Select the graph that best represents the solution set of the system of linear inequalities

Find the shortest distance, d, from the point (5, 0, −6) to the plane x + y + z = 6.

DENIUS [597]

Answer:

$\frac{7}{\sqrt{3}}$

Step-by-step explanation:

The shortest distance d, of a point (a, b, c) from a plane mx + ny + tz = r is given by:

$d = |\frac{(ma + nb + tc - r)}{\sqrt{m^2 + n^2 + t^2}} |$ --------------------(i)

From the question,

the point is (5, 0, -6)

the plane is x + y + z = 6

Therefore,

a = 5

b = 0

c = -6

m = 1

n = 1

t = 1

r = 6

Substitute these values into equation (i) as follows;

$d = |\frac{((1*5) + (1*0) + (1 * (-6)) - 6)}{\sqrt{1^2 + 1^2 + 1^2}} |$

$d = |\frac{((5) + (0) + (-6) - 6)}{\sqrt{1 + 1 + 1}} |$

$d = |\frac{(-7)}{\sqrt{3}} |$

$d = \frac{7}{\sqrt{3}}$

Therefore, the shortest distance from the point to the plane is $d = \frac{7}{\sqrt{3}}$

5 0

3 years ago

The answer to the question please

Jlenok [28]

Answer:

the answer is -2x^9

Step-by-step explanation:

i know this because of photomath lolll

8 0

2 years ago

Charlie bought 40 oz of flour for his bakery. He used 18.3 oz to make a loaf of bread, and 0.95 oz for each muffin. How many muf

Furkat [3]

Division is one of the four fundamental arithmetic operations. With the leftover flour of 7.45oz, charlie can make approximately 8 muffins.

<h3>What is Division?</h3>

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

A.) The total flour Charlie has was 40 oz, out of this he used 18.3 oz of flour. The amount of flour left now would be 21.7 (40-18.3).

Since a single muffin uses 0.95 oz of flour, therefore, the number of muffins Charlie made will be,

Number of muffins = 21.7/0.95 = 22.84 ≈ 23 muffins

B.) When Charlie had 7.45 oz of flour leftover, then the number of muffins would be,

Number of muffins = 7.45/0.95 = 7.84 ≈ 8 muffins

Hence, with the leftover flour of 7.45oz charlie can make approximately 8 muffins.

Learn more about Division:

brainly.com/question/369266

#SPJ1

8 0

2 years ago

Which function has a greater y-intercept?

Natali5045456 [20]

Answer:

Option C, both functions have an y-intersect equal to 2.

Step-by-step explanation:

When we have a function f(x), the y-intercept is the value f(0). This is the point where the graph of the function intersects the y-axis.

Then, for f(x) = -x^2 + 5*x + 2

The y-intercept is:

f(0) = -0^2 + 5*0 + 2 = 2

f(0) = 2

And for g(x) we do not have the equation, but we have the graph, so we can just look at which value of y does the graph intersects the y-axis.

We can see that the graph intersects the graph at y = 2

Then the y-intersect is: g(0) = 2

So both functions have the same y-intersect. Then the correct option is C.

4 0

2 years ago

Which statement is not true?

SVETLANKA909090 [29]

The true answer is A. all parallelograms are rectangles

6 0

3 years ago

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