Answer: First train speed shall be 42 mi/hr
Second train speed shall be 84 mi/hr
Yes it is the valid answer, it gets annoying when almost everyone enters the wrong answer for a good laugh. Either way, hope this helps! Have a spectacular day.
Step-by-step explanation:
What is the 1st train's head start in miles?
Let +s+ = the speed of the 1st train in mi/hr
From 2PM to 4PM is 2 hrs
+d%5B1%5D+=+s%2A2+
---------------------
Let +d+ = distance the 2nd train travels until
it overtakes the 1st train
From 4PM to 6PM is 2 hrs
Start time when the 2nd train leaves
---------------------
Equation for 1st train:
(1) +d+-+2s+=+s%2A2+
Equation for 2nd train:
(2) +d+=+%28+s%2B42+%29%2A2+
--------------------
Substitute (2) into (1)
(1) +%28+s%2B42+%29%2A2+-+2s+=+s%2A2+
(1) +2s+%2B+84+-+2s+=+2s+
(1) +2s+=+84+
(1) +s+=+42+
and
+s%2B+42+=+42+%2B+42+
+s+%2B+42+=+84+
------------------
The 1st train's speed is 42 mi/hr
The 2nd train's speed is 84 mi/hr
---------------------------
check:
(2) +d+=+%28+s%2B42+%29%2A2+
(2) +d+=84%2A2+
(2) +d+=+168+
and
(1) +d+-+2s+=+s%2A2+
(1) +d+-+2%2A42+=+42%2A2+
(1) +d+=+84+%2B+84+
(1) +d+=+168+
The height of a triangle is 4cm more than twice the length of the base.The area of the triangle is 35 square cm.Find the height of the triangle.
Answer:
14cm
Step-by-step explanation:
Algebra is the way!
But seriously, let's model this algebraically.
We know the that the area of a triangle is represented by:
[tex]A = \frac{1}{2} base*height[/tex]
we'll use b and h to represent base and height
[tex]A = \frac{1}{2} b*h[/tex]
Okay, so you are given the area of the triangle already. It is [tex]35 cm^2[/tex]. SO you have:
[tex]35 = \frac{1}{2} bh[/tex]
Now here's the tricky bit of the question. You have 2 unknown variables, oh no! How will you solve? The key to this is simple, in a case where you have 2 or more unknown variables, ALWAYS think to yourself, "can I represent this variable in terms of another"?
In this case you can. They tell you what the height of the triangle is, in terms of the length of the base. They tell you, height is 4 cm more than 2 times the base.
So replace h in this equation with 2b + 4.
[tex]35 = \frac{1}{2} (b)(2b+4)\\\\35 = \frac{1}{2}(2b^2 + 4b)\\ 70 = 2b^2 + 4b\\0 = 2b^2 + 4b - 70\\0 = (2)(b^2 + 2b - 35)\\0 = (b +7)(b - 5)\\\\b = 5\\b\ \neq -7[/tex]
Okay, so you know the base of the triangle is 5 cm. The question asks for height, so what you're going to do is refer back to what h is.
We found that [tex]h = 2b + 4[/tex]
sub in 5 into that:
[tex]h = 2(5) + 4 = 14[/tex]
Therefore the height of the triangle is 14cm.
Answer:
Step-by-step explanation:
Givens
Area = 1/2 B* H
B = B
H = 2*B + 4
Area = 35
Solution
35 = 1/2 * B * (2B + 4) Multiply both sides by 2
35*2 = 2*(1/2) * B * (2B + 4) Combine
70 = B(2B + 4) Remove the Brackets.
70 = 2B^2 + 4B Subtract 70 from both sides.
2B^2 + 4B - 70 = 0 Divide everything by 2
B^2 + 2B - 35 = 0 Factor
(B + 7)(B - 5)
B+7 = 0 will give a minus number. Geometry does not allow minus numbers.
B - 5 = 0
B = 5
But what you want is the height.
h = 2b + 4
h = 2*5 + 4
Answer: h = 14
Find the value of X and perimeter.
A. 140°
B. 90°
C. 70°
D. 50°
Help please
Answer:
i think the answer is d which is 50°
Manu had ₹ 120. He bought one book for ₹ 25.75 and a pen for ₹ 12.50. How much money does he have now?
Answer:
₹ 81.75
Step-by-step explanation:
Total = ₹ 120.
He bought one book for ₹ 25.75 and a pen for ₹ 12.50.
₹ 25.75 + ₹ 12.50 = ₹ 38.25
How much money does he have now?
₹ 120 - ₹ 38.25 = ₹ 81.75
₹81.75
you just minus 120 from 25.75 and 12.50
Can somebody help me pls!
Answer: C
Step-by-step explanation:
Just look at a z-score table and multiply by 100.
-> (0.308538)(100) is about 30.85%
a) the cost of. kg oranges is rs 350 how many kg of oranges can be bought for rs 665
b.). A car travel for 50 km.with the help of 5 litres of petrol how many litres of petrol is reauired to travel 120 km
A: 1.9 Kilograms of oranges for rs 665.
B: 12 liters of petrol will make a car travel 120 km.
General solution of: (1-xy)^-2 dx + [y^2 + x^2 (1-xy)^-2]dy = 0
show two solution on your answer
nonsense answer deleted
[tex] \Large \bold{SOLUTION\ 1:} [/tex]
[tex] \small \begin{array}{l} \text{First, we need to check if the given differential} \\ \text{equation is exact.} \\ \\ (1-xy)^{-2} dx + \big[y^2 + x^2 (1-xy)^{-2}\big]dy = 0 \\ \\ \dfrac{dx}{(1-xy)^2} + \left[y^2 + \dfrac{x^2}{(1-xy)^2}\right]dy = 0 \\ \\ \quad M(x, y) dx + N(x, y) dy = 0 \end{array} [/tex]
[tex] \small \begin{array}{l l}\tt\: M(x,y) = \dfrac{1}{(1 - xy)^2}, & N(x,y) = y^2 + \dfrac{x^2}{(1-xy)^2}\\ \\\tt \dfrac{\partial M}{\partial y} = \dfrac{-2(-x)}{(1 - xy)^3}, & \dfrac{\partial N}{\partial x} = \dfrac{2x}{(1 - xy)^2} + \dfrac{-2(-y)x^2}{(1 - xy)^3} \\ \\\tt \dfrac{\partial M}{\partial y} = \dfrac{2x}{(1 - xy)^3}, & \dfrac{\partial N}{\partial x} = \dfrac{2x(1 - xy)+2x^2y}{(1 - xy)^3} \\ \\\tt \: & \dfrac{\partial N}{\partial x} = \dfrac{2x}{(1 - xy)^3} \end{array} [/tex]
[tex] \small \begin{array}{l} \tt\dfrac{\partial M}{\partial y} = \dfrac{\partial N}{\partial x} \implies \text{Differential equation is exact.} \\ \\\tt \dfrac{\partial F}{\partial x} = M(x, y) = \dfrac{1}{(1 - xy)^2} \\ \tt\displaystyle F(x, y) = \int \dfrac{1}{(1 - xy)^2} \partial x = -\dfrac{1}{y} \int \dfrac{1}{(1 - xy)^2}(-y)\partial x \\ \\ \tt\:F(x, y) = \dfrac{1}{y(1 - xy)} + h(y) \\ \\ \tt\dfrac{\partial F}{\partial y} = N(x, y) = y^2 + \dfrac{x^2}{(1-xy)^2} \\ \\\tt \dfrac{\partial}{\partial y}\left[\dfrac{1}{y(1 - xy)} + h(y)\right] = y^2 + \dfrac{x^2}{(1-xy)^2} \\ \\ \tt-\dfrac{1 - xy + y(-x)}{y^2(1 - xy)^2} + h'(y) = y^2 + \dfrac{x^2}{(1-xy)^2} \\ \\ \tt-\dfrac{1 - 2xy}{y^2(1 - xy)^2} + h'(y) = y^2 + \dfrac{x^2}{(1-xy)^2} \\ \\ h'(y) = y^2 + \dfrac{x^2}{(1-xy)^2} + \dfrac{1 - 2xy}{y^2(1 - xy)^2} \\ \\ \tt\:h'(y) = y^2 + \dfrac{x^2y^2 - 2xy + 1}{y^2(1-xy)^2} = y^2 + \dfrac{1}{y^2} \\ \\ h(y) = \dfrac{y^3}{3} - \dfrac{1}{y} + C \\ \\ \tt\text{Substituting to }F(x,y),\text{we get} \\ \\ \dfrac{1}{y(1 - xy)} + \dfrac{y^3}{3} - \dfrac{1}{y} = C \\ \\ \quad \quad \text{or} \\ \\ \tt\red{\boxed{\dfrac{x}{1 - xy} + \dfrac{y^3}{3} = C} \Longleftarrow \textit{Answer}} \end{array} [/tex]
[tex] \Large \bold{SOLUTION\ 2:} [/tex]
[tex] \small \begin{array}{l} \tt\text{Since we already know that the equation is exact,} \\ \text{we can then continue solving for the solution by} \\ \text{inspection method or by algebraic manipulation.} \\ \\ \tt(1-xy)^{-2} dx + \big[y^2 + x^2 (1-xy)^{-2}\big]dy = 0 \\ \\ \tt\dfrac{dx}{(1-xy)^2} + \left[y^2 + \dfrac{x^2}{(1-xy)^2}\right]dy = 0 \\ \\ \tt\dfrac{dx}{(1-xy)^2} + y^2 dy + \dfrac{x^2}{(1-xy)^2} dy = 0 \\ \\ \tt\dfrac{dx + x^2dy}{(1-xy)^2} + y^2 dy = 0 \\ \\ \tt\text{Divide both numerator and denominator of the} \\ \tt\text{fraction by }x^2. \end{array} [/tex]
[tex] \small \begin{array}{c}\tt \dfrac{\dfrac{1}{x^2}dx + dy}{\dfrac{(1-xy)^2}{x^2}} + y^2 dy = 0 \\ \tt\\ \tt\dfrac{\dfrac{1}{x^2}dx + dy}{\left(\dfrac{1}{x}-y\right)^2} + y^2 dy = 0 \\ \\ \tt-\dfrac{\left(-\dfrac{1}{x^2}dx - dy\right)}{\left(\dfrac{1}{x}-y\right)^2} + y^2 dy = 0 \\ \\ \tt\displaystyle {\large{\int}} -\frac{d\left(\dfrac{1}{x}-y\right)}{\left(\dfrac{1}{x}-y\right)^2} + \int y^2 dy = \int 0 \\ \\ \tt\implies\tt \dfrac{1}{\dfrac{1}{x}-y} + \dfrac{y^3}{3} = C \\ \\\text{or} \\ \\ \tt\red{\boxed{\dfrac{x}{1 - xy} + \dfrac{y^3}{3} = C} \Longleftarrow \textit{Answer}} \end{array} [/tex]
#CarryOnLearning
#BrainlyMathKnower
Alice is making bracelets to sell. She plans to put 12 beads on each bracelet. Beads are sold in packages of 20.
#1. What is the least number of packages she can buy to make bracelets and have no beads left over?
#2 If each package of beads costs $5.50, how much will the beads cost for her project?
Show and Explain your work
Hint: the “T” Method works well for show and explain. Make sure you have all of the details explained. If someone only read your explanation they should know… what the question is, all of the steps needed to answer the question and what your final answer is.
Answer:
question 1 is 60 beads and question 2 is 16 dollars and 50 cents.
Step-by-step explanation:
for question 1 the are asking for the lowest common denomonator (60)
for question 2 you devide 60/20 and multiply by 5.50
3 x 5.50 = 16.5$
Find the slope of the line that passes through the two given points:
(-1, 4) and (5, 3)
A line starting in the third quadrant, crossed the x axis twice, and then ending in the first quadrant
Answer:
[tex] \frac{ - 1}{6} [/tex]
Step-by-step explanation:
[tex]slope \: = \frac{y2 - y2}{x2 - x1} \\ slope = \frac{3 - 4}{5 - - 1} \\ sope = \frac{ - 1}{ \: \: \: 6} [/tex]
Luke's house is due west of Toronto and due south of Barrie. Toronto is 16 kilometres from Luke's house and 20 kilometres from Barrie. How far is Barrie from Luke's house, measured in a straight line?
Using the Pythagorean Theorem, it is found that Barrie is 12 miles from Luke's house, in a straight line.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
This problem can be modeled by a right triangle, with [tex]l_1 = 16, l_2 = d, h = 20[/tex], hence:
[tex]h^2 = l_1^2 + l_2^2[/tex]
[tex]16^2 + d^2 = 20^2[/tex]
[tex]d^2 = 144[/tex]
[tex]d = 12[/tex]
Barrie is 12 miles from Luke's house, in a straight line.
More can be learned about the Pythagorean Theorem at https://brainly.com/question/654982
How many solutions does this nonlinear system of equations have?
Answer:
ONE “1”
Step by step:
Taking into account the definition of a system of equations, this nonlinear system of equations has one solution.
A system of equations is a set of two or more equations that share two or more unknowns. The solutions of a system of equations are all the values that are valid for all equations.
That is, to find the solution to a system of equations, you must find a value (or range of values) that satisfies all the equations in the system.
Graphically, the points where the graphs of the equations intersect will be the solutions to the system.
A system of equations with a linear equation and a quadratic equation can have two, one, or no solutions. To find its quantity, we must look for the intersection between both graphs:
If the graphs of the equations do not intersect, then there are no solutions for both equations. If the parabola and the line touch at a single point, then there is a solution for both equations. If the line intersects the parabola in two places, then there are two solutions to both equations.
In this case, you can see that the parabola and the line touch at a single point. Then there is a solution for both equations.
In summary, this nonlinear system of equations has one solution.
3. The object has the shape of a rectangular prism, but part of a face is missing.
Find the surface area of the object and show your work.
a)
Find the surface area of the complete prism.
5 cm
30 cm
20 cm
10 cm
15 cm
I need an answer
Find the measure of ∠ABC.
Answer:
170°
Step-by-step explanation:
There is a total of 180° and the angle is 10° less...
So, 180°-10° = 170°
Please 5 stars if correct!!!
I hope this helps!!!
Find the factorization of the polynomial below.
81x^2 - 18x + 1
A. (9x + 1)^2
B. (18x + 1)^2
C. (18x - 1)^2
D. (9x - 1)^2
Answer:
[tex](9x-1)^2[/tex]
Step by step explanation:
[tex]81x^2-18x+1\\\\=81x^2 - 9x-9x+1\\\\=9x(9x-1)-(9x-1)\\\\=(9x-1)(9x-1)\\\\=(9x-1)^2[/tex]
Zoe planted a walnut tree. Every week, she measures the tree and records its
growth. On the first week, the tree was 27 1/2 inches tall. On the second week, it was
29 1/4 inches tall. On the third week, it was 31 1/3 inches tall. How much did the tree
grow from the first week until it was measured on the third week? Show your work.
The tree grew about 3.83 inches between the first and third week.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
On the first week, the tree was 27 1/2 inches (27.5) tall. On the second week, it was 29 1/4 inches (29.25) tall. On the third week, it was 31 1/3 inches (31.33) tall.
The length grown = 31.33 - 17.5 = 3.83 inches
The tree grew about 3.83 inches between the first and third week.
Find out more on equation at: https://brainly.com/question/2972832
URGENT I NEED IT NOW PLEASE HELP ME!!!!
Can someone please help me with this! Thanks <3
Answer:
H
Step-by-step explanation:
If you convert these fractions into decimals:
-2 1/2 = -2.5
-2.47 = -2.47
-2/5 = -0.4
5 = 5
21/4 = 5.25
You can see that the order from lest to greatest is answer H
Hope this helps :)
What is the product of 3/4 and -6/7?
Answer:
-9/14
Step-by-step explanation:
Hey there!
Guide:
• Difference means subtract/subtraction
• Product means multiply/multiplication
• Sum means add/addition
• Quotient means divide/division
• Now that we know what “product” means… we can make the question/equation easier to solve.
3/4 × -6/7
= 3(-6) / 4(7)
= -18 / 28
= -18 ÷ 2 / 28 ÷ 2
= -9 / 14
Therefore, your answer is: -9/14
Good luck on assignment & enjoy your day!
~Amphitrite1040:)
do this only on number line
#4
-2/8=-1/43/6=1/2Refer to the attachment
#2
Mid point:-
-2/5+1/2/2-4+5/10/21/10/21/20Step-by-step explanation:
please mark me as brainlest
Adrianna has $20 in her savings account. Each week she will add $5 to it. Which equation represents this situation?
Answer:
Let y = the amount in Adrianna's savings account
Let x = the number of weeks passed
y = 5x + 20
Please help I'll mark brainliest
✿————✦————✿————✦————✿————✦————✿
So, to find the mean they added up the scores from 20 seasons and divided by 20, the number of seasons to get an average score of 10.4.
10.4 = (x1 +x2 +x3 ... +x20 )/20
Then;
10.4*(20) = (x1 +x2 +x3 ... +x20 )
208 = sum of the first 20 seasons
We want to add one more number in there, the 21st season with a score of 14. Add the 14 to the sum of the first 20 seasons and then divide by 21, the new number of seasons you're averaging.
Mean = (208+14)/21
✿————✦————✿————✦————✿————✦————✿
Answer
= 10.6
✿————✦————✿————✦————✿————✦————✿
#carryonlearning
Choose the expression that represents 3 less than 7 times a number
Answer:
7x - 3, x being the number
Step-by-step explanation:
number = x
7x - 3
Answer:
Three less than 7 times a number is 39.
Step-by-step explanation:
Solve the system of equations:
4x-5y=21
3x+10y= -53
Step-by-step explanation:
2× (4x-5y) = 21
3x+10y= -53
-------------------------
8x-10y = 42
3x+10y=-53
------------------------
11x= -11
{x=-1}
-----------------
3x+10y=-53
x=-1
3(-1)+10y=-53
-3+10y=-53
10y= -50
{y=5}
Can someone help me with this question please?
Answer:
a) 96 = 3.57√h
b) h ≈ 723.11 m
Step-by-step explanation:
a)The equation you want to solve is the model with the given values filled in.
D(h) = 3.57√h . . . . model
96 = 3.57√h . . . . . equation for seeing 96 km to the horizon
__
b)We solve this equation by dividing by the coefficient of the root, then squaring both sides.
96/3.57 = √h
h ≈ 26.891² ≈ 723.11 . . . . meters above sea level
Dustin would need to have an elevation of 723.11 meters above sea level to see 96 km to the horizon.
Shoe Size
2
4
6
8
10
12
At soccer practice, Mike asked each of his teammates to write down their shoe size.
What is the interquartile range for Mike's teammates' shoe sizes?
Answer:
2
Step-by-step explanation:
To find the interquartile range, subtract the lower quartile from the upper quartile.
The upper quartile is 7.
The lower quartile is 5.
Subtract.7–5=2
The interquartile range for Mike's teammates' shoe sizes is 2 sizes.
The interquartile range for Mike's teammates' shoe sizes is R = 2
What in Interquartile Range ( IQR )?The distance between the upper and lower quartiles is known as the interquartile range. Half of the interquartile range corresponds to the semi-interquartile range. Finding the values of the quartiles in a small data set is straightforward.
The spread of the data, or statistical dispersion, is measured by the interquartile range. The middle 50%, fourth spread, or H-spread are further names for the IQR. It is described as the spread between the data's 75th and 25th percentiles.
Given data ,
Let the interquartile range be represented as R
Now , the equation will be
Let the shoe sizes be represented as set A
A = { 2 , 4 , 6 , 8 , 10 }
Now , the upper range of the quartile is = 7
The lower range of the quartile is = 5
And , the interquartile range R = upper quartile - lower quartile
On simplifying , we get
The interquartile range R = 7 - 5 = 2
Hence , the interquartile range R = 2
To learn more about interquartile range click :
https://brainly.com/question/15686744
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The giraffes at the Liberia zoo eat 75 pounds of food per day, and 52.5 pounds per day comes from acacia leaves. How much of their diet comes from other types of leaves?
Julia, the zookeeper, used the equation 52.5 + x = 75 to find the answer. Which equation is an equivalent equation that can be used to solve the problem?
Answer:
Step-by-step explanation:
75-52.5=x
How do you write 7,100 in scientific notation
Answer:
7.1 x 10³
Step-by-step explanation:
Move your decimal so that it follows your first whole number greater than zero. The number of places you moved the decimal is the same as the exponent. Since the number 7.1 needs to INCREASE to be 7,100, then the exponent is positive.
Answer:
7.1 x 10[tex]^{3}[/tex] (note the 3 is an exponent)
Step-by-step explanation:
1. Count how many places there are to the right of 7
2. There are 3
3. Apply the formula of scientific notation a x 10[tex]^{b}[/tex]
4. 7.1 x 10[tex]^{3}[/tex] (remove all digits after 7.1
Hope this helps :)
(2)Please help with both questions
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
Let's think of the boat and wind as vectors:
Boat Vector --> [tex]\langle28cos36^\circ,28sin36^\circ\rangle[/tex]
Wind Vector --> [tex]\langle10cos22^\circ,10sin22^\circ\rangle[/tex]
Now, let's add the vectors:
[tex]\langle28cos36^\circ+10cos22^\circ,28sin36^\circ+10sin22^\circ\rangle[/tex]
Find the magnitude (the true velocity):
[tex]\sqrt{(28cos36^\circ+10cos22^\circ)^2+(28sin36^\circ+10sin22^\circ)}\approx37.78\approx38[/tex]
Find the direction (angle):
[tex]\theta=tan^{-1}(\frac{28sin36^\circ+10sin22^\circ}{28cos36^\circ+10cos22^\circ})\approx32.32^\circ\approx32^\circ[/tex]
Thus, D is the best answer
Problem 2
Recall that the angle between two vectors is [tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})[/tex] where [tex]u\cdot v[/tex] is the dot product of the vectors and [tex]||u||*||v||[/tex] is the product of each vector's magnitude:
[tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})\\\\\theta=cos^{-1}(\frac{\langle-82,47\rangle\cdot\langle92,80\rangle}{\sqrt{(-82)^2+(47)^2}*\sqrt{(92)^2+(80)^2}})\\\\\theta=cos^{-1}(\frac{(-82)(92)+(47)(80)}{\sqrt{6724+2209}*\sqrt{8464+6400}})\\\\\theta=cos^{-1}(\frac{(-7544)+3760}{\sqrt{8933}*\sqrt{14864}})\\\\\theta=cos^{-1}(\frac{-3784}{\sqrt{132780112}})\\\\\theta\approx109.17^\circ\approx109^\circ[/tex]
Therefore, C is the best answer
A rule for creating a pattern is given below. The rule begins with a number called the input and creates a number called the output.
Rule: Multiply the input by 5. Then subtract 4 from the result to get the output.
Which input and output table works for the rule?
Choose 1 answer:
(Choice A)
Input: 5 Output: 5
(Choice B)
Input: 3 Output: 7
(Choice C)
Input: 2 Output: 6
Answer:
Choice C - Input: 2 Output: 6
Answer:
C
Step-by-step explanation:
evaluate the output for the given input values using the rule
choice A
5 × 5 - 4 = 25 - 4 = 21 ≠ 5
choice B
3 × 5 - 4 = 15 - 4 = 11 ≠ 7
choice C
2 × 5 - 4 = 10 - 4 = 6 ← equals the output value
Describe how to find the sale price of an item that has been discounted 15%