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ElenaW [278]
3 years ago
13

A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits,

until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55 miles per hour, and y being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is:
55x + 35y = 200

If the car spends 2.5 hours going 35 miles per hour on the trip, how long does it spend going 55 miles per hour?

Round your answer to the nearest hundredths decimal place.
Mathematics
1 answer:
elena-s [515]3 years ago
6 0

9514 1404 393

Answer:

  2.05 hours

Step-by-step explanation:

Using the given equation with the given time, we have ...

  55x +35(2.5) = 200

  55x = 112.5 . . . . . . . . subtract 87.5

  x = 2.05 . . . . . . . . . . divide by 55

The car spends 2.05 hours at 55 mph.

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There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Write a system of equations tha
olganol [36]

Answer:

7 horses and 8 chickens

Step-by-step explanation:

To solve this, first you would need to list out all of the available ratios. Then, find out how many legs are in each option.:

14 horses and 1 chicken = 58 legs

13 horses and 2 chickens = 56 legs

12 horses  and 3 chickens = etc.

11 horses and 4 chickens

10 horses and 5 chickens

9 horses and 6 chickens

8 horses and 7 chickens

7 horses and 8 chickens = 44 legs!

6 horses and 9 chickens

5 horses and 10 chickens

4 horses and 11 chickens

3 horses and 12 chickens

2 horses and 13 chickens

1 horses and 14 chickens

5 0
3 years ago
100 points and brainest Plz help me PLZ
svp [43]

Answer:

○ C. The lines are perpendicular.

Step-by-step explanation:

In order for equations to be perpendicular, their <em>rate of changes</em> [<em>slopes</em>] must be OPPOSITE <em>MULTIPLICATIVE</em><em> </em><em>INVERSES</em>, which in this case is so:

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MULTIPLICATIVE INVERSE [RECIPROCAL]

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8 0
3 years ago
Read 2 more answers
As a sales person Jonathan is paid 50 per week +3% of the total Amount he sells. This week he wants to earn at least 100. Write
steposvetlana [31]

Answer:

The Inequality with integer coefficient for the total sales is 5000+3x\geq 10000

Hence Jonathan should make total sales of at least <u>1667</u> to earn at least 100.

Step-by-step explanation:

Given:

Amount paid per week = 50

Addition amount = 3% of Total sales.

Let the Total sales be 'x'.

∴ Additional amount = \frac{3}{100}x

Amount he wants to earn this week  \geq 100

We need to write the inequality with integer coefficient for the total sales and also to find the total sales.

Solution:

We cans say that;

Amount paid per week plus Additional amount should be greater than or equal to Amount he wants to earn this week.

framing in equation form we get;

50+\frac{3}{100}x\geq 100

Now we will make the denominator common using LCM we get;

\frac{50\times100}{100}+\frac{3}{100}x\geq 100

\frac{5000}{100}+\frac{3}{100}x\geq 100

\frac{5000+3x}{100}\geq 100

Multiplying both side by 100 we get;

100 \times\frac{5000+3x}{100}\geq 100\times 100\\\\5000+3x\geq 10000

Hence The Inequality with integer coefficient for the total sales is 5000+3x\geq 10000

On solving the above equation we get;

Subtracting both side by 5000 we get;

5000+3x-5000\geq 10000-5000\\\\3x\geq 5000

Dividing both side by 3 we get;

\frac{3x}{3}\geq \frac{5000}{3}\\\\x\geq 1666.67

Hence Jonathan should make total sales of at least <u>1667</u> to earn at least 100.

5 0
4 years ago
Use the "mixed partials" check to see if the following differential equation is exact.
Nadya [2.5K]

Answer:

The equation is exact

F(x,y) = 3x4/4  - 3xy -y2

Step-by-step explanation:

The step by step explanation and to ascertain the exactness of the differential equation is as shown in the attached file.

3 0
3 years ago
A tank contains 200 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pu
mel-nik [20]

At the start, the tank contains A(0) = 50 g of salt.

Salt flows in at a rate of

(1 g/L) * (5 L/min) = 5 g/min

and flows out at a rate of

(A(t)/200 g/L) * (5 L/min) = A(t)/40 g/min

so that the amount of salt in the tank at time t changes according to

A'(t) = 5 - A(t)/40

Solve the ODE for A(t):

A'(t) + A(t)/40 = 5

e^(t/40) A'(t) + e^(t/40)/40 A(t) = 5e^(t/40)

(e^(t/40) A(t))' = 5e^(t/40)

e^(t/40) A(t) = 200e^(t/40) + C

A(t) = 200 + Ce^(-t/40)

Given that A(0) = 50, we find

50 = 200 + C  ==>  C = -150

so that the amount of salt in the tank at time t is

A(t) = 200 - 150 e^(-t/40)

7 0
4 years ago
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