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2 years ago

3x + 4 = 5x + 10

Mathematics

1 answer:

IRINA_888 [86]2 years ago

8 0

Answer:

(-infinity, 2) U [-3]

Step-by-step explanation:

Step 1: we want to solve both equations for x. To do so, get the x variable by itself in both equations.

1.) 3x+4 = 5x+10

-6 = 2x (subtract 10 from both sides and 3x from both sides)

-3 = x (divide 2 from both sides)

2.) -5x + 7 > -3

-5x > -10 (subtract 7 from both sides)

x < 2

(divide both sides by -5, notice that dividing by a negative by a negative number flips the direction on > to < .)

Step 2: apply interval notation to these answers. Since x DOES equal -3 in equation one, it'll be in a bracket. On the contrary, since x has to be LESS THAN 2, it will have a parentheses.

So, our answer is: (-infinity, 2) U [-3]

*note the parentheses around infinity because something cannot equal infinity, it's not just one number*

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3 years ago

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balu736 [363]

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The distance of the airplane to the airport is 1421.26 miles.

Step-by-step explanation:

We are given the following information in the question:

An airplane takes off from an airport and travels 1100 miles east and then travels 600 miles north.

We could use the distance formula to calculate the distance between the airport and the airplane.

Another method that can be used is the Pythagoras theorem.

The attached image shows the scenario.

According to Pythagoras theorem:

In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

$a^2 + b^2 = c^2$ , where c is the hypotenuse of the triangle that is the side opposite to the right angle.

The distance between airport and airplane is the hypotenuse of the right angled triangle as show in the figure.

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3 years ago

Read 2 more answers