights of stairs, then runs up four flights of stairs,
and then stops. Each story of the building is 11 feet high. How many feet above the
ground is John when he stops? PLS HELP
Answer:
77 feet above the ground.
Step-by-step explanation:
After going up 11 flights, (5 +6), he goes down 8, which brings you to 3 and then back up to 7 (3 +4). Since each story is 11 feet high, you multiply 7 and 11, to get a total of 77.
PLEASE HELP PLEASE IT EASY PLEASE HELP
Answer:
$3x
Step-by-step explanation:
Trust me.
help me pleaseeee i’m begging!!!!
Answer:
The student did not complete the inverse operations correctly in Step 3
Simultaneous EQUATION 3x+2y=16 2x+y=9 PLS HELP I need answer quickly
Answer:
(2, 5 )
Step-by-step explanation:
Given the 2 equations
3x + 2y = 16 → (1)
2x + y = 9 → (2)
Multiplying (2) by - 2 and adding to (1) will eliminate the y- term
- 4x - 2y = - 18 → (3)
Add (1) and (3) term by term to eliminate y
- x = - 2 ( multiply both sides by - 1 )
x = 2
Substitute x = 2 into either of the 2 equations and solve for y
Substituting into (1)
3(2) + 2y = 16
6 + 2y = 16 ( subtract 6 from both sides )
2y = 10 ( divide both sides by 2 )_
y = 5
solution is (2, 5 )
