Two trains leave a train station traveling different directions. The first train travels 12 miles west, then 6 miles north. The second train travels 20 miles east, then 35 miles north.
a. The train station is the origin. What is the coordinate of each train?
b. Using the city center and the stop point of the first train, what is the slope of the line? Is it horizontal, vertical or neither? Write the equation of the line in slope-intercept form and standard form.
c. The city wants to build a train station 2 miles directly north of the first train station. They are going to build a train track parallel to the path the first train would’ve traveled if it were a direct route from the city center. What would be the equation of the line in slope intercept form of the new track?
Answers
The origin (0, 0) is the train station.
Part a.
The first train travels 12 miles west and 6 miles north to arrive at A.
It's coordinate is (-12, 6).
The second train travels 20 miles east and 35 miles north to arrive at B.
It's coordinate is (20, 35).
Part b.
The slope of the line from the origin to A is
m = (6 - 0)/(-12 - 0) = -1/2.
The slope is neither vertical nor horizontal.
The y-intercept is 0.
The line OA is given in slope-intercept form by
y = -(1/2)x
In standard form, the line is
y - 6 = -(1/2)*(x - (-12))
or
y - 6 = -(1/2)*(x + 12)
Part c.
The new train station is located at (0, 2) because it is 2 miles north of the old station.
If a new track is built parallel to OA, then it should have a slope of -1/2.
Because it's y-intercept is 2, its equation in slope-intercept form is
y = -(1/2)x + 2.
Answer:a. first (-12,6) second (20,35)
b. y = -1/2x, 2y + 1x = 0 (neither horizontal or vertical)
c. y= -1/2x + 2.
Step-by-step explanation:
Related Questions
A bridge hand is made up of 13 cards from a deck of 52. find the probability that a hand chosen at random contains at least 3 kings kings.
Answers
In total there are C(52, 13) ways that we can pick a hand, that is [tex] \frac{52!}{13!39!} [/tex]
2.
P(a hand contains at least 3 kings)
=P(a hand contains exactly 3 kings)+P(a hand contains 4 kings)
3.
first let's find P(a hand contains exactly 3 kings):
P(a hand contains exactly 3 kings)
=n(a hand contains exactly 3 kings)/C(52, 13)
n(a hand contains exactly 3 kings)=C(4, 3)*C(48, 10)
where C(4,3) is the total number of ways we can pick 3 out of 4 kings,
C(48, 10) is the number of picking 10 letters to complete a hand, out of the 52-4=48 non-king cards.
so P(a hand contains exactly 3 kings)=[C(4, 3)*C(48, 10)]/C(52, 13)
4. with the same reasoning as in step 3:
P(a hand contains 4 kings)=n(a hand contains 4 kings)/C(52, 13)
= [C(4, 4)*C(48, 9]/C(52, 13)
5.
P(a hand contains at least 3 kings)
=P(a hand contains exactly 3 kings)+P(a hand contains 4 kings)
=[C(4, 3)*C(48, 10)]/C(52, 13)+ [C(4, 4)*C(48, 9)]/C(52, 13)
=[tex] \frac{C(4, 3)*C(48, 10)+C(4, 4)*C(48, 9)}{C(52, 13)} [/tex]
=[tex] \frac{4* \frac{48!}{10!38!} + \frac{48!}{9!39!}}{ \frac{52!}{13!39!} } [/tex]
simplify by 38! in the denominators and 48! in the numerators :
[tex] \frac{4* \frac{1}{10!} + \frac{1}{9!39}}{ \frac{52*51*50*49}{13!39} } [/tex]
now simplify by 9! in all denominators:
[tex] \frac{ \frac{4}{10}+ \frac{1}{39} }{ \frac{52*51*50*49}{13*12*11*10*39}} [/tex]
[tex] \frac{ 0.426 }{ 9.7} =0.044[/tex]
Final answer:
The probability that a bridge hand chosen at random contains at least 3 kings is 0.0000244.
Explanation:
To find the probability that a bridge hand chosen at random contains at least 3 kings, we need to first determine the total number of possible bridge hands and then calculate the number of favorable outcomes.
The total number of bridge hands is calculated using the combination formula: C(52, 13) = 52! / (13! * (52-13)!) = 635,013,559,600.
To calculate the number of favorable outcomes, we count the number of ways we can select 3 kings and then fill the remaining 10 positions with the remaining 39 cards. The number of ways to select 3 kings is C(4, 3) = 4 and the number of ways to fill the remaining 10 positions is C(48, 10) = 17,259,390.
Therefore, the probability is given by: P(At least 3 kings) = favorable outcomes / total outcomes = (4 * 17,259,390) / 635,013,559,600 = 0.0000244.
the sum of two numbers is 70. the larger number is five less than twice the smaller number . what are the two numbers
Answers
x=2y-5
x=larger number
y=smaller number
now plug in the value of x to only have one variable in the equation...
Way to solve for y:
(2y-5)+y=70
3y-5=70
add 5 on both sides...
3y=75
divide by 3 on both sides
y=25
1st way to solve for x:
now plug in y in the original equation...
x+25=70
subtract 25 on both sides...
x=45
2nd way to solve for x:
plug in y for the second equation...
x=25(2)-5
x=50-5
x=45
answer: the two numbers are 45 and 25.
Final answer:
To find the two numbers, we created a system of equations with the sum being 70 and the larger number as five less than twice the smaller number. Solving the equations, we found that the smaller number is 25 and the larger number is 45.
Explanation:
The question asks us to find two numbers where the sum is 70, and the larger number is five less than twice the smaller number. To solve this, we'll set up a system of equations with two variables, which we'll call x and y. The first equation would be x + y = 70, since their sum is 70. The second equation is derived from the statement that the larger number is five less than twice the smaller number, which can be expressed as y = 2x - 5. Now we substitute the second equation into the first to solve for x. We get x + (2x - 5) = 70. Simplifying, we have 3x - 5 = 70, thus 3x = 75, and therefore x = 25. With the smaller number found, we can determine the larger number using the second equation y = 2(25) - 5, resulting in y = 45. Hence, the two numbers are 25 and 45.
a hallway measuring 90 feet x 7 feet requires 1/2 a fluid ounce of cleaning solutions per square foot. how much cleaning solution is required
Answers
90x7 = 630
630 x 1/2 = 315
Find the standard form of the equation of the parabola with a focus at (-4, 0) and a directrix at x = 4. (2 points)
Answers
since the focus point is at -4, 0 and the directrix is a vertical line at x = 4, is a horizontal parabola, and it opens to the left-hand-side.
now, notice the distance "p", is just 4 units, however, the parabola is opening to the left-side, thus "p" is negative, then is -4, the vertex is half-way between the focus point and the directrix.
[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} \boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})} \\\\ (x-{{ h}})^2=4{{ p}}(y-{{ k}}) \\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\ \begin{cases} h=0\\ k=0\\ p=-4 \end{cases}\implies (y-0)^2=4(-4)(x-0)\implies y^2=-16x \\\\\\ -\cfrac{1}{16}y^2=x[/tex]
PLEASE HELP ME!!! NOT GOOD AT MATH.
Answers
L = length = 8 mm
W = width = 6 mm
H = height = 4 mm
TSA = 2*(L*W + W*H + L*H)
TSA = 2*(8*6 + 6*4 + 8*4)
TSA = 208
The units are "square millimeters" often written as sq mm or "mm^2"
Answer: 208
--------------------------------
Part B)
From part A, the total surface area (TSA) was 208 square mm. If it costs $3 per square mm, then that means the total cost C is
C = (cost per sq mm)*(total surface area)
C = 3*208
C = 624
The units for the cost are in dollars. This result is assuming that there isn't any waste.
Answer: 624
--------------------------------
Part C)
Volume = Length*Width*Height
V = L*W*H
V = 8*6*4
V = 192
The units are in cubic millimeters. The notation is sometimes "cubic mm" or "mm^3"
Answer: 192
ok so what is is the square root of 1234 i dot know
Answers
sqrt(1234) = 35.1283
you don't say how it should be rounded, so round off as needed
Canada has a population that is 1/10 as large as the United States. If Canada's population is about 32 million, about how many people live in the United States? Explain the number of zeros in your answer.
Answers
Answer:
Step-by-step explanation:
Let the American Population = x
1/10 x = 32,000,000 Multiply by sides by 10
x = 320,000,000 Thirty two followed by 7 zeros is the population of America.
8meters long 4 meters wide and 2 meters deep.What is the volume of the pond.
Answers
8 x 4=32 x 2=64
The volume of the pond is 64 meters
1. 8 7/16 - (-2 4/9)
Answers
8 7/16 - (-2 4/9) =
8 7/16 + 2 4/9 =
8 7/16 = 135/16 = 1215/144
2 4/9 = 22/9 = 352/144
1215/144 + 352/144 = 1567/144 =10 127/144
A rectangle or shaped swimming pool has a perimeter of 104 feet and is 4 feet longer than 3 times its width. Find its dimensions.
Answers
______
| |
| |
| | [tex]x[/tex]
| |
| |
|_____ |
(i'm using meters instead of feet because I'm more used to it)
The perimeter of the rectangle is [tex]2x+2y[/tex]
The perimeter is 104m
∴[tex]2y+2x=104[/tex]
------------------------------------------------------------------------
It's 4 feet longer than 3 times its width.
[tex]3y=x+4[/tex]
[tex]3y-x=4[/tex]
[tex]6y-2x=8[/tex]
[tex]2y+2x=104[/tex]
[tex]6y-2x=8[/tex]
-------------------------
[tex]8y=112[/tex]
∴[tex]y=14[/tex]m
[tex]2y+2x=104 [/tex]
[tex]2(14)+2x=104[/tex]
[tex]28 +2x=104 [/tex]
[tex]2x=76[/tex]
∴[tex]x=38[/tex]m
Write the equation of a circle with a center at (–7, –7) and a radius of 7
Answers
Final answer:
The equation of a circle with a center at (-7, -7) and a radius of 7 is [tex](x + 7)^2 + (y + 7)^2 = 49.[/tex]
Explanation:
The equation of a circle is typically expressed in the form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. For a circle with a center at (–7, –7) and a radius of 7, the equation would be (x + 7)² + (y + 7)² = 7². Here, we squared the radius to get 49, which gives us the final equation (x + 7)² + (y + 7)² = 49.
rewrite y=x^2-6x+2 then state whether the vertex is maximum or minimum and give its coordinates
Answers
y=x^2-6x+2
y=(x^2-6x+9)-9+2
y=(x-3)^2-7
the vertex is at the point (3,-7), hence the minimum or maximum point is at (3,-7)
Where would we find the point (–10,0)? A. Quadrant III B. y-axis C. Quadrant II D. x-axis
Answers
A rectangular container that has a length of 30 cm a width of 20 cm and her height of 24 cm is filled with water to a depth of 15 cm when an additional 6.5 L of water are poured into the container some water overflows. How many liters of water overflow the container?
Answers
30 x 20 x 24 = 14400 cubic cm
30 x 20 x 15 = 9000 cubic cm
14400-9000 = 5400 cubic cm left
1 cubic cm = 0.001 liters
5400x 0.001 = 5.4 liters
6.5-5.4 = 1.1 liters overflow
1.1 L
Further explanationGiven:
A rectangular container that has:
a length of 30 cm,a width of 20 cm, anda height of 24 cmIt is filled with water to a depth of 15 cm.
When an additional 6.5 L of water are poured into the container, some water overflows.
Question:
How many liters of water overflow the container?
The Process:
Step-1: calculate the volume of rectangular container
[tex]\boxed{ \ V = length \times width \times depth \ }[/tex]
[tex]\boxed{ \ V = 30 \times 20 \times 24 \ }[/tex]
[tex]\boxed{ \ V = 14,400 \ cm^3 \ }[/tex]
The volume of rectangular container is 14,400 cm³, then converted to 14,4 L.
Step-2: calculate the volume of water filled in the container to a depth of 15 cm
[tex]\boxed{ \ V = length \times width \times depth \ }[/tex]
[tex]\boxed{ \ V = 30 \times 20 \times 15 \ }[/tex]
[tex]\boxed{ \ V = 9,000 \ cm^3 \ }[/tex]
The volume of water filled is 9,000³ cm, then converted to 9 L.
Step-3: calculate the volume of water overflow when an additional 6.5 L of water is poured into a container.
The volume of water overflow equals the initial water volume is added to the additional water volume then subtracted by the container volume.
The volume of water overflow = [tex]\boxed{ \ 9 \ L + 6.5 \ L - 14.4 L \ }[/tex]
Thus, the volume of water overflow of the container is 1.1 L.
Notes:
[tex]\boxed{ \ 1 \ cm^3 = 1 \ mL \ }[/tex]
[tex]\boxed{ \ 1,000 \ cm^3 = 1 \ L \ }[/tex]
[tex]\boxed{ \ 1 \ dm^3 = 1 \ L \ }[/tex]
Learn moreWhat is the volume of this rectangular prism? https://brainly.com/question/11613210Find out the area of a trapezoid brainly.com/question/2280236Find out the area of a cube brainly.com/question/12613605#Keywords: a rectangular container, has a length of 30 cm, a width of 20 cm, height of 24 cm, is filled with water, to a depth of 15 cm, an additional 6.5 L of water, are poured into the container, some water overflows, the formula, volume
How to solve this problem?
Answers
11)
x*y = -5*2 = -10, absolute value is 10
y*z = 2 * -2 = -4, absolute value is 4
10+4 = 14
A mixture of
12%
disinfectant solution is to be made from
10%
and
17%
disinfectant solution. How much of each solution should be used if
28
gallons of the
12%
solution are needed?
Answers
Gallon equation:
x+y = 28
Solution equation:
10x + 17y = (28)(12)
Solve with substitution:
y = 28-x (From 1st equation)
(Sub into 2nd equation)
10x + 17(28-x) = 336
10x + 476 - 17x = 336
-7x = -140
x = 20
y = 28-20 = 8
Therefore the solution is (20,8)
You need 20 gal of 10% solution mixed with 8 gal of 17% solution to obtain 28 gal of 12% solution.
The amount In a savings account increased from $300 to $309. What was the percent of increase?
Answers
increase = (309-300)/300 = 9/300 = 3/100 = 0.03 or 3%
2nd Method: 309/300 = 103/100 = 1.03 (increase over 1 is 0.03 = 3%)
Final answer:
The amount in the savings account increased by 3%. This was calculated by determining the amount of the increase ($9), dividing by the original amount ($300), and then multiplying by 100 to get the percent increase.
Explanation:
The question is asking to calculate the percent of increase in the amount of money in a savings account that went from $300 to $309. To determine the percent increase, you subtract the original amount ($300) from the new amount ($309) to find the amount of the increase, which is $9. Then, you divide the increase ($9) by the original amount ($300) and multiply by 100 to get the percentage:
Percent Increase = (Increase ÷ Original Amount) × 100%
Percentage Increase = ($9 ÷ $300) × 100% = 0.03 × 100% = 3%
Therefore, the percent of increase is 3%.
Find the volume: in cm 7cm high 3cm wide 2 cm long
Answers
so 7×3×2=42 cm3
hat are the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of 1728 cm^3?
Answers
The product of height and square of the radius of the open-top right circular cylindrical should be equal or more than 550 cm³ in order to hold a volume of 1728 cm³.
Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
The volume of the cylinder is = πr²h
In order to hold the volume of 1728 cm³,
πr²h ≥ 1728
r²h ≥ 550
Thus, the product of height and square of the radius of the open-top right circular cylindrical should be equal to or more than 550 cm³ in order to hold a volume of 1728 cm³.
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The table shows the values of why are different values of X which equation shows the relationship between X and y
X y
0 0
1 7
2 14
3. 21
Answers
Greatest common factor of 8 and 14?
Answers
What is the length of time a loan will last if it has a rate of 0.02, a principal of $500, and it accrued $60 of interest if Interest = Principal * Rate * Time. How would you reduce the time of the loan?
Answers
I=prt
Solve for t
T=I÷pr
T=60÷(500×0.02)
T=6 years
You can reduce the time of the loan by increasing the rate of interest
For example
T=60÷(500×0.05)
T=2.4 years
T=I÷pr
T=60÷(500×0.02)
T=6 years <-- Answer
Find a general solution to the differential equation 2y''-5y'-3y=0
Answers
2y'' - 5y' - 3y = 0
The characteristic equation is
2m² - 5m - 3 = 0
(2m + 1)(m - 3) = 0
which yields
m = -1/2, 3
Answer:
The general solution is
[tex]y(x)=c_{1}e^{-x/2}+c_{2} e^{3x}[/tex]
where c₁ and c₂ are constants.
A father is 60 years old and his son is half his age. How old was the boy when his father was four times his age?
Answers
From here, we can tell that father's age= son's age+30. We can now create the system of equations as follows.
f= s+30
f=4s
Because both define f, put the two equations together.
4s=s+30
3s=30
s=10
Final answer: The boy was 10 (and his father was 40).
Elaine's jewelry box has a volume of 36 cubic centimeters. Which of the following could be the dimensions of Elaine's jewelry box? Choose all answers that apply: A 12 cm long, 12 cm wide, 12 cm high B. 4cm long, 4 cm wide, 2 cm high C 3 cm long, 4 cm wide, 3 cm high
Answers
A. 12*12*12=1728 cm^3
B. 4*4*2=32 cm^3
C. 3*4*3=36 cm^3
Only C is correct
Answer:
Option C is the correct answer.
Step-by-step explanation:
Volume of box = Length x width x height.
Volume of box = 36 cubic centimetres.
Option A:
Length = 12 cm
Width = 12 cm
Height = 12 cm
Volume = 12 x 12 x 12 = 1728 cubic centimetres.
Option A is wrong.
Option B:
Length = 4 cm
Width = 4 cm
Height = 2 cm
Volume = 4 x 4 x 2 = 32 cubic centimetres.
Option B is wrong.
Option C:
Length = 3 cm
Width = 4 cm
Height = 3 cm
Volume = 3 x 4 x 3 = 36 cubic centimetres.
Option C is correct.
Option C is the correct answer.
Solve for the indicated variable
D = 2zv for v
Answers
v=D/(2z)
First option is correct i.e. [tex]v = \frac{D}{2z}[/tex] .
What is variable in an equation?Variable is a symbol( usually a letter) standing in for an unknown numerical value in an equation.
How to solve an equation for the variable?To solve or isolate a variable means to get the variable on one side of the equation by itself.
According to the given question
we have an equation
D = 2zv and to solve for variable v
For solving the above equation for the variable v, make the variable v on one side of the equation by itself.
⇒ [tex]\frac{D}{2z} = \frac{2zv}{2z}[/tex] ( dividing both the sides by 2z)
⇒ [tex]v = \frac{D}{2z}[/tex]
Hence, option first is correct.
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What is the answer, with the correct number of decimal places, for this problem? 4.392 g + 102.40 g + 2.51 g =?
Answers
The summation of 4.392 g + 102.40 g + 2.51 g with three decimal places is 109.302 g.
What is summation?A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There could be only two terms, but there could be one hundred, thousand, or a million.
Given the expression for sum,
4.392 g + 102.40 g + 2.51 g
⇒ (4.392 + 102.40 + 2.51)g
⇒ 109.302 g
Hence "The summation of 4.392 g + 102.40 g + 2.51 g with three decimal places is 109.302 g".
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The sum of the masses 4.392 g, 102.40 g, and 2.51 g is 109.30 g.
Explanation:A summation, which can sometimes be shortened to "sum," is the result of multiplying two or more quantities by one another. A summation always has an integer number of terms. One hundred, thousand, or a million phrases could exist, but there could only be two.
The sum of the masses 4.392 g, 102.40 g, and 2.51 g is 109.302 g.
To ensure the correct number of decimal places, we need to consider the measurement with the least number of decimal places, which is 2.51 g.
Since 2.51 g has two decimal places, we round the sum to two decimal places as well.
Therefore, the answer is 109.30 g.
Milla and Luka are 3 kilometers apart and walking toward each other. Milla's average speed is 5 kilometers per hour and Luka's is 4 kilometers per hour.
Which equation can be used to find t, the time it takes for Milla and Luka to meet?
5t + 4t = 1
5t + 4t = 3
5t – 4t = 0
5t – 4t = 3
Answers
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
Speed of Milla = 5 km per hour
Speed of Luka = 4 km per hour
Distance between Milla and Luka = 3 km
Let the time be 't'.
As we know that
[tex]Distance=Speed\times time[/tex]
So, it becomes,
Distance covered by Milla + Distance covered by Luka = Total distance
[tex]5t+4t=3[/tex]
Hence, Second option is correct.
negative 2 to the 3 power
Answers
What is the quotient (3x4 – 4x2 + 8x – 1) ÷ (x – 2)?
Answers
Answer:
the quotient of this problem is 3x^3+6x^+8x+24+47/x-2