The epicenter is located at (-5, 1) on the coordinate plane.
Explanation:To find the coordinates of the epicenter, we need to find the average of the coordinates of the three receiving stations. The x-coordinate of the epicenter is (3 - 13 - 5)/3 = -5, and the y-coordinate is (3 - 5 + 3)/3 = 1. Therefore, the epicenter is located at (-5, 1) on the coordinate plane.
Learn more about Coordinates of the epicenter here:https://brainly.com/question/14795712
#SPJ11
The coordinates of the epicenter of earthquake are (-1, 0).
The epicenter of the earthquake is the point that is equidistant from stations X, Y, and Z. This is essentially the solution to a system of three equations representing the distances from the epicenter to each of the three stations.
The equations are derived from the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] ,
where [tex](x_1,y_1)[/tex] and [tex](x_2, y_2)[/tex] are the coordinates of the two points and d is the distance between them.
For station X at (3,3), the distance to the epicenter (x,y) is 5 units. So, the equation is:
[tex](x - 3)^2 + (y - 3)^2 = 5^2 = 25 \text{ ....(1)}[/tex]
For station Y at (-13,-5), the distance to the epicenter is 13 units. So, the equation is:
[tex](x + 13)^2 + (y + 5)^2 = 13^2 = 169\text{ ....(2)}[/tex]
For station Z at (-5,3), the distance to the epicenter is 5 units. So, the equation is:
[tex](x + 5)^2 + (y - 3)^2 = 5^2=25 \text{ ....(3)}[/tex]
Solving this system of equations will give the coordinates of the epicenter.
Subtract equation (1) from equation (2), we get:
[tex](x^2+26x+169+y^2+10y+25)-(x^2-6x+9+y^2-6y+9) = 144\\\\\text{Simplifying, we get:}\\32x+16y+176=144\\32x+16y = -32\\\text{Divide by 16 on both sides of the equation, we get:}\\2x + y = -2[/tex]
Subtract equation (1) from equation (3), we get:
[tex](x+5)^2+(y-3)^2-(x-3)^2-(y-3)^2 = 0\\x^2+10x+25-(x^2-6x+9)=0\\16x + 16 = 0\\\text{Dividing by 1 on both sides, we get}\\x + 1 =0\\\text{We get:}\\x = -1[/tex]
Putting x = -1 in the equation 2x + y = -2, we get:
2(-1) + y = -2
We get,
y = 0
So, the coordinates of the epicenter of earthquake are (-1, 0).
Simplify the expression 3bx4b
How much would $400 invested at 9% interest compounded continuously be worth after 3 years? Rounded by the nearest cent
The perimeter of a parallelogram is 72 meters. The width of the parallelogram is 4 meters less than its length. Find the length and the width of the parallelogram
Answer:
Length is 20 meters and width is 16 meters.
Step-by-step explanation:
Given: Perimeter of parallelogram is 72 meters.
Width of the parallelogram is 4 meters less than its length.
To find: Length and width of the parallelogram.
Solution: Let the length of the parallelogram be x meters. So, width of the parallelogram is [tex]x-4[/tex] meters.
As per question,
[tex]x+x+x-4+x-4=72[/tex]
[tex]4x-8=72[/tex]
[tex]4x=72+8[/tex]
[tex]4x=80[/tex]
[tex]x=\frac{80}{4}[/tex]
[tex]x=20[/tex]
Hence, length of the parallelogram is 20 meters, and width of the parallelogram is [tex]20-4=16[/tex] meters.
An athlete trains on a circular track of radius 40 m and jogs 10 laps each day, 5 days a week. How far does he jog each week? Round the answer to the nearest whole number of metres.
He sum of three consecutive integers is −369−369. find the three integers.
Is the number x positive? (1) on the number line, 0 is closer to x – 1 than to x. (2) on the number line, 0 is closer to x than to x + 1?
I hope that helps!
Can the following question be considered a statistical question and why or why not? Do students at Bryan Middle School exercise?
Answer:
this is a multiple choice question with 4 answers
Yes, it specifies the population
No, it does not specify the population
Yes, it anticipates enough variability in responses
No, it does not anticipate enough variability in responses
I think the answer is.......... (Drum roll please)........... D.
Step-by-step explanation:
There is not any variability in this question it is just a yes or no question. If the question was "How long does an average person exercise for "
A square piece of cloth, which is 10 meters on a side, is cut across the diagonal to form two right triangles. What is the length of the diagonal cut?
Answer:
D
Step-by-step
The answer is the square root of 288
Ted weighs twice as much as Julie. Mike weighs three times as much as Julie. Together, Ted, Mike, and Julie weigh 210 lbs. What is the weight of each person?
Amanda drove 355 miles using 17 gallons of gas. At this rate how many gallons of gas would she need to drive 284 miles?
I need the answer Algebra question
Answer: $32
Step-by-step explanation:
add 7+9+12+4 =32
really need a answer and explanation for this
Alina is able to swim at a rate of about 2.5 miles per hour. Talia is able to swim at a rate of 1.8 meters per second. Which statement comparing the two swimmers is accurate?
1 mile 1,609 meters
Alina swims about 0.7 miles per hour faster than Talia.
Talia swims about 0.7 miles per hour faster than Alina.
Alina swims about 1.5 miles per hour faster than Talia.
Talia swims about 1.5 miles per hour faster than Alina. pls help
Answer:
Talia swims about 1.5 miles per hour faster than Alina.
Step-by-step explanation:
Since, 1 miles = 1609 meter and 1 hour = 60 seconds,
⇒ [tex]\text{ 1 miles per hour } = \frac{1609}{3600}\text{ meter per seconds}[/tex]
⇒ [tex]\text{ 1 meter per seconds } = \frac{3600}{1609}\text{ miles per hours}[/tex]
Here, The speed of Alina = 2.5 miles per hour = 2.5 × 1609/3600
[tex]=\frac{4022.5}{3600} \text{ meter per seconds }[/tex]
[tex]=1.11736111\text{ meter per seconds}[/tex]
And, the speed of Talia = 1.8 meter per second,
Since 1.8 > 1.11736111
⇒ Talia swims faster than Alina.
And, the difference between their speeds = 1.8 - 1.11736111 = 0.68263889 meter per seconds
= 0.68263889× 3600/1609 miles per hour
= 1.52734618 miles per hour ≈ 1.5 miles per hour ,
⇒ Fourth option is correct.
How do you solve -2(6x+3)=-27–5x ?
The number of minutes you can talk on a cell phone decreases as the phone's battery charge decreases.
causation
correlation
association
no relationship
The relationship described in the question between the number of minutes you can talk on a cell phone and the phone's battery charge is correlation. Correlation refers to a statistical relationship between two variables, where as the battery charge decreases, the number of minutes you can talk on the phone also decreases. It does not imply a causal relationship.
Explanation:The relationship described in the question between the number of minutes you can talk on a cell phone and the phone's battery charge is correlation.
Correlation refers to a statistical relationship between two variables. In this case, as the battery charge decreases, the number of minutes you can talk on the phone also decreases. It does not imply a causal relationship, where one variable directly causes the change in the other.
For example, if the battery is fully charged, you may be able to talk on the phone for several hours. However, as the battery charge decreases, your talk time will gradually decrease until the battery is completely drained and you can no longer use the phone.
The number of minutes you can talk on a cell phone decreases as the battery charge decreases due to a causation relationship.
The correct answer is causation. This is because there is a direct cause-and-effect relationship between the phone's battery charge and the number of minutes you can talk on the phone. As the battery charge decreases, it limits the phone's ability to function, thereby reducing the available talk time.
For example, if your phone starts with 100% battery and allows for 240 minutes of talk time, a drop to 50% battery might only allow for 120 minutes of talk time as the battery depletes. This reduction in talk time is a direct result of the decreasing battery charge, illustrating a causal relationship.
It's important to differentiate this from correlation or association, which would imply a relationship without direct causation. Here, the reduction in battery charge directly causes the reduction in talk time, proving it to be a cause-and-effect relationship.
A car dealership increased the price of a certain car by 13% . The original price was $41,200
For each handmade greeting card jacqui sells, she makes a profit of $0.35. In one week , she made a profit of $42 .she sells the cards for $0.75 each.
Part A: About how much did she earn before paying expenses?
Answer:
$ 90
Step-by-step explanation:
Given,
The profit in each card = $ 0.35,
If she sold x cards,
Then the total profit she earned = profit in each card × number of cards
= 0.35x dollars,
According to the question,
0.35x = 42
[tex]\implies x = \frac{42}{0.35}=120[/tex]
Thus, she sold 120 cards,
Now, if the selling price of each card = $ 0.75,
Hence, total earning before paying expenses
= selling price of each card × total cards
= 0.75 × 120 = $ 90
what is (4−5y)−2(3.5y−8)?
Thank you!!
Which postulate or theorem, if any, could be used to prove the triangles congruent? If not
enough information is given, write not enough information.
Answer: on d. it's, you
weren;t given enough information
Step-by-step explanation:
ur welcome.
On Monday, three hundred twenty students went on a trip to the zoo. All seven buses were filled and five students had to travel in cars. How many students were in each bus?
How many lines does wide ruled paper have?
What is the domain of the inverse of a relation?
What is −20÷45 ?−25−16−116−125
Its -25 i just did the test
In the equation b= a-2, which is the independent variable and which is the dependent variable ? Explain???? need help i don't understand
What is the vertex of the graph of the function below? y = x2 - 4x + 3
The vertex of the function y = x2 - 4x + 3 is at (2,-1). You can find this by using the formula -b/2a for the x-coordinate of the vertex and then substituting this x-value into the original equation to find the y-coordinate.
Explanation:The function you are asking about, y = x2 - 4x + 3, is a quadratic function, and the graph of a quadratic function is a parabola.
The vertex of this parabola can be found using the formula -b/2a for the x-coordinate and then substituting this value into the original equation to find the y-coordinate. For this function, the coefficients a and b (from the general form ax2 + bx + c) are 1 and -4 respectively. Using the formula, the x-coordinate of the vertex is -(-4)/2*1 = 2. We then substitute x = 2 into the original equation to find y = (2)2 - 4*(2) + 3 = -1. Thus, the vertex of the function y = x2 - 4x + 3 is at (2,-1).
Learn more about Vertex of a Quadratic Function here:https://brainly.com/question/11258039
#SPJ3
A garden table and a bench cost $1025 combined. The garden table costs $75 more than the bench. What is the cost of the bench?
Show all work please!!!!!!
1. PB (there is a line on top) is a line segment on a number line. It has endpoints at -2 and 12. What is the coordinate of its midpoint?
2. The midpoint of CD (there is a line on top) is E(-1, 0). One endpoint is C(5,2). What are the coordinates of the other endpoint?
3. Explain the distance formula. Then use it to calculate the distance between A(1, 1) and B(7, -7).
The density of an object can be calculated by dividing the object's mass by its volume. A rectangular prism has a density of 15g/cm3. The prism has a mass of 5,625 g. The length of the object is 5 cm. The width of the object is 3 cm. What is the height of the object?
density = mass/ volume
volume = mass/ density
volume = 5625 / 15 = 375 cm^3
volume = l x w x h
375 = 5 * 3 * X
375 = 15
x = 375/15 = 25
height = 25 cm
The height of the object is 25 cm and this can be determined by using the formula of density and volume.
Given :
The density of an object can be calculated by dividing the object's mass by its volume.A rectangular prism has a density of 15g/[tex]\rm cm^3[/tex]. The prism has a mass of 5,625 g. The length of the object is 5 cm. The width of the object is 3 cm.The height of the object can be determined by using the formula of density. The formula of density is given by:
[tex]\rm d = \dfrac{m}{V}[/tex]
where d is the density, m is the mass, and V is the volume.
Now, substitute the known terms in the above formula.
[tex]\rm V = \dfrac{5625}{15}= 375\;cm^3[/tex]
Now, the volume of an object is given by:
[tex]\rm V = l \times w\times b[/tex]
Now, substitute the known terms in the above formula.
375 = 5 [tex]\times[/tex] 3 [tex]\times[/tex] h
h = 25 cm
For more information, refer to the link given below:
https://brainly.com/question/6034174
What's the answer to 3/2(16n+3)=24n
For a percentage increase of 36%, state the multiplier