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solong [7]
3 years ago
9

2.1.43 A particular hybrid car travels approximately 235 mi on 5 gal of gas. Find the amount of gas required for a 705-mi trip.

The car needs allons of gas for a 705-mi trip (Type an integer or a decimal.)
Mathematics
1 answer:
o-na [289]3 years ago
7 0

Answer: 15 gallons of gas is required for a 705 miles trip.

Step-by-step explanation:

Since we have given that

Number of miles in a trip = 235 miles

Number of gallon of gas is needed = 5

We need to find the amount of gas required for 750 miles trip.

Since there is direct variation, as for increase in number of miles, amount of gas must be increased.

According to question, it becomes,

\dfrac{235}{5}=\dfrac{705}x}\\\\47=\dfrac{705}{x}\\\\47x=705\\\\x=\dfrac{705}{47}\\\\x=15\ gallons

Hence, 15 gallons of gas is required for a 705 miles trip.

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hi:) for 5(b) , I got 157.7 & 22.3 but in the answer key, the only correct answer is 157.7. I thought there should be 2 poss
n200080 [17]

Answer:

Θ = 157.7°

Step-by-step explanation:

Given

cosΘ = - 0.925

Since cosΘ < 0 then Θ is in the second or third quadrant.

Since 0° ≤ Θ ≤ 180° then Θ is in the second quadrant. thus

Θ = cos^{-1}(- 0.925) = 157.7° ← angle in second quadrant

8 0
3 years ago
Read 2 more answers
suppose a farmer encloses a rectangular region of a land next to a river. fencing will be used on 3 sieds, and none is needed al
nexus9112 [7]

Answer:

Dimensions :

x (the longer side, only one side with fence )   =  90  ft

y ( the shorter side two sides with fence )        =  45  ft

Total fence used   45 * 2  +  90    =  180 ft

A(max)  =  

Step-by-step explanation: If a farmer has 180 ft of fencing to encloses a rectangular area with fence in three sides and the river on one side, the farmer surely wants to have a maximum enclosed area.

Lets call "x" one the longer side  ( only one of the longer side of the rectangle will have fence, the other will be along the river and won´t need fence. "y" will be the shorter side

Then we have:

P = perimeter  =  180  =  2y  +  x        ⇒   y  =  ( 180 - x )  / 2        (1)

And   A (r)   =  x * y

A(x)   =  x  *  ( 180 - x ) /2       ⇒   A(x)   = (180/2) *x   -  x² / 2

Taking derivatives on both sides of the equation :

A´(x)   =  90   -  x    

Then if    A´(x)   =  0   ⇒        90   -  x    =  0     ⇒   x  =  90 ft

and from :       y  =  ( 180 - x )  / 2     ⇒     y  =  90/2

y  =  45  ft

And

A(max)  =  90 * 45    =  4050  ft²

4 0
3 years ago
Find the slope of the line passing through the points (6, -6) and (4, -4)
djyliett [7]

To find the slope (m), use the slope formula:

m=\frac{y_2-y_1}{x_2-x_1}         and plug in the two points

(4, -4) = (x₁, y₁)

(6, -6) = (x₂, y₂)

[lines usually go from left to right, so the point furthest to the left is the 1st point]

m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{-6-(-4)}{6-4}   [two negative signs cancel each other out and become positive]

m=\frac{-6+4}{6-4}

m=\frac{-2}{2}

m = -1

3 0
2 years ago
Scar goes to the gym 4 times per week. Every time he walks 5 miles on the 4 points
steposvetlana [31]

Answer:

He walks 1,060 miles on the tremil in one year.

Step-by-step explanation:

4*5=20*53=1,060

There are 53 sometimes 52 weeks in a year,2020 wise 53 so 53*20=1,060 miles.

8 0
3 years ago
When building a house, the number of days required to build varies inversely with with the number of workers. One house was buil
Helga [31]

Let d represent number of days and n represent number of workers.

We have been given that when building a house, the number of days required to build varies inversely with with the number of workers.

We know that the equation y=\frac{k}{x} represents the relation where y is inversely proportional to x and k is the constant of proportionality.  

So our required equation would be d=\frac{k}{n}

Upon substituting our given values, we will get:

19=\frac{k}{35}

k=19\cdot 35

k=665

Since constant of proportionality is 665, so our equation would be d=\frac{665}{n}.

To find the number of days it will take to build a similar house with 5 workers, we will substitute n=5 in our equation as:

d=\frac{665}{5}

d=133

Therefore, it will take 133 days for 5 workers to build a similar house.

5 0
3 years ago
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