A train leaves train station A and heads due west for 105 miles to reach train station B. Another train leaves train station A at the same time and travels 85 miles to train station C in a direction 45 north of west from station A. To the nearest mile, how far is train station C from train station B? 75 miles 109 miles 135 miles 176 miles
Answers
Answer:
135 Miles
Step-by-step explanation:
Answer:
At the nearest mile, stations B and C are 75 miles apart.
Step-by-step explanation:
In the attached image we can see all the three stations. The closest distance between stations B and C would be a straight line that can be calculate using the Cosine Rule:
[tex](BC)^2=(AB)^2+(AC)^2-2(AB)(BC)cos(\alpha)[/tex]}
Where:
AB is the distance between stations A and B
AC is the distance between stations A and C
α is the angle formed between the AC and AB railway lines
[tex](BC)^2=(105)^2+(85)^2-2(105)(85)cos(45)[/tex]
[tex]BC=75.02 miles[/tex]
So, at the nearest mile, stations B and C are 75 miles apart.
Related Questions
if a triangle has a perpendicular, does that mean it is an equilateral triangle?
Answers
Write an equation of the line that passes through point (5,6) and has a slope of 2.
Answers
The equation of the line through (5,6) has a slope of 2 will be y=2x-4.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that, the line passes through (-10,-7)and (-5,-9).
We have to find the equation of the line through given points,
The slope of the line is,
m= 2
The equation of the line is obtained as,
y-y₁=m(x-x₁)
y-(6)=-2(x-(5)
y-6=2x-10
y=2x-10+6
y=2x-4
Thus, the equation of the line through (5,6) has a slope of 2 will be y=2x-4.
Learn more about the straight line here:
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Final answer:
To find the equation of the line with a slope of 2 passing through the point (5,6), we use the point-slope formula and obtain y = 2x - 4.
Explanation:
To write an equation of a line that passes through a given point, such as (5,6), with a given slope of 2, we can use the point-slope form of a linear equation, which is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting the given point and slope into this formula, we have:
y - 6 = 2(x - 5)
Expanding this equation and solving for y, we get:
y - 6 = 2x - 10
Add 6 to both sides to find the y-intercept:
y = 2x - 4
This equation represents the line with a slope of 2 that passes through the point (5,6).
Can someone show me step by step?
Answers
Answer:
AB = JK = 49
Step-by-step explanation:
Since ABC = JKL
We know the length of AB has to equal the length of JK.
AB = JK
14x+7 = 5x+34
Subtract 5x from each side.
14x-5x +7 = 5x-5x+34
9x+7 = 34
Subtract 7 from each side
9x+7-7 = 34 -7
9x = 27
Divide each side by 9.
9x/9 = 27/9
x =3
AB = 14x+7
Substitute x=3
14(3) +7
42+7
AB = 49
100m In 9 3/5 seconds
Answers
Answer:
Speed = 10.42 m/secs
Step-by-step explanation:
We have been given with:-
Distance = 100m
Time taken = 9[tex]\frac{3}{5}[/tex] secs
1) First, we need to convert the mixed number 9[tex]\frac{3}{5}[/tex] to an improper fraction.
Method to convert a mixed number to an improper fraction
[tex]a\frac{b}{c} = \frac{c*a+b}{c}[/tex]
Applying the above formula, we get
9[tex]\frac{3}{5}[/tex] = [tex]\frac{5*9+3}{5}[/tex]
= [tex]\frac{45+3}{5}[/tex]
= [tex]\frac{48}{5}[/tex]
2) Now we need to convert [tex]\frac{48}{5}[/tex] into a decimal by dividing 48 by 5.
We get time taken as 9.6 secs
3) We need to find the speed using the below formula:-
Speed = [tex]\frac{Distance}{Time taken}[/tex]
Plugging the values of Distance and Time taken into the formula, we get
Speed = [tex]\frac{100}{9.6}[/tex]
= 10.416 m/secs
4) Upon rounding it to the nearest hundredth, we get
Speed = 10.42 m/secs
kim took a trip to china. upon leaving she decided to convert all of her yuan back into dollars. How many dollars did she receive if she exchanged 16 yuan at a rate of 8 yuan for $1
Answers
--
8x2= 16
So if 8 yuan equals $1 then 16 divided by 8 would be $2, hope this helped.
V= 2i +9j Find ||9v||
Answers
Answer:
9[tex]\sqrt{85}[/tex]
Step-by-step explanation:
9v = 9(2i + 9j) = 18i + 81j
|9v | = [tex]\sqrt{18^2+81^2}[/tex] = [tex]\sqrt{x6885}[/tex] = 9[tex]\sqrt{85}[/tex]
What is the axis of symmetry and vertex given the equation,
y=2x^2-12x+21
Answers
y = 2x² - 12x + 21 = 2(x² + 6x) + 21.
Using the complet the square method, you get:
2(x² + 6x) + 21 = 2(x² + 6x + 9) - 2*9 + 21 = 2(x + 3)² + 3.
So the axis of symmetry is: x = -3.
The vertex is: (-3, 3)
Answer: 2(x + 3)² + 3
Explanation: Axis of symmetry: x = -3 Vertex: (-3, 3)
A train travels 70 kilometers in 4 hours, and then 55 kilometers in 3 hours. What is its average speed?
Answers
Answer:
Distance = 70 + 55 = 125 kilometers
Time = 4 + 3 = 7 hours
Rate = Distance / Time
Rate = 125 / 7 = 17.8571428571 kilometers per hour
Step-by-step explanation:
The average speed:
[tex]v=\dfrac{total\ distance}{total time}[/tex]
We have
total distance = 70 km + 55 km = 125 km
total time = 4 h + 3 h = 7 h
The average speed:
[tex]v=\dfrac{125\ km}{7\ km}\approx18\ \dfrac{km}{h}[/tex]
PLZ HELP OR I FAIL MY TEST
This is a application question.
A speedboat takes 1 hour longer to go 24 miles up a river than to return. If the boat cruises at 10 miles per hour in still water, what is the rate of the current?
PLEASE DO SHOW WORK.
Answers
Answer:
time upstream=24/8=3 hours
time downstream=24/12=2 hours
Step-by-step explanation:
If R*T=D, and R is speed + or - current, how can you find the rate without the time, and how can you find the time without the rate?
THE KEY WAS WHEN WE WERE TOLD THAT IT TAKES ONE HOUR LONGER TO GO UPSTREAM THAN DOWNSTREAM BECAUSE T=D/R AND WE ARE TOLD THAT:
D/R(Upstream) minus 1 equals D/R (DOWNSTREAM)
Let x=rate of current
distance(d)=rate(r) times time(t) or d=rt or t=d/r
distance upstream=distance downstream=24 mi
rate upstream=10-x
rate downstream=10+x
time upstream=(distance upstream)/(rate upstream)=24/(10-x)
time downstream=(distance downstream)/(rate downstream)=24/(10+x)
Now, we are told that time upstream minus one hour equals time downstream. So our equation to solve is:
24/(10-x)-1=24/(10+x) Multiply both sides by (10-x)(10+x)
24(10+x)(10-x)/(10-x)-1(10-x)(10+x)=24(10-x)/(10+x)/(10+x) clear fractions
24(10+x)-(10-x)(10+x)=24(10-x) clear parens
240+24x-100-10x+10x+x^2=240-24x subtract 240 from and add 24x to both sides
240-240+24x+24x-100+x^2=240-240-24x+24x collect like terms
x^2+48x-100=0 ----------------quadratic equation in standard form
This equation can be factored:
(x+50)(x-2)=0
x=-50 mph----------------discount the negative value for speed
and
x=2 mph----------------------speed of the current
CK
10-x=10-2= 8 mph -----------------------speed upstream
10+x=10+2=12 mph--------------------------speed downstream
time upstream=24/8=3 hours
time downstream=24/12=2 hours
so 3-2=1----takes 1 hour longer upstream
Find the number of units that produce a maximum revenue, R =95x-0.1x^2, where R is the total revenue in dollars and x is the number of units sold
Answers
Answer:
[tex]x=475[/tex] units
Step-by-step explanation:
Method 1
The given revenue function is [tex]R(x)=95x-0.1x^2[/tex].
We rewrite this function in the vertex form by completing the square.
[tex]\Rightarrow R(x)=-0.1x^2+95x[/tex].
[tex]\Rightarrow R(x)=-0.1(x^2-950x)+0[/tex].
We add and subtract half the coefficient of [tex]x[/tex] multiplied by a factor of [tex]-0.1[/tex], which is [tex]-0.1(-\frac{950}{2})^2=-0.1( -475)^2[/tex] to get,
[tex]R(x)=-0.1(x^2-950x)+-0.1(-475)^2--0.1(-475)^2 +0[/tex].
We factor [tex]-0.1[/tex] out of the first two expressions again to get,
[tex]R(x)=-0.1(x^2-950x+(-475)^2)--0.1(-475)^2 +0[/tex].
We now got a perfect square.
[tex]\Rightarrow R(x)=-0.1(x-475)^2+22562.5[/tex].
Therefore the maximum revenue occurs when [tex]x=475[/tex] units were sold.
Method 2
Use derivatives to find the x-value of the maximum point.
[tex]R(x)=-0.1x^2+95x[/tex]
[tex]R'(x)=-0.2x+95[/tex]
At maximum point,
[tex]R'(x)=0[/tex]
[tex]\Rightarrow -0.2x+95=0[/tex].
[tex]\Rightarrow -0.2x=-95[/tex].
[tex]\Rightarrow x=\frac{-95}{-0.2}[/tex].
[tex]\Rightarrow x=475[/tex].
The maximum revenue is achieved when 475 units are sold in the given function R = 95x - 0.1x^2, which was determined by taking the first and second derivatives of the revenue function.
Explanation:In order to find the number of units that produce maximum revenue in the equation R = 95x - 0.1x^2, you have to differentiate the revenue function R with respect to x and set the derivative (first derivative) equal to 0 to find the critical points.
The derivative of the function R with respect to x is R' = 95 - 0.2x. Setting this equal to zero gives: 95 - 0.2x = 0. Solving for x provides x = 95/0.2 = 475. Hence, 475 units sold will maximize revenue according to the provided revenue function.
To confirm this is a maximum, you can use the second derivative test. The second derivative of R, R'' = -0.2. Since this value is negative, x = 475 indeed corresponds to a maximum point on the graph of R(x). Hence, maximum revenue is achieved when 475 units are sold.
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The Han dynasty lasted from 206 B.C. to 9 A.D. How many years did the dynasty last?
Answers
Answer:
The Han dynasty last was, 215 years
Step-by-step explanation:
Given statement: The Han dynasty lasted from 206 B.C. to 9 A.D.
To find how many years did the dynasty last.
B.C. represents Before Christ
A.D. represents After Death
To find the difference between two dates,
When the endings are the same you subtract When they are different you addYou can see that the endings in the given 206 B.C. and 9 A.D. are B.C. and A.D. are different.
Just add these 206 and 9 we get;
[tex]206 + 9 = 215[/tex] years
Therefore, 215 years did the Han dynasty last.
The ratio of boys to girls in Mr.Watson’s class is 2 to 3. There are 18 girls in his class. What is the total number of students in the class?
If the ratio of boys and girls were the same in the whole school, would it be possible that there were a total of 306 boys and 459 girls in the entire school? Why or why not?
Answers
Let's read this in a more proper way.
The number of boys in Mr. Watson's class is 2/3 the number of girls. So:
[tex]18 * \frac{2}{3} = 12\\18 + 12 = 30[/tex]
There are 30 students in Mr. Watson's class.
For this ratio to be in true in the second problem (306 boys, 459 girls), 306 must be 2/3 of 459.
[tex]459 * \frac{2}{3} = 306[/tex]
The ratio holds true for the second problem.
30 students,
Yes it is possible, because 306 is 2/3 of 459.
At the beach, Malia measured the footprints of the people who passed by. The line plot displays the length of each footprint. What fraction of the footprints measure more than a foot?
A. 11/16
B. 5/8
C. 1/2
D. 9/16
Answers
Answer: Choice B) 5/8
================================================
Explanation:
There are 10 dots that represent a measurement larger than 1/2 a foot (either the dot is over 5/8 or 3/4 or 7/8). Call this value A, so A = 10.
There are 16 dots total. Call this B, so B = 16.
Divide A over B and then reduce: A/B = 10/16 = 5/8 so that is why the answer is choice B
Coincidentally, we end up with 5/8 but that is not the same as the "5/8" as shown on the chart. It just means that if we had 8 people, the 5 of them would have a foot size larger than half a foot.
Answer:
Step-by-step explanation:
In One hour a bakery sold five muffins and nine bagels for a total of $25.50 the next hour the bakery sold three muffins and 12 bagels for a total of $28.50 let M represent the price of one muffin and B represent the cost of one bagel Draco wrote the following system of linear equations to solve for the cost of each item.
5m+9b=28.50
3m+12b=25.50
What is Draco’s error?
A.) Draco should have set the first equation equal to 25.50 and the second equation equal to 28.50.
B.) Draco should have written the first equation as 3m+9b= 25.50.
C.) Draco should have written 9b in the second equation and 12b in the first equation.
D.) Draco should have written the second equation as 5m+12b=28.50.
Answers
Answer:
Option A is the correct choice.
Step-by-step explanation:
We have been given the system of linear equations written by Draco. We are asked to find Draco's error.
Let us form a system of equations using our given information.
Let m represent the price of one muffin and b represent the cost of one bagel.
We are told that in one hour a bakery sold five muffins and nine bagels for a total of $25.50. We can represent this information in an equation as:
[tex]5m+9b=25.50...(1)[/tex]
The next hour the bakery sold three muffins and 12 bagels for a total of $28.50. We can represent this information in an equation as:
[tex]3m+12b=28.50...(2)[/tex]
Now let us see system of equations written by Draco.
[tex]5m+9b=28.50[/tex]
[tex]3m+12b=25.50[/tex]
We can see that Draco has set the price of 5 muffins and 9 bagels equal to $28.50, which is the price of 3 muffins and 12 bagels.
Therefore, Draco should have set the first equation equal to 25.50 and the second equation equal to 28.50. The correct choice is option A.
Rashida was paid $720 for 30 hours of work. How much would she be paid for 40 hours of work?
Answers
$960
720÷30=24
24×40=960
24*40=960
That’s the answer
For every 1 girl in Mr Hegarty's class there are 4 boys. What is the ratio of boys to girls in the class? Give your answer in its simplest form.
Answers
Answer:
4:!
Step-by-step explanation:
4:1 because their are 4 boys for every 1 girl
1,8,27,64._,_,_,_,_
What is the sequence?
Answers
Answer:
It is a sequence of integers cubed.
1^3 = 1
2^3 =8
3^3 = 27
4^3 =64
5^3 = 125
6^3 = 216
Step-by-step explanation:
Please help me solve this.
Answers
Answer:
The value of x is -0.5.
Step-by-step explanation:
The given equation is
[tex]-2(5x-6)+6x=4(x+4)[/tex]
Use distributive property to solve the above equation.
[tex]-2(5x)-2(-6)+6x=4(x)+4(4)[/tex]
[tex]-10x+12+6x=4x+16[/tex]
[tex]-4x+12=4x+16[/tex]
Add 4x both sides.
[tex]12=8x+16[/tex]
Subtract 16 from both sides.
[tex]-4=8x[/tex]
Divide both sides by 8.
[tex]\frac{-4}{8}=\frac{8x}{8}[/tex]
[tex]-0.5=x[/tex]
Therefore value of x is -0.5.
solve for x in simplest form 15 = 1/3(x+9)
Answers
Heya!
Your question states: Solve for x in simplest form 15 = 1/3(x+9)
Answer: X = 36
Numerical Explanation:
1. Step by step
I. 15 = 1/3(x+9)
2. Simplify both sides of the equation:
II. 15 = 1/3x + 3
3. Flip the equation:
III. 1/3x + 3 = 15
4. Subtract 3 from both sides:
IV. 1/3 x +3 = 15
-3 -3
5. Multiply both sides by 3:
V. 3 * (1/3 x) = (3) * (12)
6. Final answer:
VI. x = 36
I Hoped I Helped!
~KINGJUPITER
Answer:
x = 36
Step-by-step explanation:
Note the equal sign, what you do to one side, you do to the other. Isolate the variable, x. Do the opposite of PEMDAS:
Remember to follow PEMDAS and the left -> right rule.
PEMDAS:
Parenthesis
Exponent (& roots)
Multiplication
Division
Addition
Subtraction
----------------
15 = 1/3(x + 9)
First, multiply 3 to both sides of the equation
(15)(3) = (1/3(x + 9))(3)
(15)(3) = x + 9
45 = x + 9
Next, to isolate the x, subtract 9 from both sides
45 (-9) = x + 9 (-9)
45 - 9 = x
36 = x
-----------
36 is your answer for x.
~
what is 265 times 14.? Explain what you did.
Answers
Answer:
3710
Step-by-step explanation:
265 * 14
multiply 4 by 5, then 4 by 6, then 4 by 2 which would look like this 860
then you multiply 1 by 5, then 1 by 6, then 1 by 2 which should loo like 2650
it looks like that because for every digit you multiply by except the first you add a zero in front of it. then you add those two up which adds up to 3710 you're welcome. :}
Answer:
3,710
Step-by-step explanation:
First, write it in a multiplication form. (staking on top of each other)
First Step: Multiply the 5 and the 4 in the one's column. 20. So regroup the 2 and place the zero under the 4. Then you multiply the 5 and the one. 5. Also ad what you regrouped it to be. 7. Place that number under the 1 in 14.
Second Step: Add a zero in the ones place. Then multiply the 5 and the 1. 5. Then you multiply the 6 and the 1. 6. Then lastly multiply the 2 and the one.
Third Step: Now add the two numbers to multiplied together to get your final answer.
Have a Nice Winter Break!
:-)
You don't have to mark me as brainliest though.
Pls mark the other person as brainliest!
What property is d • e • 0 = 0
Answers
Answer:
Zero Product Property
Step-by-step explanation:
The zero product property states that anything multiplied by 0 is 0.
a car travels at an average speed of 60 mph on a trip what is the car speed in feet per second
Answers
Answer: 88 Feet Per Second
Step-by-step explanation:
Firstly you need to know 3 things:
> 60 mph = 60 Miles Per Hour
> 1 Hour = 60 mins = 60*60 = 3600 seconds
> 1 Mile = 5280 feet
Next you can change the miles to feet and hours to seconds.
60 mi/ 1 hour = 60*5280/ 3600 = 316800ft/ 3600sec
Now time to reduce that big fraction! (Or in this case just divide by 3600 sec)
316800ft/ 3600sec
= 88ft/1sec
= 88 Feet Per Second
Hope that helps!
Which linear inequality represents the solution set graphed?
A) 2y + 3x < 10
B) 2y + 3x > 10
C) 2y − 3x < 10
D) 2y − 3x > 10
Answers
Answer:
Its A.
Step-by-step explanation:
Because, I have the same question for my test online and the greater than sign with out the under marking is correct.
A 2X2 square is centered at the origin. It is dilated by a factor of 3. What are coordinates of the vertices of the square?
Answers
Answer:
The vertices are:
A' = (-3, -3)
B' = (3, -3)
C' = (3, 3)
D' = (-3, 3)
Step-by-step explanation:
Given:
A 2 x 2 square is centered at the origin.
So, the center of the square is (0, 0)
Since it is 2 x 2 square, the side of the square is 2 units.
So, the vertices of the 2 x 2 square are A (-1, -1), B(1, -1), C(1. 1), D(-1, 1)
The above square is dilated by a factor of 3.
Let's name the dilated square A'B'C'D'
To find the coordinates of the vertices of dilated square, we need to multiply each vertices of ABCD by 3.
A(-1, -1) = 3(-1, -1) = A'(-3, -3)
B(1, -1) = 3(1, -1) = B'(3, -3)
C(1, 1) = 3(1, 1) = C'(3, 3)
D(-1, 1) = 3(-1, 1) = D'(-3, 3)
Which is the equation for the linear function f in the form f(x)=mx+x that has the given values f( 1)=2,f(8)=23
Answers
f ( x ) = 3 x − 1
Hope that helps
I will be happy for you to help me with this question
Answers
Answer:
Your y-intercept is 1 and your slope is 2
Step-by-step explanation:
How to find Slope
To find your slope you have to do the change of y over the change of x. So if you go to your table find how much each value of numbers is changing by. Your y-values are changing differently, but it is fine so to get to 5 from 3 you add 2 and to get to 9 from 5 you add 4. You do the same thing for the x-values are changing differently, but it is fine, so to get to -1 from -2 you add 1 and to get to 1 from -1 you add 2. Next you will take the two values that you get on the y side which are 2 and 4 and the x side which are 1 and 2 and put them in change of y over change of x. So 4/2 with equal 2 and 2/1 equal 2. So the slope is changing by 2.
Pls ANSWER NOW HELP
Which table shows a proportional relationship between x and y?
x 1 3 4 7
y 2 5 8 14
x 2.5 3 5 6
y 5 6 10 15
x 1 2 3 4
y 4 10 12 16
x 7 14 28 35
y 1 2 4 5
Answers
The proportional relationship between x and y is;
x 7 14 28 35
y 1 2 4 5
The correct option is D.
Proportional relationships;Proportional relationships between x and y satisfy the following equation;
[tex]\rm y=kx[/tex]
Where k is some constant.
Rearranging the equation;
[tex]\rm y=kx\\\\k=\dfrac{y}{x}[/tex]
Then,
The proportional relationship between x and y is;
[tex]\rm k = \dfrac{y}{x}\\\\\rm When \ x= 7 \ and \ y= 1\\\\K=\dfrac{1}{7}\\\\\rm When \ x= 14 \ and \ y= 2\\\\K=\dfrac{2}{14}=\dfrac{1}{7}\\\\\rm When \ x= 28 \ and \ y= 4\\\\K=\dfrac{4}{28}=\dfrac{1}{7}\\\\\rm When \ x= 35 \ and \ y= 5\\\\K=\dfrac{5}{35}=\dfrac{1}{7}[/tex]
Hence, the proportional relationship between x and y is the correct option is D.
To know more about proportional relationships click the link given below.
https://brainly.com/question/14237929
Find the area of a circle who is diameter is 27 inches(use 3.1416)
Answers
Answer: The area is 572.5566
Step-by-step explanation:
27÷2=r=13.5
A=πr²
A=3.1416(π) · 13.5²(r)
A=572.5566
Answer:
Given:
Diameter= 27 inches
radius= d/2
=27/2
=13.5
Area of Circle = [tex]\pi[/tex] r² = [tex]\pi[/tex]×(13.5)² = 572.6 inches²Avery had $25.88 in her wallet. If she bought lunch with dollars from her wallet, how much money did she have in her wallet after lunch?
A. $14.38
B. $15.88
C. $15.38
D. $15.68
Answers
Answer:
B
Step-by-step explanation:
Is my unweighted 3.4 GPA good for honor roll? These are my grades:
Math: A
Finance: A
English: B
Biology: A
AP Human Geography: B
Nutrition and Wellness: A
Spanish 2: C
Answers
Answer:
You must have all A's for Honor roll.
Step-by-step explanation:
My sister is in it and she has all A's
A 3.4 unweighted GPA is generally considered good and may qualify for the honor roll, depending on your school's criteria.
Based on your grades, you have a 3.4 unweighted GPA.
To determine if this qualifies you for the honor roll, it would be best to check your school's specific requirements, as they can vary.
Typically, a 3.4 GPA is considered solid and may be sufficient for honor roll status in many high schools.
Here is a breakdown of your grades:
Math: AFinance: AEnglish: BBiology: AAP Human Geography: BNutrition and Wellness: ASpanish 2: CWhile you have mostly As and Bs, the C in Spanish 2 may affect your honor roll eligibility depending on your school's criteria.