Answers
The two trains travel for the same amount of time, but because their speeds are different, they travel different distances. The two distances add to 450 miles.
distance = speed * time
For the commuter train, you have distance d1, time t, and speed s.
For the express train, you have distance d2, time t, and speed s + 25.
The time is 6 hours, so,
For the commuter train, you have distance d1, time 6, and speed s.
For the express train, you have distance d2, time 6, and speed s + 25.
d = st
Commuter:
d1 = st
Express
d2 = (s + 25)t
Add the equations:
d1 + d2 = st + (s + 25) t
d1 + d2 = st + st + 25t
d1 + d2 = 2st + 25t
d1 + d2 = (2s + 25)t
The two distances add to 450 miles, d1 + d2 = 450, and t = 6.
450 = (2s + 25)(6)
75 = 2s + 25
50 = 2s
s = 25
The commuter train's speed is 25 mph.
The express train's speed is 50 mph.
Check:
distance = speed * time
In 6 hours, the commuter train travels d = 25 mph * 6 hours = 150 miles.
In 6 hours, the express train travels 50 mph * 6 hours = 300 miles.
150 miles + 300 miles = 450 miles.
The distances do add to 450 miles and the speed of the express train is 25 mph faster, so our answer is correct.
Related Questions
Which theorem could kari use to show the measure of angle qml is supplementary to the measure of angle snk? (1 point)?
Answers
PLEASE HELP! 10 POINTS!
Which algebraic expression represents the phrase below?
The quotient of the opposite of a number squared and three
*choices below*
Answers
Solve each system by substitution
y=-4x + 5
y= -2x + 1
Answers
x=2 and y=−3
What is the length of EF in the right triangle below
Answers
The correct answer is 24.
What is the length of leg s of the triangle below
Answers
as Pythagoras theorem, the longer side equals the 2 shorter sides add together( squared)
root 18 - 3^2 = root 18 - root 9= root 9
and root 9=3
Answer: The correct option is (B) 3.
Step-by-step explanation: We are given to find the length of the leg s in the triangle shown in the figure.
From the figure, we note that
the given triangle is a right-angled one, where
length of the hypotenuse, h = √18 units,
length of one leg, p = 3 units
and
length of the other leg, s = ?.
From Pythagoras theorem, we have
[tex]h^2=p^2+s^2\\\\\Rightarrow (\sqrt{18})^2=3^2+s^2\\\\\Rightarrow 18=9+s^2\\\\\Rightarrow s^2=18-9\\\\\Rightarrow s^2=9\\\\\Rightarrow s=3.[/tex]
Thus, the length of the leg s is 3 units.
Option (B) is CORRECT.
Assume ABC DEF. If AB = 12, BC = 15, and AC = 17, what is the length of EF? A. 15 B. 17 C. Cannot be determined D. 10
Answers
If ABC=DEF, then the answer would be A.
Answer:
Option A) EF = 15 units.
Step-by-step explanation:
We are given the following information in the question:
ΔABC ≅ ΔDEF
AB = 12, BC = 15, and AC = 17
If two triangles are congruent then they have the following properties:
AB = DE
BC = EF
AC = DF
[tex]\angle A = \angle D \\\angle B = \angle E \\\angle C = \angle F[/tex]
Hence, by congruency:
BC = EF
EF = 15 units.
Thus, option A is the correct answer.
Someone please help me ?
Answers
You earned $23.10. You would like to buy some new T-shirts. Estimate the number of T-shirts you can buy if each one costs $5.75.
Answers
Paige made $1411.75 last year by investing a total of $15,250 in two accounts: one paying 8.5% annual interest and the other paying 10% annual interest. How much did she invest in each account?
Answers
x account invested with annual interest rate 8.5%
y account invested with annual interest rate 10%
x + y =15,250 so x = 15,250 - y
0.085x + 0.1y = 1,411.75
substitute x = 15,250 - y into 0.085x + 0.1y = 1,411.75
0.085x + 0.1y = 1411.75
0.085(15,250 - y) + 0.1y = 1,411.75
1,296.25 - 0.085y + 0.1y = 1,411.75
0.015y = 115.5
y = 7,700
x = 15,250 - y
x = x = 15,250 - 7,700
x = 7,550
answer
$7,550 invested on account with annual interest rate 8.5%
$7,700 invested on account with annual interest rate 10%
Find the value of x so that the function has the given value.
r(x)=−5x−1; r(x)=19
x=
Answers
To find the value of 'x' that makes the function r(x) = 19, we need to solve the equation -5x - 1 = 19 for 'x'. After doing so, we obtain x = -4.
Explanation:This question involves finding the value of 'x' in a mathematical function provided, in order to get a specific output. The function provided is r(x) = -5x - 1 and the question states that the output r(x) should be 19. We can setup the equation -5x - 1 = 19 and solve for 'x'.
Adding 1 to both sides of the equation, we obtain -5x = 20. Dividing both sides by -5 gives x = -4. So, the value of 'x' that makes the function r(x) = 19 is x = -4.
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Find the second and third term of the arithmetic sequence -7, _, _, -22, -27, ...
A. -12, -15
B, -17, -12
C. -10, -17
D. -12, -17
Answers
Final answer:
The second and third terms of the arithmetic sequence are -12 and -17, found by adding the common difference of 5 to each succeeding term in the sequence.
Explanation:
The question is asking to find the second and third terms of an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which the difference between the consecutive terms is constant. This constant difference is known as the common difference. In the given arithmetic sequence (-7, _, _, -22, -27), we can find the common difference by subtracting two successive terms. For this sequence, the difference between -27 and -22 is -27 - (-22) = -27 + 22 = -5. This implies that to find the previous terms, we should add 5 to each term going backwards.
Starting with -22 and adding 5, we get -17 for the third term. Similarly, adding 5 again for the second term, we get -12. Therefore, the second and third terms of the arithmetic sequence are -12 and -17, respectively.
Which of these shows the result of using the first equation to substitute for y in the second equation, then combining like terms?
y = 3x
2x + 3y = 55
A. 11x = 55
B. 5x = 55
C. 9x = 55
D. 5y = 55
Answers
Answer: A(11x=55)
Step-by-step explanation:
in the equation 2x + 3y = 55, subsitute 3y for 3x, because y = 3x. this will result in the equation 2x + 3(3x) which equals 11x. so 11x=55
100/225 square feet of your bakery will be used as your storefront, where customers come to visit. the rest will be for storage and baking. In simplest form, what fraction of the space will be for storage and baking?
Someone's work
(225-110)/225
125/225
5/9
how did you get (225-110)? if it's 100/225
Answers
Answer: 5/9 will be the fraction of the space will be for storage and baking.
Step-by-step explanation:
Since area of bakery will be used as our storefront, where customers come to visit= 100/225
Thus, the total area of bakery = 225
And, the area will be used our storefront, where customers come to visit= 100
So, the remaining area which is used for storage and baking = 225 - 100 =125
So the part of area which is used for storage and baking= the remaining area which is used for storage and baking/ total area
=125/225= 5/9
which is the simplest form.
I have a right triangle they need an equation from me.the truangle is X,4,7 ... Please i need help
Answers
Final answer:
The question involves using the Pythagorean theorem to find the missing side 'X' in a right triangle with sides 'X', 4, and 7. 'X' is calculated by rearranging the theorem to X² = c² - b² and plugging in the known values. The equation simplifies to X = √33.
Explanation:
The student is asking for an equation to solve for the missing side of a right triangle, where the sides are given as 'X', 4, and 7. The Pythagorean theorem, which states that a² + b² = c², is the appropriate tool for solving this problem. Since the triangle is right-angled, we assume 'X' is one leg, 4 is the other leg, and 7 is the hypotenuse as it is the longest side.
To find 'X', we rearrange the theorem to solve for the unknown leg (X) as follows: X² = c² - b². Plugging the values into the equation gives us X² = 7² - 4² which simplifies to X² = 49 - 16, hence X² = 33. Consequently, X can be found by taking the square root of 33, which we rewrite as X = √33.
Find the dimensions of the rectangular corral split into two pens (sharing a fence) of the same size producing the greatest enclosed area given 630 630 feet of fencing.
Answers
--------------------------
| | w
| |
--------------------------
| |
| | w
--------------------------
Area = l* 2w
fence length: 3l + 4w = 630 => 3l = 630 - 4w => l = 630 / 3 - (4w/3)
=> l = 210 -4w/3
=> area = (210 - 4w/3) * (2w) = 420w - 8(w^2)/3
The maximum or minimum of a parabola of the form ax^2 + bx + c is at x = -b/2a
So, the maximum of - 8(w^2) / 3 + 420 w is at w = - 420 / ( - 2*8/3) = 78.75
and l = 210 - 4(78.75)/3 = 105.
Answer: l = 105 feet and 2* w = 157.5 feet
To find the dimensions of the rectangular corral split into two pens that produce the greatest enclosed area, use the perimeter and area formulas for a rectangle.
Explanation:To find the dimensions of the rectangular corral split into two pens that produce the greatest enclosed area, we can use the perimeter formula for a rectangle. Let L and W represent the length and width of each pen. The total fencing length will be 2L + 3W, and since it is given as 630 feet, we have 2L + 3W = 630. We can rearrange this equation to solve for one variable in terms of the other, substitute it into the area formula for a rectangle, and then find the maximum value using the first derivative test.
Using the equation 2L + 3W = 630, we can solve for L in terms of W: L = (630 - 3W) / 2. Substituting this into the area formula A = LW, we get A = (630 - 3W)W / 2. Taking the first derivative of A with respect to W, we have dA/dW = 630/2 - 3W/2. Setting this equal to zero, we find W = 105. Substituting this back into the equation 2L + 3W = 630, we can solve for L: 2L + 3(105) = 630, and simplifying gives L = 210/2 = 105.
Therefore, the dimensions of each pen that produce the greatest enclosed area are 105 feet by 105 feet.
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Through: (-4,4), perp. To y=4/5x-1
Answers
[tex]m_{0} = \frac{-1}{m} [/tex]
[tex] m_{0} = -1 / \frac{4}{5} = - \frac{5}{4} [/tex]
Use the point-slope equation to write an equation of the line perpendicular to given:
[tex]y - y_{0} = m(x- x_{0} ) [/tex]
We have a point (-4, 4). Plug in instead of [tex] x_{0} , y_{0} [/tex]:
[tex]y - 4 = - \frac{5}{4} (x+4) \\ y = - \frac{5}{4} x -1[/tex]
This is the final equation.
Is 0.33 bigger than 20/60?
Answers
To compare, let's convert 20/60 to a decimal. The decimal form of 20/60 is 0.3333 repeating.
According to the conversion, 0.33 and the fraction 20/60 are equal.
Hope this helps!
May
Suppose p = log n ( g ) p=logn(g). define an exponential relationship between p , n , p,n, and g g.
Answers
Therefore, the exponential relationship between p, n and g is given by;
[tex]g=n^p[/tex]
If you drive at 100km/hr for 6 hours, how far will you go
Answers
The distance covered by the vehicle in 6 hours will be 600 km.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
If you drive at 100km/hr for 6 hours.
Then the distance covered by the vehicle in 6 hours will be given as,
100 = Distance / 6
Distance = 100 x 6
Distance = 600 km
The distance covered by the vehicle in 6 hours will be 600 km.
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In modified boxplots, a data value is a(n) _______ if it is above q3plus+(1.5)(iqr) or below q1minus−(1.5)(iqr).
Answers
An outlier is an observation point that is distant from other observations.
In modified boxplots, a data value is a potential outlier if it is outside the range of Q3 + (1.5)(IQR) or Q1 - (1.5)(IQR). The IQR is the spread of the middle 50% of the data, calculated as Q3 - Q1.
Explanation:In modified boxplots, a data value is a potential outlier if it is above Q3 + (1.5)(IQR) or below Q1 - (1.5)(IQR). The interquartile range (IQR) is crucial in this determination, representing the spread of the middle 50 percent of the data. It is found by subtracting the first quartile (Q1) from the third quartile (Q3). For example, if Q1 is 2 and Q3 is 9, the IQR is 7. Any data value greater than 9 + (1.5)(7) or less than 2 - (1.5)(7) would be considered a potential outlier.
Constructing a box plot involves identifying these five key values: minimum value, first quartile, median, third quartile, and maximum value. The box plot visually represents the data's spread, with whiskers extending to the most extreme values within the acceptable range, and separate marks for potential outliers.
Wilma and Betty are playing a number game. Wilma tells Betty, "I'm thinking of a number between 1 and 10. If I take the number and add 4 to it and then multiply that by 3, I get 30." What number is Wilma thinking of?
Answers
(x+4)•3=30
Now solve :
(x+4)•3=30
3x+12=30
-12 -12
3x=18
/3 /3
x=6
Your answer is 6!
Hoped I helped!
To find the number Wilma is thinking of, we create an equation and solve for x.
Explanation:To solve this problem, we need to create an equation based on the information given. Let's suppose the number Wilma is thinking of is x. According to the problem, if we add 4 to x and then multiply that result by 3, we get 30. We can write this as the equation 3(x + 4) = 30. To find the value of x, we need to isolate it. First, distribute the 3 to both terms inside the parentheses: 3x + 12 = 30. Next, isolate x by subtracting 12 from both sides of the equation: 3x = 18. Finally, solve for x by dividing both sides of the equation by 3: x = 6. Therefore, Wilma is thinking of the number 6.
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Martin has 4 tickets to ICe Fantasy with the Stars. They cost him $15.75 each, plus $3.50 in handling per ticket, and $9.50 in shipping. What was the total cost of the tickets?
86.50
79.50
70.00
99.50
Answers
so each ticket cost $15.75 + $3.50 = $19.25.
There are 4 tickets, so the 4 tickets including handling
cost 4 * $19.25 = $77.00
The shipping fee is a single fee for all the tickets,
so you just add $9.50 to $77.
The total cost is $77.00 + $9.50 = $86.50
If the volumes of two similar rectangular prisms are 40mm and 135mm find the scale factor of the two rectangular prisms.
(The answers are in fraction form)
A. 1/4
B. 8/27
C. 3/5
D. 2/3
Answers
the answer is B) 8/27
The scale factor of the two rectangular prisms is 3/2 of the given problem the volumes of two similar rectangular prisms are 40 mm and 135 mm
To find the scale factor between two similar rectangular prisms, we can compare their volumes. The scale factor is the ratio of the cube root of the volumes.
Let's denote the volume of the first rectangular prism as V1 and the volume of the second rectangular prism as V2.
[tex]V1 = 40 mm^3\\V2 = 135 mm^3[/tex]
The scale factor (SF) can be calculated as follows:
[tex]SF = (V2)^{(1/3)} / (V1)^{(1/3)[/tex]
Plugging in the given values:
[tex]SF = (135)^{(1/3)} / (40)^{(1/3)[/tex]
To simplify the calculation, we can rewrite the values as prime factorization:
[tex]135 = 3^3 * 5\\40 = 2^3 * 5[/tex]
Now, let's calculate the cube roots:
[tex]SF = (3^3 * 5)^{(1/3) }/ (2^3 * 5)^{(1/3)}[/tex]
Using the property of exponents [tex](a^{(m/n) }= (a^m}^{(1/n)})[/tex]:
[tex]SF = (3^{(3/3)} * 5^{(1/3)}) / (2^{(3/3)} * 5^{(1/3)})[/tex]
Simplifying the fractions:
[tex]SF = 3 * 5^{(1/3)} / 2 * 5^{(1/3)[/tex]
The [tex]5^{(1/3)}[/tex] terms cancel out:
SF = 3/2
Therefore, the scale factor of the two rectangular prisms is 3/2 of the given problem the volumes of two similar rectangular prisms are 40 mm and 135 mm.
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can someone please simplify 81^5 = 3^x
Answers
Answer:
20
Step-by-step explanation:
:D
The value of the x is 20.
We have given that,
[tex]81^5 = 3^x[/tex]
We have to determine the value of x.
3^4 = 81
What is the exponent?Exponentiation is a mathematical operation, written as bⁿ, involving two numbers, the base b, and the exponent or power n, and pronounced as b raised to the power of n.
exponent 4 x 5 = 20
so, 3^20 = 81^5
Therefore the value of the x is 20.
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Choose the correct answers for interest in dollars and the proceeds for the following problem. Sam Sounds received a $320 discount loan to purchase a stereo. The loan was offered at 16% for 90 days. Find the interest in dollars and the proceeds for the following problem.
Answers
The Interest is $12.595 while the value of the Proceeds is $307.405
How to find the interest and proceeds?The amount of loan; A = $320
The discount rate = 16%=0.16
Time = 90 days = 90/365 year = 0.246 year
The formula of interest is;
Interest = Amount × Discount rate × Time
Thus;
Interest = 320 × 0.16 × 0.246
Interest = $12.595
Proceed = Amount - Interest
Proceed = $320 - $12.595
Proceeds = $307.405
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Answer:
12.80
307.20
Step-by-step explanation:
True or false? To begin an indirect proof, you assume the converse of what you intend to prove is true.
A. True
B. False
Answers
Answer:
The statement is false.
Step-by-step explanation:
To begin an indirect proof, you assume the converse of what you intend to prove is true. This is false.
Rather the correct answer is that to begin an indirect proof, you assume the inverse of what you intend to prove is true.
The converse can be either true or false, depending on what the original statement is, so assuming the converse is pointless.
When making bread from scratch, the recipe calls for 2/4 cup of water. If you need to make a smaller portion of the recipe, how much water would you need in order to make only 1/6 of the recipe? Give your answer as a fraction, reduced to lowest terms
Answers
1/6 * 2/4 = 1/6 * 1/2 = 1/12
You would need 1/12 cups of water in order to make only 1/6 of the recipe
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
What are Arithmetic operations?Arithmetic operations can also be specified by addition, subtraction, dividing, and multiplying built-in functions.
When making bread from scratch, the recipe calls for 2/4 cup of water. If you need to make a smaller portion of the recipe,
If a recipe requires 2/4 cup of water, then a fraction of the recipe requires 1/6 cup of water.
So the fraction of the recipe requires 1/6 cup of water as
⇒ 1/6×2/4
⇒ 2/24
⇒ 1/12
Hence, you would need 1/12 cups of water in order to make only 1/6 of the recipe.
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The posted speed limit is 55 MPH. If you’re driving 1000 feet per minute, are you going too fast?
Answers
An hour is 60 minutes, so 60 * 1000 = 60000 feet per hour.
Now change that to miles. There are 5280 feet in one mile, so just divide 60000 by 5280 to find out how many sets of 5280 there are in 60000.
60000/5280 = about 11 mph
So you aren't going too fast.
Why is x = 4 a solution to the proportion 14/x = 56/16
Answers
[tex]\large\text{Hey there!}[/tex]
[tex]\large\text{Step 1: You have to \underline{\bf{CROSS MULTIPLY}}}[/tex]
[tex]\mathsf{\dfrac{14}{x}=\dfrac{56}{16}}\\\\\mathsf{14\times16=56\times x}\\\\\mathsf{14(16)= \ \bf{\underline{224}}}\\\\\mathsf{56(x)=\underline{\bf{56x}}}[/tex]
[tex]\huge\text{We get: \bf{\underline{224 = 56x}}}[/tex]
[tex]\large\text{Step 2: }\large\text{\bf{\underline{FLIP}}}\large\text{ the new equation around}[/tex]
[tex]\huge\text{\bf{\underline{56x = 224}}}[/tex]
[tex]\large\text{Step 3: \bf{\underline{DIVIDE}}}\large\text{ both of your sides by 56}[/tex]
[tex]\mathsf{\dfrac{56x}{56}=\dfrac{224}{56}}\\\\\mathsf{Cancel\ out: \dfrac{56x}{56}\ because\ that\ gives\ us\ 1}\\\\\mathsf{Keep: \dfrac{224}{56}\ because\ it\ gives you\ the\ value\ of\ x }\\\\\mathsf{\dfrac{224}{56}=4}\\\\\mathsf{x=4}[/tex]
[tex]\boxed{\large\text{So, the reason why x = 4 for this equation is because } \mathsf{\dfrac{14}{4}}\ \& \ \dfrac{56}{16}\ \large\text{ are equal to each}}\\\boxed{\large\text{other. }}[/tex]
[tex]\mathsf{\dfrac{14}{4} = 3.5}[/tex]
[tex]\mathsf{\dfrac{56}{16} = 3.5}[/tex]
[tex]\huge\text{\bf{3.5 = 3.5}} \ \checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\dag\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]
a large bottle of dragon mouth was is 5.00 before tax and 5.30 after tax. What is the percentage of tax