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Nana76 [90]
3 years ago
5

Which graph correctly represents 3x + y > 7? NEED HELP!!

Mathematics
2 answers:
patriot [66]3 years ago
6 0
First rewrite the inequality in y = form.
3x + y > 7
Subtract 3x from both sides.
y > -3x + 7
Both graphs have a -3 slope and y intersect at 7. The only difference in the shading. Choose a test point to see if it makes the inequality true. The easiest point to choose is (0,0) if our line doesn't pass through that point.

0 > -3(0) + 7
0 > 7 is false so we want the graph where (0,0) is NOT shaded. That is the one on the left.
Andru [333]3 years ago
4 0
If the blue part is what is shaded, I'd say it's Graph B. But you can double check on a great website called "https://www.desmos.com/"

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Find the value of x in the isosceles triangle shown below.​
Ghella [55]

Answer: A, x = square root of 60.

Step-by-step explanation:

Use the Pythagorean Theorem, a^2 + b^2 = c^2.

8^2 = 2^2 + x^2

x^2 = 8^2 - 2^2

x^2 = 64 - 4

x^2 = 60

x = sqrt of 60

3 0
3 years ago
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Allen needs to prepare a compound for the patient to pick up tomorrow. He needs to mix of drug A, with of drug B and of drug C.
Phoenix [80]

Answer:

76/15

Step-by-step explanation:

Add the drug combinations together

Drug A + B + C=2/5 + 5/3 + 9/3

The L.C.M of the denominators is 15

=6+25+45/15

=76/15

Or

=5 1/15

Allen needs to prepare 76/15 compound for the patient

5 0
3 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
3 years ago
If the diameter of a golf hole is 4.25 inches, what is the approximate circumference of the hole?
shepuryov [24]
The formula for circumference is pi(diameter) or 2 x pi x radius. So you have the diameter which is 4.25. Next step you need to do is multiply it with pi which is equal to 3.14. Your equation would be C= 3.14 x 4.25.

6 0
3 years ago
Please help with this
sveticcg [70]

It should be B or C

Step-by-step explanation:

5 0
3 years ago
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