Answers
So, first you need to find how many gallons the car uses per year.
Since x is the number of gallons, this would be 15000/x.
Now, you need to multiply however many gallons the car used by 2.95 to get the cost, C.
C=2.95(15000/x) is your function for this problem.
However, this can also be written as C=[tex] \frac{44250}{x} [/tex].
Let's fill in the row for C first.
Starting with 10 mpg.
44250/10
4425
So the first value should be 4425. Keep on doing this for the rest.
Now for dC/dx, this means rate of change in C caused by a change of the value x.
Starting with 10 mpg.
-4425/10
-442.5
So in the end, the table should look like this (approximating to decimals)
[tex] \left[\begin{array}{cccccccc}x&10&15&20&25&30&35&40\\C&4425&2950&2212.5&1770&1475&1264.29&1106.25\end{array}\right] [/tex]
[tex] \left[\begin{array}{cccccccc}\\dC/dx&-442.5&-196.67&-110.635&-70.8&-49.17&-36.12&-27.66\end{array}\right] [/tex]
The driver who gets 15 mpg would benefit more because
(-44250/16)/16 = -172.85
(-44250/36)/36 = -34.14
The driver with 15 mpg saves much more money than the driver with 35 mpg.
Once again, not fully certain if that is correct, but the answer seems logical to me, and I did google a bit to check it.
Related Questions
A squirrel climbs 15 feet up a tree. He then runs 8.26 feet down the tree. How much further does the squirrel need to go before reaching the ground?
A)7.36 feet
B)7.26 feet
C)6.74 feet
D)8.11 feet
Answers
Answer:
C
Step-by-step explanation:
Forty-eight pounds of sand are used to fill 12 bags.
Miranda uses the five-step problem-solving plan. After completing the Solve step, how many pounds of sand should she find each bag will hold?
Answers
Find the length of the hypotenuse:
Answers
to find the hypotenuse on the given triangle
divide the given height ( 3sqrt(2) ) by the sin of the given angle (45)
3sqrt(2) / sin 45 = 6
answer is B. 6
The sides of a right-angle triangle are equal when the angle = 45°
[tex] a^2 = b^2 + c^2 \\ a^2 = (3 \sqrt{ 2 })^2 + (3 \sqrt{ 2 })^2 \\ a^2 = 9 \times 2 + 9 \times 2 \\ a^2 = 36 \\ a = \sqrt {36} = 6 [/tex]
Method 2:
(Optional)
Using TOA CAH SOH method
Where:
TOA is Tan θ = Opposite/Adjasent
CAH is Cos θ = Adjasent/Hypotenuse
SOH is Sin θ = Opposite/Hypotenuse
You have an angle of 45° and OPPOSITE the angle is a known length.
These are the 2 information we know.
We need to find the third information, which is the HYPOTENUSE.
Notice the capatialised words start with the letter O ans H?
Find in the TOA CAH SOH the corresponding letters, in this case SOH.
SOH is sin θ = opposite/hypotenuse
Simply substitude in the values and find the hypotenuse!
sin 45° = (3√2)/ hypotenuse
hypotenuse = (3√2) / sin 45° = 6
Answer is B.
And there you go! Both methods can be used and gives the same answer.
However the limitations to method 2 are:
1. It must be a right-angle triangle
2. An angle and a side must be given.
If you think method 2 is too confusing, stick to method 1.
Good luck!
A box with a square base and no top is to be made from a square piece of carboard by cutting 3 in. squares from each corner and folding up the sides. the box is to hold 9075 in3. how big a piece of cardboard is needed?
Answers
Final answer:
To create a box with a volume of 9075 in3, a 61 in. by 61 in. piece of cardboard is needed after cutting out 3 in. squares from each corner and folding up the sides.
Explanation:
To determine the size of the cardboard needed to construct a box with a volume of 9075 in3 when 3 in. squares are cut from each corner and the sides are folded up, we first need to express the volume of the box in terms of the dimensions of the cardboard. Let x represent the length of one side of the original square piece of cardboard. After cutting out 3 in. squares from each corner, the length and width of the base of the box will be x - 6 inches (since 3 inches are removed from each side), and the height will be 3 inches (the size of the squares cut from the corners).
The volume V of the box can be expressed as V = (x - 6)(x - 6)(3). Given that V = 9075 in3, we can set up the equation 9075 = (x - 6)2 × 3. Solving for x will give us the size of the original cardboard piece.
To solve the equation, divide both sides by 3 to isolate (x - 6)2, which gives 3025 = (x - 6)2. Taking the square root of both sides gives x - 6 = 55, so x = 61. Therefore, a 61 in. by 61 in. piece of cardboard is needed to construct the box.
An internet service provider is implementing a new program based on the number of connected devices in each household. Currently, customers are charged a flat rate of $175 per month. The new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network. Find and graph the number of devices, x, for which the cost of the new plan is less than the current plan.
Answers
The current rate is simply equal to $175 per month, let us call this as rate A:
A = 175
The new rate is $94 plus $4.50 per devices, let us call this as rate B:
B = 94 + 4.50 x
where x is the number of devices connected to the network
The inequality equation for us to find x which the new plan is less than current plan is:
94 + 4.50 x < 175
Solving for x:
4.50 x < 81
x < 18
So the number of devices must be less than 18.
- From the graph, we can actually see that the new rate intersects the current rate at number of devices equal to 18. So it should really be below 18 devices.
The number of devices connected should be less than 18 (1 to 17 devices) so that the new charges will be less than the old charge.
Given:
The old monthly charge for internet service per household is $175.
The new charges include a fixed pay of $94 plus $4.50 per connected device.
Let x be the number of connected devices.
So, the new charges can be written mathematically as,
[tex]C=94+4.5x[/tex]
Now, the new charge should be less than the old charge. This condition can be written as,
[tex]C=94+4.5x<175\\4.5x<81\\x<18[/tex]
So, the number of devices connected should be less than 18 (1 to 17 devices) so that the new charges will be less than the old charge.
See the attached graph.
For more details, refer the link:
https://brainly.com/question/18272298?referrer=searchResults
What’s angle CR PQ and CQ?
Answers
CR = CP = 17
PQ = QR = 15
CQ = x^2 +15^2 = 17^2 = x^2 + 225 = 289
x^2 = 289-225 = 64, sqrt(64) = 8, CQ = 8
There are 6 quarters in a jar .jill adds 2 quarters everyday which linear equation represents the total amount of quarters in the jar after x days
Answers
So after x days, Jill has added 2x quarters.
Which means that after x days, the total numbers of quarters in the jar is:
2x + 6.
So the linear equation that represents the total amount of quarters in the jar after x days is: f(x) = 2x + 6
Hope this helps! :)
y = 6 + 2 = 8 quarters altogether.
When x = 2, we have:
y = 6 + 2 + 2 = 10 quarters altogether.
And when x = 3, we have:
y = 6 + 2 + 2 + 2 = 12 quarters altogether.
Do you notice a pattern here? What's the relationship between the number of 2's and the value of x? How can you use that relationship to come up with a general equation?
Amanda was 48 inches She grew n inches last year and is now 56.5 inches write an expression that represents the number of inches Amanda grew
Answers
Jimmy had $4.52 to spend. He found something he wanted to buy for $6.21. How much would he need to borrow from his friend to make his purchase?
Answers
Answer:
$1.69
Step-by-step explanation:
If he wants to buy something for $6.21 but he only has $4.52, we need to find out the difference between $6.21 and $4.52.
For that, we have to subtract the smallest number from the biggest, that is
$6.21 - $4.52 = $1.69
Therefore, he would need to borrow $1.69 from his friend.
What is the measure of angle 1
Answers
What is the multiple zero and multiplicity of f(x) = x3 − 8x2 + 16x?
multiple zero = −4; multiplicity = 2
multiple zero = 2; multiplicity = 4
multiple zero = 4; multiplicity = 2
multiple zero = 2; multiplicity = −4
Answers
Answer:
B
Step-by-step explanation:
If you divide x so only x and a number remains, you will get B.
[tex]f(x) = x^{3} - 8x^{2} + 16x[/tex] has multiple zero = 4; multiplicity = 2.
What is multiple zero and multiplicity?" A multiple zero has the multiplicity which represents the number of times linear factor of multiple zero occur in the polynomial .Zero of the polynomial is associated with multiple zero."
According to the question,
Given,
[tex]f(x) = x^{3} - 8x^{2} + 16x[/tex]
Simplify the given polynomial to get the multiple zero and multiplicity,
[tex]f(x) = x^{3} - 4x^{2}- 4x^{2} + 16x[/tex]
[tex]\implies x^{2} (x-4) -4x(x-4)=0\\\\\implies (x^{2} -4x)(x-4) =0\\\\\\\implies (x) (x-4)(x-4)=0\\\\\implies x(x-4)^{2} =0[/tex]
Zero is associated with x =4.
(x-4) occur twice.
Hence, multiple zero = 4 and multiplicity = 2 of the given function.
Learn more about multiple zero and multiplicity here
https://brainly.com/question/14059007
#SPJ3
Find the missing angle.
Answers
make sure your calculator is in Degree mode.
but will run you about 36.8698976458° and 53.13010235415598°.
Evaluate the expression for x = 3 and y = 6.
5(x2 + y) + y2
Answers
Do parenthesis first
5 ( 12 ) + 6 * 2
multiply from left to right
60 + 12
add
72
5(6 + 6) + 6x2
5 x 12 + 6x2
60 + 12
72
The first side of a triangle is 2 cm longer than the second side. the third side is 5 cm shorter than twice the second side. the perimeter is 49 cm. find the length of each side.
Answers
Side 2: x
Side 3: 2x-5
Perimeter(sum of the sides)= 49 cm
(x+2)+x+(2x-5)=49
4x-3=49
4x=52
x=13
Side 1=15 cm
Side 2=13 cm
Side 3=21 cm
The sides of the triangles will be 15 cm, 13 cm and 21 cm.
What is a triangle?A closed polygon with three sides, angles and vertex is called triangle.
Given that, the first side of a triangle is 2 cm longer than the second side. the third side is 5 cm shorter than twice the second side and the perimeter is 49 cm.
Let the second side be x, then the sides will be,
x+2, x and 2x-5
∵ Perimeter = 49 cm
∴ x + 2 + x + 2x - 5 = 49
4x-3 = 49
4x = 52
x = 13
Therefore, side will be =
Side 1 = 15 cm
Side 2 = 13 cm
Side 3 = 21 cm
Hence, the sides of the triangles will be 15 cm, 13 cm and 21 cm.
Learn more about triangles, click;
https://brainly.com/question/2773823
#SPJ2
what is the slope-intercept equation of a line that has a slope of -2 and a y-intercept of (0,3)
Answers
-2 represents the constant, or slope, and +3 represents what y equals when x is zero
Hope this helps!
If she steals 100 buys 70 worth of stuff owner gives u 30 back how much did owner lose
Answers
True or false: there are infinitely many bisectors, but only one perpendicular bisector for any segment.
Answers
PLZZZZZZZZZZZZ HELP ME!!!!!!!!!!!!
Use the order of operations to simplify this expression.
4 + 0.8 × 1.5 - 3
4.2
3.3
2.2
7.2
Answers
4+1.2-3= 2.2
The cost for parking at a parking garage is $2.25 plus an additional $1.50 for each hour. What is the total cost to park for 5 hours?
Answers
The total cost to park for 5 hours is $9.75
the answer is $9.75
HELP PLEASE!
Which equation can be used to find the solution of (1/2)^2x = 32 ?
a) 1/2x=5
b) −2x=5
c) 2x = 5
d) −1/2x=5
Answers
The answer is b, not c. I just completed the quiz and got the question wrong by answering c. :/
BRAINIEST ANSWER! PLEASE! ABOUT AREA AND PERIMETER!
Answers
each little square = 1 square inch
the design takes up 21 squares so area is 21 square inches
the perimeter = 6 +2+3+3+3+5 = 22 inches
The sum of three numbers is 45 one number is 10 more than the second number it is also twice the third number find the numbers
Answers
The numbers cannot be uniquely determined with the given information.
Explanation:Let's solve this problem step by step.
Let's assume the second number is 'x'. Since the first number is 10 more than the second number, then the first number can be represented as 'x + 10'.
Since the first number is also twice the third number, the first number can be represented as '2y', where 'y' is the third number.
Now, we can form an equation using the given information: x + (x + 10) + 2y = 45
Simplifying the equation, we get: 2x + 2y + 10 = 45
Further simplifying, we get: 2x + 2y = 35
Dividing both sides of the equation by 2, we get: x + y = 17.5
Now, we have two variables and one equation, which means we have an infinite number of possible solutions. We need more information to determine the actual values of x and y.
Therefore, the numbers cannot be uniquely determined with the given information.
Helppppp plzz quickkk
Answers
he hiked 4 km east in 45 minutes
45 minutes = 3/4 of an hour
4 /.75 = 5.33
so the answer would be D. 5.3 km per hour east
A segment with endpoint a(3,1) and b(-1,1) is rotated 90° about the origin.what are the coordinates of a' and b' ? (geometry 10 a lesson 3 unit 5,if you know the answers to this whole practice pls give them to me pls and tysm)
Answers
As seen, the segment is in quadrant one and two.
For a':
a(3, 1) --> (-3, -1)
For b':
b(-1, 1) --> (1, -1)
As you can see, the coordinate's signs are reversed for each case.
Hope I helped :)
1/4x+5/3x-4=2-1/12x what is the answer ??????
Answers
the answer is x=3
x=3
have a noice day
What is the measure of angle C? 25° 30° 60° 75°
Answers
Answer:
75°
Step-by-step explanation:
A square has an area of 121 yd^2 what is the length of each side
Answers
a= 11 inches
The side of the square having an area of 121 yards² is 11 yards
What is the area of a square?
A square is a 4 sided polygon where all the sides are of equal length.
The area of the square is the square of any one of its side
Let a be the side of the square
Area of the square = a²
Given data ,
Let the area of the square be Y = 121 yards²
Now , let the side of the square be = a
And the equation for the area of the square is
Area of the square = a²
where a is the side of the square
So , substituting the values in the equation , we get
a² = 121 yards²
Taking square root on both sides , we get
a = 11 yards
Therefore , the value of a is 11 yards
Hence , The side of the square having an area of 121 yards² is 11 yards
To learn more about area of square click :
https://brainly.com/question/17707380
#SPJ5
What property of equality is used to transform equation 1 to equation 2?
Equation 1: 35 = 5x
Equation 2: 7 = x
addition Property of Equality
subtraction Property of Equality
multiplication Property of Equality
division Property of Equality
Answers
Final answer:
The division Property of Equality is used to transform Equation 1 (35 = 5x) into Equation 2 (7 = x) by dividing both sides of the equation by 5.
Explanation:
The property of equality used to transform Equation 1 (35 = 5x) to Equation 2 (7 = x) is the division Property of Equality.
This property states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal. To get from Equation 1 to Equation 2, both sides of Equation 1 are divided by 5.
Division is similar to multiplication in that it follows the same rules for signs and equality. When dividing both sides by the same number, the numerator and denominator cancel out if they are the same, leaving a value of 1.
For instance, dividing 5x by 5 will lead to x, and dividing 35 by 5 will give 7, hence 7 = x, which is Equation 2.
pleaseeeeeeeeee help meeeeeeee
Answers
foil (ab - 9)(ab + 8)
Answers
Step 1: (ab-9)(ab+8)
Step 2: ab x ab +8 x ab -9 x ab -9 x 8
Step 3: ab2 +8ab-9ab-72=
Step 4: ab2 -ab-72
solved!!! that how you would solve it everything will continue as normal
a²b² - ab - 72