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4 years ago

Which of the following inequalities is equivalent to 5 > x?

Mathematics

1 answer:

Alexxx [7]4 years ago

3 0

Answer:

x < 5

Step-by-step explanation:

What 5 > x means is that the variable x takes values less than 5, we can notice that because the narrow part of the symbol is pointing towards x, which means x is smaller than 5.

Analyzing the options:

x> 5 this tells us that x takes values greater than 5, which in fact is the opposite of what we are looking for.

5 <x this also tells us that x takes values greater than 5, not what we are looking for.

x < 5 this option does represent the same as 5 > x because in both the narrow part of the symbol points to x, indicating that x is smaller than 5, therefore this is the correct option

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A company that manufactures racing boats estimates that the profit for selling its brand is given by the following equation.

disa [49]

Answer:

$b = 10$

Step-by-step explanation:

$P(b) = -25b^3 + 750b^2 + 2500b$

This equation shows the income obtained based on the number of boats sold. We want to know the minimum number of boats that must be sold to obtain $ 75 000.

Then we must equalize the equation to 75 000 and clear b.

3 solutions will be obtained (because it is a polynomial of degree 3), and the lowest value will be taken.

$P(b) = 75000$

$-25b^3 + 750b^2 + 2500b = 75000$

Now we need to solve the equation, for that we seek to factor the polynomial

$-25b^3 + 750b^2 + 2500b - 75000 = 0$

$b^3 -30b^2 - 100b + 3000 = 0$ we divide the equation by -25

$b^2(b-30) - 100(b-30) = 0$ We take common factor b

$(b^2 -100)(b-30) = 0$ We take out common factor (b-30)

Finally the solutions are:

$b = 30\\\\b^2 -100 = 0\\\\b^2 = 100$

b = 10 and b = -10

We take the least positive solution (because you can not produce -10 boats)

Finally b = 10

The smallest number of boats that must be produced to make a profit of $ 75,000 is 10 boats.

4 0

3 years ago

In a game, the two players scored a total of 75 points. One player had 13 more points than the other player.

MissTica

the answer is 62

Step-by-step explanation:

because if you take 75 and subtract 13you get 62

3 0

2 years ago

Read 2 more answers

Use < or > to make the statement true.<br> 4/5 5/6

Daniel [21]

Answer:

4/5<5/6

Step-by-step explanation:

4/5=0.8

5/6=0.833...

4/5<5/6

6 0

3 years ago

Every student in the senior class is taking history or science. There are $200$ seniors in the class. If there are $126$ seniors

aniked [119]

Answer: 55

Step-by-step explanation:

126+129= 255

255-200=55

4 0

3 years ago

2³+2²+2÷2²+2+1=2 prove that this relation is true for any natural numbers

UkoKoshka [18]

So, this question is basically asking us "If we had an x instead of a 2, would this be true?" We can try and see what we get:

$\frac{x^3+x^2+x}{x^2+x+1}=x$

So, if we want to show this we have to change the numerator or denominator in such a way that we can cancel some common factors. Notice that $x^3+x^2+x=x(x^2+x+1)$

If we replace the factored numerator with the original one, we get:

$\frac{x(x^2+x+1)}{x^2+x+1}=x \implies \\ x=x$

Since we have an equality, this relation is proved.

3 0

3 years ago