Which of the following can be represented by the equation y = 2x?

Solve. Write the solution in interval notation. -2x>-8 and -5x<20.

Novosadov [1.4K]

Answer:

The interval notation of the solution is (-4 , 4)

Step-by-step explanation:

* Let us explain a very important point in solving inequality

- When you multiply or divide an inequality by negative number we

must reverse the symbol of the inequality

- Ex:

∵ 2 < 3

- If we multiply the both sides of the inequality by -1, then the

inequality will be -2 < -3 and this is completely wrong, so we must

reverse the symbol of the inequality

∴ -2 > -3

* Now let us solve the problem

∵ -2x > -8

- Divide both sides by -2 and remember to reverse the symbol of the

inequality

∴ x < 4

∵ -5x < 20

- Divide both sides by -5 and remember to reverse the symbol of the

inequality

∴ x > -4

- From both solutions

∴ -4 < x < 4

∴ The solution is {x : -4 < x < 4}

- Interval notation is a way of writing the solutions of inequalities

( , ) if x does not equal the end numbers

[ , ] if x equals the end numbers

[ , ) , ( , ] if x equals one of the two end numbers

* The interval notation of the solution is (-4 , 4)

4 0

3 years ago

Find the volume of the cone. Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and round yo

NeTakaya

Answer:

Volume of the cone = 130.83 cubic units

Step-by-step explanation:

The question us incomplete without the diagram of the cone and it's dimensions as this would enable us get the exact answer.

Find attached the diagram used in solving the solution.

Volume of cone = ⅓ πr²h

Radius = r = 5 unit

Height = h = 5 unit

π = 3.14

By inserting the values of each variables, we have:

Volume of cone = ⅓ × 3.14× (5)² × 5

= ⅓ × 3.14× 25×5 = ⅓ × 3.14×125

Volume of cone = (392.5)/3

Volume of cone = 130.8333

Volume of cone = 130.83 cubic units (to the nearest hundredth)

Volume of cone = 130.83 unit³

8 0

3 years ago

What are the roots of the equation? x^2+24=−11x Enter your answers in the boxes.

docker41 [41]

The correct answers are:

x=-3 and x=-8.

Explanation:

We can first write this in standard form, ax²+bx+c=0. To do this, we will add 11x to both sides:
x²+24+11x=-11x+11x
x²+11x+24=0.

Now we can factor this. Look for factors of c, 24, that sum to b, 11. Factors of 24 are:
1 and 24 (sum 25)
2 and 12 (sum 14)
3 and 8 (sum 11)
4 and 6 (sum 10).

The factors we need are 3 and 8, since they sum to 11. This gives us factored form:
(x+3)(x+8)=0.

Using the zero product property, we know that in order to have a product of 0, one or both of the factors must be 0. This means we have:
x+3=0 or x+8=0.

Solving the first equation:
x+3-3=0-3
x=-3.

Solving the second equation:
x+8-8=0-8
x=-8.

8 0

3 years ago

Read 2 more answers

The sum of two times a number and four

Leokris [45]

Twice the sum of a number and 4 is 14. In this case the numbers are added first, and the ANSWER is doubled.

8 0

3 years ago

I need help on this please

Genrish500 [490]

Answer:

ok ill private message it to you wink