Darnell's car used 8 gallons of gasoline to travel 340 miles. after a mechanic worked on the car, it used 7 gallons of gasoline to travel 350 miles. If the price of the gasoline was approximately $4.00 per gallon, how much lest to the nearst cent per mile, did it cost to run the car after the mechanic worked on it?

Answers

Answer 1

Answer: so, after the mechanic worked on it, it only does 7 gallons for 350miles, how many gallons will it be at that rate, for 340 miles then?

$\bf \begin{array}{ccll}gallons&miles\n\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\n7&350\nx&340\end{array}\implies \cfrac{7}{x}=\cfrac{350}{340}\implies \cfrac{7\cdot 340}{350}=x\implies 6.8=x$

well, each gallon is 4 bucks, for 6.8 gallons that'd be 6.8*4.

we already know that before the mechanic worked on it, it was doing 8gallons for the same 340 miles, and at 4 bucks a gallon that'd be 8*4.

how much is her savings?

$\bf \stackrel{\stackrel{\textit{gallons cost}}{\textit{before being fixed}}}{(8\cdot 4)}\qquad -\qquad \stackrel{\stackrel{\textit{gallons cost}}{\textit{after it was fixed}}}{(6.8\cdot 4)}$

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What is the inverse function of d(x)= 2x-4

Answers

Formula for inverse function:
$d^(-1)(y)=?\ny=2x-4\n2x=y+4\nx= (y+4)/(2)\n d^(-1)(y)= (y+4)/(2)$

$y=2x-4 \n Replace \ x \ by \ y:\n x=2y-4\n Isolate \ y:\n 2y=x+4\n y=(x+4)/(2)\n \n \boxed{d^(-1)(x)=(x+4)/(2)}$

Find the measure of each angle indicated

Answers

Θ≈44.29

Working:
We need to use inverse trigonometric functions to evaluate the angle
Note that tan(Θ)=o/a where
o=opposite side & a=adjacent side (the last being the hypotenuse)
The inverse being Θ=arctan(o/a)
We substitute the given sides to get Θ=arctan(4/4.1)
Put this into the calculator and the result is ≈ 44.2926806315
Rounded off to 2 decimal places: Θ≈44.29
N.B. arctan usually appears on a calculator as tan to the power of -1

Find the value of x
a) 5
b) -1
c) 6
d) 2

Answers

Answer:

a) 5

Step-by-step explanation:

x+2 = 2x-3

-x -x

2 = x-3

+3 +3

5 = x

The measure of two complementary angles are represented by x+5 and 4x - 15 find the value of x

Answers

Based on the calculations, the value of x will be equal to 20°

First and foremost, we should note that the total angles in a complementary angles equal to 90°.

In this case, we have to add the two angles that we are give and then equate them to 90°. This will be:

(x + 5°) + (4x - 15°) = 90°

x + 5° + 4x - 15° = 90°

Collect like terms

x + 4x = 90° - 5° + 15°

5x = 100°

x = 100°/5

x = 20°

Therefore, based on the calculations, the value of x is 20°

Read related link on:

brainly.com/question/17253605

complementry angles sum up to 90.
so, (x+5)+(4x-15)=90
x+4x+5-15=90
5x-10=90
5x=90+10
x=100/5
x=20

What is the value of x in the equation (x + 12) = (x + 14) – 3?

Answers

Answer: There is NO value of 'x' in the given equation.

Step-by-step explanation: We are given to find the value of 'x' in the equation below:

$(x+12)=(x+14)-3~~~~~~~~~~~~~~~~~~~~(i)$

Finding the value of 'x' in equation (i) means to find the value of 'x' for which the equation is TRUE.

The solution is as follows:

$(x+12)=(x+14)-3\n\n\Rightarrow x+12=x+14-3\n\n\Rightarrow x+12=x+11\n\n\Rightarrow x-x=11-12\n\n\Rightarrow 0=-1,$

which can NEVER be true.

So, the given equation has NO solution.

Thus, there is NO value of 'x' in the given equation.

(x + 12) = (x + 14) - 3

subtract 12 from each side

x = x + 14 - 3 - 12

Now if we subtract x from each side we see that x - x = 0. Combine the terms left over and we have -1, so

0 = -1

The answer is NO SOLUTION

24. Congratulations! You have just won a jet ski worth $8000. The depreciated value of the jet ski (V) after t years is given by V = 8000 − 725t , 0 ≤ t ≤ 11.a. Use a graphing utility to graph the equation. Include a t-chart with at least 5 key points with your accurate labeled graph.
b. After how many years will the jet ski be worth $5100? Show all of your work or explain how you came up with your answer.
c. What will be the value of the jet ski after 9 years? Show all of your work or explain how you came up with your answer.

Answers

So:

$V=8000-725t\quad \{ 0\le t\le 11\}$

*V (in dollars) stands for the depreciated or non depreciated value of the jet ski.

*t (in years) stands for the amount of time that has passed. t is greater or equal to 0 and less than or equal to 11.

-------------------

Question (a):

Now V is a function of t. V=f(t).

When t=0, V=0 --> Point:(0,0)

When t=2, V=6550 --> Point (2, 6550)

When t=4, V=5100 --> Point (4, 5100)

When t=6, V=3650 --> Point (6, 3650)

When t=8, V=2200 --> Point (8,2200)

When t=11, V=25 --> Point: (11, 25)

So as the graph V=8000-725t is LINEAR, we can draw a line through the points mentioned above.

------------------------

Question (b): After how many years will the jet ski be worth $5100?

$8000-725t=5100\n \n 8000-5100=725t\n \n 2900=725t\n \n \frac { 2900 }{ 725 } =t\n \n \therefore \quad t=4,\quad when\quad V=5100$

Answer: 4 years.

-----------------------

Question (c): What will be the value of the jet ski after 9 years?

$When\quad t=9,\n \n V=8000-725\left( 9 \right) \n \n =1475$

The answer is $1,475.00

a) $y=mx+c$
$m=gradient=-725$
$y(v)-intercept=8000$

b) $5100=8000-725t$
$2900=725t$
$t=4$
The value will be 5100 after 4 years.

c) $V=8000-725(9)$
$V=8000-6525$
$V=1475$
The value of the jet will be 1475 after 9 years.

Hope I helped bro, now i can sleep

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