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
Need help quick someone help!
A school sold a total of 250 tickets to a show. Adult tickets cost $7.25 and student tickets cost $5.50. At the end of the evening the amount of money
collected was $1,602.50. Write and solve a system of equations to determine the number of student tickets sold
В І ца
7.25x+5 5y=1,602.50
1 / 10000 Word Limit
Answer:
The system of equations is:
x + y = 250 (1)
7.25x + 5.50y = 1602.50 (2)
with x = Adult tickets
y= student tickets
Solution
Let's equation (1)
x+y=250
x=250-y (a)
subtitute x in aquation (2)
7.25(250 - y) + 5.50y=1602.50
1812.50 - 7.25y + 5.50y= 1602.50
1812.50 -1.75y = 1602.50
-1.75y = 1602.50 - 1812.50
-1.75y = -210 ↔multiply both sides by (-1) to remove the minus sign
y= 210/1.75
y= 120
Substitute y in equation (1)
x + 120 = 250
x= 250 - 120
x =130
Let's check our results in equation (1)
x + y =250
120 + 130= 250 ↔ 250 = 250
At the end of the evening they 120 students tickets and 130 adults tickets
Step-by-step explanation:
You can check the results in any of the equations
An entreprenuer sold a damage fan for 4560 thereby incurring 20% on the cost price determine the cost of the fan
Answer:
5,700
Step-by-step explanation:
Let
x = total cost of the fan
The entrepreneur incurred 20% on the cost price
Selling price = 4560
Therefore, The selling price = 80% of the total cost of the fan
4560 = 80% of x
4560 = 80/100 * x
4560 = 0.8 * x
4560 = 0.8x
x = 4560/0.8
x = 5,700
x = total cost of the fan = 5,700
The triangles shown below must be congruent.?
True or false
Answer:
True
Step-by-step explanation:
Angle-Angle-Side congruency
Answer:
A. True
Step-by-step explanation:
Since, two corresponding angles of the triangles are congruent. So, third angle will automatically be congruent. Hence, by AAA postulate both the triangles will be congruent. Therefore. Option A. TRUE is the correct answer.These tables of values represent continuous functions. For which function will the y-values be the greatest for very large values of x?
PlzzPlease help me bunnies <3
No monkey business plz. Or I will report
It's C.
The value is increasing threefold relative to the previous step.
all other function values increase by a fixed amount and are therefore linear
Why is this a function?
X Y
3. -1
0.
0
-3
-6. 2
(3 and 0 are both assigned to 0)
This is a function because each element in the domain has one and only distinct image in the co-domain.
BRANLIEST FOR CORRECT ANSWER ASAP
Complete the statement about the tables below. Then, choose a rule for each.
x y
0 5
1 7.5
2 11.25
This table represents a(n)
relationship.
Rule:
x y
0 -6
1 12
2 30
This table represents a(n)
relationship.
Rule:
Answer:
Step-by-step explanation:
First rule:- Each value of y after the first one is obtained by multiplying the previous value by 1.5, ( Note 11.25 / 7.5 = 1.5 and 7.5 / 5 = 1.5).
The relationship is : a(n) = 5 * 1.5^(n-1)
Second Rule:- Note:- 12 - (-6) = 18 and 30 - 12 = 18. So we add 18 to get the next term in this rule.
Relationship is : a(n) = -6 + 18(n - 1).
what do you means by. India gate
Answer:
The India Gate (formerly known as the All India War Memorial) is a war memoria)
Step-by-step explanation:
it's a place
Which of the expressions are equivalent to the one below? Check all that
apply.
2. (4+9)-(3.2)
A. (3.2)-(2.4) + (
29)
O B. (2+4). (2 + 9)-3.2
C. 2.4 +9-3.2
D.2.4+ (2.9) - (2.3)
Answer:
The answer is C because its the only one that adds up correctly
None of the given expressions are equivalent to (4 + 9) - (3 . 2).
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
We can simplify the given expression as:
(4 + 9) - (3 . 2) = 13 - 3.2 = 9.8
Now, we can check which of the given expressions is equivalent to 9.8:
A.
(3 . 2) - (2.4) + (2.9) = 3.7
(not equivalent)
B.
(2 + 4) (2 + 9) -3 . 2 = 84.8
(not equivalent)
C.
2.4 +9 - 3.2 = 8.2
(not equivalent)
D.
2.4 + (2.9) - (2.3) = 3.0
(not equivalent)
Therefore,
None of the given expressions are equivalent to (4 + 9) - (3 . 2).
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The complete question.
Which of the expressions is equivalent to the one below?
Check all that apply.
(4 + 9) - (3 . 2)
A. (3 . 2) - (2.4) + (2.9)
B. (2 + 4) (2 + 9) -3 . 2
C. 2.4 + 9 - 3.2
D. 2.4 + (2.9) - (2.3)
Simplify using the distributive property: 5(2x + 7). Show all of your work.
Answer:
10x + 35
Step-by-step explanation:
Given
5(2x + 7) ← multiply each term in the parenthesis by 5
= 5(2x) + 5(7)
= 10x + 35
Answer:
10x+35
Step-by-step explanation:
5×2x=10x
5×7=35
=10x+35
in a survey of 100 cars,47 were white,23 were blue and 30 were red.express each of these numbers as a percentage of the total.
Answer:
white- 47% Blue-23% Red- 30%
Step-by-step explanation:
White cars- (47/100)*100= 47%
Blue cars- (23/100)*100=23%
Red cars- (30/100)*100=30%
can someone please answer
Answer:
The answer is 49 degrees
Step-by-step explanation:
The total we are getting to is 180, we have 131. Subtract to find the missing number that makes it 180 which is 49 because 180 minus 131 is 49.
Answer:
x = 49 °
Step-by-step explanation:
These both angles are located at the straight line. So, the sum of both angles are 180 ° .
x + 131 ° = 180 °
subtract 131 ° from 180 °
x = 180° - 131 °
x = 49 °
The average height of middle school students at Seton Grove School is found to be 5.25 feet. Which sample makes this generalization valid?
Answer:
every other student who enters the school
Step-by-step explanation:
It is given that the middle school students have an average height of 5.25 feet. The students belongs to Seton Grove School.
It means that every student who comes to this school or enters the school has a height that is around 5 feet or more.
Thus we can say that every other student who enters the school has a average height of 5.25 feet.
This sample makes the generalization about the heights of the school students valid.
Answer:
c
Step-by-step explanation:
correct on edmentum / plato
Astronauts use a tool in space that weighs 5 ounces on Earth. How many grams does the tool weigh? Round your answer to the nearest hundredth.
You need to convert 5 oz into grams.
1 oz = 28.3495 g
5 oz * 28.3495 g/oz = 141.75 g
Answer: 141.75 g
PLEASEEEEEEEEE HELPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
The correct algebraic expression is [tex]8+2c[/tex] or also, [tex]2c+8[/tex] because they are the same thing.
Step-by-step explanation:
Hope this helps and,
pls let me know if it was correct.
Nadia has a $15 gift card to an online music store. Each song at the store costs $0.99. The equation m = 15 - 0.99s represents the amount of money, m, Nadia has left on the gift card after buying 5 songs. a.
The independent variable is b.
How does the amount of money left on the card change for each extra song Nadia buys?
Show your work. and the dependent variable is
Answer:
All I know is she had 10.05 left
MATH HELP PLEASE ANSWER ASAP
Step-by-step explanation:
QR = 1.5
TS = 2
TP = 3.8
RS = 1.4
PQ = 2.6
A right triangle has side lengths d, e and f as shown below use these lengths to find cos x, tan x and sin x
SOMEONE HELP ASAP PLZ
Answer:
To solve for the trigonometric functions of x, we need to recall the ratios they represent as shown below.
sin x = O/H
cos x = A/H
tan x = O/A
where O stands for opposite, A for adjacent, and H for hypotenuse. So, for example, the sine of x is equal to the side opposite of angle x over the hypotenuse. The same goes for cosine and tangent. Using the diagram attached, we have the expressions of the trigonometric functions as shown below.
sin x = f/d
cos x = e/d
tan x = f/e
Step-by-step explanation:
The trigonometric ratio's as per given side length of a triangle are as follow,
cosx = f/e , sinx = d/e , and tanx = d/f.
Let us consider triangle name as ABC,
Measure of angle ABC = x degree
Measure of angle BAC = 90 degree
Side length AB = f
Side length AC = d
Side length BC = e
For angle x ,
AC is the opposite side , AB is the adjacent side, and BC is the hypotenuse.
cosx = adjacent side / hypotenuse
= f / e
sinx = opposite side / hypotenuse
= d / e
tanx = opposite side / adjacent side
= d / f
Therefore, the value of the trigonometric ratio for the given side length of a triangle are cosx = f/e , sinx = d/e , and tanx = d/f.
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Brainliest goes to whoever answers correctly and explains also if you want extra points answer my other questions
graph 1 - clue 3
graph 2- clue 2
graph 3- clue 4
graph 4 - clue 1
Answer:
Graph 1 - Clue 3 / Kareem
the points fits neatly in between the rest of the plot
Graph 2 - Clue 2 / Paloma
same reasoning as above, located in the middleof the other points. but note that y and x are in switched order
Graph 3 - Clue 4 / Jonah
(25,10) fits just nice right in the middle of the other points. note that written as an ordered pair, or point, x has to be on the left side inside the parentheses
Graph 4 - Clue 1 / Genevieve
just fitting into the pattern on the lower right end of the plot
Which of the following is a composite number?
Ο Α. Ο
O B. 19
O C. 63
O D. 1
Answer: The letter C
Option C is correct, 63 is the composite number.
What is Number system?A number system is defined as a system of writing to express numbers.
Composite numbers are numbers that have more than two factors.
0 is not a composite number.
19 is a prime number because it is divided by itself so it is not a composite number.
63 is a composite number because it has more than two factors.
The factors of 63 are 1, 7 , 9
1 is not a prime number as it does not have factors.
Hence, Option C is correct, 63 is the composite number.
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Paul rolls a fair dice 174 times.
How many times would Paul expect to roll an odd number?
Answer:
87 times as the dice has 3even numbers and 3 odd numbers so chance is 50% so half of 174 is 87.....times
Step-by-step explanation: hope this helps
Answer:
87 times
50% of the time
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
6 numbers
1, 3, 5 are odd
3/6 in one roll
3/6 × 174 = 87
Why do some functions not have x intercepts?
A farmer has developed a new type of fertilizer. This new fertilizer costs 20
percent more to produce than the old fertilizer but has better results: The
same land now produces 25 percent more crops each year.
Which statement best describes one way the farm will be affected by using
this new fertilizer?
A. The farm's marginal cost for fertilizer will decrease.
B. The farm's marginal cost for fertilizer will increase.
C. The farm's opportunity cost for using fertilizer will decrease.
D. The farm's opportunity cost for using fertilizer will increase.
Answer:
A
Step-by-step explanation:
Marginal cost is the change in total cost as a result of increasing output by one unit
Marginal cost = Δcost / Δquantity
0.2 / 0.25 = 0.8
The marginal cost would decrease because the change in output is higher than the change in total cost
Marginal benefit would increase
Opportunity cost is the cost of the opportunity forgone when one alternative is chosen over other alternatives. There is no enough information given to determine the impact on opportunity cost
Please help the question is in the picture.
Answer:
[tex]\text{A. }\frac{5}{6}\pi x^2[/tex]
Step-by-step explanation:
The area of a sector with measure [tex]\theta[/tex] is equal to [tex]r^2\pi\cdot \frac{\theta}{360}[/tex]
Since there are 360 degrees in an angle, the measure of sector K must be 360-60=300 degrees.
What we know:
[tex]\theta[/tex] of [tex]300^{\circ}[/tex] [tex]r[/tex] of [tex]x[/tex]Thus, the area of the sector is [tex]x^2\pi\cdot \frac{300}{360}=\boxed{\text{A. }\frac{5}{6}\pi x^2}[/tex]
Need help with number one please
Answer:
answer is 4 because EJ is 4, and GJ is congruent to EJ meaning they are the same size.
OMG DUE IN 40 MINUTESSSS!!
Answer:
17 1/3 52/3
Step-by-step explanation:
3x+y=38
3x+2y=52
-y=14
y=-14
3x+-14=38
3x-14=38
3x=38+14
3x=52
3x/3=52/3
x=171\3
17 is a whole number then 1 divided by 3 . thus is x
What is the least number of apples that can be shared equally among either 6, 10 or 15 children?
Answer:
If you mean with out splitting up the apple then we could just give one apple to each child so it would look like this
6 children 6 apples
10 children 10 apples
15 children 15 apples
A ratio of peanuts to raisins is 5 to 4. A bag of the snack mix contains 200 peanuts. How many raisins are in the bag
Answer:
160 raisins
Step-by-step explanation:
First, the ratio of peanuts to raisins will be 5:4.
Next, to fine the number to multiply the 4 by, you will divide 200 by 5.
You divide the 200 by 5 because that is how many peanuts there are in the bag and the ratio is 5:4 as stated above.
So 200 divided by 5 is 40. You will take that 40 and then multiply it by 4 to get 160.
So the end result is there are 160 raisins in the bag, and the final ratio would be 200:160
there are four consecutive even numbers. The second number is represented by x. find the sum of four numbers in term of x
Answer:
Sum of the four numbers in terms of x would be 4x+4
Step-by-step explanation:
x-2 + x + x+2 + x+4 = sum
4x+4 = sum
What is DM?
22 cm
30 cm
38 cm
76 cm
Answer:
38cm
Step-by-step explanation:
38 is the answer . hope it helps.
Answer:
c. 38 cm
Step-by-step explanation: