=======================================================
Explanation:
Draw a horizontal number line. Plot point A at 0 and point B at 45 on the number line. The distance from A to B is 45 units to represent that 45 mile gap between the cities.
Let's say the trains travel to the right (aka to the east) along this number line train track. We'll place the faster train at location A, and the slower train at location B. This allows the slower train a head start. Eventually the faster train will catch up. If this was swapped and the trains still aimed to the right, then the trains will never be 10 miles apart.
-----------------------
Now we'll define two variables
x = number of hours that have elapsedy = the train's location on the number lineFor the faster train at location A, which I'll just refer to "train A" from now on, we can form the equation y = 70x. I'm using the idea that distance = rate*time to help form this equation.
For example, if x = 2 hours have passed by, then train A is at location y = 70*2 = 140 miles on the number line train track.
Train B will have the equation y = 60x+45. The 60x is formed in a similar manner compared to the 70x. The plus 45 at the end is due to the 45 mile head start. In other words, train B travels 60x miles on top of the 45 miles already done so far.
-----------------------
The two key takeaways from that last section is that we have these equations
y = 70xy = 60x+45which correspond to the locations of train A and train B in that order.
Now to the question at hand: how can we determine when the trains are 10 miles apart? The short answer is through subtraction. Moreover, we'll need to involve absolute value to ensure that distance is never negative.
So the distance expression between the trains at any given time x is:
distance between trains = |trainA - trainB|
distance = |70x - (60x+45)|
distance = |70x-60x-45|
distance = |10x-45|
Next, we set that distance expression equal to 10 and solve for x.
distance = 10 miles
|10x-45| = 10
10x-45 = 10 or 10x-45 = -10
10x = 10+45 or 10x = -10+45
10x = 55 or 10x = 35
x = 55/10 or x = 35/10
x = 5.5 or x = 3.5
-----------------------
Those two results mean that at the hour marks of 3.5 hours and 5.5 hours is when the two trains are 10 miles apart exactly.
The two trains start off being 45 miles apart. They both take off and train A will catch up to train B. Their gap will be 10 miles at the 3.5 hour mark. That gap shrinks to 0 at some point, and then grows again afterward. By the 5.5 hour mark is when the trains are again 10 miles apart. This time is when train A is in the lead and will remain so assuming the speeds stay the same.
It seems like your teacher is only concerned with when the trains are 10 miles apart for the first time and not the second. So your teacher is likely only expecting one answer and that would be 3.5 hours
Side notes:
3.5 hours = 3 hours, 30 minutes = 210 minutes.5.5 hours = 5 hours, 30 minutes = 330 minutes.Multiply by 60 to convert from hours only to minutes only.Find the greatest common factor (reverse of distributing)
Answer:
12(2A+B)=12*3
Step-by-step explanation:
Answer:
[tex]12[/tex]
Step-by-step explanation:
We know that [tex]24=12*2[/tex], [tex]12=12*1[/tex], and [tex]36=12*3[/tex].
So, we can re-write the equation as [tex]12*2*A+12*1*B=12*3[/tex].
We can factor out a [tex]12[/tex] from both sides to get [tex]12(2A+B)=12(3)[/tex].
The insides can't be simplified anymore, so the final equation is [tex]12(2A+b)=12(3)[/tex] and the gcf is [tex]\boxed{12}[/tex]
Adding/subtracting linear equations
Answer:
[tex]\sf The \: answers\: are \:attached[/tex]
_________________
Find the value of X and Y
Answer:
Step-by-step explanation:
9x-1 + 5x-15 =180, 14x-16=180, x = 14
9x-1 + y-20 = 180, 126-1-20+y =180, y = 105
An input-output machine generates the information below
a- Find the values to fill in the table for variables a and b
b- write up a rule that describes the relationship between the input output.
c- what is the value of the output and input in 20?
d- what is the value of the input when the output is 77.
Using a linear function, we have that:
a) The values are: a = 11 and b = 5.
b) The rule is:
[tex]y = 3x + 2[/tex]
c) The value of the output is 62.
d) The value of the input is 25.
The equation of a linear function is given by:
[tex]y = mx + b[/tex]
In which
m is the slope, which is the rate of change.b is the y-intercept, which is the initial value.First, we are going to solve item b to find the rule, then we solve other items.
Item b:
In the table, we have two points: (1,5) and (2,8).
The slope is given by change in y divided by change in x, thus:
[tex]m = \frac{8 - 5}{2 - 1} = 3[/tex]
Then
[tex]y = 3x + b[/tex]
Point (1,5) means that when [tex]x = 1, y = 5[/tex], and this is used to find b.
[tex]5 = 3(1) + b[/tex]
[tex]b = 2[/tex]
Thus, the rule is:
[tex]y = 3x + 2[/tex]
Item a:
a is the value of y when x = 3, thus:
[tex]y = a = 3(3) + 2 = 11[/tex]
Thus, a = 11.
b is the value of x when y = 17, thus:
[tex]3b + 2 = 17[/tex]
[tex]3b = 15[/tex]
[tex]b = 5[/tex]
The values are: a = 11 and b = 5.
Item c:
The value of the output is y when x = 20, thus:
[tex]y = 3(20) + 2 = 60 + 2 = 62[/tex]
Thus, the value of the output is 62.
Item d:
The value of the input is x when y = 77, thus:
[tex]3x + 2 = 77[/tex]
[tex]3x = 75[/tex]
[tex]x = \frac{75}{3}[/tex]
[tex]x = 25[/tex]
The value of the input is 25.
A similar problem is given at https://brainly.com/question/25004958
I need help finding the area of the smaller of the two.
Answer: The area is 12 inches
Step-by-step explanation:
If the bigger one is 24 inches, and the bigger one is two times the size of the smaller one, the smaller one is 12 iches
simplify 2m2n4p3⋅2m4n2p2
Answer:
4m8n8p6
Step-by-step explanation:
Ben wants to have his birthday at the bowling alley with a few of his friends, but he can spend no more than $80. The bowling alley charges a flat fee of $45 for a private party and $5.50 per person for shoe rentals and unlimited bowling. Write an inequality that represents the total cost of Ben's birthday for p people given his budget. Use your inequality to solve for how many people Ben can pay for (including himself) while staying within the limitations of his budget? *
Answer:
He can pay for 5 friends plus himself while staying within the budget.
Step-by-step explanation:
No parents are allowed in.
45 + 5.5p = 80 80-45=35 5.5p = 35 35/5.5 = 6.4
So he can pay for himself plus 5 people, and probably a drink.
Hope this helps!
SOLVE FOR X PLEASE ANSWE ASAP !
Answer:
x=15
Step-by-step explanation:
Rate as BRAINLIEST
JM = 4x-29
4x-29 = 6+13 +2x-18
4x -29 = 19 +2x -18
4x -29 = 1 +2x
2x -29 = 1
2x = 30
x = 15
PLEASE HELP GIVING 20 POINTS FOR BRAINLEST!!!(FIRST TO ANSWER)
what is f(5)
Answer:The F-5 is an agile, highly maneuverable, reliable supersonic fighter, combining advanced aerodynamic design, engine performance and low operating costs. ... The U.S. Navy operates the F-5 in its adversary squadrons to simulate enemy aircraft in aerial combat training exercises.
7)
Is MNO similar to PQO
Answer:
Where is your attachment or question
Solve the equation for a. 10= 1/5a+2
Answer:
it is 2.35
Step-by-step explanation:
Please help me with number 1!
[tex](x^{2} +1)(x^{2} -1)^{6}[/tex]
Answer:
(x²+1)(x²-1)⁶ = x¹⁴-5x¹²+9x¹⁰-5x⁸-5x⁶+9x⁴-5x²+1
Step-by-step explanation:
Pascal triangle 6th row for (a + (-b))⁶; ... for (x²-1)⁶
a⁶+6a⁵(b)¹+15a⁴(b)²+20a³(b)³+15a²(b)⁴+6a(b)⁵+1*(b)⁶ .. a=x² b = -1
= x¹²+6x¹⁰(-1)¹+15x⁸(-1)²+20x⁶(-1)³+15x⁴(-1)⁴+6x²(-1)⁵+1*(-1)⁶
= x¹²-6x¹⁰+15x⁸-20x⁶+15x⁴-6x²+1
(x²+1)(x²-1)⁶ = (x²+1)(x¹²-6x¹⁰+15x⁸-20x⁶+15x⁴-6x²+1)
= x¹⁴-5x¹²+9x¹⁰-5x⁸-5x⁶+9x⁴-5x²+1
i need to find the values of X but there isn’t another expression to find x for 180°
Answer:
x=5
Step-by-step explanation:
In this equation, we need to find x. According to the Vertical Angles Congruence Theorem, all vertical angles are congruent. Therefore, because angles (2x+12) and (8x-18) are vertical angles, they are congruent. We can set this up as an equation and simply solve for x:
2x+12=8x-18 Subtract 2x from both sides.
-2x -2x
12=6x-18 Add 18 to both sides.
+18 +18
30=6x Divide both sides by 6.
/6 /6
5=x
I hope this helps!! Have an amazing day :)
Answer:
x = 5
Step-by-step explanation:
The two angles have the same degree because of the Vertical Angles rule. This means that if angles are vertical, then they are congruent. Therefore, we can solve for x by setting the two angles equal to each other.
2x + 12 = 8x - 18
+ 18 + 18
2x + 30 = 8x
-2x -2x
30 = 6x
÷6 ÷6
5 = x
We can then double check this by inputing x back into the equations
2x + 12 = 2(5) + 12 = 10 + 12= 22
8x - 18 = 8(5) - 18 = 40 - 18 = 22
These check out so x = 5
I hope this helped :)
(2x+6)/5=4x−3 sove and use 5 algebric proofs of equality
x=−11/2=−5/2 1 =−5.5
X +31424=1424
What is X
100+1133232323232332323232
Answer:
1133232323232332323332
Step-by-step explanation:
Answer: 1133232323232332323332
Step-by-step explanation:
Find the angle
25 points for you plus a brainliest, thanks and 5 star
Answer:
? =64.62306
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adjacent side / hypotenuse
cos ? = 3/7
Taking the inverse cos of each side
cos ^-1 ( cos ? ) = cos ^-1 (3/7)
? =64.62306
Answer:
The angle is approximately 23°
Step-by-step explanation:
let the angle be ∆
using trigonometrical identity,
tan ∆=3/7
tan∆=0.4286
∆=tan^-1(0.4286)
∆=23.19°
Describe how to solve d = rt for t
Answer:
t = d/r
Step-by-step explanation:
Given the equation, d = rt for t:
Switch sides:
rt = d
Divide both sides by r to isolate t:
[tex]\frac{rt}{r} = \frac{d}{r}[/tex]
t = d/r
MARKING BRAINLEIST IF YOUR ANSWER IS CORRECT!
Answer:
1 /5
Step-by-step explanation:
What Did The Acorn Say When It Grew Up?
Answer:
The picture is to small.
Step-by-step explanation:
To small.
How do I use FOIL? I get lost every time...especially with exponents
what is the answer to 56,763 rounding to the nearest thousand
Answer:
60000
Step-by-step explanation:
56763 so you're going to take that number and you're going to run it to the nearest thousands by doing that you're going to take the six and six is either closest to zero or 10 and it is closer to 10 which would be your answer so you're going to add these zero replacing the six seven six and three in the equation and making me five of six by adding the one from the number 10 if you have any other questions text me if that doesn't make sense
If 1llm, find the value of y
Answer:
y = 70°
Step-by-step explanation:
4x - 50 and 2x + 30 are equal, because they are corresponding angles
4x - 50 = 2x + 30
4x = 2x + 80
2x = 80
x = 40°
The angle below 2x + 30 = y, because they are vertical angles
Since we know what x is, we can substitute x from 2x + 30
And since two angles that take up a line are 180°, we can add them
2(40) + 30 + y = 180
80 + 30 + y = 180
110 + y = 180
y = 180 - 110
y = 70
-Chetan K
the distance of a trip
An airport offers free parking for 30 minutes and then charges $2.00
for each hour after that. How is the price for parking related to the
total time a car is parked?
write an equation for each relationship
Answer:
T-.5 = x (200)
Step-by-step explanation:
Let T = total time in hours
30 mn = .5 hours 30 /60 = .5
$ 2.00 is the rate per hour.
so T − .5 = the time that will be charged at the rate
Therefore the total charge is then
T − .5 × 2.00
Solve the system.
x + 4y +z = 12
y – 3z = -7
z = 3
Enter your answer as an ordered triple.
([ ? ], [ ], [ ]
Answer:
([ 1 ], [ 2 ], [ 3 ])
Step-by-step explanation:
y – 3z = -7; z = 3 => y = 2
x + 4y +z = 12 => x + 4(2) + 3 = 12 => x = 1
([ 1 ], [ 2 ], [ 3 ])
What is (5⁴) (5³) simplified
Answer:
5^7 or 78125
Step-by-step explanation:
Whats the distance between the points (5,5) and (-1,8)
Answer:
6.71
Step-by-step explanation:
Using the distance formula:
[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
= √(-1-5)^2 + (8-5)^2
= √36 + 9
= √45
= 3√5 <- Optional
= 6.70820393
≈ 6.71
Hope this helps and be sure to have a wonderful time ahead at Brainly! :D
Answer:
[tex]3\sqrt{5}[/tex]
Decimal form: 6.70820393 …
Step-by-step explanation:
The length of this line can be found by using the distance formula:
[tex]{\sqrt (}(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2})[/tex]
Step 1: Plot the coordinates of both points.
Step 2: Evaluate the x-axis and y-axis distance between the points.
Step 3: Square both results.
Step 4: Add the squared results.
Step 5: The answer lies in the square root of the equation.
ײ+6×+9=0 in Discriminant and nature of the roots
Answer:
D = 0, x = -3
Step-by-step explanation:
D = b*b - 4ac = 36 - 4*9 = 36 - 36 = 0
x = -b/2a since D = 0, so
x = -6/2 = -3
a baker is making cupcakes. he has 36 pounds of dough. each cupcake is made from ⅙ pound of dough. how many cupcakes can be made?
explain with answer
Answer:
First you have to understand a one cupcake has 1/6 pound of dough.
Then to calculate the number of cupcakes, divide the total 36 pounds of dough by a 1/6 pound.
36/(1/6)
= 36 ×(6/1)
= 216 cupcakes
Answer: 216 cupcakes can be made
Step-by-step explanation:
Given information
36 pounds of dough in total
⅙ pound of dough per cupcake
Set variables
Let x be the number of cupcakes that could be made
Set equations from given information
Total = unit × number
36 = (1/6) × x
Multiply 6 on both sides to isolate [x] variable
36 × 6 = (1/6) × x × 6
216 = 1 × x
[tex]\boxed{x=216}[/tex]
Hope this helps!! :)
Please let me know if you have any questions