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2 years ago

Solve the equation, if possible. 1. 2x + 2(4x - 2) + 3x = x + 3(x – 8) + 4x

Mathematics

1 answer:

MAXImum [283]2 years ago

5 0

Answer:

x=-4

Step-by-step explanation:

Distribute and expand everything in brackets.

2x+2*4x+2*-2+3x=x+3*x+3*-8+4x

2x+8x-4+3x=x+3x-24+4x

Solve like terms

13x-4=8x-24

Place like terms on same side.

13x-8x=-24+4

Solve for x

5x=-20

x=-4

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Jake is using a horse trailer to take his horses to his new ranch. 1 Horse= 1,200 lb Trailer= 2,700 lb Jake's truck can tow a ma

Kitty [74]

Answer:

Jack can take only 1 horse on his trailer to be towed by the truck without going over the maximum weight the truck.

Step-by-step explanation:

Given:

Weight of 1 horse = 1,200 lb

Weight of trailer = 2,700 lb

Jacks'truck can tow a maximum of 5000 pounds.

To find the maximum number of horses Jack can take in his trailer without going over the maximum weight his truck can tow.

Solution:

Let the maximum number of horses that Jack can take be = $x$

Using unitary method to find weight of $x$ horses.

If 1 horse weights = 1,200 lb

Then $x$ horses will weight in lbs = $1,200\times x = 1,200x$

Total weight of horses and trailer in lbs = $1200x+2700$

Since the maximum weight the truck can tow = 5,000 lb, so the inequality can be given as:

$1200x+2700\leq5000$

Subtracting both sides by 2700.

$1200x+2700-2700\leq5000-2700$

$1200x\leq2300$

Dividing both sides by 1200.

$\frac{1200x}{1200}\leq\frac{2300}{1200}$

$x\leq1.91$

From the inequality solution for $x$ , we can conclude that Jack can take only 1 horse on his trailer to be towed by the truck without going over the maximum weight the truck.

3 0

3 years ago

On a certain route, an airline carries 8000 passengers per month, each paying $70.A market survey indicates that for each $1

son4ous [18]

Answer:

The maximum revenue is $661,250.

Step-by-step explanation:

The total revenue (R) is the product between the number of passengers (N) and the price of each ticket (P), so the inicial revenue is:

R = N * P = 8000 * 70 = $560,000

For each 1$ increase in the ticket, the airline loses 50 passengers, so if we call "x" the increase in the ticket price, we have that the revenue equation will be:

R = (8000-50*x) * (70+x) = 560000 + 8000*x - 50*70*x -50x2

R = -50*x2 + 4500*x + 560000

The value of x that gives the maximum value of a quadratic function is found using the formula:

x = -b/2a

where a and b are coefficients of the quadratic equation (in our case, a = -50 and b = 4500)

So the value of x that gives the maximum revenue is:

x = -4500 / (-100) = 45

Using this value in the revenue equation, we have that the maximum R is:

R = -50*45^2 + 4500*45 + 560000 = $661,250

(To get this revenue, the ticket will cost 70+45 = $115 and there will be 8000-50*45 = 5750 passengers)

3 0

2 years ago

Nesterboy [21]

Answer:

Step-by-step explanation:

Answer

2/3

Explanation

For f(x) = g(x) we should equate the two functions to get the value of x.

f(x) = g(x)

−3x + 4 = 2

-3x + 4 - 4 = 2 - 4

-3x = -2

Dividing by -3 on both sides;

(-3x)/-3 = (-2)/-3

x = 2/3

7 0

3 years ago

Speed, Time, and Dis

serious [3.7K]

Answer:

3 hours

Step-by-step explanation:

Recall:

Distance = speed x time

we are given that speed = 18 km/h and distance = 54 km.

hence,

54 = 18 x time (divide both sides by 18 and rearrange)

time = 54/18 = 3 hours

7 0

3 years ago

Explain how to compute 3/4 x 4/5 using one diagram.

Drupady [299]

Answer:

The simplified form of given expression is 3/5.

Step-by-step explanation:

The given expression is

$\frac{3}{4}\times \frac{4}{5}$

We need to find the product of two factions using diagram.

For 3/4, draw a box and divide it in 4 equal parts by using vertical lines. The color three parts of it.

For 4/5, draw a box and divide it in 5 equal parts by using horizontal lines. Then color the four parts of it.

Now combined both boxes and shown below.

From the below figure it is clear that

The number of common shaded small boxes = 12

Total number of small boxes = 20

The required fraction is

$Fraction=\frac{\text{Number of common shaded small boxes}}{\text{Total number of small boxes}}$

$Fraction=\frac{12}{20}$

Cancel out common factor.

$Fraction=\frac{3}{5}$

Therefore, the simplified form of given expression is 3/5.

5 0

2 years ago