All categories

3 years ago

If a is a solution of abs(x+3)>4, then is a also a solution of x+3>4?

Mathematics

1 answer:

Alexandra [31]3 years ago

7 0

Answer:

Yes

Step-by-step explanation:

After solving for the two values of a, the second inequality gives a value inside the range of the first inequality.

You might be interested in

An Elevator descends into a mine shaft at the rate of 5m/min. If the descend starts from 15m above the ground, how long will it

zhenek [66]

First of all, assuming that the "ground level" is 0;

The lift is not starting from 0, so we also need to account for the extra 15 meters above the ground the lift is.

The total distance the lift would cover in the downward direction: 15+350=365m

Now, you know that the lift covers 5 m/min

Therefore, 5x=365 (ignoring units because they can complicate things)

x=365/5
x=73 minutes

Therefore, they would take 73 minutes to reach 350 m deep into the ground with a starting position 15 m above the ground.

Hope I helped :)

5 0

3 years ago

A store plans to sell two different game consoles, the YuuMi and the ZBox. The store’s wholesale cost for a YuuMi is $250, and t

strojnjashka [21]

9514 1404 393

Answer:

Constraints: x + y ≤ 250; 250x +400y ≤ 70000; x ≥ 0; y ≥ 0
Objective formula: p = 45x +50y
200 YuuMi and 50 ZBox should be stocked
maximum profit is $11,500

Step-by-step explanation:

Let x and y represent the numbers of YuuMi and ZBox consoles, respectively. The inventory cost must be at most 70,000, so that constraint is ...

250x +400y ≤ 70000

The number sold will be at most 250 units, so that constraint is ...

x + y ≤ 250

Additionally, we require x ≥ 0 and y ≥ 0.

A profit of 295-250 = 45 is made on each YuuMi, and a profit of 450-400 = 50 is made on each ZBox. So, if we want to maximize profit, our objective function is ...

profit = 45x +50y

A graph is shown in the attachment. The vertex of the feasible region that maximizes profit is (x, y) = (200, 50).

200 YuuMi and 50 ZBox consoles should be stocked to maximize profit. The maximum monthly profit is $11,500.

4 0

3 years ago

A 500-kg car has 25,000 joules of kinetic energy. What is its speed?

Lelu [443]

(m.v^2)/ 2 = 25000
<=> 500.v^2 = 50000
<=> v^2 = 100
<=> v = 10 m/s

7 0

3 years ago

14 is the GCF of anumber M and 210. What are possible values of M?

Cloud [144]

<span>14 = GCF of M and 210
M = possible values

GCF = Greatest common denominator
Now, let’s start decomposing
=> 210 | 2
=> 105 | 2
=> 35 | 5
=> 7 | 7
=> 1

Thus, 2 x 3 x 5 x 7 = 210

Now let’s find the factors of 14
=> 14 | 2
=> 7 | 7
=> 1

Thus, 2 x 7 = 14

Notice that’s there’s no 14 in 210 shown factors, but the only GCF found is 7.
Thus, the value of M that we’re looking for is infinite. All numbers that has the GCF of 7 are applicable.</span>

6 0

4 years ago

Which equation represents the equation of the parabola with focus (-3 3) and directrix y=7?

Artemon [7]

Answer:

The equation $y=\frac{-x^2-6x+31}{8}$ represents the equation of the parabola with focus (-3, 3) and directrix y = 7.

Step-by-step explanation:

To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).

Using the distance formula $d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }$ , we find that the distance between (x, y) is

$\sqrt{(x+3)^2+(y-3)^2}$

and the distance between (x, y) and the directrix y = 7 is

$\sqrt{(y-7)^2}$ .

On the parabola, these distances are equal so, we solve for y:

$\sqrt{(x+3)^2+(y-3)^2}=\sqrt{(y-7)^2}\\\\\left(\sqrt{\left(x+3\right)^2+\left(y-3\right)^2}\right)^2=\left(\sqrt{\left(y-7\right)^2}\right)^2\\\\x^2+6x+y^2+18-6y=\left(y-7\right)^2\\\\x^2+6x+y^2+18-6y=y^2-14y+49\\\\y=\frac{-x^2-6x+31}{8}$

6 0

3 years ago