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3 years ago

Which system of linear inequalities is graphed?

Mathematics

1 answer:

ANEK [815]3 years ago

8 0

To determine the system of inequality that has been graphed, we need to be very smart.

Observe that all the equations are the same.

Also note that all the lines are solid. This should tell you that the inequities should involve.

$\ge \:or\: \le$

Therefore the answer is between option A and B.

So we choose a point in the solution region to discriminate between A and B.

Let us choose the origin since that is easy to evaluate.

We substitute into option A to get.

$y\le 3x-1\:and\: x+ 3y \ge 6$

$0\le 3(0)-1\:and\: 0+ 3(0) \ge 6$

$0\le -1\:and\: 0\ge 6$

The above statements are false

We now substitute into option B

$y\ge 3x-1\:and\: x+ 3y \le 6$

$0\ge 3(0)-1\:and\: 0+ 3(0) \le 6$

$0\ge-1\:and\: 0 \le 6$

Both statements are true, therefore the correct answer is option B.

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How do I find the length of AB?

Anit [1.1K]

I assume #3 is 19 because the slope of the line is still the same.
Hope this is right and it helps! I'm not very sure though.

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3 years ago

If f(x) = x² – 5, evaluate: f(x+h)-f(x)/<br> h

Likurg_2 [28]

The first derivative of the function f(x) = x² - 5 is equal to f'(x) = 2 · x.

<h3>How to find the derivative of a quadratic equation by definition of derivative</h3>

In this question we have a quadratic function, in which we must make use of the definition of derivative to find the expression of its first derivative. Then, the procedure is shown below:

f(x) = x² - 5 Given

f' = [(x + h)² - 5 - x² + 5] / h Definition of derivative

(x² + 2 · x · h + h² - 5 - x² + 5) / h Perfect square trinomial

(2 · x · h + h²) / h Associative, commutative and modulative properties / Existence of additive inverse

2 · x + h Distributive, commutative and associative properties / Definition of division / Existence of multiplicative inverse

2 · x h = 0 / Result

The first derivative of the function f(x) = x² - 5 is equal to f'(x) = 2 · x.

To learn more on derivatives: brainly.com/question/25324584

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2 years ago

Which point is a distance of 5 units from the point (1,9)

Vesna [10]

I believe it's 5,6

Hope this helped!

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3 years ago

Jeff is baking a cake. The recipe says that he has to mix 32 grams of vanilla powder to the flour. Jeff knows that 1 cup of that

ella [17]

To determine the excess amount, subtract 32 from 85.33 which has a numerical value of 53.33 grams.

7 0

2 years ago

Find Distance (4,6) (-4,-3)

vampirchik [111]

Answer:

$\sqrt{145}$

Step-by-step explanation:

The distance formula states that the distance between two points $(a,b)$ and $(c,d)$ is $\sqrt{(a-c)^2+(b-d)^2}$ .

The two points we have are $(4,6)$ and $(-4,-3)$ . Plugging these numbers into the distance formula, we have

$\sqrt{(4-(-4))^2+(6-(-3))^2$ .

Simplifying with order of operations, first using the distributive property, gives

$\sqrt{(4+4)^2+(6+3)^2$ .

Squaring and adding gives

$\sqrt{(4+4)^2+(6+3)^2}=\sqrt{8^2+9^2}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\sqrt{64+81}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\boxed{\sqrt{145}},$

which is the answer in simplest form. This also rounds to about 12.04.

7 0

2 years ago