Essay Question.
You are purchasing a new car. In order to determine which car will provide maximum savings, you’ve researched miles per gallon (mpg) ratings of cars. If gas is $3.45 per gallon and you drive an average of 18,000 miles per year, the following rational equation is given:
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a. You will find the gallons of gas consumed by the old car in one year when you divide \(\frac{18,000}{old\;miles\;per\;gallon}\).
b. The amount of dollars you would save in the first year by switching to the 27 mpg car is $1,150.
c. The amount of dollars you would save after 5 years is $5,750.
d. Yes, the additional savings in gas be worth the extra $3000 over a 5 year loan.
e. The gas mileage your new car would have to be if you saved $800 per year over your 18 mpg current car is 23.4 mpg.
How to evaluate the rational equation?Based on the information provided about the car that would provide maximum savings, the following rational equation models the situation:
\(g(x)=3.45(\frac{18,000}{old\;miles\;per\;gallon})-3.45(\frac{18,000}{new\;miles\;per\;gallon})\)
Note: "g(x) is used for calculating the amount of dollar savings for one year for driving a car that gets higher miles per gallon rate."
Part a.
Based on the rational equation, we can logically deduce that the expression \(\frac{18,000}{old\;miles\;per\;gallon}\) would help to determine the gallons of gas consumed by the old car in one year.
Part b.
The amount of dollars you would save in the first year by switching to the 27 mpg car can be calculated as follows:
\(g(x)=3.45(\frac{18,000}{18})-3.45(\frac{18,000}{27})\)
g(x) = 3,450 - 2,300
g(x) = $1,150.
Part c.
The amount of dollars you would save after five years can be calculated as follows:
f(5) = 5g(x)
f(5) = 5 × $1,150
f(5) = $5,750
Part d.
\(g(x)=3.45(\frac{18,000}{27})-3.45(\frac{18,000}{33})\)
g(x) = 2,300 - 1,881.82
g(x) = $418.18.
f(5) = 5g(x)
f(5) = 5 × $418.18
f(5) = $2,090.9
Next, we would subtract the cost in 5 years as follows;
Difference = $5,750 - $2,090.9
Difference = $3,659.1.
Therefore, $3,659.1 is greater than $3,000, so an additional savings is worth it.
Part e.
Lastly, we would determine the gas mileage your new car would have to be if you saved $800 per year over your 18 mpg current car;
\(800=3.45(\frac{18,000}{18})-3.45(\frac{18,000}{y})\)
800 = 3,450 - 62,100/y
62,100/y = 3,450 - 800
62,100/y = 2,650
y = 62,100/2,650
y = 23.4 mpg.
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Related Questions
For what value of x is the following expression
sinx
undefined for Os x <211?
1+COS X
Answers
Answer:
ti 5
Step-by-step explanation:
its 5
Which rule explains why these triangles are
congruent?
U
T
V
W
AAS
ASA
SAS
SSS
These triangles
cannot be proven
congruent.
Answers
These triangles can be proven congruent by using ASA RULE.
What is congruent triangles and its rules ?
When two triangles are congruent, their three sides and their three angles match precisely.
If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.
ASA rule stands for Angle-Side-Angle rule which means two angles and a side of both triangles are equal.
Main Body:
In ΔTUV and ΔTWV
VT =VT ----(1)
∠VTU=∠TVW -----(2)
As TUVW is a parallelogram
so, ∠T = ∠U
hence, ∠TVU =∠VTW ----(3)
taking equation 1, 2,3
therefore, ΔTUV ≅ ΔTWV by ASA rule which means by Angle- Side- Angle rule.
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Use the distributive property to write an expression equivalent to 6(53).
plsplspls help
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one hundred and twenty-one million, six hundred and nine
Answers
Answer: 121,000,609.
I need the answer this is pre cal
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The transformations are:
Vertical shift of 3 units.Vertical dilation of scale factor 2Horizontal shift of 1 unit (assuming the horizontal axis is in units of pi)Which are the transformations applied to the parent sine function?The general sine function is:
y = sin(x)
The first thing we can see, is that the amplitude is not 1 like in the parent sine function, in this case the amplitude goes from the top value to the midline, so it is:
A = 5 - 3 = 2
Then we can write:
y = 2*sin(x)
So this is a vertical dilation of scale factor 2
We also can see the midline is at y = 3 instead of at y = 0, so we have a vertical shift of 3 units up to get.
y = 2sin(x) + 3
Finally, we can see that the function starts decreasing after x = 0, so we have a shift of 1 (the horizontal axis is in units of pi)
y = 2*sin(x + 1) + 3
That is the graphed function.
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Start with x and cube it
Answers
Answer:
x to the power of 3
Step-by-step explanation:
The surface area of a sphere is 900pi cubic cm. What is the length of its diameter.
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The length of the diameter of the sphere is 30 cm.
The surface area of a sphere is given by the formula:
\(A = 4\pi r^2\)
where A is the surface area and r is the radius of the sphere.
We are given that the surface area of the sphere is 900π cubic cm. Therefore:
\(A = 4\pi r^2 = 900\pi\)
Dividing both sides by 4π, we get:
\(r^2 = 225\)
Taking the square root of both sides, we get:
r = 15
The diameter of the sphere is twice the radius, so:
d = 2r = 30
Therefore, the length of the diameter of the sphere is 30 cm.
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George is reading a book that is 420 pages long. he reads 45 pages on the first day and the remaining pages in the book in 15 days. during that time he will read an equal number of pages each day. how many pages will he read each day?
Answers
Answer:
maybe 30 cause i cant tell if this is a trick question or not
Step-by-step explanation:
30 cause 420 divided by 15 =30
i dont really know the answer to this
Please help with this math question!
Answers
Answer:
5. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
What number is halfway between 0 and negative 20
Answers
Hope this helps!
:)
HELP NEEDED ASAP
answer these problems (image provided)
1. What is the volume of the first cube?
What do you know about the sides of a cube?
2. What is the volume of the cube with sides of 24m?
3. What is the volume of the cube with sides of 7m?
4. What is the combined volume of these 2 cubes?
5. How much more gold do you get in the better option?
Answers
Step-by-step explanation:
1 15625 m
2 13824 m
3 343 m
4 14167 m
5 cube with 25 m
awnser the qusetion 9iu523hb5hn33
Answers
The order of the matrices of each product is given as follows:
AB is nonexistent, BA is nonexistent.
How to apply multiplication of matrices?Multiplication of matrices is applied multiplying the rows of the first matrix by the columns of the second matrix, and hence the number of columns of the first matrix must be equal to the number of rows of the second matrix.
For the product AB, we have that:
A has four columns.B has two rows.Hence the product is nonexistent.
For the product BA, we have that:
B has four columns.A has two rows.Hence the product is nonexistent.
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What is the solution to –2(8x – 4) < 2x + 5?
x > x is greater than StartFraction 1 Over 6 EndFraction.
x < x is less than StartFraction 1 Over 6 EndFraction.
x > 6
x < 6
Answers
Answer:
-8<2x+5
Step-by-step explanation:
-2 times 8x= -16x
-2 times 4=-8
-16-(-8)<2x+5
-16-(-8)=-8
-8<2x+5
Answer:
\(x > \frac{1}{6} \)
Step-by-step explanation:
The solution is in the image
Which of the following coordinates is located in Quadrant I?
(-3,-4)
(-1,2)
(4,6)
O
(2,-1)
Answers
Answer:
(4,6)
Step-by-step explanation:
quadrant 1 always has positive coordinates so the only one with all positive coordinates is (4,6)
Assume you get a 15-year $165,000 mortgage loan at 8.2% interest, with monthly payments. Use the amortization registers of your calculator to find the balance after payment 100.
$66,878.13
$98,101.87
$97,176.29
$92,695.87
Answers
Which statement describes a unit rate?
A. Sarah rides her bike 12 miles and walks 3 mile
B. Sarah rides her bike 14 miles per 1 hour.
C. Sarah rides her bike 35 miles per 4 hours.
D. Sarah rides her bike - mile in 10 minutes.
Answers
A farmer earns $___ for each orange she sells. She had to pay $___ for fertilizer. Part A: Rewrite the description by filling in the blanks with values of your choice to show the amount of money the farmer could earn selling any number of oranges, n. Make sure the values you choose make sense for this situation. (6 points) Part B: Write an algebraic expression from your written description used in Part A. Let n stand for the number of oranges. (6 points)
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Part B: The algebraic expression for the amount of money the farmer could earn selling any number of oranges, n, is 0.20n - 25.
The x and y intercepts for the linear equation x – 2y = -8 is
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Answer:
x- intercept = - 8 , y- intercept = 4
Step-by-step explanation:
to find the x- intercept let y = 0 in the equation and solve for x
x - 2(0) = - 8
x - 0 = - 8
x = - 8 ← y- intercept
to find the y- intercept let x = 0 in the equation and solve for y
0 - 2y = - 8
- 2y = - 8 ( divide both sides by - 2 )
y = 4 ← y- intercept
Find the volume of the space inside the right cylinder that is not filled by the right cone below.
AC=16
BD=17
Answers
9514 1404 393
Answer:
D. 640 m³
Step-by-step explanation:
The height CD of the cone is found using the Pythagorean theorem.
BC² + CD² = BD²
8² + CD² = 17²
CD = √(289 -64) = 15
The volume of the cylinder is ...
V = πr²h
The volume of the cone is ...
V = 1/3πr²h
So, the portion of the cylinder not occupied by the cone is ...
V = (πr²h) -(1/3πr²h) = (2/3)πr²h
V = 2/3(π)(8 m)²(15 m) = 640π m² . . . . . matches choice D
Which graph shows an image and preimage after reflecting across y = -x ? *
Option 1
Option 2
Option 3
Option 4
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The graph which correct shows an image and pre-image after reflecting across the line; y = -x as required in the task content is; Option 1.
Which answer choice represents an image and pre-image after a reflection across y = -x?It follows from the task content that the answer choice which correctly represents an image ajd pre-image after reflecting across the line; y = -x.
First it is noteworthy to know that the line; y = -x is one which passes through the origin and has a negative slope of; -1.
On this note, by observation; when the line y = -x is drawn; the graph which represents the image and pre-image after reflecting across the line; y = -x is; Option 1.
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many many many questions from me....
Answers
Answer:
B is the answers for the question
Step-by-step explanation:
please mark me as brainlest
write the letter of the correct answers on your answer sheet. Find the next three terms in each sequence. Example 10,15,20,25,
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Answer:
30, 35 and 40
Step-by-step explanation:
The given sequence 10, 15, 20, 25... is an arithmetic sequence
nth term of an arithmetic sequence Tn = a +(n-1)d
a is the first term = 10
d is the common difference = 15-10 = 20-15 = 5
n is the number of terms
For the 5th term
T5 = 10 + (5-1)*5
T5 = 10+4(5)
T5 = 10+20
T5 = 30
For the 6th term
T5 = 10 + (6-1)*5
T6 = 10+5(5)
T6 = 10+25
T6 = 35
For the 7th term
T7 = 10 + (7-1)*5
T7 = 10+6(5)
T7 = 10+30
T7 = 40
Hence the next 3 terms are 30, 35 and 40
Select the correct answer.
Which point is a reflection of 01-4, -6) across the x-axis and the -axis?
a) point a
b) point b
c)point c
d)point d
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Answer:
If we have a point (x, y), a reflection across the x-axis converts the point to (x, -y)
While a reflection across the y-axis converts the point to (-x, y)
Then if we apply both of these transformations to our point, the reflection of (x, y) across the x-axis and then across the y-axis is (-x, -y)
Then the reflection of (-4, -6) across these two axes, is:
(- (-4), - (-6)) = (4, 6)
The correct option is B.
Given that cos(θ)=−2√13/13, and θ is in Quadrant II, what is sin(θ)?
Report your answer as a rationalized fraction.
Answers
The value of sin(θ) = 3√13/13
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
if cos(θ) = adj/hyp = 2√13/13
then
2√13 = adj, hyp = 13
opp = √ 13²- 2√13)²
= √169- 52
= √117
= √13 × 9
= 3√13
since the θ is in second quadrant, cosine will be negative and sine will be positive
therefore sin(θ) = 3√13/13
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10
El tiempo aproximado en caminar de tu casa (C) a la de tu amigo (A) pasando por la tienda (T)
es de 14 minutos; Si caminas a la misma velocidad, ¿Cuántos minutos te tomará caminar
directamente a la casa (C) de tu amigo (A)? Redondea al entero más cercano.
500yd
A
700yd
Answers
Respuesta:
10.0 minutos
Explicación paso a paso:
Distancia total recorrida caminando de C a A pasando por T:
500 yardas + 700 yardas = 1200 yardas
Tiempo necesario para recorrer 200 yardas = 14 minutos
Caminando directamente de C a A:
La distancia se puede obtener usando una relación trigonométrica:
Hipotenusa = √ (opuesto² + adyacente²)
Hipotenusa = √500² + 700²
Hipoteno = 860.23252 yardas
Por eso ; Si
1200 yardas = 14 minutos
860.23252 yardas = x
Multiplicar en cruz:
1200x = 12043,255
x = 12043,255 / 1200
x = 10.036 minutos
El tiempo necesario para caminar directamente será: 10.0 minutos
Appliances Plus purchased a washing machine for a cost price of $480, if they mark it up 38% what will the retail price be?
Answers
Answer:
$662.4
Step-by-step explanation:
Markup Percentage = (Markup / Cost)
1.38 = (Markup / 480)
1.38 * 480 = $662.4
Find the slope (-7,4) and (-7,-8)
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Answer: The slope for this line is not defined.
Step-by-step explanation: We can find the slope of a line using the formula m = y2 -y1/x2 - x1
here, (x1,y1) = (-7,4)
and, (x2,y2) = (-7,-8)
now, m= -8-4/-7+7
m = -12/0
So, the slope for this line is not defined as we are getting zero in the denominator.
You were asked to factor 16x^4 + 25. Which of the following is true? ANSWER ASAP
Answers
Answer: Please explain what you mean by "Which of the following is true?"
Overall, This is the step to solve the equation.
Step-by-step explanation:
16x4=64
64+25=89
Reuben has been saving $6 each week. Today he spent $90 of the savings, and he now has $48 left. For how many weeks has he been
saving?
(a) Write an equation that could be used to answer the question above.
First, choose the appropriate form. Then, fill in the blanks with the
Answers
Answer:
23 weeks
Step-by-step (x = weeks)
90 + 48 = 138
divide 138 by 6 to find out how many weeks he'd been saving up .
that gives you 23 but to turn it into an equation
6x - 90 = 48
+ 90 +90
6x = 138
_ _
6 6
x = 23 again x meaning weeks
Find the equation of the linear function represented by the table y0 5 10 15 x 1 2 3 4
Answers
Answer:
y = 5x
Step-by-step explanation:
The first step is to find the slope. The table shows an increase of 5 on the x-axis and 1 on the y-axis. Our slope is 5/1 or 5
The y-intercept is 0 because when x=0, y=0. The value of y is the y-intercept.