The train should travel at a speed of 30√5 miles/hour on a 300-mile trip to minimize the total cost for the trip?
Given the cost per hour for fuel to run is v^2/15 dollars:
Labor cost=$300 per hour
Calculate the velocity to travel on a 300-miles trip:
Total time t=Distance/speed
=300/v
t=300/v
Total cost=(fixed cost*time)+(variable cost*time), where fixed cost is $300 per hour and variable cost is v^2/15 dollars , and time t=300/v
Total cost=(300*300/v)+((v^2/15)*(300/v))
=(90000/v)+(300v/15)
Now, to minimize the total cost on a 300-mile trip, we differentiate the total cost with respect to the velocity:
Let the d/dv of total cost be C(v):
C(v) =(-90000/v^2+300/15=0
(-90000/v^2+300/15)=0
90000/v^2=300/15
90000/v^2=20
v^2=90000/20
v^2=4500
v=√4500
v=30√5 miles/hour
Hence, the speed is 30√5 miles/hour
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PLEASSEEEEEEEEE Solve for x ax^2-2ax+(a+1)=0
i hope that this helps :)
Find the value of x!
××1=× 123 =×/1= the value of x is one
standard to slope intercept form
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{2}{5} x - 2[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 8x - 20y = 40[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: - 20y = 40 - 8x[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 20y = 8x - 40[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{8}{20} x - \frac{40}{20} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{2}{5} x - 2[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
An inequality is shown below.
4x + 2<2x +9
Which graph shows the solution to the inequality?
O A
O
O
B. -
C.
OD
01
N
01
w.
0123
56
8 9 10
8 9 10
+
7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
Answer: Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x < 7/2
Step-by-step explanation: graph included in link
The graph which shows the solution of the inequality 4x + 2 < 2x + 9 is the graph B.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
The given linear in equality is,
4x + 2 < 2x + 9
Find the solution set of the inequality.
Operate the like terms together.
Subtracting both sides by 2x,
2x + 2 < 9
Subtracting both sides by 2,
2x < 7
Dividing both sides by 2,
x < 3.5
Hence the correct graph is B.
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The point J(-2,2) is rotated 270° clockwise around the origin. What are the coordinates of the resulting point, J'?
Check the picture below.
screenshot of question below
1. The slope is -2.
2. The slope is 1.
3. cost of 1 yards fabric is $6.49.
4. The average speed is 65 miles/ h.
What is slope?
The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,
The slope of line is the measure of steepness or the direction of line the coordinate plane.
m = Δy/Δx
where, m is the slope
1. The co- ordinates of the graph is (0, 0) and (-1, 2)
slope = (2-0) / (-1 - 0) = 2/ (-1) = -2
Thus, the slope is -2.
2. The co-ordinates of the graph is (0, 0) and (4, 4)
slope = (4 - 0) / (4- 0) = 4/4 = 1
Thus, the slope is 1.
3. cost of 7 yards fabric = $45. 43
cost of 1 yards fabric = 45. 43/7
= $6.49
4. Distance = 325 miles
Time = 5 hours
So, average speed = 325 / 5
= 65 miles/ h
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a local salesman receives a base salary of $875 monthly. he also receives a commission of 10% on all sales over $1800. how much would he have to sell in a month if he needed to have a monthly income of $1500?
The total sell in a month if salesman needed to have a monthly income of $1500 is $894657.14.
What is termed as the sales commission?Sales commission is indeed the amount of cash as well as money paid to salespeople for exceeding a predetermined sales target. For instance, a company may agree to pay it's own salespeople a 4% commission on monthly sales exceeding Y.The total monthly earnings for salespeople can be calculated as follows:
Monthly salary = base salary + sales commission
Given that what a local salesman generates a base salary of $875 and a 10% sales commission on any and all sales above $1,800, the salesman must make the following sales in order to earn $1500 in a given month:
Let the sales done by 'x'.
Then,
875 + 7% (x - 1800) = 1500
875 + (7/100) (x - 1800) = 1500
7(x - 1800) = 62500
x - 1800 = 8928.7
x = 894657.14
Thus, the total sell in a month if salesman needed to have a monthly income of $1500 is $894657.14.
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the________ is the side right triangle that is directly across from the right angle
You survey people in a city to determine whether they support the construction of a new baseball stadium. The exact percent of all people in the city who support the construction of the stadium is likely between 24% and 38%. How many people did you survey? Round your answer to the nearest whole number.
The number of the people did we survey = 12/19
What is whole number?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers.
The set of whole numbers is 0 through 9 (inclusive). Every value in this set is an example of a whole number. Examples are 0, 15, 53, and so forth.
To convey a thorough grasp of more complicated number identifiers like real, rational, and irrational numbers, whole numbers are employed as building blocks. Calculations can be made simpler and issues can be resolved more quickly by rounding decimal numbers to the next whole number.
According to question,
the exact percentage of the people is between 24% and 38%
24%÷ 38%
=0.24/0.38
=12/19
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James sells 6 cupcakes for £5
Maddie sells 4 cupcakes for £3.50
Which is better value?
You must show all your working.
Given the function f(x) = 8x + 4, find each of the following. f(5), f(-8), f(0)
Answer:
44, -60, 4
Step-by-step explanation:
8(5) + 4 ---- 40 + 4 ---- 44
8(-8) + 4 ---- -64 + 4 ---- -60
8(0) + 4 ---- 0 + 4 ---- 4
SOLVE pleeeeease essy points
always substitute the function
(for example here we have) h(x) with its value
goodluck :)
Hello!
Since h(x) = -3x + 2 and h(x) = -4
[tex]\hookrightarrow \text{Thus: } -3x + 2 = -4[/tex]
Let's solve:
[tex]-3x + 2 = -4\\-3x = -4-2\\-3x=-6\\x = 2[/tex]
Hope that helps!
PLEASE HELP! WILL MARK BRAINLIEST!Jackson biked k kilometers. Maria biked 8 more kilometers than Jackson. Peter biked 2 fewer kilometers than Jackson.Drag and drop the expressions into the boxes to write an expression that represents the total number of kilometers Jackson, Maria, and Peter biked in all.------ + ------ + ------k812k + 10k + 8k + 2k−8k−2
We already know that Jackson biked k kilometers.
Maria biked 8 more kilometers than Jackson, which means that she biked
[tex]k+8[/tex]Peter biked 2 fewer kilometers than Jackson, which means that he biked
[tex]k-2[/tex]To get the total all of them biked, we add those expressions together.
[tex]k+(k+8)+(k-2)[/tex]4. Find the perimeter and the area of the
trapezoid.
18 cm
33.3 cm
31.5 cm
32.4 cm
8.7 cm
The perimeter and area of the given trapezoid are 92.4 cm and 420.525 cm².
What is a trapezoid?An open, flat shape with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel.So, the area and perimeter of the trapezoid:
The perimeter of the trapezoid formula: P = a + b + c + d
P = a + b + c + dP = 8.7+18+33.3+32.4P = 92.4 cmThe area of the trapezoid formula: a+b/2 × h
A = a+b/2 × hA = 8.7 + 18/2 × 31.5A = 420.525 cm²Therefore, the perimeter and area of the given trapezoid are 92.4 cm and 420.525 cm².
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Write the sentence as an equation.
341 is the same as the product of k and 273, minus 79
Write in standard form the equation of the line with the given slope through the given point. slope = 6; (1/2,2)
we are given m=6 and a point MEANING WE CAN SUBSTITUTE THE KNOWNS TO GET C IN THE EQUATION Y=MX+C
[tex]2 = 6( \frac{1}{2} ) + c \\ 2 = 3 + c \\ c = 2 - 3 \\ c = - 1[/tex]
THEREFORE
[tex]y = 6x - 1[/tex]
IS THE ANSWER.
HOPE THIS HELPS
PLS HELP I WILL MARK BRAINLEIST
Volume of the sphere = 17157.28 cubic centimeters
How to calculate the volume of a sphere?
Given:
Diameter (d) = 32
r = d/2 = 16
We know that the volume of a sphere is,
[tex]V=\frac{4}{3} \pi r^{3} \\\\ = \frac{4}{3} (3.14) (16)^{3}\\\\=17157.28 cm^{3}[/tex]
What is the volume of a sphere?
A sphere's capacity is measured by its volume. The sphere has a three-dimensional, rounded shape. Its shape is defined by its three axes, which are the x, y, and z axes. Since the cross-section of the sphere is a circle, the volume in this situation is dependent on the radius or diameter.To learn more about volume of a sphere, refer:
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[tex]\huge\boxed{\sf 17157.28} \\\\\\\displaystyle \sf Converting\ d\ to\ r\\\\r=\frac{d}{2} =\frac{32}{2} =16\\\\Calculating\ the\ volume \\\\V=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi \times 16^{3} \approx 17157.28 \\\\[/tex]
What is the weight of 6yards of fabric
Answer:6.1 ounces
Step-by-step explanation:
The distance around Earth's equator is
4.00 x 104 km. The distance around the Moon's
equator is 6.8 x 103 km. What is the difference
between these distances?
The difference between distance around Earth's equator and distance around the Moon's equator is 284.4.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. We frequently employ subtraction in our daily lives. Subtraction is used, for instance, to determine how much money was spent on the products we purchased, how much money is still in our possession, or how much time is left to complete a task.
Given Data
The distance around Earth's equator is
4.00 x 104 km
= 416 km
The distance around the Moon's equator is
6.8 x 103 km
= 700.4
Difference = Distance around Earth's equator - Distance around the Moon's equator
Difference = 700.4 - 416
Difference = 284.4
The difference between distance around Earth's equator and distance around the Moon's equator is 284.4.
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Given a Figure whose points are A(4, 5), B(2, -1), C(0, 0), D(-4, -1).
What would be the image of that figure if it goes under a reflection across the line y = 1, what is the
coordinate of B'?
A. B'(2, 3)
B. B'(3, 1)
C. B'(-2,3)
D. B'(2, -3)
Answer:
B' (2,3)
Step-by-step explanation:
See the pictures below. B was two units below y = 1 so B' needs to be 2 units above y = 1. That places the point at (2,3)
Create an equation with one solution of x = −7
All help is appreciated :)
The most appropriate choice for linear equation will be given by -
8x - (x - 35) = 2x - (7 + x) is the required equation with x = -7
What is linear equation?
At first it is important to know about algebraic expression
Algebraic expression consist of numbers and variables connected with addition, subtraction, multiplication and division.
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Let y be filled in the gap
8x - (x -35) = 2x - (y + x)
8x - x + 35 = 2x - y - x
7x + 35 = x - y
putting x = -7
7(-7) + 35 = -7 -y
y = -49+35 + 7
y = 7
8x - (x - 35) = 2x - (7 + x) is the required equation with x = -7
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What percentage of this shape is shaded?
5x/6 = 30 solve for x simplify your answer as much as possible
Answer:
x = 36
Step-by-step explanation:
Simplify:To find the value of 'x', isolate 'x'.
[tex]\sf \dfrac{5}{6}x = 30\\\\ \text{Multiply both sides by 6,}\\\\ 5x = 30*6\\\\\text{Divide both sides by 5,}\\\\ x = \dfrac{30*6}{5}\\[/tex]
x = 6 * 6
x = 36
Write an equation of the line passing through point P(0, 0) that is perpendicular to the line y = -9x-1.
y =
The equation of the line passing through P(0, 0) perpendicular to y = -9x - 1 will be [tex]y = \frac{1}{9}x[/tex]
The given question states that the line passes through the point P(0, 0) perpendicular to the line y = -9x - 1. We have to find out the equation of the line. We have to find the equation in slope-intercept form.
We know the slope intercept is: y = mx + b
Also, given the perpendicular line has slope m₂ = -9 according to slope-intercept form. And we know that perpendicular lines have a slope that is equal to the negative reciprocal.
So, the Slope of the line m₁ = Negative reciprocal of the slope of the perpendicular line.
=> [tex]m_{1} = -\frac{1}{m_{2} }[/tex]
=> [tex]m_{1} = -\frac{1}{(-9)}[/tex]
=> [tex]m_{1} = \frac{1}{9 }[/tex]
We get the slope [tex]m_{1} = \frac{1}{9 }[/tex]. Also, it is given that the line passes through (0, 0) so the y-intercept b = 0. Putting these values in slope-intercept form, we get:
=> y = mx + b
=> [tex]y = \frac{1}{9} x[/tex]
Hence, the equation of the line is [tex]y = \frac{1}{9} x[/tex]
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Rewrite the equation in Ax+By=C form.Use integers for A, B, and C.y-4=6(x-6)
The question wants us to represent your the equation y - 4 = 6()
A shirt can be stitched using 3 2/5 m of cloth. How much cloth is required for stitching 15 such shirts?
A 50 m
B 55 m
C 51 m
D none of the above
Help me with this please
Answer:
v = -1.5
Step-by-step explanation:
[tex]v = 2 + ( -7 \times .5) = - 1.5[/tex]
The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Use the constraints of the real-world situation to predict the height of the water balloon at 15 seconds. Use complete sentences to support your answer.
The representation of the linear model shows that the height of the balloon after 15 seconds is 0 feet.
In statistics, the term "linear model" has several meanings depending on the situation.
Since it refers to regression models the most, the phrase is frequently used synonymously with a linear regression model. When used in time series analysis, the phrase has a different meaning. In each case, "linear" refers to a subclass of models for which it is possible to significantly reduce the complexity of the underlying statistical theory.The water balloon is hurled from a height of 40 feet above, as can be seen from the linear model.
The balloon now ascends to a height of 70 feet before returning to ground due to gravity.
The balloon drops to the earth and makes a splash after about ten seconds.
Therefore, the balloon will remain at the ground for some more time.
As a result, according to the linear model, the balloon's height at time 15 seconds is always 0 feet.
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What is the slope of the line that passes through the points (2, 8) and
(-3, 14)? Write your answer in simplest form.
Answer:
-6/5
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (14 - 8)/(-3 - 2)
slope = 6/(-5)
slope = -6/5
The solution is -6/5
The slope of the line that passes through the point A ( 2 , 8 ) and B ( -3 , 14 ) is slope m = -6/5
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the first point be A
Now , the value of A is A ( 2 , 8 )
Let the second point be B
The value of B is B ( -3 , 14 )
And , the slope of the line between 2 points is given by the formula,
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 14 - 8 ) / ( -3 - 2 )
On simplifying the equation , we get
Slope m = 6 / ( -5 )
Slope m = -6/5
Therefore , the slope of the line is m = -6/5
Hence , The slope of the line that passes through the point A ( 2 , 8 ) and B ( -3 , 14 ) is slope m = -6/5
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What kind of transformation converts the graph of f(x)=3x+9 into the graph of g(x)=3x–10?
The transformation of the functions from f(x) to g(x) is translate 7 units right and 2 units up
How to determine the transformation?The equations of the functions are given as
f(x) = 3x + 9
g(x) = 3x - 10
Let the translations from f(x) to g(x) be h and k
So, we have
g(x) = f(x + h) + k
This gives
f(x + h) = 3(x + h) + 9 + k
Open the brackets
f(x + h) = 3x + 3h + 9 + k
Substitute f(x + h) = 3x + 3h + 9 + k in g(x) = f(x + h) + k
g(x) = 3x + 3h + 9 + k
This means that
3x + 3h + 9 + k = 3x - 10
Evaluate the like terms
3h + 9 + k = - 10
This gives
3h + k = - 19
Express -19 as -21 + 2
3h + k = -21 + 2
Express 21 as 3 * 7
3h + k = -3 * 7 + 2
By comparison, we have
h = -7 and k = 2
This means that the transformation is 7 units right and 2 units up
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