=======================================================
Work Shown:
x = number of miles
2x = cost of traveling x miles, at $2 per mile, without including the $3 fee
2x+3 = total cost now including the $3 entrance fee, without tip
2x+3+1 = total cost plus $1 tip
2x+4 = amount you spent
2x+4 = 20
2x = 20-4
2x = 16
x = 16/2
x = 8
You traveled 8 miles.
Hey there! I'm happy to help!
Let's represent the number of miles traveled with the variable m.
We see that it will cost $2 for every mile, so for if we drive 8 miles, it will cost $16, 9 will be $18, and so forth. So the relationship is that the cost will be double the money, so what we have here is 2×m. In algebra, you can simply write variable multiplication as just putting the numbers next to each other, so 2m will be that part of the equation.
We see that the initial cost of the taxi is $3.
3
We are going to be adding our $2 per mile to this amount (2m).
3+2m
And we will add our $1 tip.
3+2m+1
And this is equal to $20.
3+2m+1=20
We can combine the 3 and the 1 to give us 4.
4+2m=20
So, we see that 2m+4 is equal to 20. If we subtract that four from 20, we will see that 2m is equal to 16.
We remember that our cost from mileage is double the miles, so if 16 is double something, we just divide by two!
16/2=8
So, this means that we traveled 8 miles!
Have a wonderful day and keep on learning! :D
9. Maria usually pays $3.10 per pound for her favorite granola. Which of the answers below is
a better deal?
A. 2 pounds for $6.49
B. 3 pounds for $10
C. 5 pounds for $14.75
D. 8 pounds for $28
What’s the answer
Answer:
c
Step-by-step explanation:
The answer is C. To find the answer all you need to do is divide the money per pound for each option until you find the lowest deal.
A is not a good deal because its about $3.14 for a pound
B is not a good deal because its about $3.33 per pound
D is not a good deal because its $3.50 per pound
C IS a good deal because it's $2.95 per pound
Answer:
c
Step-by-step explanation:
The answer is C. To find the answer all you need to do is divide the money per pound for each option until you find the lowest deal.
A is not a good deal because its about $3.14 for a pound
B is not a good deal because its about $3.33 per pound
D is not a good deal because its $3.50 per pound
C IS a good deal because it's $2.95 per pound
Calculus (yet again)!
The water level of a certain body of water is changing at a rate of [tex]W(t) = \frac{1}{2}cos(3 - \frac{t}{2})[/tex] inches per hour, where t represents hours since 12 a.m.
What is the average hourly number of inches that the water level changes for this lake in one day?
I'm pretty sure that the number of inches that the water changes in one day would be represented by [tex]\int\limits^2_0 {W(t)} \, dt[/tex] (where the number on top of the integral is a 24), but how would I set up an integral for the average hourly number of inches? Thank you so much!
Answer:
The average hourly number of inches that the water level changes per day is about 0.0231 inches per hour.
Step-by-step explanation:
The water level of a certain body of water is changing at a rate represented by the function:
[tex]\displaystyle W(t) = \frac{1}{2}\cos \left( 3- \frac{t}{2}\right)[/tex]
Where W is measured in inches per hour and t represents hours since 12 A.M.
And we want to determine the average hourly number of inches that the water level changes for the lake in one day.
Recall that the average value of a function is given by:
[tex]\displaystyle f_\text{avg} = \frac{1}{b-a} \int_{a}^{b} f(x) \, dx[/tex]
Hence, the find the average hourly number of inches that the water level changes in one day, we simply need to find the average value of W from t = 0 to t = 24.
Substitute:
[tex]\displaystyle W(t)_{\text{avg}} = \frac{1}{(24)-(0)} \int_{0}^{24} \frac{1}{2}\cos \left(3 - \frac{t}{2}\right) \, dt[/tex]
Simplify:
[tex]\displaystyle W(t)_{\text{avg}} = \frac{1}{24} \int_{0}^{24} \frac{1}{2}\cos \left(3 - \frac{t}{2}\right) \, dt[/tex]
Evaluate using u-substitution. We can let:
[tex]\displaystyle u = 3 - \frac{t}{2} \Rightarrow du = -\frac{1}{2}\, dt\Rightarrow -2\, du = dt[/tex]
Hence:
[tex]\displaystyle W(t)_{\text{avg}} = -\frac{1}{24} \int_{3}^{-9} \cos u \, du[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} W(t)_{\text{avg}} &= \frac{1}{24}\int_{-9}^{3} \cos u\, du \\ \\ &= \frac{1}{24}\left(\sin u\Big|_{-9}^{3}\right) \\ \\ &= \frac{1}{24}\left(\sin3 - \sin -9\right) \\ \\ &=\frac{1}{24}\left(\sin 3 + \sin 9\right) \\ \\ &\approx0.0231 \end{aligned}[/tex]
In conclusion, the average hourly number of inches that the water level changes per day is about 0.0231 inches per hour.
This is finding the midpoint. Please help
Answer:
hence the required midpoint of the given line is (9,5)
Answer:
[tex]( \frac{6 + 2}{2} +\frac{12 + 8}{2}) = ( \frac{8}{2} + \frac{20}{2} ) = (4 \: comma10)[/tex]
The answer is :(4, 10)
Find the equation of the tangent of x^2- xy + y^2 =7 at (-1, 2)
Answer:
It is 3y = 4x + 10
Step-by-step explanation:
Let's first get the slope of the curve.
[ slope is the derivative of the equation ]
[tex] {x}^{2} - xy + {y}^{2} = 7[/tex]
introduce dy/dx :
[tex] \frac{d}{dx} ( {x}^{2} - xy + {y}^{2} ) = \frac{d}{dx} (7) \\ \\ 2x - (y + \frac{dy}{dx} ) + 2y \frac{dy}{dx} = 0[/tex]
make dy/dx the subject:
[tex]2x - y - \frac{dy}{dx} + 2y \frac{dy}{dx} = 0 \\ \\ 2y \frac{dy}{dx} - \frac{dy}{dx} = y - 2x \\ \\ \frac{dy}{dx} (2y - 1) = y - 2x \\ \\ \frac{dy}{dx} = \frac{y - 2x}{2y - 1} [/tex]
At point (-1, 2):
[tex] \frac{dy}{dx} = \frac{2 - 2( - 1)}{2(2) - 1} \\ \\ slope = \frac{4}{3} [/tex]
but a tangent has the same slope as the curve:
[tex]y = mx + c[/tex]
m is the slope
c is the y-intercept
At (-1, 2):
[tex]2 = ( - 1 \times \frac{4}{3} ) + c \\ \\ c = 2 + \frac{4}{3} \\ \\ c = \frac{10}{3} [/tex]
equation:
[tex]y = \frac{4}{3} x + \frac{10}{3} \\ \\ { \boxed{3y = 4x + 10}}[/tex]
Answer:
Step-by-step explanation:
Here is an other way:
z=f(x,y)=x²-xy+y²-7=0
[tex]\dfrac{\partial f(x,y)}{\partial x} =2x-y\\\\\dfrac{\partial f(x,y)}{\partial y} =-x+2y\\\\\\\dfrac{dy}{dx} =-\dfrac{\dfrac{\partial f(x,y)}{\partial x} }{\dfrac{\partial f(x,y)}{\partial y}} =-\dfrac{2x-y}{-x+2y} \\\\(-1;2)\\Slope=-\dfrac{2*(-1)-2}{1+2*2} =\dfrac{4}{5} \\\\y-2=\frac{4}{5} (x+1)\\\\\\\boxed{y=\dfrac{4x}{5} +\dfrac{14}{5} }[/tex]
The following table shows the amount of money earned by the key club from a car wash. Use the table to determine what the rate of change is if the amount of money made is dependent on the number of cars washed.
Answer:
Can u help me
Step-by-step explanation:
With my maths question
The domain for f(x) and g(x) is the set of all real numbers
Let f(x) = 3x + 5 and g(x) = x^2
Find (f + g)(x).
Answer:
3x square + 5 is your answer
Solve the following problem. Round to one decimal place if necssary.
Answer:
x = 16.1051577
Step-by-step explanation:
tan0 = opp/adj
tan0 = 14/x
tan(49)× 14 = 16.1051577
is 3.4567, 3.4567... irrational or rational
Answer:
Irrational
Step-by-step explanation:
Because irrational this number do not repeat so there for it is not rational.
Find the equation of the line that is perpendicular to y=-2x+1 and contains the point (8, 2).
Answer:
y = 1/2x - 2
Step-by-step explanation:
In order for a line to be perpendicular to another, the lines must have opposite reciprocal slopes.
Example of an opposite reciprocal slope: -2 ⇒ 1/2
Insert the information into the point-slope formula:
[tex]y-y_1=m(x-x_1)\\\\y-2=\frac{1}{2}(x-8)\\\\y-2=\frac{1}{2}x-4\\\\y=\frac{1}{2}x-2[/tex]
2sinx/2cosx-secx=tan2x
Answer:
hope it help u
Step-by-step explanation:
2sinx/(2cosx – secx)
=2 sinx/(2cosx–1/cosx)
as secx = 1/ cosx
multiplying both the denominator and numerator by cost,we get
2sinxcosx/( 2cos^2x –1) =cos2x
since,2sinxcosx = sin2x and 2cos^2 –1=cos2x
2sinxcosx/(2cos^2x– 1)= sin2x/ cos2x = tan2x
WHATS 9+10??????????????
Ben took part in a 45km bicycle race.Ben cycled at a speed of v km/h for the entire race.Express the time taken by Ben in terms of v.
Answer:
(45/v) hours
Step-by-step explanation:
that is the answer yep
Answer:
45/v =t
Step-by-step explanation:
Cuz the normal formula is
V= d/t
Therefore
t= d/v
And u know D = 45km so..
t=45/v
Which statement is supported by the graph?
The bicycle has speed but not velocity.
The bicycle is moving at a constant velocity.
The bicycle has a displacement of 3 m.
The bicycle is not in motion.
Answer:
The correct answer is D. The bicycle is not in motion.
Step-by-step explanation:
In the position-time graph we can see that the position of the cycle hasn't changed when the time has changed (e.g. when time changes from 2s to 3s, the position remains 3m). Therefore, we can conclude that the cycle is not moving, and therefore answer D. is correct.
Answer:
its d
Step-by-step explanation:
What’s the answer to this? Please send help
Answer:
B
Step-by-step explanation:
giải phương trình :
-4x-8x>0
Answer:
[tex]x < 0[/tex]
Step-by-step explanation:
[tex] - 4x - 8x > 0[/tex]
➡️ [tex] - 12x > 0[/tex]
➡️ [tex]x < 0[/tex]
calculate the area of the classroom.area =l×b
answer it plz
step by step plz
Answer:
I HOPE IT WILL HELP YOU A LOT.
Have a great day ahead.
When the sum of the internal angles of a polygon is 10 right angles, then how
many sides does it have?
Answer:
7 sides
Step-by-step explanation:
formula for sum of interior angles
(n-2)× 180= 10 right angles
(n-2)× 180 = 900
n-2= 900÷180
n= 5+2
n= 7
10q - 20 is equivalent to _____.
2(q - 10)
10(q - 20)
10(q - 2)
what is equivalent expression to 0.112 - 16/75 A -0.112 + 16/75 B -0.112 (-16)/75 C 0.112 + (-16)/75
Answer:
C
Step-by-step explanation:
0.112 + (-16)/75 is equivalent to 0.112 - 16/75
Find tan A of a RIGHT TRIANGLE with side lengths b = 8 and c = 12
-5.025, -square root of 25, -5 1/2, -11/2 least you greatest
answer =-51/2,-11/2,-5.025,-✓25
-✓25=-5
-11/2=-5.5
-51/2=-25.5
-5.025
look at the adjoining figure and write 2 pairs of intersecting lines.
Answer:
Line AB and Line GHLine CD and Line FFConcept:
Intersecting lines are lines that overlap upon only one point. The number of lines can be two or more.
Intersecting lines can intersect at any angle.
Solve:
There are in total four intersecting points in the given figure.
As we can see from the figure, any two lines would intersect each other
Therefore, 2 pairs of intersecting lines can be any pairings of lines that are not in the same orientation.
Line AB and Line GHLine CD and Line FFHope this helps!! :)
Please let me know if you have any questions
Solve for x: |4x + 12| = 16 (5 points)
Group of answer choices
x = 7, x = −7
x = 1, x = −1
x = 1, x = −7
x = −1, x = 7
X= 1 , X= –7
I hope I helped you^_^
if (2x,3y) =(8, 9),find x and y
Answer:
x = 4, y = 3
Step-by-step explanation:
Equating corresponding coordinates , gives
2x = 8 ( divide both sides by 2 )
x = 4
and
3y = 9 ( divide both sides by 3 )
y = 3
Write an equation in slope-intercept form of a line that passes through the point (-4,9) and has a slope of 1/2.
Answer:
y = 1/2x + 11
Step-by-step explanation:
y = 1/2x + b
9 = 1/2(-4) + b
9 = -2 + b
b = 11
You use a crowdfunding website to raise money. the website keeps 5% of each donation. Five of your friends each donate the same amount.e total funding you receive is $47.50. How much does each friend donate?
Answer:
Step 1:
Let x represent the amount of each friend donate
Website keeps = 5%
Total funding I receive = $ 47.50
4.75x = $47.50
Step 2:
4.75 = $47.50 - Write the equation
[tex]\frac{4.75x}{4.75}[/tex] = [tex]\frac{47.50}{4.75}[/tex] - Divide both sides of the equation by 4.75
The solution is x = 10
ANSWER: Each friend donates $10
hope this helps Have a good day.
Each friend donates $10.
It is required to find How much does each friend donate.
What is arithmetic?The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.
Given :
The website keeps 5% of each donation.
Five of your friends each donate the same amount.
Total funding receive is $47.50.
Let x represent the amount of each friend donate
According to question we have,
4.75x = $47.50
Divide both sides of the equation by 4.75 we get,
x = 10
Therefore, each friend donates $10.
Learn more about arithmetic here:
brainly.com/question/24423838
#SPJ2
Simplify (ab)(ab)(ab)(ab).
ab 4
a 4b 4
4ab
Answer:
[tex] {a}^{4} {b}^{4} [/tex]
Step-by-step explanation:
[tex](ab) \times (ab) \times (ab) \times (ab)[/tex]
[tex] {a}^{1 + 1 + 1 + 1} {b}^{1 + 1 + 1 + 1} [/tex]
[tex] = {a}^{4} {b}^{4} [/tex]
marginal relative frequency example?
Answer:
Marginal relative frequency is the ratio of the sum of the joint relative frequency in a row or column and the total number of data values. Remember, the marginal frequency numbers are the numbers on the edges of a table, kind of like the margins are the areas on the edge of a paper.
why can u write both addition expression and subtraction expression for the situation
Answer:
It depends if the number is an integer {-1,+7,-7}
e.g -7+4
these numbers are integers that is why you can write both addition and subtraction expressions