The rate of the passenger train must be 45 miles per hour, and the rate of the freight train must be 30 miles per hour.
Let's denote the rate of the passenger train as "P" and the rate of the freight train as "F". We are given that the passenger train's rate exceeds the freight train's rate by 15 miles per hour. Therefore, we can write the following equation:
P = F + 15
We are also given that the two trains start from points that are 300 miles apart and meet after 4 hours. We can use the formula distance = rate × time to set up two equations:
Distance covered by the passenger train: P × 4
Distance covered by the freight train: F × 4
Since they meet each other, the sum of their distances should add up to 300 miles:
P × 4 + F × 4 = 300
Substituting P = F + 15 into the equation, we can solve for F:
(F + 15) × 4 + F × 4 = 300
4F + 60 + 4F = 300
8F = 240
F = 30
Now that we have the rate of the freight train, we can substitute it back into the equation P = F + 15 to find the rate of the passenger train:
P = 30 + 15
P = 45
Therefore, the rate of the passenger train must be 45 miles per hour, and the rate of the freight train must be 30 miles per hour.
For such more questions Train Rates
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Pleaseee helpp!!
Jack manages a café. Each day he buys watermelons and mangoes in the (respective) ratio of 3:2. If on one day he buys 200 mangoes how many water melons would he have bought?
Answer:
300 watermelons
Step-by-step explanation:
3:2 ratio
3 is water melons and 2 is mangoes.
200 mangoes were purchased.
200/2=100
The unit rate is 100, so multiply 3 by 100, which is 300.
So Jack bought 300 watermelons, and 298 of which will be devoured by yours truly.
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hope it helps
pliss give me the aswer
Answer:
AA
Step-by-step explanation:
AA
Answer:
15+ 8d
After d day,she has read 15 +8d pages
There are 9 students in a class: 2 boys and 7 girls. If the teacher picks a group of 4 at random, what is the probability that everyone in the group is a girl?
The triangle pictured below represents a community garden, which is surrounded on
3 sides by a fence. Find the perimeter of the fence.(Please provide Explanation)
A)4
B)62
C)88
D)336
Answer:
88
Step-by-step explanation:
10a-9=14a-25
10a-14a=-25+9
-4a=-16
a=4
10(4)-9+14(4)-25+6(4)+2
40-9+56-25+24+2
88
which Venn diagram is shaded to represent the event L AN N
Answer:
I'm not 100% sure but I think its A
Express the following in the form a +bi, where a and b are real numbers:
[tex] \sqrt{24 + 10i} [/tex]
Another accepted answer is -5-i, but if your teacher wants only one answer, then I'd go for 5+i
======================================================
Work Shown:
[tex]\sqrt{24+10i} = a+bi\\\\\left(\sqrt{24+10i}\right)^2 = (a+bi)^2\\\\24+10i = a^2+2abi+b^2i^2\\\\24+10i = a^2+2abi+b^2(-1)\\\\24+10i = a^2+2abi-b^2\\\\24+10i = (a^2-b^2)+(2ab)i\\\\[/tex]
Equating terms, we have this system
[tex]\begin{cases}24 = a^2-b^2\ \text{.... real terms}\\10 = 2ab\ \text{.... imaginary terms}\end{cases}[/tex]
Solve the second equation for b to get b = 5/a
Plug that into the first equation to solve for 'a'
[tex]24 = a^2-b^2\\\\24 = a^2-\left(\frac{5}{a}\right)^2\\\\24 = a^2-\frac{25}{a^2}\\\\24a^2 = a^4-25\\\\0 = a^4-24a^2-25\\\\a^4-24a^2-25 = 0\\\\(a^2-25)(a^2+1) = 0\\\\(a-5)(a+5)(a^2+1) = 0\\\\[/tex]
Setting each factor equal to zero would lead to...
a-5 = 0 solves to a = 5a+5 = 0 solves to a = -5a^2+1 = 0 solves to a = i and a = -iWe're told that 'a' is a real number, so we ignore the solutions "a = i and a = -i". The only possible solutions are a = 5 and a = -5
If a = 5, then,
b = 5/a = 5/5 = 1
So
[tex]\sqrt{24+10i} = a+bi = 5+1i = 5+i[/tex]
or in short,
[tex]\sqrt{24+10i} = 5+i[/tex]
-----------------
If a = -5, then b = 5/a = 5/(-5) = -1
So it's very possible that we could also say
[tex]\sqrt{24+10i} = -5-i\\\\[/tex]
If you wanted to combine the two we would use the plus/minus notation like so
[tex]\sqrt{24+10i} = \pm(5+i)\\\\[/tex]
This is due to (5+i)^2 and (-5-i)^2 both having the same result of 24+10i. Hence the plus/minus. If your teacher wants one answer only, then I'd go for 5+i, as we could consider it a "principal" square root in a sense.
hey! i’ll give brainliest please help
Answer: A would be your answer.
Step-by-step explanation: Internal conflict is when you have a problem with yourself and this means your not intercating with others.
PLEASE HELP! Choose one answer
Answer:
c
Step-by-step explanation:
Interquartile range or IQR is the range of the "box" in the graph. So we have 54 and 36 so we subtract 54-36.
So we get 18.
im sorry for asking so many questions, but please help
Answer:
x=110˚
Step-by-step explanation:
We need to first find the other degree inside the triangle
first add 45˚ and 65˚
which is 110˚
subtract 110˚ with 180˚
which is 70˚
So we find x since a straight line is 180˚
subtract 70 and 180
which is 110˚
Hoped I helped!
Answer:
110 degrees
Step-by-step explanation:
A triangle is 180 degrees. So if the missing angle is 70, and 70+x=180 then x=110
Which value(s) of x are solution(s) of the equation below
Hi there!
[tex]\large\boxed{x = -1}[/tex]
We can solve by multiplying each term to get a common denominator:
[tex]\frac{1}{x - 4} + \frac{x}{x - 2} = \frac{2}{x^2-6x+8}[/tex]
[tex]\frac{x -2}{(x - 4)(x - 2)} + \frac{x(x - 4)}{(x - 2)(x - 4)} = \frac{2}{x^2-6x+8}[/tex]
Since the denominators are all the same (x² - 6x + 8 factors to (x - 2)(x - 4)), we can ignore them temporarily and solve the numerator:
x - 2 + x(x - 4) = 2
Simplify:
x - 2 + x² - 4x = 2
x² - 3x - 4 = 0
Factor:
(x - 4)(x + 1) = 0
x = -1, 4
For the values of x to be a solution, they cannot cause the denominator to be equal to 0, so:
(x - 2)(x - 4) = 0
x = 2, 4. These values result in a denominator of 0, which is undefined.
Thus, the only solution is x = -1.
PLEASE HELP
Write a recursive formula for each sequence.
1, -2, -2, 4, -8, -32, 256, ...
PLEASE HELP
WILL MARK AS BRAINLISTS
Step-by-step explanation:
1*-2=-2, -2*-2=4, -2*4=-8, -8*-32=256
WILL GIVE BRAINLIEST!
Ms. Sally is ordering sets of place-value blocks for the 3rd, 4th, 5th graders. She want one set for each student, and there are 6 sets of blocks in a carton. How many cartons should Ms. Sally order?
3rd grade - 48 students
4th - 43 students
5th - 46 students
6th - 50 students
Answer:
32 cartons
Step-by-step explanation:
Total sets needed
48 + 43 + 46 + 50 = 187
Cartons needed
187 / 6 = 31 1/6
need 32 cartons
Answer:
32 cartons
Step-by-step explanation:
add up all of the students = 187
divide by 6 = 187/6 = 31.16
round = 32 cartons
please help me with these two problems I need help
Answer:
24 area
18.80983669 perimeter
Step-by-step explanation:
1 (6*3/2)*2(1*3/2)+(4*3)
2 trust me
PLEASE HELP ME this is very difficult for me.
Answer:
∆ADE ≈ ∆ DCF
I hope this helps
Drag the tiles to the boxes to form correct pairs.
Match each operation involving Rx) and g(x) to its answer.
(t) = 1 - 22 and g(x) = V11 — 41
Answer:
[tex](g + f)(2) = \sqrt 3 - 3[/tex]
[tex](\frac{f}{g})(-1) = 0[/tex]
[tex](g + f)(-1) = \sqrt{15}[/tex]
[tex](g * f)(2) = -3\sqrt 3[/tex]
Step-by-step explanation:
Given
[tex]f(x) =1 - x^2[/tex]
[tex]g(x) = \sqrt{11 - 4x[/tex]
See attachment
Solving (a): (g + f)(2)
This is calculated as:
[tex](g + f)(2) = g(2) + f(2)[/tex]
Calculate g(2) and f(2)
[tex]g(2) \to \sqrt{11 - 4 * 2} = \sqrt{3}[/tex]
[tex]f(2) = 1 - 2^2 = -3[/tex]
So:
[tex](g + f)(2) = g(2) + f(2)[/tex]
[tex](g + f)(2) = \sqrt 3 - 3[/tex]
Solving (b): [tex](\frac{f}{g})(-1)[/tex]
This is calculated as:
[tex](\frac{f}{g})(-1) = \frac{f(-1)}{g(-1)}[/tex]
Calculate f(-1) and g(-1)
[tex]f(-1) = 1 - (-1)^2 = 0[/tex]
So:
[tex](\frac{f}{g})(-1) = \frac{f(-1)}{g(-1)}[/tex]
[tex](\frac{f}{g})(-1) = \frac{0}{g(-1)}[/tex]
[tex](\frac{f}{g})(-1) = 0[/tex]
Solving (c): (g - f)(-1)
This is calculated as:
[tex](g + f)(-1) = g(-1) - f(-1)[/tex]
Calculate g(-1) and f(-1)
[tex]g(-1) = \sqrt{11 - 4 * -1} = \sqrt{15}[/tex]
[tex]f(-1) = 1 - (-1)^2 = 0[/tex]
So:
[tex](g + f)(-1) = g(-1) - f(-1)[/tex]
[tex](g + f)(-1) = \sqrt{15} - 0[/tex]
[tex](g + f)(-1) = \sqrt{15}[/tex]
Solving (d): (g * f)(2)
This is calculated as:
[tex](g * f)(2) = g(2) * f(2)[/tex]
Calculate g(2) and f(2)
[tex]g(2) \to \sqrt{11 - 4 * 2} = \sqrt{3}[/tex]
[tex]f(2) = 1 - 2^2 = -3[/tex]
So:
[tex](g * f)(2) = g(2) * f(2)[/tex]
[tex](g * f)(2) = \sqrt 3 * -3[/tex]
[tex](g * f)(2) = -3\sqrt 3[/tex]
im really struggling with this, i need A on this test please help me!
Question 2 options:
If XY is 4 m and WZ is 9 m, the exact volume of the cone is ___π square meters.
Answer:
150.8 m³
48π m³
Step-by-step explanation:
V = πr²h/3
V = π · 4² · 9/3
150.8 m³
please help me im gonna have to do this over again if i get it wrong
[tex]1\frac{1}{2}[/tex] [tex]batches[/tex]
➛➛➛➛➛
[tex]\frac{1/2}{1} =\frac{3/4}{x}[/tex]
[tex]\frac{1}{2} =\frac{3}{4x}[/tex]
[tex]cross~multiply[/tex]
[tex]4x=2(3)[/tex]
[tex]\frac{4x}{4} =\frac{6}{4}[/tex]
[tex]x=\frac{3}{2} =1\frac{1}{2}[/tex]
✂----------------hope it helps...have a great day!!What is the value of this expression? 27+4×(8−4) Enter your answer in the box.
Answer:
43.
Step-by-step explanation:
Follow PEMDAS (Parentheses, exponents, multiply, divide, add, subtract). First you do 8-4 which is 4, then you multiply 4 by 4 which is 16 since you multiply next, then you add 27 to 16 which then gets you to 43.
Element X is a radioactive isotope such that every 13 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 90 grams, how long would it be until the mass of the sample reached 62 grams, to the nearest tenth of a year?
Answer:
The mass of Element X will reach 62 grams in 7.0 years.
Step-by-step explanation:
We can find the time of decay of Element X by using the exponential decay equation:
[tex] \frac{dm}{dt} = -\lambda t [/tex]
The solution of the above equation is:
[tex]m_{(t)} = m_{0}e^{-\lambda t}[/tex] (1)
Where:
t: is the time =?
λ: is the decay constant
[tex]m_{(t)}[/tex]: is the mass at time t = 62 grams
[tex]m_{0}[/tex]: is the initial mass = 90 grams
First, we need to calculate λ
[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex] (2)
Where [tex]t_{1/2}[/tex] is the half-life = 13 years
By entering equation (2) into (1) and solving for "t" we have:
[tex]\frac{m_{(t)}}{m_{0}} = e^{-\frac{ln(2)}{t_{1/2}}*t}[/tex]
[tex]ln(\frac{m_{(t)}}{m_{0}}) = -\frac{ln(2)}{t_{1/2}}*t[/tex]
[tex]t = -ln(\frac{m_{(t)}}{m_{0}})(\frac{t_{1/2}}{ln(2)}) = -ln(\frac{62}{90})(\frac{13}{ln(2)}) = 7.0 y[/tex]
Therefore, the mass of Element X will reach 62 grams in 7.0 years.
I hope it helps you!
3/4 + (1/3 ÷ 1/6) - (-1/2)
Please give answer as a fraction
Answer: 13/4
Step-by-step explanation: it was 3.25 and that as a fraction is 13/4
3/4 + ( 1/3 × 6 ) + 1/2 =
3/4 + 2/4 + ( 2 ) =
3 + 2/4 + 8/4 =
5/4 + 8/4 =
5 + 8/4 =
13/4
What is the distance between (7,2) and (-3,2)?
A.8
B.12
C.4
D.10
Answer:
The answer is D
......(don't mind this it's because it says that it needs to be 20 characters long) but the answer is D
4 1/2 = 1 1/2n = plsss answer
Answer:
Step-by-step explanation:
n = 3
Answer: n= 3
Step-by-step explanation:
i hope this helped :))
sub duplicate ratio of 4:9
Answer:
sub duplicate ratio of
4:92:3hope it helps
stay safe healthy and happy...which elevation is higher 8 feet below sea level or 13 feet below sea level
Answer: 8 feet below sea level is higher
Step-by-step explanation:
What term describes the elements that sets have in common in a Venn diagram?
What is the 1st step in evaluating this expression? 12 divided by (7.4 - 3.6) + 8 -2= *
Answer:
The 1st step in evaluating the expression is doing the equation in the paranthesis. PEMDAS states we do the paranthesis 1st.
need help pls and ty
Answer:
95 square units
Step-by-step explanation:
Area of a triangle formula:
A = 0.5bh
Given:
b = 19
h = 10
Work:
A = 0.5bh
A = 0.5(19)(10)
A = 9.5(10)
A = 95
P L E A S E A N S W E R A S A P T H A N K S
Answer:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
55 divided by 10 = 5.5 around 5
Add all your numbers
Divide by the many numbers there are, go by the exact value or estimate if needed.
KLM is isosceles. Calculate the segment EF from the data in the drawing.
HELP!!
Answer:
4.5 cm
Step-by-step explanation:
KL = LM as triangle is isosceles
LM = KM as LF = FM = KN = NM, so the triangle is equilateral
EF ║ NM as LE⊥EF and LN⊥NM
EF is half the midsegment as ∠KLN ≅ ∠MLN, and LN is angle bisector of ∠KLM
Midsegment is half the side length, and all sides are 18 cm.
EF = 1/2(1/2*18) = 4.5 cm
Help Find kif (2, k) lies on the line with equation 2x + 7y = 41
Answer:
i think 11y
Step-by-step explanation: