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2 years ago

Which graph shows the solution to the inequality Negative 3 x minus 7 less-than 20

Mathematics

2 answers:

Aleksandr-060686 [28]2 years ago

6 0

Answer:

A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10.

Step-by-step explanation:

we have

$-3x-7$

Solve for x

Adds 7 both sides

$-3x$

Divide by -3 both sides

Remember that

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

$x> 27/(-3)\\x>-9$

The solution is the interval (-9,∞)

therefore

A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10.

Lisa [10]2 years ago

5 0

Answer:

A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10.

Step-by-step explanation:

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A study shows that, over the course of a lifetime, the average salary of college graduates is greater than the average salary of

iogann1982 [59]

Answer: The word "ensures" implies that it is certain.

In the case of the study, they simply found that the average salary is greater for college graduates. This doesn't mean that in every case the college graduate makes more money.

The problem is the word "ensures". Our study doesn't show certainty only a general pattern.

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2 years ago

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Chris and Ben walked home from school. The distance Chris walked,in miles, is represented by point C on the number line. Ben wal

Xelga [282]

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2 years ago

What is r = wp, for p

weqwewe [10]

<span>What is r = wp, for p
</span>r = wp...divide both sides by w
so then p = r/w

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2 years ago

Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer d

andrey2020 [161]

Answer:

The maximum value is 1/27 and the minimum value is 0.

Step-by-step explanation:

Note that the given function is equal to $(xyz)^2$ then it means that it is positive i.e $f(x,y,z)\geq 0$ .

Consider the function $F(x,y,z,\lambda)=x^2y^2z^2-\lambda (x^2+y^2+z^2-1)$

We want that the gradient of this function is equal to zero. That is (the calculations in between are omitted)

$\frac{\partial F}{\partial x} = 2x(y^2z^2 - \lambda)=0$

$\frac{\partial F}{\partial y} = 2y(x^2z^2 - \lambda)=0$

$\frac{\partial F}{\partial z} = 2z(x^2y^2 - \lambda)=0$

$\frac{\partial F}{\partial \lambda} = (x^2+y^2+z^2-1)=0$

Note that the last equation is our restriction. The restriction guarantees us that at least one of the variables is non-zero. We've got 3 options, either 1, 2 or none of them are zero.

If any of them is zero, we have that the value of the original function is 0. We just need to check that there exists a value for lambda.

Suppose that x is zero. Then, from the second and third equation we have that

$-2y\lambda = -2z\lambda$ . If lambda is not zero, then y =z. But, since $-2y\lambda=0$ and lambda is not zero, this implies that x=y=z=0 which is not possible. This proofs that if one of the variables is 0, then lambda is zero. So, having one or two variables equal to zero are feasible solutions for the problem.

Suppose that only x is zero, then we have the solution set $y^2+z^2=1$ .

If both x,y are zero, then we have the solution set $z^2=1$ . We can find the different solution sets by choosing the variables that are set to zero.

NOw, suppose that none of the variables are zero.

From the first and second equation we have that

$\lambda = y^2z^2 = x^2z^2$ which implies $x^2=y^2$

Also, from the first and third equation we have that

$\lambda = y^2z^2 = x^2y^2$ which implies $x^2=z^2$

So, in this case, replacing this in the restriction we have $3z^2=1$ , which gives as another solution set. On this set, we have $x^2=y^2=z^2=\frac{1}{3}$ . Over this solution set, we have that the value of our function is $\frac{1}{3^3}= \frac{1}{27}$

4 0

2 years ago

an original piece of art work is 3 feet by 2.5 feet. a reprint of the artwork is 6 inches by 5 inches. are the pieces similar? i

RoseWind [281]

For this case we observe that the dimensions of the original piece are:
3 feet
2.5 feet
Let's multiply these dimensions by a scale factor k:
3 * k
2.5 * k
We match the new dimensions with their respective values:
3 * k = 6
2.5 * k = 5
Clearing k we have:
k = 6/3 = 2
k = 5 / 2.5 = 2
Since the value of k is the same, then the pieces are similar.
Answer:
The pieces are similar.
The ratio of their corresponding side lengths is:
k = 2

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2 years ago