Answer:
The speed of the normal train is 60 kilometers per hour.
Step-by-step explanation:
Let suppose that both trains move at constant speed and cover the same distance. Then, we have the following identity:
[tex]v_{1}\cdot t_{1} = v_{2}\cdot t_{2}[/tex] (1)
Where:
[tex]v_{1}, v_{2}[/tex] - Average speeds of the express train and the normal train, in kilometers per hour.
[tex]t_{1}, t_{2}[/tex] - Travel times of the express train and the normal train, in hours.
In addition, there is the following relationship between average speeds:
[tex]v_{1} = v_{2} + 90[/tex] (2)
By (2) in (1), we have the following expression for the average speed of the normal train:
[tex](v_{2} + 90) \cdot t_{1} = v_{2}\cdot t_{2}[/tex]
[tex]90\cdot t_{1} = v_{2} \cdot (t_{2} - t_{1})[/tex]
[tex]v_{2} = \frac{90\cdot t_{1}}{t_{2}-t_{1}}[/tex]
If we know that [tex]t_{1} = 4\,h[/tex] and [tex]t_{2} = 10\,h[/tex], then the average speed of the normal train is:
[tex]v_{2} = 90\cdot \left(\frac{4\,h}{10\,h - 4\,h} \right)[/tex]
[tex]v_{2} = 60\,\frac{km}{h}[/tex]
The speed of the normal train is 60 kilometers per hour.
Can someone help me please really need help? I’ll help you back please & thanks
"You want to purchase a North Face jacket for $180. You have already saved $115 and can set aside $13 a week.
Write and solve an inequality to find the number of weeks, w, it will take you to save at least $180.
Answer:
115 + 13w [tex]\geq[/tex] 180
Step-by-step explanation:
A bagel shop sold 8 plain bagels and 13 rye bagels. What is the ratio of the number of rye bagels to the number of plain bagels sold?
Answer:
13 : 8
Step-by-step explanation:
Number of plain bagels sold = 8
Number of rye bagels sold = 13
Ratio of the number of rye bagels to the number of plain bagels sold = 13 : 8
Also written as
13/8
Or
13 to 8
A bagel shop sold 8 plain bagels and 13 rye bagels. What is the ratio of the number of rye bagels to the number of plain bagels sold?
Answer: It is 13: 8.
Find the percentage decrease ???
Step-by-step explanation:
Price of a book costing sh.250
reduced to sh.200
percentage decrease on the price = (250-200)/250×100
= 20%
...yea i just need help (:
Answer:
2/3-4
3 1/3
-1*3.3=-3.3
-3 1/3 divided by 5/6
-4
so a
Hope This Helps!!!
Answer:
-2/3+4÷5/6
-2+12÷3÷5/6
10/3÷5/6
10/3x6/5
2/1x2/1
4/1
4
Step-by-step explanation:
hope this is helpful
A typical serving of fish is 4 ounces. What is this serving size in grams?
Answer:
the answer is 113.398 grams
________ collect money from investors, create capital, and offer various investment options.
Fill in the blank
its 2 words
[tex]\sf\purple{Mutual \:funds}[/tex] collect money from investors, create capital, and offer various investment options.
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
solve for x. round to the nearest tenth. If necessary
Answer:
x = 14
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA [Right Triangles Only] sinθ = opposite over hypotenuseStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ = 30°
Opposite Leg = 7
Hypotenuse = x
Step 2: Solve for x
Substitute in variables [sine]: sin(30°) = 7/x[Multiplication Property of Equality] Cross-multiply: x = 7/sin(30°)Evaluate: x = 14Answer:
x = 14
Step-by-step explanation:
Given :-
θ, angle = 30°Hypotenuse = xopposite side = 7Solution :-
Since, it's right triangle we can use trignometery equations;
In this case we need to use sine equation.
sin θ = opposite side / hypotenuse
plug the values
sin 30° = 7 / x.
cross multiplication
x = 7 / sin 30°
Evaluate
x = 7 / 0.5
x = 14
Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 5.15 ft at midnight, rises to a
high of 10.2 ft falls to a low of 0.1 ft, and then rises to 5.15 ft by the next midnight
What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the
situation?
Enter your answer in the box
Answer:
f(x)=5.05 sin((pi/12)x) + 5.15
Step-by-step explanation:
how do i solve for x with an equation that says 19 = x - 3
Answer: x = 22
Step-by-step explanation: Since x is unknown, we want to isolate it and determine what it equals. We know that x - 3 gives us 19, but we don't want to know what x - 3 is, just x. So we can add three to both sides of the equation, to get our answer and keep it balanced. As a result, we get x = 22
Answer:
x = 22
Step-by-step explanation:
19 = x - 3
Add 3 to each side
19 + 3 = x - 3 + 3
Simplify
22 = x
how much water should be added to one liter of pure ammonia to make a mixture of 50% ammonia
Answer:
I assume that this is a math question not a chemistry question...
In math I assume the answer is 1 liter....
total = 2 liters (1 liter water 1 liter ammonia )
If this is a chemistry question there is a difference between total
volume, and total weight, which would not result in the answer being 1 liter
Step-by-step explanation:
A turkey has a mass of 6 kilograms. A bag of sweet potatoes has a mass of 2 kilograms. How many more grams does the turkey weigh than the sweet potatoes?
Answer:
the correct answer is 4,000 grams
Question 5 of 10
In the diagram below, 30 is parallel to XY. What is the value of x?
769
Answer:
D
Step-by-step explanation:
a and 76° are corresponding angles and are congruent , then
x = 76° → D
Tasha is planning an expansion of a square flower garden in a city park. If both the length and the width of the original garden are each increased by *3m*, the new total area of the garden will be *49* squared meters. Find the length of each side of the original garden.
Answer:
4 m
Step-by-step explanation:
Since the flower garden is square :
Both length and width are equal :
Let :
Original side length = x
Increased length = x + 3
Area of square = s² (s = side length)
New area = 49 m²
That is ;
(x + 3)² = 49
Original length, x can be calculated thus ;
Take square root of both sides
x + 3 = √49
x + 3 = 7
x = 7 - 3
x = 4
Hence, original length of each side = 4 m
The sum of Aini’s age and Wani’s age is 62 years old. Three years later, Aini’s age is three times Wani’s age. How old is Aini now?
Answer:
48 years old
Step-by-step explanation:
a + w = 62
a+3 = 3(w+3) =>a+3=3w+9
=> a-3w = 6
a+ w = 62
a- 3w= 6
________-
4w = 56
w = 14
so, the Aini's age now is 62-14 = 48 years old
semoga membantu
During a sale, a store offered a 20% discount on a stereo system that originally sold for $320. After the sale, the discounted price of the stereo system was marked up by 20%.
Answer:
354 $ is correct
Step-by-step explanation:
your v id dead
Question 24 Multiple Choice Worth 1 points)
(8.01 MC)
Two lines, A and B, are represented by equations given below:
Line A: y = x - 4
Line B: y = 3x + 4
Which of the following shows the solution to the system of equations and explains why?
0 (-3,-5), because the point satisfies one of the equations
0 (-3,-5), because the point lies between the two axes
(-4,-8), because the point satisfies both equations
(-4, -8), because the point does not lie on any axis
Given:
The system of equations is:
Line A: [tex]y=x-4[/tex]
Line B: [tex]y=3x+4[/tex]
To find:
The solution of given system of equations.
Solution:
We have,
[tex]y=x-4[/tex] ...(i)
[tex]y=3x+4[/tex] ...(ii)
Equating (i) and (ii), we get
[tex]x-4=3x+4[/tex]
[tex]-4-4=3x-x[/tex]
[tex]-8=2x[/tex]
Divide both sides by 2.
[tex]-4=x[/tex]
Substituting [tex]x=-4[/tex] in (i), we get
[tex]y=-4-4[/tex]
[tex]y=-8[/tex]
The solution of system of equations is (-4,-8).
Now verify the solution by substituting [tex]x=-4, y=-8[/tex] in the given equations.
[tex]-8=-4-4[/tex]
[tex]-8=-8[/tex]
This statement is true.
Similarly,
[tex]-8=3(-4)+4[/tex]
[tex]-8=-12+4[/tex]
[tex]-8=-8[/tex]
This statement is also true.
Therefore, (-4,-8) is a solution of the given system of equations, because the point satisfies both equations. Hence, the correct option is C.
Find the reciprocal of 9.
the reciprocal of 9 is 1 divided by 9, i.e. 1/9
Maverick wants to rent some office space for 5 years. The lease states that the
annual rent is $75,000 for the first year and will increase by 7.25% each
additional year of the lease. What will the total rent be for the entire 5-year
lease? Round your answer to the nearest hundredth.
Answer:
$106,426.01
Step-by-step explanation:
Use the compound amount equation A = P(1 + r)^t and take as your answer the total amount after 5 years. Here the principal is $75,000, the interest rate is 0.0725 and the number of years (t) is 5:
A = $75,000(1 + 0.0725)^5, or
A = $75,000(1.0725)^5, or
A = $106,426.01
Answer:
$434,907.04 or $435,179.37 depending on your teacher's rounding.
Step-by-step explanation:
The rent for the first year is given as $75,250.
For the second year, the rent will increase by 7.25%, so the rent will be:
$75250 + 0.0725 ($75,250) = $80,705.63
Using the calculation for the previous year, continue the formula.
The rent increases by 7.25% for the third year, so:
$80,705.63 + 0.0725 ($80,705.63) = $86,556.79
Fourth Year:
$86556.79 + 0.0735 (86556.79) = $92,918.71
Fifth Year:
92918.71 + 0.0735 (92918.71) = 99748.24
Add these all together to get the final rent after the 5 year lease:
75,250 + 80.705.63 + 86,556.79 + 92,918,71 + 99,748.24 = 435,179.37
I need help with my math! Can you please help me!!
Answer:
[tex]y=-|x-1|+3[/tex]
Step-by-step explanation:
The graph of the function ([tex]y=|x|[/tex]) can be described as a perfect (v) shape composed of two lines with the equation ([tex]y=x[/tex]) and ([tex]y=-x[/tex]) with a range of ([tex]y\geq 0[/tex]). In the depicted graph, this function has undergone some transfomrations. The general format for a transformation of an absolute value function is the following;
[tex]y=(+-)n|x-k|+h[/tex]
The function can be inverted if the sign of (n) is (-). As per the given graph, the function is inverted, thus the answer will have a (-) sign in front of it. One can see that the (n) value has to be (1) or rather not present since the function has no scaling factor.
[tex]y=-|x|[/tex]
The function has been shifted (k) units to the right, one can see that the given function's vertex is (1) unit to the right, thus the equation of the function has a (1) in the position of (k).
[tex]y=-|x-1|[/tex]
The function is shifted (3) units up, thus the position of (h) is occupied by a (3).
[tex]y=-|x-1|+3[/tex]
Therefore the following answer choice is correct, as it fits all of the requirements;
[tex]y=-|x-1|+3[/tex]
f(4) =
If g(x) = 2, x =
<
A squirrel has a 75% chance of finding food when it is sunny, but only a 25% chance of finding food when it is raining. Suppose there is a 50% chance of rain. What is the probability that a squirrel will find food?
Answer:
The probability is 0.5
Step-by-step explanation:
If there is a 50% chance of rain, then there is also a 50% chance of not rain.
Now let's write all the probabilities:
(just take the percentage and divide it by 100%)
Probability of rain: p = (50%/100%) = 0.5
probabiity for the squirrel to find food when it rains: q = (25%/100%) = 0.25
Then the joint probability, this is, the probability that rains and that the squirrel finds food, is equal to the product of these two probabilities, this is:
P1 = 0.5*0.25 = 0.125
And we also have the case where there is no rain.
Probability that does not rain: p' = (50%/100%) = 0.5
Probability that the squirrel finds food if doesn't rain: q = (75%/100%) = 0.75
The joint probability is:
P2 = 0.5*0.75 = 0.375
The total probability that the squirrel will find food is equal to the sum of the probabilities of the squirrel finding food if there is rain, and the probability of the squirrel finding food if there isn't rain, so the total probability is:
P = P1 + P2 = 0.125 + 0.375 = 0.5
Figure PQRS is a parallelogram. The expressions represent the measures of the angles in degrees.
Parallelogram P Q R S is shown. Angle Q is (20 + 2 x) degrees and angle R is (6x) degrees.
What is the value of x?
5
10
20
25
Given:
In parallelogram PQRS, [tex]m\angle Q=(20+2x)^\circ,\ m\angle R=6x^\circ[/tex].
To find:
The value of x.
Solution:
In a parallelogram, the consecutive interior angles are supplementary angles.
In parallelogram PQRS,
[tex]m\angle Q+m\angle R=180^\circ[/tex] (Supplementary angles)
[tex](20+2x)^\circ+(6x)^\circ=180^\circ[/tex]
[tex](20+8x)^\circ=180^\circ[/tex]
[tex]20+8x=180[/tex]
Subtracting 20 from both sides, we get
[tex]8x=180-20[/tex]
[tex]8x=160[/tex]
Divide both sides by 8.
[tex]\dfrac{8x}{8}=\dfrac{160}{8}[/tex]
[tex]x=20[/tex]
Therefore, the correct option is C.
Answer:
c
Step-by-step explanation:
The sum of two numbers is 10. The larger number is 4 times the smaller number. What are the two numbers?
Let x = the smaller number.
Let y = the larger number.
Which two equations represent the system for this word problem?
Equation 1:
Equation 2:
Step-by-step explanation:
everything can be found in the picture
Answer:
Step-by-step explanation:
Which two equations represent the system for this word problem?
Equation 1:
✔ x + y = 10
Equation 2:
✔ y = 4x
PLEASE HELP BRO IM LOSING MY MIND (if u could explain how with the answer THATD be sick)
Answer:
y = (x+3)(x+2)(x+1)
Step-by-step explanation:
so how to determine that...
1) it has to be a third order equation (x^3) since it changes direction two times
2) it crosses the x axis at -1,-2,-3 so (x-1),(x-2),and (x-3) are factors
AB and CF are parallel find x
Show CLEARLY how you got your answers with reasons
Answer:
x = 152°
Step-by-step explanation:
∠ BDE = ∠ ABD = 76° ( alternate angles )
Since DE = BE then Δ BDE is isosceles with base angles congruent
∠ DBE = ∠ BDE = 76°
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
x is an exterior angle of the triangle, then
x = 76° + 76° = 152°
Please answer i will give brainliest
Which is a better estimate for the height of a 5-story building?
a. 15 centimeters b.15 meters
Answer:
b. 15 meters
Step-by-step explanation:
This doesn't involve a lot of math, just some common sense. 15 centimeters is about the size of a pencil so that is definitely not the answer. Therefore, 15 meters would be the correct choice.
Answer:
B bro
Step-by-step explanation:
simplify
[tex] \frac{2e + f}{8e - 2e {}^{2} } \times \frac{4e - e {}^{2} }{2ef + f {}^{2} } [/tex]
The answer is 1/2f
my answer is in the image above
a=10^x, b=10^yanda^y^*b*x=100then2xy=?
Answer:
Here is your answer
Step-by-step explanation:
xy = 1
Hope you like it : )
