the table represent a linear function

X Y
-2 -2
-1 1
0 4
1 7
2 10
what is the slope of the function?
-3
-2
3
4

In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line:

In your case line m is not parallel to the plane A and is not embedded in the plane, then the intersection is the point. Since point X is common point of the line m and the plane A, then the intersection of plane A and line m is point X.

Answer: correct choice is C.

Point X as it is the only point common in the both , Therefore Option C is the correct answer.

The point of intersection is the unit place where the two lines or planes meet each other .

In the given figure it can be seen that the the intersection of plane A and line m is given by Point X as it is the only point common in the both.

Therefore Option C is the correct answer.

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The value of k is 18, If -3 is a zero of P(x) = 2x^3 + 3x^2 - kx - 27.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

-3 is a zero of P(x) = 2x^3 + 3x^2 - kx - 27

so,

We can just input the value of -3 into the equation to find value of k.

now, we get,

0=2(-3)^3 + 3(-3)^2 +3k -27

27= -54 +27 + 3k

27= -27 = 3k

27+27 = 3k

54/3 = k

18 =k

Hence, The value of k is 18, If -3 is a zero of P(x) = 2x^3 + 3x^2 - kx - 27.

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We have that for the Question "Two angles are supplementary and have a ratio of 1:4. what is the size of the smaller angle" it can be said that  the size of the smaller angle is

x=36 degree

From the question we are told

Two angles are supplementary and have a ratio of 1:4. what is the size of the smaller angle

Generally the equation for "Two angles are supplementary"   is mathematically given as

[tex]180=x+y\\\\Therefore\\\\x=\frac{1}{5}*180\\\\x=36[/tex]

Therefore

the size of the smaller angle is

x=36

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The sides of the right angle triangle are 20, 48, and 52.

We have given that,

The hypotenuse of a right triangle is 8 feet less than three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg.

Suppose the shortest leg is x, the hypotenuse is then 3x-8, and the longer leg is 2x+8

We use the Pythagorean theorem

[tex]hypotenous^2=side^2+side^2[/tex]

Therefore by using Pythagorean theorem

[tex]x^2+(2x+8)^2=(3x-8)^2\\x^2+(4x^2+32x+64)=(9x^2-48x+64)\\4x^2-80x=0[/tex]

x=0 or x=20

So the sides are 20, 48, and 52.

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The function rule in slope-intercept form is y = 3x + 9.

The function rule in slope-intercept form is given by the equation y = mx + b, where m represents the slope of the line and b represents the y-intercept.

In this case, the given y-intercept is 9, so b = 9.

The slope of the line is 3, which means that for every increase of 1 on the horizontal axis (x-axis), there is a rise of 3 on the vertical axis (y-axis). Therefore, m = 3.

Putting these values into the slope-intercept form, we get the function rule to be y = 3x + 9.

Answer:

B (-∞, -21]

Step-by-step explanation:

edge

If two or more points are collinear they lie on the same plane.

Collinear points are points that lie on the same straight line. In other words, if three or more points are collinear, they can be connected by a straight line.

Collinear points are important in geometry and are used in many geometric proofs and constructions. The concept of collinearity is also used in other fields, such as physics and engineering, where it is used to describe the motion of objects along a straight line or to define the direction of forces acting on an object.

Given data ,

Let the points be represented as A , B and C

Now , when A , B and C are lying on the same line , we say the points are collinear or collinear points

So , If two or more points are collinear they lie on the same plane.

Hence , the collinear points are solved

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Answer:

So, the point-slope form of the equation that represents the line passing through the points [tex]\((-6,4)\) and \((2,0)\)[/tex] is:

[tex]\[ y - 4 = -\frac{{1}}{{2}}(x + 6) \][/tex]

Explanation:

To find the equation of the line passing through the points [tex]\((-6,4)\) and \((2,0)\)[/tex] , we can use the point-slope form of the equation of a line:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

Where [tex]\((x_1, y_1)\)[/tex]  is a point on the line, and [tex]\(m\)[/tex] is the slope of the line.

First, let's find the slope [tex]\(m\):[/tex]

[tex]\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \][/tex]

Using the coordinates of the given points:

[tex]\[ m = \frac{{0 - 4}}{{2 - (-6)}} \][/tex]

[tex]\[ m = \frac{{-4}}{{2 + 6}} \][/tex]

[tex]\[ m = \frac{{-4}}{{8}} \][/tex]

[tex]\[ m = -\frac{{1}}{{2}} \][/tex]

Now that we have the slope, let's choose one of the given points to plug into the point-slope form. We'll use [tex]\((-6,4)\):[/tex]

[tex]\[ y - 4 = -\frac{{1}}{{2}}(x - (-6)) \][/tex]

[tex]\[ y - 4 = -\frac{{1}}{{2}}(x + 6) \][/tex]

[tex]\[ y - 4 = -\frac{{1}}{{2}}x - 3 \][/tex]

Now, let's simplify and put the equation in slope-intercept form:

[tex]\[ y = -\frac{{1}}{{2}}x - 3 + 4 \][/tex]

[tex]\[ y = -\frac{{1}}{{2}}x + 1 \][/tex]

To find the intervals over which a function is increasing, you need to find its derivative, set it greater than 0 and solve for x. The solutions give the intervals where the function is increasing.

In mathematics, to find the intervals over which a function is increasing, you first need to find its derivative. The derivative of a function at a certain point gives the slope of the tangent line at that point. If the derivative is positive, the function is increasing. If it's negative, the function is decreasing.

For example, let's say we have a function f(x) = x^3 - 3x. The derivative of this function is f'(x) = 3x^2 - 3. To find the interval where the function is increasing, we set the derivative greater than 0 and solve for x: 3x^2 - 3 > 0. The solution to this inequality gives the intervals over which the function is increasing .

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Option D is not justified because living in water doesn't necessarily mean that the snakes are fish. This logical fallacy is known as the undistributed middle. Options A, B, and C present logically justified conclusions.

The conclusion that is not justified by the previous pair of statements is found in option D: 'All fish live in the water. Some snakes live in the water. Some snakes are fish.' In this scenario, the fact that some snakes live in the water does not logically lead to the conclusion that those snakes are fish. This is because belonging to the category 'fish' is not determined simply by living in water. Therefore, the conclusion is not supported by the given premises.

In contrast, for options A, B, and C, the conclusions are logically justified by the premises:

Each of these sets uses deductive reasoning to draw conclusions that are supported by the premises. However, option D is an example of a logical fallacy known as the undistributed middle, leading to an erroneous conclusion.

To determine the number of units produced by Assembly Line A when Line B produces 555 units, we use the ratio of their production rates (45/37) to find that Assembly Line A would produce 675 units.

The question asks how many units Assembly Line A produces when Assembly Line B produces 555 units, given that Line A produces 45 units in the same time that it takes Line B to produce 37 units. To find the answer, we can use the concept of ratio and proportion.

Since Line A produces 45 units at the same time Line B produces 37 units, we have a ratio of 45/37. With Line B producing 555 units, we can set up a proportion to find how many units Line A produces:

45/37 = x/555

Multiplying both sides of the equation by 555, we get:

x = (45/37) * 555

Calculating the value of x gives us:

x = 675

Therefore, Assembly Line A produces 675 units in the same time that Assembly Line B produces 555 units.